THE GEM-E3 MODEL FOR THE EUROPEAN UNION
Coordination:
National Technical University of Athens
Prof. P. Capros
T. Georgakopoulos main researcher
A. Filippoupolitis researcher
S. Kotsomiti researcher
G. Atsaves computer support
Core Teams
Catholic University of Leuven (Center for Economic Studies)
Prof. S. Proost
D. Van Regemorter
Centre for European Economic Research (ZEW)
Prof. K. Conrad
T. Schmidt
Contributing teams
IDEI (University of Toulouse) (N. Ladoux, M. Vielle, A. Bousquet)
Stockholm School of Economics (Prof. L. Bergman, C. Nilsson)
ERASME (Prof. P. Zagame)
University of Strathclyde (Prof. P. McGregor, K. Swales)
Partially funded by the European Commission, Programme JOULE, DG-XII/F1. Contact person: P. Valette.
The GEM-E3 model:
Reference Manual
NATIONAL TECHNICAL UNIVERSITY OF ATHENS
The GEM-E3 model reference manual
For further information contact:
Prof. P. Capros
National Technical University of Athens
42 Patission St.
10682 Athens, Greece
E-mail: [email protected]
Table of Contents
C H A P T E R 1 : THE GEM-E3
MODEL FOR THE EU MEMBER
STATES
Data sources
114
The IO table
116
Introduction
1
The SAM
121
Policy analysis support
3
Foreign trade data
125
Design Principles
5
Dynamic calibration
126
On-going model developments
C H A P T E R 2 :
PRESENTATION
13
MODEL
Introduction
14
Core model structure
15
Environmental Module
40
C H A P T E R 3 : IMPERFECT
MARKETS AND ECONOMIES OF
SCALE
C H A P T E R 6 : CALIBRATION OF
MODEL EXTENSIONS
Data for the environment
128
Emission coefficients
132
C H A P T E R 7 : MODEL
CALIBRATION
Calibration structure
145
Values of elasticities
146
Calibration of imperfect competition
159
Production
63
Firm-specific demand
66
C H A P T E R 8 : MODEL
IMPLEMENTATION
Firm pricing behaviour
68
Model Implementation in SOLVER
166
Price-cost margins
69
Model Implementation in PATH
166
C H A P T E R 4 : PROTOTYPE
MODEL EXTENSIONS
C H A P T E R 9 : FUTURE MODEL
DEVELOPMENTS
World closure
72
Endogenous growth
83
Endogenous energy-saving investments
93
Labour market
98
The financial/monetary sector
105
Energy sub-model
108
CHAPTER 5: DATA AND
NOMENCLATURE
168
C H A P T E R
1 0 : REFERENCES
170
1
Chapter
The GEM-E3 model for
the EU member states
An overview of the reference manual is presented in this chapter
The model’s theoretical position and its main
design characteristics
I N T R O D U C T I O N
This presentation describes the basic features and characteristics of the GEM-E3
General Equilibrium Model for Energy-Economy-Environment interactions. The
model, partly financed by the European Commission1, is being used to evaluate
policy issues for the European Commission. Applications of the model have been
(or are currently being) carried out for several Directorate Generals of the
European Commission (economic affairs, competition, environment, taxation,
research). At present, the model version 2.0 is operational for EU-15 memberstates, while further development is under way.
GEM-E3 is an applied general equilibrium model for the European Union
member states taken individually or as a whole, which provides details on the
macro-economy and its interaction with the environment and the energy system2.
It is an empirical, large-scale model, written entirely in structural form. The model
computes the equilibrium prices of goods, services, labour and capital that
simultaneously clear all markets under the Walras law. Therefore, the model
follows a computable general equilibrium approach. The main features of the
model are as follows:
1
JOULE programme, Coordinator P. Valette (DG-XII/F1).
The model is the result of a collaborative effort by a consortium involving National Technical
University of Athens (coordinator), the Catholic University of Leuven (Centre for Economic Studies),
Univ. Mannheim and the Centre for European Economic Research (ZEW) as the core modelling team.
A team of the Commissariat à l’ Energie Atomique made significant contributions, now active within
IDEI (University of Toulouse). Other project participants include Univ. Strathclyde, Stockholm School
of Economics, ERASME (Ecole Centrale de Paris) and Université Catholique de Louvain (CORE).
2
The model extensions to represent market imperfections and economies of scale were carried out by
the National Technical University of Athens (coordinator), the Catholic University of Leuven and
Middlesex University.
• GEM-E3 is a multi-country model, treating separately each EU-15
member-state and linking them through endogenous trade of goods
and services.
• GEM-E3 includes multiple industrial sectors and economic agents,
allowing the consistent evaluation of distributional effects of policies.
• GEM-E3 is a dynamic, recursive over time, model, involving dynamics
of capital accumulation and technology progress, stock and flow
relationships and backward looking expectations.
In addition, the model covers the major aspects of public finance including all
substantial taxes, social policy subsidies, public expenditures and deficit financing,
as well as policy instruments specific for the environment/energy system. A
financial/monetary sub-model optionally complements the real side of the model3
and operates as an overall closure, following the IS-LM methodology.
The model determines the optimum balance of energy demand and supply,
atmospheric emissions and pollution abatement, simultaneously with the
optimising behaviour of agents and the fulfillment of the overall equilibrium
conditions. In this sense, the interactions between the economy, the energy
system and the environment are evaluated.
The results of GEM-E3 include projections of full Input-Output tables by
country, national accounts, employment, capital, monetary and financial flows,
balance of payments, public finance and revenues, household consumption,
energy use and supply, and atmospheric emissions. The computation of
equilibrium is simultaneous for all domestic markets of all EU-15 countries and
their interaction through flexible bilateral trade flows.
A major aim of GEM-E3 in supporting policy analysis, is the consistent evaluation
of distributional effects, across countries, economic sectors and agents. The
burden sharing aspects of policy, such as for example energy supply and
environmental protection constraints are fully analysed, while ensuring that the
European economy remains at a general equilibrium condition.
The rest of the paper is organised as follows: Section 2 describes the current and
potential uses of the model and illustrates the type of issues that the model is
designed to deal with. Section 3 presents the design principles of the model in the
framework that classifies general equilibrium models, so as to compare to other
approaches that are available in the literature. Section 4 presents the specific
implementation of the latest model version, describes the benchmark data to
which the model is calibrated and presents the model software and solution
algorithm. Section 5 is by far the largest in size. It starts from a brief general
The Catholic University of Leuven and the Centre for European Economic Research (ZEW)
developed the environmental module.
3
This is only one of the several possible alternative closure rules embedded in GEM-E3.
2
presentation of the model structure and then proceeds to present in detail the
technical aspects of the model. Section 6 is the concluding part of the paper, in
which two of the exercises carried out with the model are presented. These
concern the evaluation of the Single Market Programme of the EU and the impact
of the revision of the minimum excise taxes on energy products.
P O L I C Y
A N A L Y S I S
S U P P O R T
The advantages of computable general equilibrium models for policy analysis4,
compared with traditional macro-economic models5, are now widely admitted6.
The general equilibrium models allow for consistent comparative analysis of policy
scenarios since they ensure that in all scenarios, the economic system remains in
general equilibrium. In addition, the computable general equilibrium models
incorporate micro-economic mechanisms and institutional features within a
consistent macro-economic framework, and avoid the representation of behaviour
in reduced form. This allows analysis of structural change. Particularly valuable are
the insights in distributional effects and in longer-term structural mechanisms.
Main Applications of the GEM-E3
model
•
The ex-post evaluation of the
impact of the Single Market
Programme7.
•
The study of the revision of the
minimum excise taxation for energy
products for the European Union
member states8.
•
The study of the possibility for a
“double dividend” for environment
and employment9.
•
The evaluation of the macroeconomic implications of the
European Union’s targets for the
Kyoto negotiations for greenhouse
gas mitigation.
•
The examination of the impact of
creating a market of tradable
pollution permits.
The relevance and type of insights that can be gained
from the GEM-E3 model have already been
demonstrated in its use for several issues that are of
primary interest for the European Union.
By directly mapping economic theory the GEM-E3
model offers a quantified framework that uniquely
characterises a policy case, through its impact on
social welfare. Under reasonable assumptions, this
welfare can be measured through the use of model
variables such as trade flows, investment,
consumption and GDP. In this way, an unobservable
construct, such as the welfare function, can be
translated into a quantifiable measure of satisfaction.
GEM-E3 is a general-purpose model that aims to
cope with the specific orientation of the policy issues
that are actually considered at the level of the
European Commission. Therefore it is modularly
built allowing the user to select among a number of
alternative options depending on the issue under
study.
4
See Borges A.M. (1990)
5
For example, Valette P. and Zagame, eds. (1994)
6
See Capros P., Karadeloglou and G. Mentzas (1989) and (1990) for a formal comparison.
7
See Capros, Georgakopoulos et. al. (1997a)
8
See Capros, Georgakopoulos (1997b)
9
See Capros, , Georgakopoulos et al. (1994) and (1995)
3
The main types of issues that the model has been designed to study
are:
• The analysis of market instruments for energy-related
environmental policy, such as taxes, subsidies, regulations,
pollution permits etc., at a degree of detail that is sufficient for
national, sectoral and Europe-wide policy evaluation.
• The evaluation of European Commission programmes that aim
at enabling new and sustainable economic growth, for
example the technological and infrastructure programmes.
• The assessment of distributional consequences of
programmes and policies, including social equity, employment
and cohesion targets for less developed regions.
• The consideration of market interactions across Europe, given
the perspective of a unified European internal market, while
taking into account the specific conditions and policies prevailing
at a national level.
•
Public finance,
stabilisation policies and their implications on
trade, growth and the behaviour of economic agents.
• The standard need of the European Commission to periodically
produce detailed economic, energy and environment policy
scenarios.
Policies that attempt to address the above issues are analysed as counterfactual
dynamic scenarios and are compared against baseline model runs. Policies are then
evaluated through their consequences on sectoral growth, finance, income
distribution implications and global welfare, both at the single country level and
for the EU taken as a whole.
The GEM-E3 model intends to cover the general subject of sustainable
economic growth, and supports the study of related policy issues. Sustainable
economic growth is considered to depend on combined environmental and
energy strategies that will ensure stability of economic development.
The model intends, in particular, to analyse the global climate change issues (as
far as Europe is concerned), a theme that embraces several aspects and
interactions within economy, energy and environment systems. To reduce
greenhouse gas emissions, CO2 emissions in particular, it is necessary to achieve
substantial gains in energy conservation and in efficiency in electricity generation,
as well as to perform important fuel substitutions throughout the energy system,
in favour of less carbon intensive energy forms.
4
Moreover, within the context of increasingly competitive markets, new policy
issues arise. For example, it is necessary to give priority to market-oriented policy
instruments, such as carbon taxes and pollution permits, and to consider marketdriven structural changes, in order to maximise effectiveness and alleviate macroeconomic consequences. Re-structuring of economic sectors and re-location of
industrial activities may be also induced by climate change policies. This may have
further implications on income distribution, employment, public finance and the
current account.
The model is designed to support the analysis of distributional effects that are
considered in two senses: distribution among European countries and distribution
among social and economic groups within each country. The former issues
involve changes in the allocation of capital, sectoral activity and trade and have
implications on public finance and the current account of member states. The
latter issues are important, given the weakness of social cohesion in European
member-states, and regard the analysis of effects of policies on consumer groups
and employment. The assessment of allocation efficiency of policy is often termed
“burden sharing analysis”, which refers to the allocation of efforts (for example
taxes), over member-states and economic agents. The analysis is important to
adequately define and allocate compensating measures aiming at maximising
economic cohesion. Regarding both types of distributional effects, the model can
also analyse and compare coordinated versus non coordinated policies in the
European Union.
Technical progress and infrastructure can convey factor productivity
improvement to overcome the limits towards sustainable development and social
welfare. For example, European RTD strategy and the development of panEuropean infrastructure are conceived to enable new long-term possibilities of
economic growth. The model is designed to support analysis of structural features
of economic growth related to technology and evaluate the derived economic
implications for competitiveness, employment and the environment.
G E M - E 3
M O D E L
D E S I G N
P R I N C I P L E S
The General Equilibrium Modelling Approach
The distinguishing features of general equilibrium modelling derive from the
Arrow-Debreu10 economic equilibrium theorem and the constructive proof of
existence of the equilibrium based on the Brower-Kakutani theorem11.
Figure 1: Fixed point and the
tâtonnement process
The Arrow-Debreu theorem considers the
economy as a set of agents, divided in
suppliers and demanders, interacting in several
markets for an equal number of commodities.
Each agent is a price-taker, in the sense that
the market interactions, and not the agent, are
10
See Arrow K.J. and G. Debreu (1954).
11
See Kakutani S. (1941).
5
setting the prices. Each agent is individually defining his supply or demand
behaviour by optimising his own utility, profit or cost objectives.
The theorem states that, under general conditions, there exists a set of prices that
bring supply and demand quantities into equilibrium and all agents are fully (and
individually) satisfied. The Brower-Kakutani existence theorem is constructive in
the sense of implementing a sort of tâtonnement process around a fixed point
where the equilibrium vector of prices stands (see Figure 1). Models that follow
such a process are called computable general equilibrium models.
In theory, the computable and the optimisation equilibrium models
are equivalent: the former, represented as a system of simultaneous
equations, corresponds to the first order optimum conditions of the
mathematical programming problem. Motivated by the long-term
character of the climate change issue, several new optimisation
models have been constructed recently12. The computable general
equilibrium models however, are more common for two reasons:
their computer solution is easier; they enable a straightforward
representation of policy instruments and market-related institutional
characteristics, therefore they enrich policy analysis.
It has been demonstrated that the Arrow-Debreu equilibrium can also be obtained
from global (economy-wide) optimisation that implements Pareto optimality and
uses the equilibrium characterisation introduced by Negishi13. Models that follow
this methodology, have the form of mathematical programming14 and are called
optimisation equilibrium models†.
In applied policy analysis, the so-called “closure rule15” problem has been often
taken as a drawback of general equilibrium models, as the results are depend on
the choice of the closure rule. As a matter of fact, a number of earlier approaches
have been classified according to the type of closure rules that they were adopting
(neoclassical, neo-Keynesian etc.).
A recent trend in computable general equilibrium modelling consists of
incorporating an IS-LM mechanism (termed also macro-micro integration), that
has been traditionally used in Keynesian models. J. De Melo, Branson and F.
Bourguignon, and independently P. Capros et al. have proposed the ensuing
hybrid models16. These models often incorporate additional features that enhance
their short/medium term analysis features, such as imperfect competition in some
See Manne A. (1978) and (1990), Nordhaus W. D. (1990), Dewatripont et al. (1991), Proost S. and D.
Van Regemorter (1992).
12
13 See Negishi (1962).
14
For example see Dorfman et al. (1958), Ginsburgh and Waelbroeck (1981).
15
See Dewatripont M. and G Michel (1987), and Lysy F.J. (1983).
16
See for example Bourguignon F., Branson, De Melo (1989), and Capros et al. (1985) and (1990).
6
markets, financial and monetary constraints, rigidity in wage setting and
dynamically adjusting expectations. The IS-LM closure of computable equilibrium
models overcomes the limitation of an arbitrary closure rule, which must
otherwise be adopted. In addition it provides insight into financial market
mechanisms and related structural adjustment, allowing for a variety of choices of
a free monetary variable that can then determine the level of inflation. These
models have been often used for the evaluation of stabilisation packages.
Facilitated by the explicit representation of markets, the computable general
equilibrium models have been often extended to model market imperfections and
other economic mechanisms that deviate from the Pareto optimality frontier.
Some authors used the term “generalised equilibrium modelling”17 to underline the
flexibility of the computable equilibrium paradigm, regarding the extensions
aforementioned, but also the possibility to represent and even mix different
market clearing regimes within a single model. In general, these possibilities enrich
the analytical capability of the model regarding structural change and its relation to
market distortions, for example price regulations, cost-depending price setting, etc.
The extensions that allowed the introduction of alternative market clearing regimes gave the
possibility for introducing elements of the new trade economic theory within CGE models18.
From the simple static open-economy models of the 70s, it was now possible to develop
sophisticated multi-country models where benefits from the exploitation of the potential for
economies of scale and from the intensification of competition due to trade liberalisation are
explicitly represented.
Similar methodological approaches have also lead to the incorporation of
mechanisms reflecting endogenous technology evolution dynamics19. This issue
however is at the frontier of current research activities and although the theoretical
literature is expanding, few attempts have been made to include endogenous
growth in a full-scale applied CGE model. Another are of interest, namely labour
market imperfections20, have also been introduced through the representation of
the bargaining power of labour unions21, while capital mobility regulations are also
be taken into account in some models.
The current stream of CGE models, through its modular design, encompasses the
whole area of modern economics going much beyond the standard neo-classical
17
For example see Nesbitt D. (1984) on energy system applications.
Helpman and Krugman (1985) describe the theoretical framework, while Winters and Venables (eds.)
(1992), Baldwin (1992) and Dewatripont and Ginsburgh (eds.) (1994) give examples of applications.
Baldwin and Venables (1995) provide an overview of recent attempts.
18
The work of Romer P.M. (1990) is one of the first expositions of the new growth theory. Grossman
G., Helpman E. (1991) provide the first systematic survey of incorporating endogenous growth
mechanisms that is further elucidated by Barro (1995).
19
20 The book “The new macroeconomics” Dixon and Rankin (eds.) (1995) includes an overview of many
of the recent attempts.
Recent attempts to introduce wage bargaining processes have been introduced in the WARM (see
GRETA (1995)) and the WORLDSCAN models.
21
7
economics on which the first generation of CGE models was confined. This new
generation of model design is the inspiration behind the development of the
GEM-E3 model.
Main Characteristics of the GEM-E3 Model
During the past fifteen years there has been a substantial growth in the use of
empirical general equilibrium models for policy analysis. Equilibrium models have
been used to study a variety of policy issues, including tax policies, development
plans, agricultural programs, international trade, energy and environmental policies.
A range of mathematical formulations and model solution techniques has been
used in these modelling experiences. The design of GEM-E3 model has been
developed following four main guidelines:
1. Model design around a basic general equilibrium core in a modular
way so that different modelling options, market regimes and closure
rules are supported by the same model specification.
2. Fully flexible (endogenous) coefficients in production and in
consumer’s demand.
The World Bank -type of models constitutes the major bulk of
equilibrium modelling experiences. This type of models was usually
used for comparative static exercises. The World Bank and
associated Universities and scientists have animated a large number
of such modelling projects, usually applied to developing countries.
Principal representatives of this group are J. De Melo, S. Robinson,
R. Eckaus, S. Devarajan, R. Decaluwe, R. Taylor, S. Lusy and
others22.
These models however do not use full-scale production functions but rather work
on value added and their components to which they directly relate final demand.
1. Calibration to a base year data set, incorporating detailed Social
Accounting Matrices as statistically observed.
2. Dynamic mechanisms, through the accumulation of capital stock.
The GEM-E3 model has the starts from the same basic structure as the standard
World Bank models†. Following the tradition of these models, GEM-E3 is built on
the basis of a Social Accounting Matrix23 and explicitly formulates demand and
supply equilibrium.
See Adelman, I. and S. Robinson (1982), Dervis K., et al. (1982), Lewis J. D. and Shujiro Urata
(1984), Devarajan S. and H. Sierra (1986), Robinson S. (1986), Condon T. et al. (1987), Adelman I. And
S. Robinson (1988), Devarajan S. (1988), De Melo J. (1988), De Melo J. and S. Robinson (1989), S.
Robinson (1989), Devarajan S. et al. (1990) and (1991).
22
23
See Decaluwe B. and A. Martens (1987 and 1988).
8
The generalised Leontief type of model was first formulated
empirically in the work of D. W. Jorgenson24 who introduced
flexibility in the Leontief framework, using production functions
such as the translog. The work of D. W. Jorgenson inspired many
modelling efforts, in which particular emphasis has been put to
energy. For example, P. Capros and N. Ladoux in France, the
OECD (GREEN and WALRAS), L. Bergman in Sweden and K.
Conrad in Germany developed such models 25.
Technical coefficients in production and demand are flexible in the sense that
producers can alternate the mix of production not only regarding the primary
production factors but also the intermediate goods. Production is modelled
through KLEM (capital, labour, energy and materials) production functions
involving many factors (all intermediate products and two primary factors -capital
and labour). At the same time consumers can also endogenously decide the
structure of their demand for goods and services. Their consumption mix is
decided through a flexible expenditure system involving durable and non-durable
goods. The specification of production and consumption follows the generalised
Leontief type of models† as initiated in the work of D. Jorgenson.
The model is not limited to comparative static evaluation of policies. The model is
dynamic in the sense that projections change over time. Its properties are mainly
manifested through stock/flow relationships, technical progress, capital
accumulation and agents’ (backward looking) expectations 26.
The model is calibrated to a base year data set that comprises of full Social
Accounting Matrices for each EU country that is built by combining InputOutput tables (as published by EUROSTAT) with national accounts data. Bilateral
trade flows are also calibrated for each sector represented in the model, taking into
account trade margins and transport costs. Consumption and investment is built
around transition matrices linking consumption by purpose to demand for goods
and investment by origin to investment by destination. The initial starting point of
the model therefore, includes a very detailed treatment of taxation and trade†.
Total demand (final and intermediate) in each country is optimally allocated
between domestic and imported goods, under the hypothesis that these are
considered as imperfect substitutes. This is often called the “Armington”
24
See Hudson E. and D.W. Jorgenson (1974).
See Hudson E. and D.W. Jorgenson (1977), Jorgenson D.W. (1984), Capros P. and N. Ladoux
(1985), Blitzer C.R. and R. S. Eckaus (1986), Conrad K. and I. Henseler-Urger (1986), Bergman L.
(1988) and (1989), Jorgenson D.W. and P.J. Wilcoxen (1989), Conrad K. and M. Schroder (1991),
OECD (1994).
25
A recent generation of general equilibrium models involves rational expectations where the model is
solved inter-temporally i.e. all time-periods together. A recent example of such a model is the G-Cubed
model (see McGibbin and Wilcoxen, 1995)
26
9
assumption27. To cover analysis of European Union’s unifying market, the model
is simultaneously multinational (for European Union) and specific for each
member-state. To this respect the model follows the methodology of the models
that are developed to study tax policy and international trade (see box in previous
page).
Models designed to study trade and fiscal policy do not necessarily
represent the full detail of production technologies and consumption
patterns, but instead put emphasis on public budgeting and
international trade links. They implement a dynamic multi-period
structure and they often solve inter-temporally to determine optimal
taxation28. International trade and multi-country models determine
equilibrium as an allocation driven by prices. Shoven, Whalley and
others are among the main authors. The equilibrium models for
international trade have been applied to policy analysis raised by
GATT conventions, by the USA-Mexico trade issues, the USAJapan trade, the EEC market unification and others29.
GEM-E3 considers explicitly market-clearing mechanisms, and related price
formation, in the economy, energy and environment markets. Following a microeconomic approach, it formulates the supply or demand behaviour of the
economic agents regarding production, consumption, investment, employment
and allocation of their financial assets. The model as a result of supply and demand
interactions in the markets computes prices. Through its flexible formulation, it
also enables the representation of hybrid or regulated situations, as well as perfect
and imperfect competition.
†Models with imperfect competition are a rather recent addition to
the literature of CGE models. They are usually based on the concept
of product varieties as this derived from the theory of industrial
organisation and the concept of economies of scale which provided
an elegant micro-economic framework for including non-linearity in
production and consumption30. Such models have been developed
mainly in Europe to study the impact of European unification.
Similar techniques have been utilised to study the labour market
imperfections. The concept of product varieties has also been
27
See Armington (1969).
See Shoven J.B. and Whalley J. (1972) and (1974), Shoven J.B. (1973), Fullerton et al. (1981), Piggot J.
and Whalley J. (1985), and Pereira A.M. and J. B Shoven (1988).
28
See Taylor L., S. L. Black (1974), Zalai E. (1982), Shoven J.B. and Whalley J. (1984) and (1992),
Whalley J and B. Yeung (1984), Deardoff A.V. and R.M Stern (1986), Harris R.G. (1986), Spenser J.E.
(1986), Smith A. and A. Venables (1988), Wigle R. (1988), Devarajan S. et al. (1991), Hinojosa-Ojeda R.
and S. Robinson (1991), Mercenier J. (1991).
29
See Dixit and Stiglitz (1977) for a pioneer exposition of the notion of product varieties and J. Tirole
(1988) for its use in industrial organisation.
30
10
utilised to endogenise technical progress in a number of theoretical
models.
The current model version for example, incorporates sectors in which only a
limited number of firms operate under oligopoly assumptions†. Firms in these
sectors operate under non-constant returns to scale involving a fixed cost element,
endogenously determine their price/cost mark-ups based on Nash-Bertrand or
Nash-Cournot assumptions. Firms in these sectors can make profits or losses
which will alter the concentration and firm size in the sector. Demand then is also
firm specific in the sense that changes in product varieties directly affect the utility
of the consumers.
Institutional regimes, that affect agent behaviour and market clearing, are explicitly
represented, including public finance, taxation and social policy, as well as
monetary policy. All common policy instruments affecting economy, energy and
environment are included. Model closure options mainly investments/savings
equality are varied according to capital or labour mobility across sectors/countries,
external sector possibility of adjustment and the possibility for a
financial/monetary closure31.
The model is general and complete, in the sense that it includes all agents, markets
and geographic entities that affect European economic equilibrium. The model
attempts also to represent goods that are external to the economy32 as for example
damages to the environment.
The internalisation of environmental externalities is conveyed either through
taxation or global system constraints, the shadow costs of which affect the
decision of the economic agents. The current version of GEM-E3 links global
constraints to environmental emissions changes in consumption or production
patterns, external costs/benefits, taxation, pollution abatement investments and
pollution permits. The current version of GEM-E3 evaluates the impact of policy
changes in the environment in the sense of calculating atmospheric emissions† and
damages and determines costs and benefits in the sense of an equivalent variation
measurement of global welfare.
†The recent awareness about the greenhouse problem motivated the
emergence of several empirical models for the analysis of economyenvironment interactions. For example, the work of W. Nordhaus,
D. Jorgenson and Wilcoxen, A. Manne and Richels, Blitzer and
Eckaus, K. Conrad, L. Bergman, S. Proost and Van Regemorter33
31 See Agenor et al. (1991), Bourguignon F. et al. (1989) and Capros et. al. (1990) for the
financial/monetary closure to a CGE model.
32 On accounting for externalities, see the report of the EXTERNE project, European Commission
(1995).
See W. Nordhaus (1994), D. Jorgenson and Wilcoxen (1990), A. Manne and Richels (1997), S. Proost
and Van Regemorter (1992).
33
11
have focused on the economic conditions for obtaining CO2
reduction by means of a carbon-related tax. Such a policy issue needs
to be addressed by ensuring consistent representation of the
interactions between the economy, the energy system and the
emissions of CO2.
A counterfactual simulation is characterised through its impact on consumer’s
welfare, as this is computed through the equivalent variation of his welfare
function. The equivalent variation can be, under reasonable assumptions, directly
mapped to some of the endogenous variables of the model such as consumption,
employment and price levels. The sign of the change of the equivalent variation in
each member state and the for the EU as whole, gives then a measure of the
policy’s impact and burden sharing implications.
The GEM-E3 model is built in a modular way around its central CGE core. It
supports defining several alternative regimes and closure rules without having to
re-specify or re-calibrate the model. The most important of these options are
presented below:
Alternative behavioural/closure options in GEM-E3
• Multiple linked countries or single country
• Capital mobility across sectors and/or countries, or no capital mobility
• Demand structure reflecting segmented/ partially integrated/ totally integrated multicountry markets
• Flexible or fixed current account (with respect to the foreign sector)
• Flexible or fixed labour supply
• Market for pollution permits national/international, environmental constraints
• Fixed or flexible public deficit
• IS-LM closure
• Nash-Bertrand or Nash-Cournot or perfect competition assumptions for market
competition regimes
12
D I R E C T I O N
O F
O N - G O I N G
M O D E L
D E V E L O P M E N T S
As already explained the GEM-E3 model provides a modular platform on which
several modelling extensions can be incorporated. Further modelling
developments are envisaged in relation with the policy inquiries as actually prevail
in Europe: sustainable development and burden sharing in the presence of
externalities, unemployment, economy integration and the management of
transition, and how to influence the evolution of technology and growth.
The above naturally dictate the main axes of on-going development of the GEME3 model:
1. The disaggregated specification of the labour market in labour skills
and of consumption in income classes along with the explicit
incorporation of imperfect competition in the labour market, to
reflect for example the bargaining power of unions.
2. The endogenous representation of technology evolution and the
process of innovation as the potential outcome of conscious effort of
the economic agents and its diffusion across countries/sectors. This
can allow for potential growth, which is often called in the literature
“endogenous growth” being of key importance for assessing the
longer-term implications of policy issues.
3. The engineering representation of the energy system, through a
separate energy sub-module (following a mixed-complementarity
approach) that will be integrated in the model.
4. The extension of the model to incorporate the accession countries
and their gradual adaptation to the single market.
13
2
Chapter
Model presentation
The structure of this chapter is as follows: The
core model structure is presented first. Seven
model extensions (either operational or at an
advanced point of development are presented
afterwards. These are:
Model Extension
Current Status
(end 1997)
Environmental
module
Operational. Implemented
in main model version
Representation of
market
imperfections
Operational. Implemented
in model version GEME3-SM
World Closure
Operational. Usually used
as sensitivity test.
Endogenous
Technology
Evolution
Two prototype versions
operational. Full
incorporation of
endogenous growth
mechanisms planned for
1998-99.
Labour market
imperfections and
disaggregation
Specifications ready.
Implementation planned
for 1998.
IS/LM closure
Operational. Not
implemented in main
model version.
Engineering
representation of
energy
Prototype version under
construction. Planned
incorporation in main
model version early 1998.
A technical presentation of the model is given
in this chapter.
Introduction
The GEM-E3 model, is an operational, empirical model,
which follows the computable general equilibrium
methodology. The model aims at representing the
interactions between the economy, the energy system and
the environment. It clears the markets either at countryspecific level (European Union member-states) or Europewide. At present, version 2.0 of GEM-E3 is operational,
while further development is underway.
The CGE framework requires that all markets clear
through prices. This procedure is usually called
price-adjustment of the markets. The core version of the
model assumes a prefect competition regime for this priceadjustment of markets, in particular for the markets of
commodities. Under such a perfect competition regime a
single representative firm is considered per sector
producing a commodity. The core version of the model
assumes an imperfect competition regime only for the
labour market. Extensions of the model have assumed that
some sectors operate under an oligopolistic competition
regime. In that case, the single representative firm (per
sector) assumption is replaced by a consideration of a finite
number of firms per sector and the corresponding
commodity varieties.
The core model version, which is a stylised CGE model
integrating the environment, constitute version 2.0 of the
model, which has been used in a number of studies, in
particular regarding CO2 mitigation policies. This core
14
model version is presented in this chapter.
The model version GEM-E3-IM incorporates imperfect competition, economies
of scale, product varieties and market integration. This version has been used for
the evaluation of the European single market. It is presented in the next chapter.
Several prototype versions of the model have been also constructed, as part of
research activity with GEM-E3.
Two of these activities have dealt with the model closure. One of the model
versions introduced a world closure, in which the rest of the world reacts upon the
equilibrium obtained in the European Union by adjusting prices and supply. This
closure has been tested through a number of sensitivity analysis runs. Another
model version has introduced a financial-monetary sub-model that acts as a
closure of the model. The closure completes an IS-LM type of economic
mechanism and allows for the analysis of implications of public budget financing
on the real-side of the economy (through the endogenous re-adjustment of the
interest rate). The IS-LM closure is operational and has been used in early studies
on stabilisation and public deficit policies.
Two other activities have dealt with the endogenous representation of technology
evolution. Technology is perceived in the model through factor productivity, as
extended to all inputs to the production process. In one of these activities, the
endogenous investment on energy efficiency improvement has been modelled.
The corresponding operational version of the model has been used for the
analysis of CO2 mitigation policies in the EU. Another activity formulated an
endogenous growth link connecting productivity growth to R&D expenditure. An
operational model version exists and has been tested in a number of sensitivity
analysis runs.
Finally, two research directions are under development, for which specifications
and first prototypes are currently available. The first concerns the disaggregation
of labour and the representation of labour market imperfections influenced by the
bargaining power of unions. The second concerns an engineering-oriented
modelling of energy supply and price formation. Both sub-models will be
incorporated in the core model version by 1998.
General Presentation of the Core Model
The model clears simultaneously the markets of commodities and primary factors
(labour, capital). The equilibrium prices for these markets are explicitly computed,
so the model is able to support policy analysis of taxation and consider alternative
price setting circumstances.
The demand and supply functions, interacting across the markets, represent
micro-economic behaviour of economic agents. These are producers, consumers,
government and foreign sector. The producers are identified as sectors (columns)
of an Input-Output framework. They aim at maximising their profits in the short
15
run, and they are constrained by physical capital stock (fixed within the current
period) and available technology. Producers can change their physical capital stock
over time, by means of investment. Producers are also demanders of goods,
services, capital and labour.
The consumers are identified as households and are grouped in social categories
(not available in the present model version that includes one representative
household). Households’ demand for goods and services is a part of final demand
of the Input-Output framework. Households aim at maximising their intertemporal utility under an inter-temporal budget constraint. On this basis, the
derived steady-state formulation is included in the model, defining their level of
consumption, savings and leisure. Therefore, they also define their supply of
labour force.
The behaviour of the government is largely exogenous and concerns public
expenditure, public investment, taxation, subsidies and social policy.
Seen from the perspective of a single country, the behaviour of the foreign sector
depends on the economic conditions of other countries. The model considers
simultaneously the European Union countries as linked together and, moreover,
their links with the rest of the world. It is constructed as a single system of
equations that incorporate simultaneously the equilibrium markets of all European
countries. Endogenous foreign trade links the countries forming a closed loop.
This is formulated in a way to ensure, in all cases, equality between imports by one
country and the corresponding exports of another country (in volume and value),
a condition that corresponds to a trade matrix with zero trade deficit (in value) at
the global level.
At an equilibrium point, supply equals demand in all markets and prices are such
that all agents optimise their behaviour. At that point, all producers achieve zero
profits and all consumers fully use their budget. Moreover, that point corresponds
to a distribution of revenues and payments across the economic agents. Their final
economic balance may be in a surplus or deficit situation, depending on their
consumption and savings decisions. The model is designed in such a way that the
algebraic sum of agents' surplus or deficit is equal to zero, at the equilibrium point.
This corresponds to the Walras law.
At a given non equilibrium situation, the Walras law is not necessarily satisfied.
Moving towards the equilibrium point, the model activates appropriate adjustment
processes for all agents, so as to reach an equilibrium that satisfies the Walras law.
The type of adjustment process, that achieves consistency of transactions at the
macro-economic level, is often called macro-closure. In a traditional CGE model,
the model builder has to choose a particular macro-closure, because the model has
exactly one degree of freedom, since the equilibrium depends only on relative
prices (the price level that is set, is called numeraire). That choice of macro-closure
is particularly important for appraising the model properties and can characterise a
model independently of the way markets clear. GEM-E3 generally follows the
investment-savings global closure, which can be optionally expanded through a
16
detailed financial/monetary system by country (often called the IS-LM closure).
Figure 1 illustrates the overall structure of the GEM-E3 model.
Figure 1: The overall structure of the GEM-E3 model
Imports
Exports
P
E
U
N
|Goods
Market
Equilibrium
B
V
L
I
I
Consumption
Domestic
R
O
C
Investment
Labour
Market
Labour
Labour
Investment N
P
M
O
Revenues
E
L
N
I
T
Income Flows and Transfers
Allocation across Economic Agents
C
A
Y
L
Households
Government
Consumers
Foreign
Investment Financing
Real Interest Rate
IS-LM
The Social Accounting Matrix
I
The definition of economic agents and their transactions follows the framework
of a Social Accounting Matrix - SAM (a schematic representation is provided in
Figure 2). A SAM is an extended Input-Output table, which is complemented by a
table of income flows and transfers between agents. A SAM ensures consistency,
completeness and balance of flows from production to the agents and back to
consumption. The design of a SAM characterises the disaggregation details of a
computable general equilibrium model.
17
Figure 2: Social Accounting Matrix (SAM)
PAYMENTS
SECTORS
SECTORS
AGENTS
INTERMEDIATE
CONSUMPTION
FINAL DEMAND
RECEIPTS
AGENTS
REVENUES
FROM SECTORS
TRANSFERS
SURPLUS OR DEFICIT
BY AGENT
The construction of the SAM is the starting point of the model building work. In
the base year, the definition of the set of prices is such that the balance of flows in
the SAM is satisfied in both constant and current currency. The balance is
conceived as the equality between the sum by row and the sum by column. In
addition, a SAM ensures the fulfilment of the Walras law in the base year, since by
construction the algebraic sum of surplus or deficits of agents is equal to zero. To
understand the notation used, Figure 3 gives a more detailed presentation of the
SAM framework, as used in GEM-E3.
The SAM of GEM-E3 represents flows between production sectors, production
factors and economic agents. The production sectors produce an equal number of
distinct goods (or services), as in an Input-Output table. Production factors
include, in the SAM, only primary factors, namely labour and capital. These are
rewarded by sharing sectoral value added. The economic agents, namely
households, firms, government and the foreign sector, are owners of primary
factors, so they receive income from labour and capital rewarding. In addition,
there exist transactions between the agents, due to taxes, subsidies and transfers.
The agents partly use their income for consumption and investment, and form
final domestic demand. The foreign sector also makes transactions with each other
sector. These transactions represent imports (as a row) and exports (as a column)
of goods and services. The difference between income and spending (in
consumption and investment) by an economic agent determines his surplus of
deficit.
18
Figure 3: The Social Accounting Matrix
REVENUES
EXPENDITURES
→
↓
Sectors
Factors
Agents
Investment
& Stocks
Total
expend.
intermediate
consumption
0
demand for goods
for consumption
and exports
demand for
goods for
investment
total demand of
goods
rewarding of factors
from value added by
sector
0
income transfers
from foreign
0
indirect taxes,
VAT, subsidies,
duties and
imports
0
factor payments to
agents according
ownership
income transfers
between agents
0
0
0
Total
Revenues
total supply of goods
total payments of
factors
total revenues
minus investment
and stocks
total spending of
agents
Surplus or
Deficit
0
0
lending (+ or -)
capacity by sector
(Sum = 0)
0
Goods
from
Sectors
Factors
(labour
and
capital)
Agents
Gross
Savings
total factor
revenues
total income of
agents
0
Model Core structure
C O N S U M P T I O N
In every period, households allocate their total income between consumption of
goods (both durables and non-durables) and services and savings. They receive
income by providing labour services to firms and the government but they also
receive several non-wage transfers (interest payments from assets, dissemination of
firms profits, social benefits, transfers from other countries). Households’
behaviour is modelled through one representative consumer for each EU country.
Her behaviour is assumed to be formed as a sequential decision tree: based on
myopic assumptions about the future she decides the amount of leisure that she is
wishing to forsake in order to acquire the desired amount of income (thus also
defining labour supply behaviour). Disposable income is then optimally allocated
between consumption and savings. At the second level of the decision process
consumption is subdivided into demand for specific goods. The consumption
structure is presented in Figure 4.
The consumption-leisure choice of the households is considered as being derived
from an optimal control problem. In that the consumer wishes to maximise her
intertemporal utility subject to an intertemporal budget constraint defining her
total available resources. It is assumed that at the end of her life she will have no
savings left.
19
The GEM-E3 implementation involves the following LES (Cobb Douglas) utility
function1:
U = ∑ (1 + stp ) ⋅ (β H ⋅ ln (HCDTOTVt − CH t ) + β L ⋅ ln (LJVt − CLt ))
−t
t
where HCDTOTV represents the consumption of goods (in volume), LJV the
consumption of leisure in year t , stp the subjective discount rate of the
households, or social time preference, CH the subsistence quantity of consumption,
CL the subsistence quantity of leisure, and BH and BL the respective shares of
consumption and leisure on the potential disposable income of the households
(YDISP + PLJ ⋅ LJV ) .
Figure 4: The consumption structure of the GEM-E3 model
Total Income
Disposable income
Leisure
Savings
Labour Supply
Investment in
dwellings
Monetary Assets
Consumption
Durable goods
• Cars
• Heating Systems
• Electric Appliance
Non-durable goods and
services
•
•
•
•
•
Consumption of non-durables
linked to the use of durables
•
•
•
•
•
•
Food
Clothing
Housing
Housing furniture and
operation
Medical care and health
expenses
Purchased transport
Communication
recreation, entrertainment etc.
Other services
Fuels and power
Operation of transports
Equations without numbering are not included in the model text, as they are only intermediate steps
used for the derivation of other formulas.
1
20
The general specification of the problem can be written as follows:
∞
Max U = ∫ f (c t )e − ρt dt
0
where ρ represents the subjective rate of time discount. The
consumer then chooses a time path of consumption ct that
maximises his utility subject to the following budget constraint:
BC = wt + rt a t − c t
where wt is the wage income, rt is the real interest rate, and at is the
asset accumulation. Although this problem can readily be solved2 it is
often easier to solve its discrete time approximation3.
The expenditure choice is subject to the following budget constraint, which states
that all available disposable income will be spent either now or some time in the
future:
∑ (1 + r ) ⋅ (HCDTOT
−t
t
− CH t ⋅ PCI t + PLJ t ⋅ LJVt − CLt ⋅ PLJ t )
t
= ∑ (1 + r ) ⋅ (YTRt + PLJ t ⋅ LTOTt − PCI t ⋅ CH t − CLt ⋅ PLJ t )
−t
t
where r is the nominal discount rate used, YTR is the total available income of
the households from all sources, excluding wages and PLJ ⋅ LTOT is the value of
their total time resources.
Assuming in the above equation that, at the aggregate level, the values at the right
hand side increase at constant rates (say, according to the wage rate), then,
remembering that for a given year (for example t=0) the following identity holds
YTR + PLJ ⋅ LTOT = YDISP + PLJ ⋅ LJV , the right hand side of the above
becomes:
For a detailed presentation of the derivation of the demand functions using optimal control see C.
Lluch (1973). The results obtained are identical to the ones presented below.
2
3
A similar formulation can also be found in Jorgenson et. al (1977).
21
∑ (1 + r ) (1 + f ) (YDISP
−t
t
0
+ PLJ 0 LJV0 − PCI 0 CH 0 − CL0 PLJ 0 )
t
 1+ r 

= (YDISP0 + PLJ 0 LJV0 − PCI 0 CH 0 − CL0 PLJ 0 ) ⋅ ∑ 
t
 1+ r
= 
1+ f
−t
1 + f 
−t

 (YDISP0 + PLJ 0 LJV0 − PCI 0 CH 0 − CL0 PLJ 0 )

where the first factor in the above equation is the inverse of the real discount rate,
1
which we assume equal to the real interest rate .
r
Taking the Lagrangian of the above problem (maximise utility subject to the
budget constraint) the first order conditions are obtained. These comprise of the
budget constraint, plus the two derived demand functions.
(1 + stp )−t ⋅ β H ⋅ (HCDTOTt − CH t ) − λ ⋅ (1 − r )−t ⋅ PCI t
(1 + stp )−t ⋅ β L ⋅ (LJVt − CLt ) − λ ⋅ (1 − r )− t ⋅ PLJ t
=0
=0
the value of the Lagrangian multiplier λ can be found by summing up these
equations over time, and substituting them into the budget constraint.
Expressing now the above equations for the current time period (t=0) and using
the value of the multiplier, the two demand functions to be used in the model are
obtained:
CV = CH +
βH
stp
(YDISP + PLJ ⋅ LJV − Obl )
r PCI ⋅ (β H + β L )
(1)
LJV = CL +
βL
stp
(YDISP + PLJ ⋅ LJV − Obl )
r PLJ ⋅ (β H + β L )
(2)
where Obl = PCI ⋅ CH + PLJ ⋅ CL is the minimum obliged consumption.
Given the fact that the model is calibrated to a base year data set in which
households have a positive savings rate, STP is computed to be less than
RLTLR . The savings rate computed from the above is not fixed but rather
depends on such factors as the social time preference, the real interest rate and the
relative shares of consumption and leisure in total potential disposable income.
Total consumption is further decomposed into demand for specific consumption
goods. Two main types of goods are identified: durable and non-durable4. The
rationale behind this distinction is the assumption that the households obtain
4
The specification follows Conrad and Scroder (1991).
22
utility from consuming a non-durable good or service and from using a durable
good. So for the latter the consumer has to decide on the desired stock of the
durable as based not only on the relative purchase cost of the durable, but also on
the cost of the related non-durable commodities (as for example fuels for cars or
for heating systems).
The consumer allocates her expenditures in order to minimise her expenditure
function given a specific level of utility U . Through this procedure one demand
function is derived for each consumption category defining desired consumption
of non-durable (including the amount needed to operate the durable) and desired
stock of durable goods. Non-durable goods and services are denoted by the index
ND while durable by the index DG.
The expenditure function in GEM-E3 has the following form:
E (U , p, SDG ) = ∑ PC ND ⋅ γ ND + U ⋅ ∏ (SDG − γ DG )
− β DG
ND
DG
⋅ ∏ PC ND
β ND
ND
where U is the level of utility, PC is the price for the durable and non-durable
goods, SDG is the stock of durable, γ is the minimum obliged consumption and
β is the elasticity in private expenditure by category. By minimising the above
function we obtain the Hicksian derived demand functions for the non-durable
goods:
 β
HCFV ND = γ ND +  ND
 PC ND
 

 ⋅  HCNDTOT − ∑ PC ND ⋅ γ ND 
ND

 
The demand for durable goods is obtained by differentiating the above
expenditure function with respect to the stock of each of the durable. This
quantity represents the amount of non-durable goods that the consumer is willing
to forsake for one extra unit of the particular durable:


β DG  HCNDTOT − ∑ PC ND ⋅ γ ND 
∂E

ND

=−
∂SDG
SDG − γ DG
where HCFV is the demand for durable goods and non-durable goods and
HCNDTOT is the consumption of non-durable goods.
To calculate the desired stock levels of the durable goods, this quantity is set equal
to the marginal cost of holding one more unit of a durable goods for one period.
The marginal cost is the user costs (or rental equivalent cost) of the durables and
include interest charge, deterioration in the stock and property taxes. The desired
stock level of the durables is:
 β DG
SDG = γ DG + 
 PDUR DG
 

 ⋅  HCNDTOTV − ∑ PC ND ⋅ γ ND 
ND

 
23
(3)
while the durable user cost (PDUR ) is:
PDUR DG = PC DG ⋅ (r + δ DG ) + TX PROP , DG ⋅ (1 + r )+
∑γ
LND
⋅ PC LND , DG
(4)
LND
where r is the real interest rate, δ DG is the replacement rate for durable goods,
TX is the property tax for the durables and LND is the set defining all linked
non-durable goods.
The last part of the user cost equation links some non-durable goods to the use of
durables. Energy is the main linked non-durable good. Energy complements the
use of durables in order for them to provide a positive service flow. Consumption
of energy does not affect the expenditure of durables through the change in
preferences but rather through the additional burden in the user cost. The
demand for linked non-durable goods, coupled with the use of the durable is then:
LLNDC ND = ∑ λ DG ⋅ (θ ND , DG SHINV )
(5)
DG
where λ DG measures the proportion of the consumption of the linked nondurable good that is used along with the durable so as to provide positive service
flow, θ ND, DG represents the minimum consumption of the non-durable that is
needed for a positive service flow to be created. If there is no need for nondurable good the θND , DG in the first equation of the linked non-durables becomes
zero formulating with that way the demand for non-linked non-durable goods.
Therefore:
 β
HCFV ND = CH ND +  ND
 PC ND
+ LLNDC ND


  HCNDTOT − ∑ PC ND ⋅ γ ND 
ND


(6)
Total households’ expenditure is then the sum of consumption (for non-linked
non-durables) plus investment in durables plus consumption in non-durables used
with durables.
C = HCNDTOT + ∑ HCFV + LLNDC
(7)
DG
where
∑ HCFV
represents the change in stocks of durables or in other words,
DG
the net investment that is necessary to move towards the long run equilibrium
durable goods levels. Assuming a rate of replacement δ , this investment is equal
to:
HCFV DG = SHINV DG − (1 − δ ) ⋅ SHINV DG [− 1]
24
(8)
Evaluation of Changes in Consumers’ Welfare
Every policy simulation can be uniquely characterised by its effect on the welfare
index, or more specifically through the implied equivalent variation change. Giving
the index A in a policy simulation and B in the reference situation, the equivalent
variation of the scenario is given as:
(
)
(
)
(
EVt U tA ,UT = C tH U tA , PCI tB , PLJ tB − C tH U tB , PCI tB , PLJ tB
)
for every time period t. Summing over the whole time period, the present value of
the equivalent variation is obtained:
(
)
T
A
A 
 1
EV = e −γ ⋅η0 ∑ 
⋅ ∆PCI tB ⋅ ∆PLJ tB e γ ⋅U t − e γ ⋅U t 
t = 0 1 + ρ

(9)
where
 PCI tB
∆PCI = 
B
 PCI 0
B
t



βH
 PLJ tB
and ∆PLJ = 
B
 PLJ 0
B
t



βL
represents weighted changes in the consumer’s price index and the valuation of
leisure (equal to net wage rate) between the reference and the counterfactual
simulation.
F I R M S
B E H A V I O U R
Domestic production is formulated for all varieties of commodities. A type of
commodity corresponds to a sector in those sectors where perfect competition is
assumed to prevail, hence in all the sectors of the core model version 2.0. In
oligopolistic competition sectors as formulated in the GEM-E3-IM model version
(see next chapter), several varieties of commodities are produced by a sector, each
variety corresponding to one firm of the sector. In any case, the definition of
sectors follows the sectoral decomposition of the Input-Output table.
In the core model version where perfect competition prevails in all sectors a single
representative firm is assumed to operate. Each sectors is assumed to produce a
single homogeneous good, which is differentiated from any other good in the
economy and is supplied to a market for this good. To produce that good, the
sector purchases all goods and two primary production factors, namely labour and
capital.
All production factors (all goods and the two primary factors) are endogenous and
their purchase depends on relative factor prices. The substitution possibilities
across production factors depend on a pre-specified separability scheme that is
presented in Figure 5. The production-nesting scheme retained for the core model
version has been specified on the basis of a literature survey related to
econometric estimation of flexible functional forms for production functions. As a
CGE model is calibrated, the choice of flexible functional forms is not possible,
since this involves a large number of degrees of freedom, related to the values of
25
parameters. The econometrics on flexible forms provides information on the
substitutability or complementarity of production factors.
For example, in Figure 5 a close connection between electricity and capital is
retained, along with a weaker relationship between electricity and other energy
fuels. Also, a strong relationship between labour, raw materials and non-electricity
fuels has been retained to capture the on-going restructuring in heavy energy away
from traditional heavy-energy intensive processes.
Figure 5: Production nesting scheme in the GEM-E3 model5
Production (output)
Labour
Energy
Materials bundle
Capital
Agriculture
Ferrous, ore, metals
Electricity
chemicals
Other en. intensive
Electrical goods
Transport equip.
Other equipment
Consumer goods
Coal
Oil
Fuels
Gas
Labour
Materails
Fuels bundle
Labour
Building/Constr.
Telecommunication
Credit & insurance
Materials
Credit & insurance
Market services
Non-market services
The optimal production behaviour can be represented in a primal or
dual formulation. Their equivalence, under certain assumptions, can
be easily verified within the theory of production behaviour.
Specifically, the production part of the model consists of both the
primal and dual production functions, the n derived demand
functions, where n is the number of production factors taking part in
the production process, and the zero profit equation. In that way, a
system of n+3 equations is created where n+1 are needed for its
5 Production factors are denoted by bold letters and are in rectangle. Round boxes represent
intermediate bundles of goods with no physical relevance.
26
solution. Given any functional form for the production possibility
frontier the following equations specify the producer’s demand for
production factors:
(
XDi = f XI i j , K i ,t , Li , e t
)
where XDi is domestic supply of good i by sector i , XI i j is
intermediate consumption of good j by sector i , K i ,t is capital
cost (fixed within the current period t ), Li is labour force, e t
denotes technical progress which is separately embedded in each
production factor and f is any functional form obeying a set of
standard assumptions;
Pi
∂XDi
= PI i j computing XI i j
j
∂XI i
where Pi is the selling price of good i and PI i j is the purchasing
price of good j used as intermediate consumption by sector i ;
Pi
∂XDi
= PLi computing Li
∂Li
where PLi is the unit cost of labour force used by sector i ;
Pi XDi = ∑ PI i j XI i j + PLi Li + PK i K i
j
computing PK i , where PK i is the effective rate of return of
capital of sector.
The sectoral firm decides its supply of goods or services given its selling price and
the prices of production outputs.
The production technology exhibits constant return of scale in the perfect
competition sectors. The firm supplies its good and selects a production
technology so as to maximise its profit within the current year, given the fact that
the firm cannot change the stock of productive capital within this period of time
(or is constrained by totally available capital in case of capital mobility). The firm
can change its stock of capital the following year, by investing in the current one.
Since the stock of capital is fixed within the current year, the supply curve of
27
domestic goods is upwards sloping and exhibits decreasing return to scale6. The
current model version implements a putty-putty scheme and does not represent
capital vintages.
The production scheme adopted in GEM-E3 is based on a CES neo-classical type
of production function and assumes nested separability involving capital (K),
labour (L), energy (E), and materials (M). Energy and materials are included in the
intermediate consumption (IOV), following the sectoral classification of the
model.
The choice of nesting scheme of production in GEM-E3 has been guided by
available econometric estimations of KLEM production functions for European
Union countries.
The primal production function has the following form:
σ
XD PR
1
σ −1 σ −1
σ −1
 1

= δ1σ, PR ⋅ ( KAV PR ⋅ e tgk PR ⋅t ) σ + δ2σ, PR ⋅ LEM PRσ 


(10)
where XD PR is the domestic production, KAV PR is the fixed capital stock,
LEM PR is the Labour-Energy-Materials bundle in production,σ is the elasticity
of substitution between KAV PR and LEM PR , tgk is the technical progress of
capital, and δ1,PR andδ2,PR are scale parameters derived from the base year data
set. The scale parameters are calibrated using the observed values and volumes and
the substitution elasticities:
(
δ1, PR = VSH KAV , XD
(
)
σ
δ1, PR = 1 − VSH LEM , XD
0

 KAV PR

⋅
0

 XD PR
)
σ
1− σ
and
0
 LEM PR

⋅

0
 XD PR

1− σ
where VSH KAV , XD and VSH LEM , XD are the base year value shares of capital and
Labour-Energy-Materials bundle in production respectively.
The dual function representing the unit production cost, on the other hand, is
expressed as follows:
This description applies only to the most rigid of the capital mobility assumptions that are available in
the model variants, where capital is assumed immobile across sectors and countries in static terms.
When capital is assumed malleable across sectors and/or countries, then the capital stock by sector can
adjust even in static terms, but the overall capital resources available to the economy (of the country or
the EU as a whole) within each time-period are constant.
6
28
1
PD PR
1− σ
1− σ

1− σ 
 PK PR 
= δ1, PR  − tgk PR ⋅t 
+ δ 2, PR ⋅ PLEM PR 
e



where PD PR is the deflator in domestic production and PK PR and PLEM PR are
the effective capital rate of return for fixed capital and the deflator of LabourEnergy-Materials bundle respectively. This equation is not used in the model, since
PD PR will be computed in a subsequent section as the equilibrium price that
clears the goods market. The derived demand for the Labour-Energy-Materials
bundle is:
LEM PR
 PD PR 
= XD PR ⋅ δ LEM , PR ⋅ 

 PLEM PR 
σ1
where δLEM , PR is the scale parameter estimated from the base year data with a
similar way of the estimation of δ1,PR and δ2,PR
KAV PR = XD PR ⋅ δ KAV , PR
 PD PR 
⋅

 PK PR 
σ2
⋅ e tgk PR ⋅t ⋅(σ 2 −1)
(11)
σ2
 PD PR 
Equation ( KAV PR = XD PR ⋅ δ KAV , PR ⋅ 
 ⋅ e tgk PR ⋅t ⋅(σ 2 −1)
 PK PR 
(11)) is then used to compute the rate of return of capital (in the model
version with fixed sectoral capital stock) or the demand for capital (if capital is
assumed mobile). In the latter case the rate of return of capital PK PR will be
computed as the equilibrium price that equalises demand and supply of capital7.
Similar formulas can be derived for the other levels of the nesting scheme of the
production function, always linking the demand for a factor at a lower level of the
nesting scheme to the bundle to which it belongs. Finally a cost-minimising
demand for each production factor (all intermediate goods, capital and labour)
(
ENLPR = f XDPR , δ ENL , PR , PELPR , PD PR , e tgePR ⋅t ⋅(σ 2 −1)
(
LAV PR = f XDPR , δ LAV , PR , PLPR , PD PR , e tgl ⋅t ⋅(σ 2 −1)
(
)
)
IOVE PR , BR = f XDPR , δ IOVE , PR , PIOBR , PD PR , e tgi⋅t ⋅(σ 2 −1)
(
(12)
(13)
)
IOVM PR , BR = f XDPR , δ IOVM , PR , PIOBR , PD PR , e tgi⋅t ⋅(σ 2 −1)
(14)
)
(15)
The equilibrium of the various markets that are represented in the model are discussed in a later
section.
7
29
where ENLPR is the demand for electricity, PELPR is the corresponding deflator,
tge PR is the technical progress in energy use, LAV PR is the labour demand, PLPR
is the unit cost of labour and tgl PR is the technical progress of labour. EN PR is
the demand for energy, PE PR is the unit cost of energy. The last two equations
represent the demand for intermediate consumption of commodity BR used in
the production of sector PR ( IOV PR, BR ) with PIO BR being the unit cost of the
intermediate good. The unit labour cost is computed through the average wage
rate that comes from the equilibrium of the labour market.
PLPR = f (WR)
(16)
Under the above specification, the zero profit condition is always satisfied (and
hence not included in the model text):
PD PR ⋅ XD PR = PK PR ⋅ KAV PR + PLEM PR ⋅ LEM PR + ∑ IOV PR ⋅ PIO PR
PR
I N V E S T M E N T
The comparison of the available stock of capital in the current year with the
desired one (based on backward looking expectations about the evolution of the
economy), determines the volume of investment decided by the firms.
Investment serves to expand capacity for the next year and replaces obsolete
capital stock, which is determined by means of a fixed rate of replacement δ . An
investment matrix with fixed technical coefficients transforms investment by
sector into demand for capital goods, which contribute to the formation of total
final demand for goods and services.
The desired stock of capital in the next year is derived from profit
maximisation seeking to achieve an optimal level of long run rate of
return of capital, given expectations about future user’s cost of
capital. The optimal long-run rate of return of capital is derived
according to Ando-Modigliani formula8 involving the real interest
rate augmented by the depreciation rate.
In the model variant without capital mobility, capital is fixed by sector,
KAVi, t = fixed from previous period
while when capital is mobile, capital stock is derived from the production function,
under a global capital stock constraint (defined over the area of capital mobility).
In this case, there is only one average rate of return of capital for the economy,
which is the shadow price of the constraint defining total available capital stock.
The amount of capital allocated to the sector is then the one to which the optimal
amount is compared.
8
See Ando, Modigliani et.al (1974).
30
The optimal capital stock is obtained using the optimal long-run rate of return of
capital PINVPR ⋅ ( r + δ1 )σ .
KAV i ,t derived from PD i
∂XD i
= PINVi ( r + δi )
∂KAV i , t
where KAV i , t is the desired stock of capital, PINV i is the unit cost of
investment of sector i , r is the market interest rate and δi is the replacement
rate of capital stock in sector i .
The difference between KAVi ,t and KAV i , t together with the producers’
expectations is used to define sectoral investment:


KAVPR
INVVPR = 
T 1/ σ  ⋅
 (1 − (1 − δ1 ) ) 
(17)



PK PR
⋅ (1 + STGR )T ⋅ etpk ⋅T ⋅( σ −1) − (1 − δ1 )T 

σ
PINV
r
⋅
+
(
)
δ

PR
1


where T is the duration of the time period , PINV PR is the cost of investments
and STGR PR is the expected growth rate of the sector.
The next period capital stock is given by the equation:
 1 − (1 − δ1 ) T 
 ⋅ INVV PR
KAVC PR = (1 − δ1 ) T ⋅ KAV PR + 
δ1


(18)
The same investment function applies to imperfect competition sectors as well.
D E M A N D
General Specification
Total domestic demand is constituted by the demand for products by the
consumers, the building of investments, the producers (for intermediate
consumption) and the public sector.
Total demand is allocated between domestic products and imported goods,
following the Armington specification. According to the Armington specification9,
sectors and consumers use a composite commodity that combines domestically
produced and imported goods, which are considered as imperfect substitutes. The
buyer of the composite good seeks to minimise his total cost and decides the mix
of imported and domestic products so that the marginal rate of substitution equals
to the ratio of domestic to imported product prices. The buyer’s total cost is called
absorption. In GEM-E3 we assume that the buyer’s decision is uniform
throughout the economy, therefore we apply Armington specification at the level
of total domestic demand for each sector.
9
See Armington (1969).
31
GEM-E3 employs a nested commodity aggregation hierarchy, in which sector’s i
total demand is modelled as demand for a composite good or quantity index Yi ,
which is defined over demand for the domestically produced variant ( XXDi ) and
the aggregate import good ( IMPi ). At a next level, demand for imports is
allocated across imported goods by country of origin and finally (in the sectors
with imperfect competition) between firms in the country of origin. Domestic
demand for domestic goods is also allocated across firms. See Figure 6.
Figure 6: Nesting Scheme of Demand
Demand Structure
The minimum unit cost of the
composite good determines its selling
price. This is formulated through a
CES unit cost function, involving the
selling price of the domestic good,
which is determined by goods market
equilibrium, and the price of imported
goods, which is taken as an average
over countries of origin. By applying
Shephard’s lemma, we derive total
demand for domestically produced
goods and for imported goods.
Domestic Consumers (final and
intermediate)
Demand for goods and services
Domestically produced
goods
Imported goods from
EU or RW
Goods from EU
Goods from RW
Split in EU countries
Domestic firms
Other EU firms
RW firms
The specification described above corresponds to the model variant where EU
markets are assumed segmented. Another alternative assumption that is available
as an option in GEM-E3, is that consumers treat all EU products (whether
domestic or imported) as close (in the case of the “market integration” variant of
the model) or perfect (in the case of the “advanced market integration” variant of
the model) substitutes. In the latter case consumers allocate their demand across a
pool comprising of all firms situated within the EU, without being interested in
the country of origin but only on relative prices. In what follows only the
specification reflecting segmented markets is presented.
Demand is allocated between domestic and imported goods according to the
following CES functional form:
σx
YPR
σ x −1 σ −1
1
σ x −1
 1
 x
σ
σx
σx
σ
= δ1, PR ⋅ ( XXD PR ) x + δ2 , PR ⋅ ( IMPPR ) x 


where XXD PR represents the demand for domestic production, IMPPR is the
demand for imports, δ1,PR and δ2,PR are scale parameters estimated from the base
year data related with the value shares of XXD PR and IMPPR in the demand for
composite good YPR . Finally, σ x is the elasticity of substitution between domestic
and imported goods. The corresponding dual formulation is:
32
PYPR
[
( 1− σ )
( 1− σ )
1
=
δ σ ⋅ PIMPPR + (1 − δ )σ ⋅ PXD PR
AC
]
1
1− σ
(19)
where PYPR stands for the absorption price of composite good, PIMPPR is the
price of imported good PR computed as an average over all trading partners, and
PXD PR is the price of the domestically produced good. AC is a scale parameter
in the Armington function.
The budget constraint is this case, simply states that total expenditures are split
between domestic and imported commodities.
PYPR ⋅ YPR = PXD PR ⋅ XXD PR + PIMPPR ⋅ IMPPR
The optimal demand for domestic and imported goods is obtained by employing
the Shephard’s lemma.
XXD PR = YPR ⋅ AC
IMPPR = YPR ⋅ AC
B I L A T E R A L
T R A D E
F L O W S
( σ x −1 )
( σ x −1)
⋅ (1 − δ )
⋅δ
σx
σx
 PYPR 
⋅

 PXD PR 
 PYPR 
⋅

 PIMPPR 
σx
(20)
σx
(21)
Bilateral trade flows are treated in GEM-E3 endogenously. Imports demanded by
the EU countries from the rest of the world are supplied by the latter flexibly.
However, the EU countries consider the optimal allocation of their total imports
over the countries of origin, according to the relative import prices. Each country
buys imports at the prices set by the supplying countries following their export
supply behaviour. Of course, the supplying countries may gain or loose market
shares according to their price setting. When importing, the EU countries
compute an index of mean import price according to their optimal allocation by
country of origin. This means import price is then compared to the domestic
production (this corresponds to an Armington assumption).
The model is not covering the whole planet and thus the behaviour of the rest of
the world (RW) is left exogenous. Imports demanded by the rest of the world
depend on export prices set up by the European Union countries, while exports
from the rest of the world to the EU sold at an exogenous price. The imports
demanded by the RW are flexibly satisfied by exports originating by the EU. The
latter consider the profitability of exporting to the rest of the world, exporting to
EU or addressing the goods to their markets. Via these profitability considerations,
the EU countries set their export prices as mentioned above. Within the
European Union, exports are considered homogeneous. This means that the
producer sets a single export price for the European Union countries and another
export price for the rest of the world.
The model ensures analytically that, under the above assumptions, the balance of
trade matrixes in value, and the global Walras law, are verified in all cases. A trade
33
flow from one country to another matches, by construction, the inverse flow. The
model ensures this symmetry in volume, value and deflator. It is obvious, then,
that the model guarantees (in any scenario run) all balance conditions applied to
the world trade matrix, as well as the Walras law at the level of the planet (see
Figure 7).
Import demand is allocated across countries of origin using again a CES functional
form. In equation below, EU and CO denote the countries. Index EU refers to
European Union countries, while index CO also includes the rest of the world10.
1
PIMPPR , EU

 1−σ
(1− σ )
= ∑ β σ ⋅ PIMPO BR
, EU , CO 
 CO

(22)
Figure 7: Trade matrix for EU and the rest of the world
EXPORTER
IMPORTER
TOTAL
IMPORTS
ARMINGTON-TYPE MIX
OF IMPORTS BY ORIGIN
THROUGH RELATIVE EXPORT PRICES
TOTAL EXPORTS
COMPETITIVENESS EFFECTS
EXPORT PRICES FROM
DOMESTIC PRICES
BY COUNTRY
COUNTRY-SPECIFIC
DEMAND BASED ON
RELATIVE PRICES
where PIMPPR , EU denotes price of total imports of good PR demanded by
country EU, PIMPO PR , EU , CO denotes import price of good PR of country EU
originating from country CO, β is the share parameter for Armington and σ is
the elasticity of substitution.
IMPOPR , EU , CO
∂PIMPPR , EU
=
IMPPR, EU
∂PIMPOPR , EU , CO
∀EU ≠ RW
(23)
computing IMPOPR , EU , CO
where IMPOPR , EU ,CO denotes imports of good PR demanded by country EU by
country CO .
34
IMPO PR , RW , EU = α RW
 PWEO PR , RW , EU 

⋅
 PWEO PR , EU , RW 
ε RW
(24)
where IMPO PR , RW , EU denotes imports of good PR of the rest of the world
originating from country EU, α RW is a scale parameter for export demand of the
rest of the world, PWEOPR , RW , EU is the exogenous price of good PR set by the
rest of the world, and PWEOPR , EU , RW is the export price of good PR set by
country EU to the rest of the world.
EXPO PR , CO , EU =
IMPO PR , EU , CO
(25)
EX EU ⋅ EX CO
The previous equation is the one that satisfies the Walras law by equating the
exports of sector PR of country CO to country EU with the imports of sector PR
of country EU from country CO not only in volume but in value as well.
EXPOTPR , EU = ∑ EXPO PR , EU .CO
(26)
CO
where EXPOTPR , EU is the total exports of good PR from country EU and
EXPO PR , EU ,CO denote exports of good PR from country EU to country CO.
F I R M S ’
P R I C I N G
B E H A V I O U R
Firms address their products to three market segments namely to the domestic
market, to the other EU countries and to the rest of the world. Prices are derived
through demand/supply interactions. In any iteration of the model run and before
global equilibrium is achieved, producers face demand for their products. To this
demand they respond with a price. For the PC sectors, since these operate under
constant returns to scale and the number of firms is very large, this price depends
only on their marginal cost of production.
In the core model version a simple specification is followed in which firms do not
differentiate their pricing according to the market segment to which they address
their products, but rather set a uniform price. Differentiation of prices according
to the market segment is formulated in the GEM-E3-IM version of the model.
The producer is assumed not to differentiate his price according to the market to
which he sells his products11. He therefore sells his products at the same price
(equal to his marginal cost reduced by the amount of production subsidies that he
receives).
A simplified version of the model is presented. In reality a number of additional factors are also
present such as the existence of non tariff barriers and the fact that exporting a unit of a good implies
using a number of related banking services and transport costs.
10
Another model variant incorporates a constant elasticity of transformation (CET) function. In this
variant firms try to maximise their profits from selling their commodities, so the prices they address to
different markets are different.
11
35
PXD PR = PD PR ⋅ (1 + TXSUB PR )
(27)
PEX PR = PD PR ⋅ (1 + TXSUB PR )
(28)
where PXD PR denotes domestic supply price addressed to domestic demand,
PEX PR is domestic supply price addressed to exports and TXSUB PR is the rate
of subsidies.
D E R I V E D
P R I C E S
Derived prices are those depending on leading prices, which are derived from
market equilibrium. On derived prices appropriate taxation is applied, to form
prices as perceived by consumers. The main leading price is that of the composite
good PYPR . Depending on the destination of a commodity, differentiated
taxation may be applied, as for example indirect taxation τ PR or VAT. The prices
of goods at intermediate consumption are given in (29), while the prices of goods
in final consumption are computed through (30) for households and (31) for
government. Finally, (32) defines the prices of goods used to build investment.
PIOPR = PYPR + τ PR
(29)
PHCPR = ( PYPR + τ PR ) ⋅ (1 + vat PR ) ,
(30)
where vat PR is a rate of value added tax imposed on good PR .
PGCPR = PYPR + τ PR
(31)
PINVPPR = PYPR + τ PR
(32)
The unit cost of investment by sector of destination (owner) depends on its
composition in investment goods (by sector of origin). This structure is
represented by a set of fixed technical coefficients tcf PR , BR :
PINV BR = ∑ tcf PR, BR ⋅ PINVPPR
(33)
PR
I N C O M E
F L O W S
A N D
A G E N T S ’
S U R P L U S
The formation of income flows among agents is formulated according to the
definitions of the Social Accounting Matrix. The model formulates in a detailed
way a large number of transfers across economic agents12. Income flows,
combined with expenditures in consumption and investment are used to compute
surplus or deficit for each economic agent. Government receives revenue from
indirect taxation, custom duties, direct taxation and social contributions.
Government spends for public consumption and investment and transfers social
benefits to other agents:
The model follows a more detailed Social Accounting Matrix than the simplified outline given in this
paper.
12
36
SURPLUS G =
∑ IOV PR , BR + HC PR

 BR

τ PR 
∑

+ ∑ tcf ⋅ INVV BR + INVH PR + INVG PR 
PR

BR


[
+ ∑ vat PR ⋅ ( PYPR + τ PR ) ⋅ HC PR + ( PINVH PR + τ PR ) ⋅ INVH PR
PR
+ ∑ TXDUTEU ,CO ⋅ PIMPOPR , EU ,CO ⋅ IMPO PR, EU
]
(34)
EU
− HTRA − ∑ ( PGCPR ⋅ GCPR + PINVPPR ⋅ INVGPR )
+ τs ⋅ ∑ PL PR ⋅ LAV PR
PR
PR
where τs is the rate of social security contribution, HTRA denote income
transfers from government to households, GC PR is government consumption,
and PGC PR is the price of government consumption. Finally, SURPLUS h
∀h = G , H , F , W denote surplus or deficit of, respectively, government,
households, firms and foreign sector;
SURPLUS H = HTRA + ∑ PL PR ⋅ LAV PR ⋅ (1 − τ i ) − PC ⋅ HCT
PR
− ∑ TINV PR ⋅ PINV PR ⋅ INVV PR
(35)
PR
where TINV is part of investments financed by the households (usually
investment in dwellings), HCT is total household consumption and INVV is
value of investments.
SURPLUS F =
∑ PK
PR
PR
⋅ KAV PR − ∑ PINV PR ⋅ INVV PR
(36)
PR
SURPLUS W = ∑ PIMPO PR ⋅ IMPO PR − ∑ PEX PR ⋅EXPOTPR
PR
(37)
PR
The model is constructed in such a way that the sum of the consumer surpluses is
zero, in other words the Walras law is always satisfied. This needs not be an
additional model equation, but rather is respected by the construction of the
model as it involves full redistribution of profits (or zero profits) and full spending
of income available for consumption.
T H E
C U R R E N T
A C C O U N T
One of the model versions allows for a free variation of the balance of payments,
while the exchange rate is kept fixed. This assumption is equivalent to the small
open economy13 hypothesis for the EU taken as a whole, vis-à-vis the rest of the
world.
13
Namely, that each EU member state is price taker in imports and non-price maker in exports.
37
An alternative approach, implemented in the GEM-E3 model as an option, is to
set the current account of the EU with the rest of the world (RW) (as a percentage
of GDP) to a pre-specified value, in fact a time-series set of values. This value is
the one obtained, as a result, from the baseline scenario. As a shadow price of this
constraint, a shift of the real interest rate at the level of the EU is endogenously
computed. This shift is proportionally applied to the real interest rates of each
member-state.
E Q U I L I B R I U M
O F
T H E
R E A L
P A R T
Figure 8: Equilibrium in Markets
The equilibrium of the real part is achieved simultaneously
in all the markets following a cobweb process as in Figure
8. In the goods market the equilibrium condition refers to
the equality between the supply of the composite good,
p
related to the Armington equation, and the domestic
demand for the composite good. This equilibrium
q
combined with the sales identity, guarantees that total
resource and total use in value for each good are identical. The equilibrium
condition serves then to determine domestic production. For the sectors in which
imperfect competition is assumed to prevail, the equilibrium is determined at the
level of the firm.
D
S
The equilibrium of the goods markets involves an equality between production
and demand quantities at the sectoral level (in the core model version, or that the
firm level in the GEM-E3-IM version). This condition serves to compute the unit
cost of production (that is of course related to the selling price).
XD PR = XXD PR + EXPOTPR serving to compute PD PR
(38)
xdf PR = xxdf PR + exot PR serving to compute PD PR
(39)
Being within a price-driven equilibrium regime, the labour market is influenced by
the slope of labour supply (as decided by households simultaneously with
consumption and leisure). In this sense, the model assumes that the entire
unemployment is voluntary. However, the model also assumes that, if the
economic conditions are favourable, the households can supply more labour
force, since they have spare time. This concept is used to reflect unemployment
that prevails in European countries, which is further represented by a relatively
high real wage rate elasticity of labour supply. In other terms, we assume that additional
labour force is available to enter the market with some flexibility, but under competitive
equilibrium conditions.
The labour supply is not, nevertheless, totally elastic. This elasticity can be thought
of, as representing the bargaining power of the already employed people. A high
bargaining power would entail that an increase of the labour demand would lead
to an important increase in the wage rate, without any additional employment.
The other extreme would be for the wage rate to remain constant and the
38
employment to increase to cover the whole labour demand. The elasticity used in
the model, falls between these two extremes.
On the demand side we have the labour demanded by firms (as derived from their
production behaviour). The equilibrium condition serves to compute the wage
rate.
∑ LAV
PR
= TOTTIME − LJV serving to compute WR
(40)
PR
which is the average nominal wage rate used to derive the labour cost PLPR 14.
In the case of capital mobility across sectors and/or countries an additional market
is defined: producers demand an amount of capital (as derived from their costminimising behaviour), while the total stock of capital available is fixed within the
time period. The equilibrium of the market defines then the average uniform rate
of return of capital across the area of capital mobility.
If capital is mobile across sectors only then:
KAV _ Supply = ∑ KAV PR
(41)
PR
computing an average country-wide rate of return of capital, while if capital is
perfectly malleable across countries as well:
KAV _ Supply = ∑ ∑ KAV PR
(42)
EU PR
KAV _ Supply is the total amount of capital stock available, fixed within the time
period.
Another market that can be activated in the model is the pollution permits
market15. The supply in this case is fixed, equal to the amount of permits available
within the country (in the case where the permit market in national) or within the
EU (if permits are assumed tradable EU-wide). The demand comes from the
decision of the economic agents (in this case firms and households) that through
cost-minimisation in production, compare the cost of abating emissions (and
perhaps selling permits) to the cost of acquiring an additional unit of permits. The
equilibrium in this case defines the uniform permit price.
14
Other model variants include a Philips curve, fixed labour supply and fixed wages.
15
For a description of the pollution permits see the description of the environmental module..
39
Environmental Module
I N T R O D U C T I O N
The objective of the environment module is to represent the effect of
environmental policy on the EU economy and on the state of the environment.
The current version only covers atmospheric emission related to the energy use
and conversion.
Compared to other currently available models, the aim of the introduction of an
environment module is to improve the analysis in the following four directions:
• Integrated analysis of environmental and energy objectives on a
European scale, e.g. energy security versus clean air.
• Representation of a larger set of environmental policy
instruments at different levels: standards, taxes, tradable permits;
international, national, sectoral.
• Integrated analysis of different environmental problems:
simultaneous analysis of global warming and acid rain policy.
• Comparative evaluation of source and receptor oriented: damage
valuation versus uniform emission reductions.
The environmental sub-model focuses on three important environmental
problems:
1. Global warming through CO2 emissions
2. Problems related to the deposition of acidifying emissions
3. Ambient air quality linked to acidifying emissions and ozone
concentration.
Hence, we consider energy-related emissions of CO2, NOx, SO2, VOC1 and
particulate, which are the main source of air pollution. Combustion processes
almost exclusively generate the pollutants. Regarding the problem of global
warming, CO2 is responsible for more than 60% of the radiate forcing (IPCC,
1990). In a later stage other GHGs (CH4, CFC, N2O) will be introduced in the
model.
VOC are only partly generated by energy using activities; other important sources are the use of
solvents in the metal industry and in different chemical products but these emissions are not taken into
account here.
1
40
Figure 1: Flow chart of the environmental module
•
•
•
Policy support component
Taxes
Pollution permits
Emission constraints
Abatement costs
Behavioural component
behaviour
Pollution abatement
Energy and economic activities
Emissions
State of the environment
component
transportation
Transportation model
concentration
Dose-Response function
Damages
Monetary valuation function
External costs
•
•
Model use
Cost effectiveness analysis
• Cost benefit analysis
Assessment of policy instrument
Figure 1 provides a general scheme of the structure of the environmental submodel of GEM-E3.
The environment module contains three components:
1. a “behavioural” component, which represents the effects of different
policy instruments on the behaviour of the economic agents; e.g.
additive (end-of-pipe) and integrated (substitution) abatement;
2. a “state of the environment” module, which uses all emission information
and translates it into deposition, air-concentration and damage data.
This component was constructed on the basis of information available
from different sources, but mainly from the EC-project ExternE.
There is at this stage no feedback from the state of the environment
to the behavioural part of the model;
41
3. a “policy-support component”, which includes representation of policy
instruments related to environmental policy, such as taxation, tradable
pollution permits and global constraint emissions; through policy
instruments, emissions may influence on the behaviour of economic
agents as formulated in the model.
Emission factors and other data related to the pollutants (CO2, NOx, SO2, VOC
and PM) are differentiated by country, sector, fuel, and type of durable good (e.g.
cars, heating systems). The links to inputs to production or consumption only
concern the use and conversion of energy. Non-energy sources of emissions, like
refinery and other processing are treated separately.
To be able to evaluate excise taxes on energy, the energy content of fuels and
electricity is also considered.
For private consumption the major links between energy inputs and consuming
durable goods are specified as follows: cars and gasoline; heating systems and oil;
coal, gas and electricity; electrical appliances and electricity.
The model covers three explicitly specified mechanisms of emission reduction:
•
End-of-pipe abatement (where appropriate technologies are available),
•
Substitution between fuels and/or between energy and non-energy inputs,
and
•
Emission reduction caused by sectoral and/or consumption restructuring.
The explicit formulation of a cost function in the supply side of the GEM-E3
model eases the representation of the effects of emission or energy based
environmental policy instruments on economic behaviour. The costs induced by
the environmental policy instruments act on top of production input costs.
Derived demand for intermediate goods is derived from the unit cost function
that takes these environmental costs into account. Similarly the demand of
households for consumption categories is derived from the expenditure function,
which is derived from utility maximisation. Hence, the environment-related policy
instruments convey effects on prices and volumes of equilibrium.
The model takes into account the transboundary effects of emissions through
transport coefficients, relating the emissions in one country to the
deposition/concentration in other countries. For secondary pollutants as the
tropospheric ozone, this formulation needs to consider the relation between the
emission of primary pollutants (NOx emissions and VOC emissions for ozone)
and the level of concentration of the secondary pollutants.
Damage estimates are computed for each country and for the EU as a whole,
making the distinction between global warming, health damages and others. The
data for damages per unit of emission, deposition or concentration and per person
42
as well as their monetary valuation are based on the ExternE project of the EC
Joule programme.
T H E
‘ B E H A V I O U R A L ’
M O D U L E
Mechanisms of emission reduction
There are three mechanisms that affect the level of actual emissions in the model:
• End-of-pipe abatement (SO2, NOx, VOC and PM): end-of-pipe
abatement technologies are formulated explicitly through abatement
cost functions associated to production sectors. These cost functions
differ across sectors, durable goods, and pollutants but not between
countries. It is assumed that these abatement technologies are
available all over Europe at uniform costs. The data come from
bottom-up studies. As the cost of abatement is an increasing function
of the degree of abatement, the sectors and countries differ according
to the country- or sector-specific abatement efforts already assumed
to be undertaken in the base year.
• Substitution of fuels (all fuels): as the production of the sectors is
specified through nested CES-functions, some degree of substitution
between production factors is allowed. The demand for production
inputs depends on relative factor prices and is therefore influenced by
additional costs conveyed by environmental policy or constraints. For
example, a shift may occur away from ‘expensive’ energy inputs
towards less costly inputs. Of course, substitutions may occur not only
among the energy inputs but also between energy and non-energy
production factors (raw materials, labour or capital).
• Production or demand restructuring: in a general equilibrium
framework sectors and countries are interdependent. Environmental
constraints (through standards, taxes or other instruments) imply
additional costs that differ across sectors or countries as they have
different possibilities for substitution or abatement. This situation may
further imply restructuring, for example by inducing a decline of a
sector or a shift of demand to some countries. The net effects on the
environment or the economy may be important.
The firm's behaviour
The abatement activities are modelled as implying additional costs related to the
production inputs that cause pollution (affecting for example the costs of energy
use). Through this mechanism, the abatement activities enter in the decision
process of the firm. The purchase price of energy is augmented with abatement
cost and a tax, representing the user’s cost of energy. This is used in the firm’s
choices about production factors. Of course, the price of energy, exclusive taxes
and abatement cost, is used to value the delivery of the energy sectors to the other
sectors. As the abatement cost is defined in constant terms, a deflator is also
introduced to compute the abatement cost per unit of energy.
Regarding the modelling of abatement activities, the installation of abatement
capacities has been considered as an expenditure of the firms but not as an
43
investment. Certainly the abatement is not a productive investment for the firm,
but as a capacity, we would need to formulate the dynamics of accumulation and
retirement. However, as the available abatement cost functions are in terms of
levelised costs, we preferred to formulate abatement as expenditure.
The abatement expenditure requires commodities (goods and services). The
demand for inputs to abatement expenditures is modelled in the following way:
• Sectoral abatement expenditure is split in demand addressed to
delivery sectors through fixed coefficients.
• These inputs are added to intermediate demand of the sector and are
priced as all other intermediate deliveries.
The consumer's behaviour
• The modelling of the environment in the demand side is similar to
that of the firm, with the exception of the transfer of payments of
environmental tax revenues to the government. While in case of firms,
the environmental tax revenues are transferred by the branch causing
the pollution to the government, in the case of households this
transfer is done by the branch delivering the product causing pollution
to the household. The environmental tax is therefore perceived as all
other indirect taxes paid by households. Therefore the price of energy
in the consumer allocation decision includes the abatement cost and
the tax and represents the user's cost of energy. The price of delivery
of energy to the household includes the pollution and/or energy tax;
while the cost of abatement is formulated in a way similar to that of
the producers.
The abatement expenditure of households is modelled as in the production
sectors. The allocation to sectoral deliveries is done through fixed coefficients and
is priced as other deliveries. Of course, the abatement materials are not added to
private consumption and do not contribute to consumer’s utility. They, however,
influence the choice of durable goods as they indirectly affect their cost of use.
Cost and price functions: End-of-pipe abatement costs
The average abatement costs are levelised as annuity payments. The parameters in
the corresponding equations are based on bottom-up engineering data. The database has been constructed for Germany and then extrapolated to the other
countries, taking into account the initial abatement levels in these countries relative
to that of Germany.
The cost functions are considered in marginal abatement cost terms:
γ
mc~pab, s (a p , s ) = β p , s ⋅ (1 − a p , s ) p ,s ,
where
44
: Degree of abatement of pollutant π of sector σ ,
a p ,s
(
β p ,s , γ p ,s
: Estimated parameters β p,s ≥ 0, γ
p, s
)
≤0 .
( )
c pab,s a p , s .2
By integrating the above formula one obtains the average cost curve ~
− β p ,s
~
c pab,s a p ,s =
⋅ 1 − a p ,s
1 + γ p ,s
( )
(
)
γ
p , s +1
+ K p ,s
The degree of abatement απ , s can be exogenous or determined through the
implicit equation, imposing equality between marginal cost of abatement and tax.
The typical slope of the cost curves is depicted by Figure 2 (the example shows
the unit abatement cost curve of the electricity sector in DM per reduced kilogram
of SO2).
Figure 2: Unit costs of abatement in DM per reduced kg of SO2
Abatement costs for SO2
(electricity sector)
6
unit costs
5
4
3
2
1
1,00
0,90
0,80
0,70
0,60
0,50
0,40
0,30
0,20
0,10
0,00
0
degree of abatement
The abatement cost function of sector σ for pollutant π , given the output Xs of
this sector and the degree of abatement απ ,σ is then
( )
( )
(
)
~
~ ab
C pab, s = ~
cpab, s a p , s ⋅ a p , s ⋅ EM ppot
, s = cp , s a p , s ⋅ a p , s ⋅ ∑ ef p ,i , s ⋅ µ i , s ⋅ α i , s ⋅ X s ,
i
where
ef p ,i ,s : Emission factor for pollutant π of input i in sector σ ,
2
This simplification requires the assumption of constant returns to scale.
45
µ i ,s
: Share of energetic use of demand of input i .
~
These costs involve an additional intermediate demand ABI p,i ,s ; the allocation of
these costs to the delivering sectors is based on of fixed coefficients3. The main
deliveries for abatement technologies are investment goods, energy (due to a
decrease in efficiency) and services (maintenance).
~
~
ABI p,i , s = tab p ,i ,s ⋅ C pab, s ,
where
tabp,i ,s : Share of deliveries of sector i for abatement of pollutant p in sector s
( ∑ tabp,i ,s = 1 ).
i
The deflator or price of abatement cost per unit of energy by branch is
determined by the prices of the required intermediate inputs.
PCpab,s = ∑ tabp,i,s ⋅ (1 + ti ,s ) ⋅ PYi ,
i
where ti ,s indicates the indirect tax rate.
This allows calculating the average abatement cost per unit of energy by branch in
value, associated to the abatement level:
ab ~ ab
c ab
p, s = PCp ,s ⋅ c p,s
This cost is further used to compute the user cost of energy that the firms and
households consider in their decision process regarding derived demand for
inputs.
~
~
For the variables Cpab,s and ABI p,i ,s the corresponding values Cpab,s and ABI p ,i,s
are evaluated similarly.
By including the expenditure for abatement in the determination of intermediate
~ :
demand one obtains the following input-output coefficients α
i ,s
Abatement is therefore not directly increasing the GDP, as it would be the case if one would treat
abatement measures as investment.
3
46
α~ i , s =
~
α i , s ⋅ X s + ∑ ABI p ,i , s
p
~
X s + ∑ ABI p ,i , s
,
p ,i
where α i ,s is the Input-Output coefficient without environmental policy impacts.
If an environmental policy is linked to taxes or permits, the are not only costs for
emission reduction but for the actual emission caused as well ( Χ πεφ, σ ).
( )
( )
(
)
( a ) depends on a
ef
C pef, s = cpef, s a p , s ⋅ (1 − a p , s ) ⋅ EM ppot
, s = cp , s a p , s ⋅ (1 − a p , s ) ⋅ ∑ ef p ,i , s ⋅ µ i , s ⋅ α i , s ⋅ X s
The unit cost of an actually emitted unit of a pollutant c efp, s
i
p ,s
p ,s
and the type of policy instrument imposed. Emission taxes and permits lead to a
c efp, s ap,s greater than zero, whereas an emission standard (for example an upper
( )
bound on emissions) implies no extra cost to the remaining emissions
( c efp, s ap,s =0).
( )
The total costs of emission of pollutant p emitted by sector s are
Cpem, s = Cpab,s + Cpef,s
The end-of-pipe abatement costs of households are specified similarly except that
emissions and abatement are considered per type of durable goods; i.e. for each
durable a separate abatement cost function is specified. The costs of the
consumption inputs are equal to the prices of the deliveries to households (by
consumption category). Abatement expenditure of households are further split
into demand for goods and services addressed to the supply side of the economy.
Cost and price functions: User cost of energy
In the following we consider emissions that are generated from energy
consumption.
The use cost of energy is a function of the price of the energy input and of the
additional costs per unit of energy. The latter are linked to emission from that
energy input or the energy content of that input, depending on the nature of
environmental policy instrument. For example, the excise tax on energy may be
proportional to actual emissions or proportional to energy content. To this one
must add the costs of abatement depending on the rate of abatement and the
baseline emission (and/or energy) coefficient.
Introducing a new variable for the user cost, PFUi, s , for each branch s and each
energy input i , we can compute:
47
PFU i ,s = (1 + ti , s ) ⋅ PYi + c sen ⋅ eci ⋅ χ i ,s +
∑ ([(1 − a )⋅ c (a ) + a
p,s
ef
p,s
p,s
p,s
]
⋅ c ab
p , s (a p , s ) ⋅ ef p ,i , s ⋅ µ i , s
)
p
where
csen
: Tax on energy,
eci
: Coefficient for energy content of energy input i (equal across sectors),
χ i ,s
: Share of energy related use of input i in sector s .
The use costs of energy product will further influence the choice of energy
products and other inputs (as it is used in the price-function of the energy
aggregate Fs ).
The price of the energy aggregate PFs is then
1
1−σ F

1−σ 
,
PFs = ∑ δ σi ,sF ⋅ PFU i ,s F 
 i

where
δi
: Distribution parameter of energy component l
σF
: Elasticity of substitution
PFU i = PFU i g (t ) : Price-diminishing technical progress.
i
The input price for electricity is affected by an energy tax only (use of electricity
causes no emissions).
PELs = PELU s = (1 + t El ,s ) ⋅ PYEl + c sen ⋅ ec El ⋅ χ El , s
Electricity and the fuels aggregate are components of the unit cost function PDs .
Hence, a more restrictive environmental policy which increases PFUi, s and PFs
or PELs , will cause an increase in the unit cost and consequently in the deflator of
total demand, PYs .
The price (1 + t i ,s ) ⋅ PYi remains the delivery price of energy by the energy
sectors, entering the valuation of Fi ,s . This implies that the sector generating
emission transfers the environmental tax revenues, if there are any, to the
government and not the branch delivering the energy product, as is the case for
48
the other production taxes. The environmental taxes are of course attributed as a
burden to the branch generating the pollution.
As already mentioned, the specification of the environmental costs and decisions
of household is very similar to those of the firms. In absence of any
environmental constraint, the user cost price pdur j is specified according to the
following equation:
(
)
pdurj = p j r + δ j + ⋅t jprop ⋅ (1 + r ) + ∑ ϑ l , j ⋅ ~
pl , j ,
l
where
r
: Interest rate,
δj
: Depreciation rate of durable good j ,
t jprop
: Property taxes for durable j ,
ϑ l , j : Minimum consumption of non-durable l that is linked to the use of
durable j
~
pl , j
: Price of linked non-durable good l including value added tax.
If emission costs are imposed on households, the user cost of durable goods is
increased by the costs of abatement as well as by the costs implied by the actual
emissions.
~
pl , j = pl + c en ⋅ ecl + ∑
p
([(1 − a ) ⋅ c (a ) + a
p, j
ef
p, j
p, j
p, j
( )]
)
⋅ cab
⋅ ef p , l , j ⋅ µ l , j .
p, j ap, j
Abatement decision
Based on the above specification, the firm’s decision whether to abate or to pay
taxes can be derived from profit maximisation.
max
X s , v i ,s , a p ,s
Gs ,
where
Gs = PX s ⋅ X s − VCs
(with VCs as variable cost function).
49
To ease the notation in the following presentation an input price PYi act is defined
that includes emission and/or energy-taxes as well as indirect taxes.4
PYi act = (1 + t i ) ⋅ PYi + c sen ⋅ eci ⋅ χ i , s +
∑ [ef
p ,i , s
)]
(
ef
⋅ µ i , s ⋅ c ab
p , s (a p , s ) ⋅ a p , s + c p , s (a p , s ) ⋅ (1 − a p , s )
p
The variable cost function VC s is then given by
n+2
VCs = ∑ vi ⋅ PYi act ,
i =1
where
vi ,s : Intermediate demand of input i by sector s .
As the indices n + 1 and n + 2 denote labour and capital, PYnact
+1 is equal to PL
act
and PYn +2 is equal to PK post . We suppress the notification of intervals in the
following equations.
The first order conditions of the profit maximisation serve to determine supply
and the degree of abatement. For the description of the environmental module
only the latter is of interest.
As the abatement costs are not distinguished by inputs, the formula for the
optimal degree of abatement of pollutant p can be reduced to the following
expression:
∂G s
∂a p ,s
r
∂VC s ∂PY act
= − r act ⋅
=
∂a p , s
∂ PY
[
]


ef
∂  (c ab
p , s (a p , s )⋅ a p , s + c p , s (a p , s )⋅ (1 − a p , s )) ⋅ ∑ ef p ,i , s ⋅ µ i , s 
i

− ∑ vi , s ⋅ 
∂a p , s
i
(
)
= − ∑ v i , s ⋅ ef p ,i , s ⋅ µ i , s ⋅
i
( ( )
( )(
ef
∂ c ab
p , s a p , s ⋅ a p ,s + c p ,s a p , s ⋅ 1 − a p , s
∂a p , s
))
=0
4
Assuming linear-homogenity of the cost function
r
VCs X s , PY act , as , K fix
(
) with respect to
output (quasi-fixed capital stock) eases the solution of the maximization problem considerably. (see
SCHRÖDER, MICHAEL (1991): ‘Die volkswirtschaftlichen Kosten von Umweltpolitik: Kosten
Wirksamkeitsanalysen mit einem Angewandten Gleichgewichtsmodell’, Heidelberg, Physika.).
50
⇒
⇒
(
)=0
ef
∂ c ab
p , s (a p , s )⋅ a p , s + c p ,s (a p , s ) ⋅ (1 − a p , s )
∂a p , s
ab
ef
ef
mc ab
p , s (a p , s )⋅ a p , s + c p , s (a p , s ) + mc p , s (a p , s )⋅ (1 − a p , s ) − c p , s (a p ,s ) = 0
ef
env
ef
Hence, given an exogenous emission tax rate of t env
p ,s ( c p , s = t p , s and mc p , s = 0 )
the (cost minimising) degree of abatement a p , s can be derived (numerically) by
the following implicit equation:
∂G s
ab
env
= mc ab
p , s (a p ,s )⋅ a p , s + c p , s (a p ,s ) − t p , s = 0
∂a p , s
The abatement decision of households can be derived similarly. To reduce the
complexity of the analytical solution, it is assumed that only the fixed part of the
linked non-durable demand is affected by the end-of-pipe emission reduction
measures. Hence, the degree of abatement is independent of the prices and
quantities of the linked consumption.
The derivation of the cost minimising degree of abatement can be reduced
according to the following expressions:5
∂u~
∂u~ ∂z j ∂p durj
=
=0
∂a p , j ∂z j ∂p durj ∂a p, j
⇒
⇒
∂p durj
∂a p , j
= ∑ ϑl , j ⋅ ef p ,l , j ⋅ µ l , j ⋅
(
)=0
ef
∂ c ab
p , j (a p , j )⋅ a p , j + c p , j (a p , j )⋅ (1 − a p , j )
∂a p , j
l
ab
ef
ef
mc ab
p , j (a p , j )⋅ a p , j + c p , j (a p , j ) + mc p , j (a p , j ) ⋅ (1 − a p , j ) − c p , j (a p , j ) = 0
ef
env
ef
Under an exogenous emission tax t penv
, j ( cp , j = t p , j and mc p , j = 0 ), the optimal
degree of abatement a p, j is given by the following implicit equation:
( )
( )
ab
env
mcab
p , j a p , j ⋅ a p , j + cp , j a p , j = t p , j
T H E
O F
‘ S T A T E
T H E
E N V I R O N M E N T
’
M O D U L E
General structure
The ‘state of the environment’ module has as main objective the computation of
the emissions, their transportation over the different EU countries and the
monetary evaluation of the damages caused by the emissions and depositions. The
analysis is conducted on a marginal basis, i.e. it assesses the incremental effects and
costs compared to a reference situation.
This assumption is not very restrictive as the disposable part of the linked non-durable goods is
typically very small (around 5 to 10 %).
5
51
The ‘state of the environment’ module proceeds in three consecutive steps:
1. the computation of emissions of air pollutants from the different
economic activities, through the use of emission factors specific to
these activities;
2. the determination of pollutants’ transformation and transportation
between countries, i.e. the transboundary effect of emissions;
3. the assessment value of the environmental damages caused by the
incremental pollution compared to a reference situation in monetary
terms.
For each step of the environmental module, the equations and the type of data
needed will be briefly described, the sources of the data and their manipulation are
described in Chapter 5.
Emissions
All emission calculations start from the potential emission EM ppot, s that a sector s
produces before end-of-pipe measures have been undertaken. These emissions are
linked to the endogenous output, the price-dependent (endogenous) input
coefficient, the exogenous emission factor and the share of the energy use in input
demand.
EM ppot
, s = ∑ ef p ,i , s ⋅ µ i , s ⋅ α i , s ⋅ X s
ι ∈Ι ,
i
where
εφπ ,ι ,σ
: Emission factor for pollutant π using input ι in the production of
sector σ ,
εφπ ,ι ,σ = 0 for ι ≠ emission causing energy input,
µ ι ,σ
: Share of energetic use of demand of input ι in sector σ ,
α i , s ⋅ X s : Intermediate demand of input ι for output X s in sector σ ,
I
: Set of inputs.
For the households we similarly have:
EMH ppot, j = ∑ ef ph,i , j ⋅ µ ih, j ⋅ ϑ i , j ⋅ z jfix
i ∈Ij ,
i
where
52
ef ph,i , j : Emission factor for pollutant π using linked non-durable good ι to
operate durable good j , ef ph,i , j = 0 for ι ≠ emission causing energy input,
µ ih, j
: Share of energy use of demand of linked non-durable good ι to operate
durable good j ,
ϑ i , j ⋅ z jfix : Fixed part of the demand for linked non-durable good ι induced by
use of durable good j .
i ∈ I j : Set of non-durable goods linked to the use of durable good j .
Installing abatement technologies reduces total emissions. With respect to the
degree of abatement specified above one obtains the abated emissions EM ab
p ,s or
EMH pab, j .
EM pab, s = a p ,s ⋅ EM ppot
,s
and
EMH pab, j = a hp , j ⋅ EMH ppot, j
The remaining actual emissions ( EM efp,s or EMH pef, j ) are then given as residual:
(
)
ab
pot
EM pef, s = EM ppot
, s − EM p ,s = 1 − a p ,s ⋅ EM p ,s
and
(
)
ab
pot
EMH pef, j = EMH ppot
, j − EMH p , j = 1 − a p , j ⋅ EMH p , j
The actual emissions of primary pollutants are therefore related to the use of
energy sources, the rate of abatement, the share of energy use of the demand of
input i and the baseline emission coefficient of a pollutant.
Hence, for every pollutant, sector and fuel, a reference baseline emission factor is
used, relating the baseline emissions before abatement to the energy use. For
GEM-E3, the emission factor must be related to the energy consumption in
monetary value. A conversion factor (from energy unit to monetary unit) is
calculated from the energy price in the model base year. Moreover, at the
aggregation level of GEM-E3, energy consumption by sector includes both energy
causing emissions and energy not causing emissions, therefore a parameter
reflecting the fraction of energy use of the energy consumption (the parameter µ
53
in the equations above) is computed in the data calibration6. The abatement level
has been assumed equal to zero in the calibration year for the model. The
procedure for the computation of the model’s environmental database is
described in Chapter 5. The data have been recently updated and extended to all
EU countries and pollutants considered (including VOC, particulates and
tropospheric ozone).
Transport and transformation of emissions
The transboundary nature of pollutants needs accounting for the transport of
SO2, NOx, VOC and particulates emissions between countries. In case of
tropospheric ozone (a secondary pollutant), besides the transboundary aspect, the
relation between VOC and NOx emissions, the two ozone precursors, and the
level of ozone concentration has also to be considered.
In theory, the concentration/deposition (IM) of a pollutant ip in a grid g at time t
is a function of the total antropogenic emissions before time t, some background
concentration7 (BIM) in the country, and other parameters such as meteorological
conditions, as derived in models of atmospheric dispersion and of chemical
reactions of pollutants:
IM ip,g (t) ≡ imip,g ( EM p,c (t ′ ≤ t), BIMip,g (t),.. ∀ p, c) ,
The equations are introduced in static terms in the model and are linearised
through transfer coefficients TPC which reflect the effect that the emitted
pollutants in the different countries have on the deposition/concentration of a
pollutant ip in a specific grid, so as to measure the incremental
deposition/concentration, compared to a reference situation:
∆IMip,g = ∑∑ TPC p,ip [g,c] ⋅ ∆EM p,c
p
,
c
where TPC[g,c] is an element of the transport matrix TPC with dimension GxC.
In the models the grids considered are the countries and deposition-concentration
levels are average by country.
The transport-deposition coefficients for SO2 and NOx emissions are derived
from EMEP budgets for airborne acidifying components, which represent the
total deposition at a receptor due to a specific source. Basically, the EMEP model
is based on a receptor orientated one layer trajectory (Lagrangian) model of acid
deposition at 150-km resolution. Characteristics of the various pollutants and their
transport across countries, as well as atmospheric conditions are taken into
The statistical problem of correspondence between an Input-Output table and Energy Balances is a
complex one. In Input-Output tables values of intermediate consumption may aggregate several
components of the energy balances. For example, in the oil sector, the use of crude oil in refineries,
used as raw material for the conversion to oil products, corresponds to intermediate consumption of oil
product from the oil sector. Therefore the aggregate value includes crude oil and oil consumption for
heating or cogeneration activities in refineries. However, only the latter emit pollutants.
6
7 Resulting from natural emissions and emissions from geographic parts that are not included in the
country set.
54
account. For particulates, Mike Holland (ETSU, 1997) has estimated country to
country transfers of primary particulates. His computations are based on a simple
model that accounts for the dispersion of a chemically stable pollutant around a
source, including deposition by wet and dry processes. To convert deposition into
air concentration, use was made of linear relations estimated by Mike Holland
(1997). These data are given in Chapter 5.
Tropospheric ozone is a secondary pollutant formed in the atmosphere through
photochemical reaction of two primary pollutants, NOx and VOC. The sourcereceptor relationship is not as straightforward as for acid deposition. However, it is
recognised (EMEP, 1996) that there is a relatively strong linearity between change
in ozone concentration and change in its precursors emissions (both VOC and
NOx), allowing an approximation through linear source-receptor relationships.
The transformation matrix, established by EMEP, is given in Chapter 5.
It would be useful to include the distinction by source of emission, for instance
between emissions from mobile sources and/or low height stationary sources as
opposed to high stack sources as it is expected that the deposition of pollutants
per unit emitted will be different in each case. However, there is no information
available at this moment that allows making such distinction.
For the problem of global warming, the global atmospheric concentration matters
and it is only a function of the total anthropogenic emission of greenhouse gases:
∆CCip,g (t) = ∆ CCip (t) = ccip ( ∆TA EM p (t ′ ≤ t)..∀p) .
Then, the concentration of GHG's (greenhouse gases) must be translated into
radiate forcing R and global temperature increase ∆T,
R(t)= f 1 ( ∆CCip (t) ∀ip) ,
∆T(t)= f 2 (R(t)) .
Damages and their valuation: General structure
The approach followed is entirely based on the data derived from the ExternE
project, though they are used at a much more aggregated level.
The damage occurs when primary (e.g. SO2) or secondary (e.g. SO4) pollutants are
deposited on a receptor (e.g. in the lungs, on a building) and ideally, one should
relate this deposition per receptor to a physical damage per receptor.
In practice, dose-response functions are related to (i) ambient concentration to
which a receptor is submitted, (ii) wet or dry deposition on a receptor or (iii) ‘after
deposition’ parameters (e.g. the PH of lake due to acid rain). Following the
‘damage or dose-response function approach’, the incremental physical damage
DAM per country is given as a function of the change in deposition-concentration
(acidifying components or ozone concentration in the model), as follows:
55
∆DAM cACID,d (t) = damcACID,d ( ∆ IMip,c (t),.. ∀ ip) ,
In the case of global warming, damage is a function of the temperature rise,
c
(t) = damcGLOBWAR,d ( ∆T(t),.. ) .
∆DAM GLOBWAR,d
The damages categories considered in the model are
1. damage to public health (acute morbidity and mortality, chronic
morbidity, but no occupational health effect)
2. global warming
3. damage to the territorial ecosystem (agriculture and forests)
4. damage to materials, being treated in a very aggregated way at this
stage.
The impact on biodiversity, noise or water is not considered, either because there
are no data available that could be applied to this respect or because air pollution is
only a minor source of damage for that category.
For the monetary valuation of the physical damage, a valuation function VAL for
the physical damage is used:
VAL co (t) = val co ( ∆ DAM co,d (t),.. ∀d) .
The economic valuation of the damage is based on the willingness-to-pay concept.
For market-related goods, the valuation can be performed using the market price.
When impacts occur on non-market goods, two broad approaches have been
developed to value the damages. The first one, the contingent valuation approach,
involves asking people open- or closed-ended questions for their willingness-topay in response to hypothetical scenarios. The second one, the indirect approach,
seeks to recover values for the non-marketed goods by examining market or other
types of behaviour that are related to the environment as substitutes or
complements.
It is clear that measuring environmental costs at the global involves several
problems, which are extensively discussed in ExternE. They are related to the
transferability of the results from specific studies, time and space limits, the
uncertainty, the choice of the discounting factor, the use of average estimates
instead of marginal estimates and the aggregation. However, despite all these
limitations, it is possible, according to ExternE, to provide a quantified assessment
of the environmental costs.
56
Impact on public health
The ExternE project retains, as principal source of health damages from air
pollution, particulates8 resulting from direct emission of particulates or due to the
formation of sulphates (from SO2) and of nitrates (from NOx), and ozone. Health
damages come also as a direct effect of SO2 whereas the direct effect from NOx
because is likely to be small. The assessment of health impacts is based on a
selection of exposure-response functions from epidemiological studies on the
health effects of ambient air pollution (both for Europe and the US). They are
reported in the ExternE report (1997) and summarised hereafter.
Table 1: Health impact of pollutants from ExternE (in cases/(yr-1000peopleµg/m3 for morbidity and %change in annual mortality rate/µg/m3)
Pollutant
Effect
PM10
Acute mortality
0.00399
Rate
ug/m3
Respiratory hospital admissions
0.00207
Congestive heart failure
0.00277
Ischaemic heart disease
0.00263
Cerebro-vascular hospital admission
0.00504
ERVs for COPD
0.00720
ERVs for asthma
0.01290
Hospital visits for childhood croup
0.02910
RADs
0.39920
Bronchodilator usage by children for asthma
0.77500
Bronchodilator usage by adults for asthma
6.51600
Cough in asthmatic children
2.66900
Cough in asthmatic adults
6.70400
Wheeze in asthmatic children
1.02900
Wheeze in asthmatic adults
2.42400
Chronic mortality
0.03860
Chronic bronchitis in adults
0.03920
Change in prevalence of children with bronchitis
0.32200
Change in prevalence of children with chronic cough
0.41400
O3
Acute mortality
0.00938
1 hr ppb
Respiratory hospital admissions
0.01132
ERVs for asthma
0.02100
Minor RADs
0.15600
Change in asthma attacks (days)
29.00000
Symptom days
66.00000
SO2
Acute mortality
0.00719
ug/m3
Respiratory hospital admissions
0.00020
There is still discussion within ExternE on how to valuate the mortality impacts,
through the concept of the “value of a statistical life” or “value of years of life
lost”. The valuation of morbidity is based on estimates of WTP to avoid health
related symptoms, measured in terms of respiratory hospital admissions,
PM10, i.e. particulates of less than 10 µg/m3 aerodynamic diameter, is taken as the relevant index of
ambient particulate concentrations.
8
57
emergency room visit, restricted activity days, symptom days, etc. and their
respective costs. The figures used in ExternE are summarised in Table 2.
Table 2: Valuation of mortality and morbidity impacts in ExternE (ECU 1990)
Mortality
Statistical life
Lost life year
Acute Morbidity
Hospital admission for respiratory and pulmonary (COPD) symptoms
Emergency room visit (ERV) or hospital visit for childhood croup
Restricted activity days (RAD)
Symptoms of chronic bronchitis or cough
Asthma attacks or minor symptoms
Chronic Morbidity
Chronic bronchitis/asthma
Non fatal cancer/malginant neoplasm
Changes in prevalence of cough/bronchitis in children
2600000
94000
6600
186
62
138
31
87000
375000
187
Putting the impact and valuation data together, an estimation of the health damage
figure per incremental pollution can be computed for PM10 (direct and indirect),
for SO2 (direct) and ozone (cf. Table 3).
Table 3: Damage from an increase in air pollution (106 ECU per 1000 persons)
from an increase of one µg/m3 of PM10 concentration
Lost life
Stat. Life
from an increase of one µg/m3 of SO2 concentration
Lost life
Stat. Life
from increase of one ppb of ozone concentration
Lost life
Stat. Life
0.005358
0.133383
0.000693
0.022306
0.002433
0.030630
Other impacts: Impact on terrestrial ecosystems (agriculture and forest)
Damage on agriculture and forest is done by foliar uptake or due to acid
deposition on the soil. Damage related to chronic exposure is usually different
from the acute injury. It is often not possible to accredit damage to a specific
stress agent and multiple stress hypotheses have been proposed (climate, pests,
pathogens). In some areas plants have been found to grow better in the presence
of low levels of fossil fuel related pollution than without any pollution because
sulphur and nitrogen are essential nutrients for living organisms (fertilisation). At
higher concentrations however pollutants interfere with plant functions and cause
damage. A given dose of a pollutant will produce a variable response depending
on a wide range of factors: species affected, age of the organism, other pollutants,
time of day or season, temperature, water status, light conditions, soil and plant
nutrient status, heavy metals in the soil, etc. Moreover, especially in agriculture
land, action is taken to counteract the effect of pollution. These different elements
make it very difficult to assess the impact of incremental air pollution.
The ExternE gives the following table for the importance of pollutants for
different damage categories.
58
Table 4: Importance of pollutants per damage category
SO2
forests
XX
crops
XX
fisheries
0
natural flora
XX
NOx
X
X
0
X
NH3
X
X
0
X
O3
XXX
XXX
0
XXX
Total acid
XXX
X
XXX
XXX
Total N
XXX
0
XX
XXX
0: not ecologically significant
X: indirect effects
Source: ExternE
XX: significant effects in some areas
XXX: direct and significant effects in large areas of Europe
A G R I C U L T U R E
F O R E S T S
ExternE has examined in detail the assessment of the direct impact of SO2 and O3
on yield for a limited number of crops (rye, oats, barley, peas, beans and wheat).
They made use of exposure-response functions, applied on the increased liming
requirement to compensate for acid deposition and on the reduced nitrogenous
fertiliser requirements through deposition of oxidised N. They did not take into
account interactions with pathogens, pests or other pollutants.
As there are limited acceptable approaches to predict forest response to pollution,
ExternE has made tentative estimations of the forest damage, more with a
methodological objective than with the objective to give complete results for the
assessment of the forest damage. Their approach is based on the critical load/level
concept to identify the sensitive areas and on correlation measures between forest
damage and critical load/level excess.
Impacts on materials
Discoloration, material loss and structural failure are the main impact categories
for most materials, which result from interactions with acidifying substances like
SO2 and NOx, particulates and ozone. The impact is highly dependent on the
material in question: buildings, textile, paper, etc.
ExternE considers that discoloration and structural failure resulting from pollutant
exposure are likely to be small, though there are no specific studies estimating
these possible damages. Therefore their analysis has been limited to the effect of
acidic deposition on corrosion, the direct effect of SO2 and the effects of acidity
resulting from SO2 and NOx. Damage from ozone has not been considered
because further research is still needed on ozone formation and on the effects of
ozone on materials.
The materials for which damage have been considered are calcareous stone,
mortar, paint, concrete, aluminium and galvanised steel and the study concentrates
on ‘utilitarian’ buildings (houses, shops, factories, offices and schools), buildings of
aesthetic or cultural merit were not considered. Specific dose-response functions
for each material were derived from a literature survey: 14 dose-response functions
were selected, linking the deterioration of materials to SO2 and O3 concentration,
acidity and meteorological conditions.
59
Damage to territorial ecosystems and materials in GEM-E3
Because of the big uncertainty related to dose response functions even aggravated
by the aggregation necessary for GEM-E3, it was impossible to derive a damage
impact coefficient and an associated valuation term it for each category of damage.
Moreover first results from ExternE showed that they were relatively less
important than public health impact. Therefore Mike Holland (ExternE, ETSU)
computed an average damage cost per person from ExternE detailed
computations to be used in GEM-E3.
Table 5: Damage from an increase in air pollution (106 ECU per 1000 persons)
From an increase of one µg/m3 of sulphite
concentration
From an increase of one µg/m3 of nitrite
concentration
0.0028
0.0018
Global Warming
For global warming, estimates of the marginal cost of one ton of carbon emitted
in the period 2000 to 2010 range between 7$/ton of C (Nordhaus, 1993) to over
150$/ton of C (Cline, 1992). This high range result more from differences in the
basic assumptions than in the methodology. Important assumptions are the
discount rate, the rate of population growth, the rate of technical progress in
general and the development of carbon free energy sources in particular. A more
complete discussion about global warming damage estimates is presented in
ExternE, in the context of the coal fuel cycle. The estimate used in GEME3 is
22.8$/ton of C for the World and 5.38$ for Europe (Fankhauser, 1993).
I N S T R U M E N T S
A N D
P O L I C Y
D E S I G N
Type of instruments
Three types of instruments can be addressed: taxes, tradable pollution permits,
and emission standards (upper bounds on sectors and/or countries).
Many European countries use standards to curb SO2 and NOx emissions or to
impose efficiency standards, while also market-based instruments like taxes or
permits are considered. To be able to test various designs of these instruments, the
model was kept as flexible as possible.
Standards can be imposed at the level of countries, sectors, and/or durable goods
(i.e. cars, heating systems, electrical appliances). They are based on technical
restrictions concerning for example the concentration of a pollutant in the flue gas
of a combustion process or a maximum gasoline consumption limit for cars (e.g. 5
litres per 100 km). They can also take the form of global emission constraints. A
complementarity approach is adopted to formulate these standards or constraints.
The associated endogenous shadow cost acts proportionally to emissions to
impose additional cost charges to producers or consumers. The model’s algorithm
searches for that value of the shadow cost which will render the constraint
binding.
In this sense, the model supports tax simulations given the tax rate or a
quantitative limit to be reached. In the latter case, the tax rate is computed
60
endogenously, which might help to trace the tax rate corresponding to a
quantitative goal.
Permit markets for primary pollutants are specified and can be activated in the
model. While the total supply of permits is given by the quantitative policy limit
and a grand-fathering approach, the demand for permits is linked to the demand
for commodities that provoke emission. The endogenously computed permit
price equilibrates demand and the fixed supply. Auctioning of the permits can also
be considered in the model as it is equivalent to a tax.
Base of instrument
While standards can be imposed on emissions or energy use, taxes and permits
can be based on emissions, energy content, depositions, and damage. There is a
wide range of tax proposals concerning the tax base to be used. This includes pure
energy taxes, pure emission taxes, and mixtures of both with varying weights of
the two.
The permit market designs suggested by environmental economists range from
undifferentiated emission permits to regionally differentiated emission permits.
GEM-E3 is able to analyse undifferentiated emission permits and ambient
discharge permits. The latter consider the source and the sink of an emission
geographically (on a country level). It is also intended to analyse permit systems
that are based on the damage caused in the countries. This application could give a
rough estimation of the economic effects and the financial transfers due to an EUwide implementation of the polluter-pays-principle.
Practical design of the instrument
Using market-based policy instrument requires a range of information about how
these instruments should be implemented practically. This includes e.g. the
purpose of tax receipts or the principle how permits should be allocated initially.
Principally there are many ways of refunding the receipts raised by emission
and/or energy taxes. Not all of them are reasonable and only a few are in the
current political discussion. In GEM-E3 the following refunding mechanisms
were introduced and tested:
• government keeps the tax receipts and reduces public deficit
• government uses receipts for public consumption and investment (e.g.
in hope to reduce unemployment)
• lump sum transfer to households
• tax reform 1: social security rates are reduced according to the tax
receipts (double dividend analysis)
• tax reform 2: taxes on firms and capital income are lowered according
to the tax receipts
61
In all tax reform analysis, it is possible to verify explicitly that public deficit is not
inflicted if the tax base erodes. This is usually very likely as taxes on emissions are
expected to reduce the latter and therefore the tax receipt.
For the permit markets a variety of designs is possible. The initial allocation of
permits can be based on the grand-fathering principle or on auctioneering. In a
grand-fathered allocation permits are given free of charge to the polluters
according to their actual emissions or a comparable rule. If permits are sold by
auction, an additional income for the government is raised, for which again an
appropriate refunding mechanism has to be chosen (not interesting at this level of
analysis because it is equivalent to a tax). Other aspects, like the duration of
permits (limited or unlimited) etc., are supported by the current version of the
model.
Institutional setting and scope
This aspect concerns institutional level of the political goal to be achieved as well
as the sectoral and/or geographical scope that should be addressed by the
instrument. GEM-E3 supports the simulation of market-based instruments
(permits and taxes) on a national and/or on the multinational level. The
multinational level can cover a selection of some countries only (e.g. expected
forerunners in emission reduction like Denmark, Belgium and Germany) or the
entire EU-11 or EU-15. This feature can be used for permit markets as well. They
can be installed on a national and/or a multinational level where permits are traded
between sectors and countries. All kinds of exemptions can be simulated, i.e. taxes
and permits can be introduced for some sectors or the households only.
62
3
Chapter
Model Extensions:
Imperfect Markets and
Economies of Scale
1
The presentation given in Chapter 2 for the core model structure is
extended to cater for imperfect competition. This is a standard feature of
the model variant GEM-E3-IM. In what follows only the changes in
specification with respect to the main model text are presented.
GEM-E3-IM Version: Model Description
To represent potential economies of scale,
in some sectors, a simple model of average
Average cost curve
cost functions is assumed, so as to also
facilitate numerical calibration. Following
Pratten, it is assumed that, in these sectors,
the total cost function is composed of a
Marginal cost curve
variable cost and a fixed cost part2.
Scale
Production technology, as illustrated in the
Initial
Firm with
MES
position
a higher
figure, is assumed to exhibit constant
market
returns of scale, implying that the variable
share
cost part of the cost function determines a
variable average cost that coincides to the marginal cost function.
Cost
P R O D U C T I O N
Firm-internal economies of scale in the sense of decreasing unit costs are
introduced by incorporation of a recurrent annual fixed-cost element. Before the
first unit of output can be produced using the production technology, fixed
amounts of output-independent production factors must be hired in addition to
variable, output-dependent input requirements just to maintain a firm’s capacity to
produce and sell its output variant. A firm’s total cost function then takes the
form:
This development has been carried out by NTUA and KUL. Valuable contributions were made by D.
Willenbockel (Middlesex University) and E. Zalai (University of Budapest).
1
2
See Pratten (1988).
63
Costf PR = { m arg inal cos t function} ⋅ xdf PR + fixed cos tf PR
(1)
where the marginal cost function is identical to the one that corresponds to the
PC sectors, only now at the individual firm level, depending only on the prices of
the production factors, F is the total fixed cost and Lif, m , K i f, m , XI i f, m are
respectively fixed amounts of labour services, capital services and intermediate
inputs, which are constant parameters numerically calibrated in accordance with
the existing extraneous evidence on cost-scale relationships by industry. The
volume of production of the individual firm is denoted by xdf .
Firms in the imperfectly competitive sectors set optimal profit-maximising price
mark-ups on marginal cost for each market segment they address, based on their
conjectures of their rivals’ reactions to their own actions. Hence price cost margins
depend on the assumed type of oligopolistic competition and vary endogenously
with market share variations and changes in the competitive environment. Each of
the individual firms choose the optimal mix of production factors so as to
minimise its variable cost.
 Min




s. t .

var
PD PR ⋅ xdf PR = ∑ PIO PR , BR iovf PR
, BR
BR
(
var
var
+ PL PR ⋅ lavf PR
+ PK PR ⋅ kavf PR
var
var
var
xdf PR = CES iovf PR
, BR , kavf PR ,t , lavf PR
)
where PD PR is the marginal cost of production, xdf PR is the volume of
var
var
var
production of the firm, kavf PR
, lavf PR
, iovf PR
is the variable part of the firmspecific demand for production factors (capital, labour, intermediate inputs
respectively). Following the same methodology as in the PC sectors (see previous
section, equations 11-15), demand for production factors is derived.
Total demand by firm for production factors is then the sum of the variable part
as derived from the cost-minimising production schedule of the producer and the
fixed part, which is calibrated using engineering evidence3:
var
KAVf PR = kavf PR
+ kavf PRfix
(2)
var
IOVf PR = iovf PR
+ iovf PRfix
(3)
var
LAVf PR = lavf PR
+ lavf PRfix
(4)
As all firms in the same location and industrial sector are assumed symmetric,
industry-level input requirements are simply the n-fold of the respective firm-level
requirements. Industry level totals for output and output-depended factors are:
The fixed part of production is different for each sector and does not necessarily includes the use of
all production factors.
3
64
XD PR = n PR ⋅ xdf PR
(5)
IOV PR , BR = n PR ⋅ IOVf PR, BR
(6)
LAV PR = n PR ⋅ LAVf PR
(7)
Total fixed cost by sector is:


Fixed CostPR = nPR ⋅  KAVf PRfix + LAVf PRfix + ∑ IOVf PRfix, BR 


BR
(8)
The firms can make positive profits or losses:
profitf PR = PS PR xd PR − ∑ PI PR, BR ⋅ xif PR , BR + PL PR ⋅ lf PR
BR
+ PK PR kf PR , t − fixed cos tf PR
(9)
The total profit (or loss) of the sector is then added to (subtracted from) the
capital value added of that sector and distributed to the rest of the economy
according to the SAM.
Due to its explicit dynamic character and the associated endogenisation of
investment, the incorporation of entry and exit processes in the model is an
intricate problem to which the existing literature provides no guidance, since most
of the existing models apart from GEM-E3 perform comparative static analyses.
In GEM-E3 the number of identical firms in the sector varies endogenously in the
model. If profits are positive, then new firms may decide to enter into the market
while negative profits will induce a higher industrial concentration to exploit
economies of scale potential and reduce fixed costs. Two ways for this adjustment
of the number of firms are supported in the model:
• Instantaneous adjustment: In this model variant, the number of firms
adjusts within the year so that net profits (inclusive of fixed costs) are
taken always equal to zero in the equilibrium. In that case equation (9),
is used to evaluate the industrial concentration consistent with zero
profits.
• Partial dynamic adjustment: The number of firms is assumed constant
within each time period, but profits/losses will affect the number of
firms in the next. Firm numbers change according to a dynamic
adaptation mechanism
(
n i ,t +1 = n i ,t + g ⋅ n ⊗ i ,t − ni ,t
)
(10)
65
where n ⊗ i ,t is the number of firms consistent with zero profits in the industry. In
this modelling option firms are allowed to make profits/losses according to
equation (9).
D E M A N D :
F I R M S P E C I F I C
D E M A N D
Consumers (i.e. firms, in intermediate consumption and investment, private
consumers and the government, in final demand) all may benefit from product
variety expansion and can achieve efficiency gains, in the volume and costs of their
consumption.
In this sense, technical progress due to increasing specialisation is endogenously
modelled, as an indirect consequence of the expansion of product variety. While in
production a decrease in industrial concentration (increase of the number of
firms) will incur proportional increases in the demand for production factors, the
effect on demand is non-linear. Households are assumed to be attracted by
product variety (they prefer two units of consumption coming from two varieties
to the same amount coming from one variety), while use of new varieties in
intermediate consumption and investment generates gains similar to factor
productivity gains. An increase in the number of varieties available in the market
means that same volume of demand (or the same level of utility) can be satisfied
by a lower volume of goods. This will have an additional positive effect on the
economy, since it entails that capacity constraints are relaxed and economic
growth can ensue.
The model specification follows the work of Dixit and Stiglitz, whose approach on
product diversity has proved quite useful in many contexts where product
differentiation is of primary importance.
According to this approach, demand for the domestically produced variant
( XXD PR ) and imports distinguished by country of origin IMPO PR , EU , CO are
further disaggregated into demand for firm-specific varieties4. So for the IC
sectors, XXD PR and IMPO PR , EU , CO become themselves aggregators defined over
sector’s PR demand for the output of each individual firm. Correspondingly, the
prices PXD PR and PIMPO PR , EU , CO , associated with XXD PR and
IMPO PR , EU , CO , become also aggregate prices. The specification chosen in GEME3 imposes a constant (and equal) elasticity of substitution between any pair of
varieties within the same sector.
Firms in the same country and sector are symmetric in the sense that they utilise
the same technology, so that in the equilibrium, for any two given firms k and ë
located in sector PR of country EU:
k
λ
k
λ
xxd PR
, EU = xxd PR , EU and exot PR , EU = exot PR , EU
4
(11)
Note that that in all equations apart from the trade equations, the country suffix is omitted.
66
k
k
where exot PR
, EU denotes the firm-specific exports of the firm and xxd PR , EU the
production oriented to the domestic market.
Given a sector’s total demand for aggregate domestically produced goods, the
following equation further allocates it across firms:
sPR
XXD PR
s PR
sPR −1 s −1
 nPR
 PR
s PR −1
sPR
= ∑ ( xxdf PR )
= n PR ⋅ xxdf PR

 k

PXDPR is then dual associated price index
1
PXDPR
 n PR
 1− s PR
1− sPR
= ∑ ( pxdf PR )1− sPR 
= n PR
⋅ pxdf PR
 k

1
(12)
where n PR is the number of firms s PR is the elasticity of substitution between
firm-specific product varieties. These are assumed as close but not perfect
substitutes5 so s PR >> 1. The derived demand function for individual firm-specific
products is derived from applying Shephard’s lemma to the unit cost function:
xxdf PR = XXD
k
PR
 PXD 
⋅

 pxdf 
sk
(13)
EU , RW
The bottom level nesting for bilateral imports IMPO PR
is:
σ EU
IMPO PR , EU , CO
σ EU −1 σ −1
 EU
 nk
= ∑ ( impof PR , EU , CO ) σ EU 


=n
σ EU
σ EU −1
⋅ impof PR, EU ,CO
and the associated price indices:
1
PIMPO PR, EU ,CO
 nk
 1−σ EU
= ∑ ( pimpof PR, EU , CO )1−σ EU 


=n
1
1− σ EU
(14)
⋅ pimpof PR, EU , CO
again the firm-specific volume of imports is derived from Shephard’s lemma
applied to the previous equation:
5
See Willenbockel (1994) for a survey of numerical values for this elasticity.
67
impof PR , EU , CO = IMPO PR , EU , CO
 PIMPO PR , EU ,CO 

⋅
 pimpof PR , EU , CO 
σ EU
(15)
Equations above exemplify the discussion about efficiency gains from increasing
variety. While for example, a doubling in the number of domestic firms will cause,
ceteris paribus, each firm to produce the half the amount it was producing before.
Demand for domestic goods on the other hand, can now be satisfied using less
than half from each of the firms:
xxf
new
 1
= 
 2
s
s −1
⋅ xxdf
old
 1
<   ⋅ xxdf
 2
old
This effect unleashes productive resources and leads to economic growth in the
context of general equilibrium with constraints on primary factor supply.
Trade matrix equilibrium in volume implies that the imports of country EU
demanded from country CO from firm k would be equal to the demand for
exports that firm k in country CO faces from country EU .
exo k PR , EU ,CO = impo k PR ,CO , EU ,
(16)
Total volume of EU exports of firm k in sector PR is then:
PR , k
PR ,k
exot EU
= ∑ exo EU
, EU
(17)
EU
F I R M S ’
P R I C I N G
Firms address their products to three market segments namely to the domestic
market, to the other EU countries and to the rest of the world. Prices are derived
through demand/supply interactions.
B E H A V I O U R
I N
I M P E R F E C T
M A R K E T S
Along the iterations of the model run, before global equilibrium is achieved,
producers face a volume of demand for their products. To this demand they
respond with a price. For the IC (imperfect competition) sectors, that face
increasing returns and the number of firms is limited, pricing also depends on the
intensity of competition (reflected in the number of firms and the elasticities of
substitution) and the share that each firm has on the market. At the next iteration
consumers observe the new set of prices and re-optimise their demand allocation
addressing a different demand. This process continues until the marginal cost of
production ( PD ) which is the market equilibrium price, becomes such that
demand and supply are equalised.
In the IC sectors, price/cost margins are different by market segment as they vary
endogenously depending on number of firms that compete in the same market,
market shares and the volume of demand.
Firms in the imperfectly competitive sectors set optimal profit-maximising price
mark-ups on marginal cost for each market segment, based on their conjectures of
68
their rivals’ reactions to their own actions. Hence price/cost margins depend on
the assumed type of oligopolistic competition regime and vary endogenously with
changes in the relative market shares and in the competitive environment (as for
example a shift from segmented to integrated markets).
An imperfectly competitive firm in sector PR is able to set three separate markups for home sales, exports to the EU and exports to the rest-of-the-world.
Correspondingly, there are three separate Lerner-type first order conditions for a
profit maximum describing the optimal relationships between price and marginal
cost in each market segment.

1 
PXD PR ⋅ 1 −
 = PD PR
 ψdo PR 
(18)

1 
PEX PR ⋅ 1 −
 = PD PR
 ψeu PR 
(19)

1 
PEX PR , RW 1 −
 = PD PR
 ψrw PR 
(20)
where PD PR (the marginal (unit) cost of production) is used throughout, because
the products oriented to all markets are supposed to be produced using identical
technology and ψdoPR , ψeuPR ,ψrw PR , respectively, are the perceived elasticities
of demand with respect to domestic, European, and international market.
S P E C I F I C A T I O N
O F
P R I C E - C O S T
M A R G I N S 6
To compute the perceived price elasticities of demand it is necessary to make
some assumption on what the firms perceive their rivals reactions to be. Several
types of oligopolies have been proposed in the literature. GEM-E3 includes both
the Nash-Bertrand and the Nash-Cournot oligopoly assumptions as model
variants7. The rest of the section presents the Nash-Cournot model variant.
Perceived price elasticities can change endogenously as they depend on a number
of factors:
• changes of the competitive environment
• through a regime switch from market segmentation to market
integration or to full market integration or
A more detailed explanation of the derivation of mark-up pricing rules in the context of general
equilibrium models can be found in D. Willenbockel (1994).
6
7 In the Cournot model a firm operates under the assumption that its rivals do not alter their supply
quantities as a result to changes in the firm’s supply. On the other hand, the firm conjectures that its
rivals prices will change. This expected price change, called “conjectural variation” is assumed zero in
the Bertrand case.
69
• through changes in the number of firms
• changes in the share of domestic and imported goods in final demand,
or across imported goods
It is reasonably assumed that individual firms do not have full information about
the complex determination of the volume of the composite good Y, or that the
cost of gathering this information coupled with the complexity of finding their
“true” demand functions, precludes them from making use of all available
information. Instead firms are characterised by bounded rationality at this stage
and make simplifying working assumptions when they decide their optimal supply
strategy. Specifically firms are taken to assume that top-level composite demand at
any sector, is governed by a constant elasticity demand function.
YPR = α PR ⋅ ( PYPR )
Ω PR
(21)
Setting Ù to zero that firms ignore the effects of changes in their prices on toplevel demand, while Ù=1 is equivalent to assuming that firms perceive total
expenditure values to be unaffected by their actions. The perceived elasticity in the
domestic market is considered to be:
ψdo PR , EU =
−1
1
S EU
(22)
+ γ S ,σ X + VSH XXD ,Y ⋅ γ σ X ⋅ Ω
where
1− σ
 PXD EU  x
PXD EU XXD EU
S EU =
= δ EU 
is the share that all domestic firms

PYEU YEU
 PYEU 
have in the domestic market, σ x is the Armington elasticity of substitution at the
top level, N EU is the total number of firms, and σ i elasticity of substitution
between domestic and EU commodities. The other parameters in the above are
defined as follows:
γ S ,σ3 =
1  1
1
⋅
− 
N EU  S EU σ 3 
γ σ X ,Ω =
1  1
1
⋅
− 
N EU  σ X Ω 
VSH XXD ,Y =
XXD PR , EU ⋅ PXD PR , EU
YPR , EC ⋅ PYPR , EC
70
The EU price elasticity perceived by an individual firm, is the weighted average
over the perceived elasticities of the demand functions of the various EU
countries.
IMPO PR, EC , EU ⋅ EXO EU
EXO EC
EXPOTEU PR , EU
SEG
ψeu PR
, EU = ∑
EC
⋅ φSEG
(23)
where:
φSEG =
γ σ 3, σ 4 =
−1
 1

+ γ S ,σ 3 + V S H I M P O , I M P E U ⋅ γ σ 3 ,σ 4


 S EU

 + VSH


I M P O , I M P ⋅ γ σ 4 ,σ X + V S H I M P O , Y ⋅ γ σ X ⋅ Ω 
 1
1
1
⋅
−  and γ σ 4 ,σ X =
N EU
 σ3 σ 4 
1
N EU
VSH IMPO , IMPEU =
VSH IMPO , IMP =
VSH IMPO ,Y =
 1
1 
⋅
−

 σ4 σ X 
IMPO PR , EC , EU ⋅ PIMPO PR , EC , EU
IMPEU PR , EC ⋅ PIMPEU PR , EC
IMPO PR , EC , EU ⋅ PIMPO PR , EC , EU
IMPPR , EC ⋅ PIMPPR , EC
IMPO PR , EC , EU ⋅ PIMPO PR, EC , EU
YPR , EC ⋅ PYPR , EC
Finally, the perceived elasticity for the international market is:
ψrw PR, EU =
−1
−1
1  1
1
+
⋅
− 
S PR , EU N EU  S PR, EU σ 4 
71
(24)
4
Chapter
Prototype Model
Extensions
This Chapter presents a number of GEM-E3 model extensions or
prototype mode versions involving the following:
• The specification of the behaviour of the rest of the world so as to
close the loop in foreign trade;
• The endogenous representation of factor productivity changes; implying
energy savings;
• The endogenous treatment of technology evolution and endogenous
growth;
• The labour market disaggregation and imperfect competition;
• The financial/monetary closure of the model;
• The engineering representation of the energy system.
Model Extension 1: World Closure
I N T R O D U C T I O N
In open-economy applied general equilibrium models the specification of foreign
trade and of the behaviour in the rest of the world (RoW) is an important feature.
In the literature a distinction is made between multi-country and single-country
models8. While the former are mainly designed to analyse global issues, the latter
takes the perspective of a single country. Multi- and single-country models differ
also with regard to the modelling of trade determinants, i.e. the way of modelling
export and import behaviour. In multi-country models, or world models
respectively, production and demand are specified for all countries participating in
trade. All regions covered by the model are linked together by bilateral world trade
matrices or trade pools. In comparison, in single-country models the behaviour in
the RoW is modelled rather roughly. Typically, a ‘closure rule’ for trade with the
external sector is incorporated, i.e. a crude specification of the RoW’s import8
Shoven and Whalley (1992) give an overview on recent multi-country and single-country models.
72
demand and export-supply functions which is usually completed by a balance-ofpayments condition (Shoven and Whalley 1992, p. 81).
As recent studies indicate, the closure rule chosen in a general equilibrium model,
and thus in the GEM-E3 model as well, may be of particular importance for
simulation results9.
The GEM-E3 model includes 14 EU countries and the RoW covering all other
industrialised regions and all developing countries. It is not a global model, as the
behaviour of the RoW is kept exogenous in large parts. World production and
export prices are fixed, i.e. export supply is assumed to be perfectly price elastic.
This assumption reflects price-taking behaviour of the EU vis-à-vis RoW. But, as
price-taking behaviour is accompanied by product differentiation due to the
Armington assumption, the price level in the European Union is not completely
determined by the world market (and exchange rates). Thus, an exogenous rise in
foreign export prices would affect the EU-wide price level only partly.
Another important aspect in the GEM-E3 model is the modelling of interactions
between macroeconomic developments in the EU and the foreign sector.
Actually, the only feedback is a price elastic foreign demand for EU exports.
Optionally, for the long-term analysis, an additional feedback mechanism can be
introduced by a balance-of-payments constraint.
Basically, the assumption that the export prices of the RoW remain constant,
independent from the amount of imports demanded by the EU, is rather
restrictive. It should be taken into consideration that the EU-15’s share of the
entire world trade volume (measured on merchandise imports and imports of
commercial services) is around 40%. Bearing in mind that the share of EU intraregional trade flows in total merchandise imports is around 64%, the share of
extra-EU imports in world merchandise imports is still around 19% (WTO 1996).
Thus, it seems reasonable to assume that trade activities of the EU affect world
prices.
The objective of this chapter is to clarify the relationship between the foreign
sector and the EU economy in the GEM-E3 model. For reasons of simplicity, the
analysis is based on the (real) standard version of the GEM-E3 model (Version
2.0) where money and asset markets are excluded. This has the advantage that any
policy-induced change is fully reflected by changes in real variables, and is not
absorbed by money market effects.
Whalley and Yeung (1984) examine how results from policy simulations depend on the assumptions
about international trade, using a simple numerical example. The external sector specifications vary
according to the elasticity of the foreign supply curve. They include as extremes the large country
assumption and the small, price taking country formulation in which the country has only marginal
influence over its terms of trade. Calculating the equilibrium effects of a distorting capital tax Whalley
and Yeung yield a substantial sensitivity of results in terms of welfare gains to the external sector
specification. Whereas in case of the large country assumption the terms of trade loss offsets the gain
from the removal of a distorting tax, in case of the small country assumption the domestic gain is at its
highest.
9
73
In what follows we present some convenient concepts of world closure as
discussed in the literature and applied in some recent CGE models. Then we deal
with the specification of the foreign trade system incorporated in the GEM-E3
model. Then some changes in the foreign trade system are discussed and tested to
the sensitivity of results. For reasons of comparability, our sensitivity analysis is
fully based on a co-ordinated double dividend policy with a EU-wide 10%
reduction of CO2 emissions.
T H E O R E T I C A L
C O N S I D E R A T I
O N S
Approaches of a world closure in the literature
In recent years the ‘world closure issue’ has received some attention in literature
on CGE trade models. Several external closure rules for single-country models,
including the domestic or home country and the external sector (RoW), have been
described and assessed according to their appropriateness for empirical work. The
first three closure mechanisms, explained below, are analysed in more detail in
Whalley and Yeung (1984), the last one is discussed in de Melo and Robinson
(1989).
The first approach presented by Whalley and Yeung is based on a simple twocommodity formulation without national product differentiation and non-traded
goods. Foreign import demand and foreign export supply functions are
characterised by constant price elasticities.10
ε
PEX 
(1) IM row = IM row,0 ⋅ 
 ,
 e 
(2) EX row = EX row, 0 ⋅ ( PEX row ) γ ,
−∞ < ε <0,
0<γ <∞
(foreign import demand)
(foreign export supply)
where IM row and EX row are imports demanded and exports supplied by RoW.
IM row,0 and EX row,0 denote base year imports and exports of RoW. PEX (in
domestic currency) is the price received by the domestic country for exports to
RoW. Domestic prices are derived from the zero profit conditions and are cost
covering prices. As e denotes the exchange rate from domestic into foreign
PEX
is the world price for exports from the domestic country to RoW.
e
denotes the world price paid by the home country for foreign exports. ε
currency,
PEX row
and γ represent the own-price elasticities of foreign import demand and foreign
export supply.
Whalley and Yeung introduce a zero trade balance condition in order to close the
system.
(3) (e ⋅ PEX row ) ⋅ EX row = PEX ⋅ IM row
(balance-of-payments condition)
Thus, in equilibrium the value of RoW’s exports equals the value of its imports.
This implies equalisation of the value of exports and imports, too.
In the following equations, notation has been brought into line with the nomenclature used in the
GEM-E3 model. Variables without indices refer to the domestic country.
10
74
Whalley and Yeung (1984, p. 130) point to the fact that equation system (1) to (3)
"can be misleading both in creating an appearance of monetary non-neutralities,
and in potentially leading to misspecification of intended elasticity values". They
explicitly show that the trade balance constraint for the external sector must be
taken into consideration when estimating or selecting foreign export demand and
import supply elasticities because this constraint establishes an analytical
interrelation between both elasticities. In consequence, the ‘true’ elasticities
generated by the equation system differ from the parameters ε and γ in (1) and
(2).
The second closure rule proposed by Whalley and Yeung (1984, p. 134f.) differs
from the first rule mainly in two aspects. Firstly, the assumption of homogeneous
goods is given up by introducing product differentiation on the import side
following the Armington assumption. According to this, the domestic import
demand function is characterised in a simplified version by constant own price
elasticity.11 Secondly, the domestic economy is faced with fixed world prices for
imports (price-taking behaviour for imports)12.
Whalley and Yeung demonstrate that for this specification the problem of
misspecification of trade elasticities may arise in a similar way.
Like in the first rule, foreign import demand is a downward-sloping function with
constant own price elasticity less than infinite. Domestic export prices are given as
cost covering prices from zero profit conditions of the model, i.e. export prices
are determined domestically and translated into foreign currency by the exchange
rate. A zero trade balance equation completes the system. The system is described
by the following equations:
(4) IM row = IM row , 0 ⋅ 
ε
PEX 
 ,
 e 
−∞ < ε <0
(foreign import demand)
S
(5) IM = EX row
= IM D
(equilibrium condition)
(6) IM D = IM 0 ⋅ (e ⋅ PEX row )η , −∞ < η <0
(domestic import demand)
(7) PEX row = PEX row
(foreign export supply)
(8) (e ⋅ PEX row ) ⋅ IM = PEX ⋅ IM row
(balance-of-payments condition)
IM row,0 and IM 0 are base year imports of RoW and the home country, IM D
S
denotes the domestic import demand, while EX row
represents export supply of
RoW. PEX row , which is fixed at PEX row , denotes the price of RoW’s exports in
Usually, import demand functions in CGE models do not have a constant price elasticity but are
specified, for example, as CES (constant elasticity of substitution) functions.
11
This implies that RoW supplies any amount of goods demanded by the home country at fixed world
prices.
12
75
PEX
e
denotes the price of exports of the home country in foreign currency. ε and η
foreign currency; (e ⋅ PEX row ) is the domestic price for imports from RoW.
are the foreign and the domestic import demand price elasticities. In equilibrium
the balance of payments is satisfied and the price vectors PEX and PEX row
guarantee that excess demands equal zero.
As shown in Whalley and Yeung (1984, p. 132), equation system (4) to (8) leads to
the following reduced form elasticities
(9)
∂IM row PEX
ε ⋅η
⋅
=
∂PEX IM row (ε + η + 1)
and
(10)
∂IM
PEX row
ε ⋅η
⋅
=
.
IM
(ε + η + 1)
∂ PEX row
Thus, Whalley and Yeung show that foreign and domestic import demand
elasticities are, if the balance-of-payments condition is satisfied, not independent as
suggested by equation system (4) to (7), but are a single parameter. They criticise
that most of the world closure rules are described as if they allowed incorporating
given foreign and domestic import demand elasticities while simultaneously
meeting a trade balance condition. Furthermore, Whalley and Yeung point out
that in the two-good case the foreign and the domestic supply curves that are
constructed to satisfy external sector equilibrium conditions at any set of prices lie
one on top of the other. In exactly the same way, the restrictions given by
balanced trade should be considered in econometric estimations. Incidentally, this
point is picked up and confirmed by de Melo and Robinson (1989, p. 48).
Basically, in the GEM-E3 model the trade relations between EU-14 and RoW are
specified in close analogy to the second rule (see above). Whalley and Yeung, in
particular, take an econometric point of view. However, the pure econometric
problem of identification or misspecification of elasticity parameters is less relevant
as the GEM-E3 model is not an econometric model. Additionally, in an 18 sector
model any change in one market will be cushioned by reactions in the remaining
17 markets so as to satisfy the balance-of-payments constraint. Thus, the relation
of elasticities is less significant as in a two-good model framework. And finally, the
trades balance constraint, and thus the closure rule as well, can be turned off in the
GEM-E3 model.
The third closure rule proposed by Whalley and Yeung (1984, p. 134f.) is
characterised by the inclusion of non-tradable goods, by price-taking behaviour
and by missing product differentiation for tradable goods. Thus, in a two-good
case the foreign offer curve is a straight line with a slope given by the world prices
of traded goods, while the domestic offer curve incorporates some degree of
elasticity. Whalley and Yeung argue that this rule is unpalatable for empirical work
on large countries because of the small-country assumption. In addition, its
76
specification of import demand is unable to address the problem of intra-industry
trade.
De Melo and Robinson have applied the fourth rule presented here. De Melo and
Robinson (1989) extended the standard assumption of product differentiation on
the import side to the export side. They introduce ‘symmetric’ product
differentiation, using a CES (constant elasticity of substitution) function for
domestic aggregate import demand and a CET (constant elasticity of
transformation) function for the domestic export transformation function.
Furthermore, three assumptions are made: the small-country assumption, i.e. the
domestic country can sell or purchase any amount of imports and exports at fixed
world prices, the assumption of a fixed aggregate output (full employment) and
the assumption of a zero balance of trade.
De Melo and Robinson show that the specification is theoretically well behaved. It
implies intersecting supply curves: the balance-of-trade condition defines the
foreign supply curve as a straight 45° line (choosing units so that world prices for
exports and imports equal one) while the domestic supply curve is well-behaved
with an elasticity depending on both elasticity of substitution and transformation.
Thus, the problem of identical supply curves arising from the second rule can be
avoided. But, similarly to the third rule, the small-country assumption restricts the
application of this rule to small-country models.
All models described above, introduce a fixed trade balance for the external sector
with a flexible exchange rate variable that clears the foreign exchange market.
Alternatively, the exchange rate can be fixed while the trade balance is allowed to
adjust in order to retain equilibrium on the foreign exchange market. As Francois
and Shiells (1994, p. 32) note, ideally, in general equilibrium models the current and
capital accounts and the exchange rate would be determined endogenously.
However, this more complex approach is not widely used in CGE models. A third
alternative, chosen for the (real) standard version of the GEM-E3 model without
money market, is a fixed exchange rate system, which is combined with a fixed or
a variable current account. In the first case, the long-term real interest rate, or
national prices respectively, adjust as to satisfy the trade balance equilibrium.
The Armington assumption
CGE trade models differ widely in the specification of import demand. Whereas
in some models imports and competing domestic goods are treated as perfect
substitutes according to the Heckscher-Ohlin model, in some others the
Armington assumption of national or of firm-level product differentiation is
employed13. Models differ also with respect to the functional forms used. Some
apply nested or non-nested CES functional forms, while some apply flexible,
functional forms such as the almost ideal demand system (AIDS). Armington
(1969), and most CGE modellers, have given preference to CES functions as
these require relatively less estimation or calibration effort and as regularity
conditions (global concavity) are satisfied. On the other hand, the AIDS
13In
the GREEN model, for example, the Armington specification is implemented for all import goods
apart from crude oil for which homogeneity across countries of origin is assumed. This is due to
relatively low transportation costs, e.g. compared to natural gas or coal (Burniaux et al. 1992).
77
overcomes the restrictions imposed by the CES by giving up constancy and pairwise equality of substitution elasticities (see Francois and Shiells 1994, Shiells and
Reinert 1993).
However, the majority of empirically based CGE models have introduced the
Armington assumption of national product differentiation, often using CES
functions with two levels of nesting14. The nested specification includes an upperlevel function that specifies a country’s demand for the composite of imports
(aggregated over all countries) relative to domestic substitutes. The lower-level
function defines allocation of imports on competing foreign sources, i.e. countries
(Lächler 1985, p.74, Shiells and Reinert 1993, p. 300).
The upper-level Armington elasticity measures the sensitivity of a country or
industry competitive position in international trade and controls the degree to
which the country’s price system is ruled by foreign prices. The higher the sectoral
upper-level elasticity the higher the degree of demand responsiveness to relative
prices. Ultimately, the Armington assumption gives small-country models more
reality as it provides a degree of autonomy in the domestic price system while
preserving all the features of standard neo-classical models (de Melo and Robinson
1989, p. 56).
The wide use of the Armington assumption in practice is motivated by two
further advantages. First, it addresses the phenomenon of intra-industry trade
flows that is, since the post-war liberalisation of world trade, observable to an
increasing extent in the international trade data. Instead of increasing specialisation
according to Heckscher-Ohlin, countries simultaneously increase exports and
imports of goods that are classified in the same commodity category, even if an
industry is highly disaggregated. This phenomenon of cross hauling can be
explained by qualitative differences between domestic and foreign goods,
geography or transportation costs (Shoven and Whalley 1992, p. 187). A second
reason for the popularity of the Armington assumption is that difficulties, such as
unrealistically extreme specialisation effects, due to homogeneous products and
linear production possibility frontiers, can be avoided (see Shoven and Whalley
1992, p. 230, de Melo and Robinson 1989, p. 49).
However, among economists and econometricians scepticism against the
Armington concept has been arising. Some criticise that the empirical relevance of
cross hauling, and thus the theoretical justification of the Armington concept,
mainly depends on the level of data disaggregation. Thus, the question focuses on
which aggregation level is appropriate to the concept of an industry (Lächler 1985,
p. 75). Besides, some authors describe the Armington approach as a "simple,
restricted and ad hoc (but effective) means of capturing the rigidities apparent in
observed trade flows patterns" (Abbott 1988, p. 67). In a similar way Norman
14Some
CGE models, for example the Deardoff and Stern model, assume a single level CES function
where domestic production competes with an aggregate of imports. Some other CGE models, for
example the models of Cox and Harris, Sobarzo, and Roland-Holst, Reinert, and Shiells, have adopted
the non-nested specification in order to describe national product differentiation. Here, the two-tiered
utility function is fitted together into one level by assuming that utility is a function of domestic output
and imports from each separate source (Shiells and Reinert 1993, p. 301,303).
78
argues (1990, p. 726) as follows: "Typically, the Armington approach is used within
perfectly competitive models; and must be regarded as a purely ad hoc means of
describing intra-industry trade flows and reducing the sensitivity of trade flows to
changes in relative prices - essentially, it is an attempt to capture supply-side
imperfections through modification of the model demand side". Norman
supports the abandon of the Armington assumption, instead incorporating
imperfect competition based on firm-level product differentiation. In their general
equilibrium model Trela and Whalley (1994, p. 263) also refrain from using the
Armington assumption, but treat products as homogeneous referring to “strong
and often artificial terms-of-trade effects” the Armington assumption induces in
numerical results.
S P E C I F I C A T I O N
O F
F O R E I G N
T R A D E
I N
T H E
G E M - E 3
Table 1 illustrates the characteristics of the foreign trade system of the GEM-E3
model. International prices that clear domestic and foreign product markets are
not completely determined by the model but are partly exogenous. World import
demand depends on international terms of trade only, but does not include any
variable measuring RoW’s economic performance, e.g. in terms of world income.
S T A N D A R D
V E R S I O N
Table 1: Import demand and export supply in the GEM-E3 model
European Union
Rest of the World
Import demand
=> finite price elastic
=> depending on international price
relations and EU economic
performance (e.g. income)
Export supply
=> finite price elastic
=> export prices given by
cost-covering domestic
production prices
=> finite price elastic
=> depending on international price
relations
=> perfectly price elastic
=> exogenous
In this section alternative specifications for the rest-of-the world are presented.
These concern two main changes in the core model specification:
S E N S I T I V I T Y
T O
F O R E I G N
T R A D E
S P E C I F I C A T I O
N S
•
An additional price equation for exports from RoW to EU is introduced.
Instead of fixed world prices for exports, the EU is faced with a finite, price
elastic, export supply function.
•
The foreign import demand function is changed by introducing a link between
the activity level of the domestic (EU) and the foreign (RoW) economy15.
Specification of RoW's export supply
In this section the assumption of a perfectly price elastic export supply function of
the RoW is given up. Instead, for each sector a foreign export supply function
with constant own-price elasticity is introduced:
(23)
EX row = EX row ,0 ⋅ (PEX row ) , 0 < γ < ∞ ,
γ
Variations in the degree of substitution between goods entering the sectoral aggregate import
demand functions of both EU countries and RoW are an integral part of the sensitivity analysis of the
model results. As they however do not impose any changes in the model specification they are included
in the chapter concerning the values of the elasticities.
15
79
where EX row,0 denotes exports of the base year. γ is the RoW’s export supply
elasticity, i.e. an increase in the sectoral export price by 1% would increase the
supply of exports by γ %. Solving equation (23) for PEXrow yields
1
(24)
PEX row
 EX row  γ
 , 0 <γ <∞.
=
 EX row, 0 
In the following, equation (24) is introduced as an additional price equation for all
sectors in the GEM-E3 standard model version. Now prices of exports from
RoW are no longer fixed, but may increase with the amount of RoW's exports, or,
because of equation (20), with the amount of EU-14 imports respectively.
Obviously, introducing this new specification can lead to substantial changes in
simulation results, in particular if the policy-induced impacts on EU imports are
substantial.
The new specification is tested for three alternative parameter values of γ (see
Table 2). For reasons of simplicity, γ is not differentiated among sectors.
Table 2: Values of parameter γ for sensitivity analysis
Case 0:
Sector
1 - 18
Standard version of
GEM-E3
Case 1:
Case 2:
Case 3:
Halved values Central values Doubled values
∞
0.5
1
2
Econometric studies indicate that the own-price elasticity of export supply is
below 1. Diewert and Morrison (1989, p. 207), for example, estimated the own
price elasticity of export supply for the U.S. economy. They obtained as result that
γ stayed nearly constant between 0.32 and 0.375 over the sample period 19671982. Hence, Case 1 with γ = 0.5 seems to be most close to reality and might be
interpreted as an upper limit value.
Specification of RoW’s import demand
In the standard version of the GEM-E3 model neither production and neither
consumption nor domestic supply in RoW is endogenous. Domestic demand for
domestically produced goods that enters RoW’s import demand function is given,
too. Hence, no linkage to the economy’s activity level is incorporated in RoW’s
import demand specification. Thus, in contrast to the EU import demand
specification, import demand of RoW depends alone on relative prices (terms-oftrade).
The idea behind the specification presented below is to introduce an additional
endogenous variable in the foreign import demand function, which measures the
economic performance of RoW. As in the standard version of the GEM-E3
80
model production of RoW is fixed, RoW’s exports are used as ‘activity variable’
entering import demand. However, as RoW’s actual exports are completely
determined by import demand of EU-14, RoW’s import demand is no longer
influenced exclusively by EU country-specific export prices, but also by the
amount of imports demanded by EU-14.
The specification represents a rough attempt to provide RoW’s import demand
function with more flexibility and empirical evidence as economic interactions
between the two regions are now taken into account. If in reality, for instance, the
economy of EU-14 expands and income rises, EU-imports will rise, too, because a
part of additional income will be spent for additional imports. This in turn implies
a rise in exports of RoW. Up to this point, the interactions are covered by the
standard model version. However, in addition to that, in reality an increase in
RoW’s exports would result in an increase in RoW’s income, and thus in an
increase in RoW’s import demand as well. This feedback mechanism which is
ignored in the standard model version has been included in the new specification
presented in the following.
The specification of XXDrow is changed by relating RoW’s production to RoW’s
exports. First, we assume that production in RoW XDrow is a function of RoW’s
exports EX row
(25)
XDrow = β ⋅ ( EX row )ϕ .
ϕ may be interpreted as elasticity of RoW’s production to RoW’s exports which
measures the degree of linkage between EU and foreign economy. It is assumed
that the share of RoW’s exports in RoW’s production, θ , and thus the share of
domestically sold and domestically produced goods in domestic production,
(1 − θ ) , is fixed. With this assumption, substituting (25) in (18) leads to equation
(26)
(26)
IMProw , k
 PXDrow ⋅ e k 
= ( EX row ) ⋅ α k ⋅ 

 PEX k ⋅ erow 
ϕ
where α k = (1 − θ ) ⋅ β ⋅ δm row ,k ⋅
δx1, row
δx 2 ,row
σ row
∀k, k = 1,...,14,
is calibrated to the observed benchmark
data.
In order to specify ϕ equation (26) is used as a regression equation with RoW’s
exports as an explanatory (exogenous) and RoW’s production as a dependent
(endogenous) variable. The regression coefficients β and ϕ are estimated by the
least-square method. The empirical database comprises of time-series of RoW’s
exports and production indices (see Table A-1 in the Appendix). A lack of data
occurred concerning production data of sector 1 (agriculture), sector 13 (building
and construction), sector 14 (telecommunication services), sector 15 (transports),
sector 16 (credit and insurance), sector 17 (other market services), and sector 18
(non market services).
81
Elasticity ϕ has been estimated for energy intensive goods industries (sector 6, 7,
8) ( ϕ$ = 0.47 ), equipment goods industries (sector 9, 10, 11) ( ϕ$ = 0.57 ) and
consumer goods industries (sector 12) ( ϕ$ = 0.25 ). The elasticity values of the
remaining sectors were calculated as a linear average over these three estimates
( ϕ = 0.43 ).
In the following, the sectoral estimates of ϕ are used as central values with
sensitivity analysis around (Case 1, Case 2 and Case 3 in Table 3). Case 0 includes
the standard version of the GEM-E3 model, in which ϕ is set to 0 for all sectors.
Table 3: Sectoral values of parameter ϕ for sensitivity analysis
Sector
1 - 5, 13 - 18
6-8
9 - 11
12
Case 0:
Standard version of
GEM-E3
0
0
0
0
Case 1:
Case 2:
Case 3:
Halved values Central values Doubled values
0.22
0.24
0.29
0.13
82
0.43
0.47
0.57
0.25
0.86
0.94
1.14
0.50
Model Extension 2: Endogenous representation
of technology evolution and growth
16
I N T R O D U C T I O N
Introduction
T H E
D Y N A M I C S
Although the representation of technology evolution as the outcome of conscious
efforts by the economic agents is still under development, a prototype model
extension attempts to formulate an endogenous representation of total factor
productivity changes in the model and their linkage to economic growth. Through
this extension it is possible that R&D expenditure (considered as an exogenous
policy control) can influence economic growth. The prototype model is one of
the first attempts in building a CGE model with endogenous growth concepts.
O F
T E C H N O L O G Y
E V O L U T I O N
In recent years, theoretical and empirical work on economic growth has
reappeared on the macroeconomic agenda. However, the process of economic
growth is far from being fully understood. Wide differences still exists between the
levels of the gross domestic product of various countries. Growth rates of real
capita GDP are also diverse.
The two main issues in the theoretical and empirical studies of economic growth
relate to the attempt to discover the determinants of growth performance and
analyse, therefore, whether convergence exists.
The ideal way to distinguish between the old versus the new growth models would
be through empirical investigations. However, to date these studies have not been
performed very successfully in the literature, if they have ever really been tried.
Because the authors, in empirical analysis of growth determination, study different
sets of countries, with aggregates of different years and different explanatory
variables, the cross-country studies are not very homogeneous. The plethora
diversity makes it difficult to discern consistent relationships and compare the
results of studies, as noted by LEVINE and RENELT (1992):
"There does not exist a consensus theoretical framework to guide
empirical work on growth, and existing models do not completely
specify the variables that should be held constant while conducting
statistical inference on the relationship between growth and the
variables of primary interest. This has produced a diverse and
sometimes unwieldy literature, in which few studies control for the
variables analysed by other researchers".
However, the tests of the convergence hypothesis illustrates that it is ex-post
possible to identify "convergence clubs" among groups of countries but it hardly
justifies generalised convergence. BAUMOL (1986) found evidence that poor
countries grow faster than rich, but De LONG (1988) argues that this is due to ex16
This extension has been developed by IDEI, University of Toulouse
83
post sample selection bias, since the data was expanded to include countries that
ex-ante appeared rich.
The consensus that scientific and technical knowledge is an important factor in
economic growth seems to be reinforced. This is illustrated largely in the literature
focusing on the social return of R&D in an more general approach than the
productivity literature does 17 Recent development in R&D literature recognise the
existence of externalities or spillover effects in the knowledge creation process.
This phenomenon is crucial for both modeling and policymaking purpose,
because it can explain why firms, sectors, economies engage too much or too little
R&D effort.
The extensive empirical literature attempts to resolve this question empirically
using micro data on R&D and productivity (See GRILICHES 1992). This
empirical micro literature, then, seems to provide a clear answer: firms underinvest in R&D. Endogenous growth theory provides a potentially devastating
criticism of the approach taken in the productivity literature. The empirical results
as reviewed by GRILICHES are almost all based on a neo-classical theory of
growth in which R&D is simply an alternative form of capital investment. The
typical approach of this literature is to cumulate R&D expenditure into an R&D
stock, include that stock in the production function, estimate its marginal product,
and interpret the estimate as the rate of return of R&D. This simple capital-based
approach to R&D ignores distortions due to monopoly mark-ups, intertemporal
knowledge spillovers, congestion externalities, and creative destruction. Given the
overall misspecification inherent in this approach, we may in fact have very little
information on the true social rate of return to R&D and its relationship to private
return.
Moreover the theoretical approaches such as endogenous growth theory
represented by ROMER (1990), AGHION and HOWITT (1992) and
GROSSMAN and HELPMAN as well the I-O literature by TIROLE (1988) are
unable to provide an unambiguous answer to the sign, much less the magnitude,
of the net distortion to R&D, because there are incentives working to promote
both over and under investment in R&D.
Even if economic growth has many facets, and despite the difficulties in modeling
endogenous growth in a general equilibrium model, there exists convincing
empirical evidence that in a world with international trade in goods and services,
with cross investment among countries and with an intensive communication and
diffusion of knowledge, the productivity of a particular country will depend not
only of its own R&D effort but also of the foreign R&D activity. Following this
idea COE and HELPMAN developed an econometric model and show that
R&D spillovers effects are very important.
This is just an observation and not a proof. Other aspects of growth needs also to be clarify regarding
the question whether higher growth precedes higher investment, a lower fertility rate and a higher
human capital accumulation.
17
84
Endogenous growth mechanisms into the GEM-E3 model
From the theoretical point of view we define a model incorporating endogenous
growth mechanisms as a model which creates growth sustainability by maintaining
the long run marginal productivity of capital above a positive level. Different
researches have tried to explain the existence of a sustained growth in an
economy. Among the papers in the literature the one of GROSSMAN and
HELPMAN [1991] (see also the Joseph SCHUMPETER Lecture of HELPMAN
[1992]) appears as an interesting approach for at least two reasons. Firstly,
GROSSMAN and HELPMAN « concentrate on mechanisms that link the
growth performance and the trade performance of nations in the world
economy ». Secondly COE and HELPMAN [1995] have tried to give some
empirical evidences to their theoretical development that could be useful for our
purpose.
About the first point there is no much to say. Since the GEM-E3 model is a
model for Europe, it seems intuitively reasonable to take into account the role of
international trade in the economic development of the different nations, which
compose the EU. It is useful to mention the second point because empirical
studies are very rare in the literature on endogenous growth.
We follow hereafter a very simple plan. First we briefly outline the theoretical
support used by COE and HELPMAN in their empirical study. Second we will
describe the very simple model they use, the data they provide and the results they
obtain. Finally we show how this study can be used as a basis for implementation
of simple endogenous growth mechanisms into the GEM-E3 model.
Theoretical aspects of the GROSSMAN and HELPMAN model.
The theoretical model used by COE and HELPMAN and widely discussed in
GROSSMAN and HELPMAN is clearly an innovation-driven growth model that
is a model in which the SOLOW residual results from the accumulation of
knowledge. Using a model of differentiated products, GROSSMAN and
HELPMAN show that cumulative R&D explains at least most of the variation in
Total Factor Productivity (TFP) where TFP is defined in an usual way as,
TFP = log Y − β log K − (1 − β ) log L ,
(1)
with β defined as the share of capital in GDP.
Taking this general result into account, the following equation can be estimated,
log TFP = α 0 + α d log S d ,
(2)
where S d is the domestic R&D capital stock.
But, such a specification is not satisfactory because many of the inputs used in
production in a given country are manufactured by trade partners. Then the
international trade is a way through which a given country increases its stock of
knowledge. It follows that the foreign stock of knowledge, S f , defined as the
85
imports-share-weighted average of the domestic R&D capital stocks of trade
partners, is a relevant independent variable to be added in equation (2) to obtain,
log TFP = α 0 + α d log S d + α f log S f .
(3)
But as mentioned by COE and HELPMAN this specification « may not capture
adequately the role of international trade » because, when estimated on pooled data, it
does not reflect the idea that the more a country imports the more it may benefit
from foreign R&D. COE and HELPMAN propose then a modified specification
of (3),
log TFP = α 0 + α d log S d + α f mi log S f ,
(4)
where mi is the share of imports in GDP for country i.
From (4) it appears that the elasticity of TFP with respect to the domestic R&D is
α d while the elasticity of TFP with respect to foreign R&D is α f mi . It is clear
that the latter elasticity varies across countries while the former is constant across
countries.
We will show later how specification (4) must be used for including endogenous
growth mechanisms in the GEM-E3 model. For the moment let us note that this
specification could be relevant because it allows for endogenous differentiation of
TFP variations across countries.
Data and results from the COE and HELPMAN model.
Our survey on empirical analysis of endogenous growth shows that the
methodology developed by COE and HELPMAN (1995) was probably one of
the few attempts to provide empirical results within a tractable model allowing to
link technical innovation with economic growth.
Moreover, data sources cover 20 OECD countries plus Israël hence provide
estimates for all the countries present in GEM-E3. For all these countries (U.S.,
Japan, Germany, France, Italy, U.K., Canada, Australia, Austria, Belgium,
Denmark, Finland, Greece, Ireland, Israel, Netherlands, New Zealand, Norway,
Portugal, Spain, Sweden and Switzerland) COE and HELPMAN use R&D
expenditure data from the OECD's Main Science Technology Indicators others data are
from specific countries like US, Japan... provided by their Ministry of Labor
statistics. The period is 1971-1990, which is quite large and sufficiently recent for
our purpose. These data are reported in table A.1. of the COE and HELPMAN
paper (p.877). The data show that total factor productivity, domestic R&D capital
stock, foreign R&D capital stock and imports share in GDP increases significantly
during the period. Except the imports share in GDP trends are neither uniform
across countries nor uniform over time.
COE and HELPMAN have constructed TFP measures using (1) where Y is value
added in the business sector, K is the stock of business sector capital and L is
employment in the business sector.
86
The business sector Domestic R&D capital stocks are also reported in this paper
for each year and for all the countries. The corresponding estimates are based on
OECD data on R&D expenditures. Nominal R&D expenditures are converted
into real expenditures using an R&D price index deflator defined as a weighted
average of an implicit deflator for business sector output and an index of average
business sector wage. R&D capital stock is then defined as the beginning of period
stock constructed by using the perpetual inventory model. Data are finally
converted into U.S. dollars and normalised at 1 in 1985.
The foreign R&D capital stocks, also reported in the paper, are constructed as
weighted averages of the domestic R&D capital stocks of each 21 countries by
using bilateral imports shares reported in table A.4 of the paper.
Different results corresponding to different specifications are given in the paper.
We only report here pooled cointegrating regressions that are based on equation
(4).
In this model, the impact of domestic R&D is allowed to differ between the
largest seven economies compared with the other 15 economies, while
constraining the impact of the foreign R&D stock to be the same for all countries
Table: Coe and Helpman estimates.
TOTAL FACTOR PRODUCTIVITY ESTIMATION RESULTS18
log S d
0.078
G 7.log S d
0.156
m.log S f
0.294
Standard error
0.044
R2
0.651
R 2 adjusted
0.630
Towards a specification of endogenous growth mechanisms.
Specification (4) cannot be used in the GEM-E3 model as it is. Indeed, the
definition (1) of TFP as the Solow residual used by COE and HELPMAN, assumes a
Cobb-Douglas specification while actually the GEM-E3 model uses a CES
specification for the producer behaviour. To bypass this problem, it would be
useful to re-estimate (4) with a new specification for constructing TFP. This seems
highly time consuming and not really relevant.
Another way to proceed is to consider that the COE and HELPMAN estimates
of (4) provides good estimates of the TFP growth rate with respect to the growth
In this table, G7 is a dummy variable introduced for allowing the impact of domestic R&D to differ
between the largest seven economies compared with the other economies.
18
87
rates of domestic and foreign R&D capital stocks. This means that the following
new relation must be used,
∆S f
∆S d
∆TFP
= αd
+ α f mi
.
TFP
Sd
Sf
(5)
Including relation (5) into the GEM-E3 model allows us to differentiate TFP
variations across countries. But, it remains to provide a specification to
endogenously estimate the R&D capital stock inside the GEM-E3 model.
The simplest way to do that is to assume that R&D expenditures are a constant
share of GDP over time which can be differentiated by country or not because it
does not differ greatly across countries. Such an hypothesis is consistent with the
observed data used by COE and HELPMAN (R&D expenditures average about
1.5% of GDP with a maximum of about 2%, see p. 862 of their paper op. cit.) and
can be interpreted as a constant rate of saving hypothesis.
To construct real R&D capital expenditures it remains then, to define price index
for R&D. The one used by COE and HELPMAN is simply,
PR = 0.5P + 0.5W ,
(6)
where P is the deflator for business output sector and W is an index of average
business sector wages. Note that specification (6) could be easily refined but an
acceptable simpler way is to take the price of GDP as a proxy for PR.
R&D Capital stock is defined as the beginning of period stock using the perpetual
inventory model,
S t = (1 − δ )S t −1 + Rt −1 ,
(7)
where R is the real R&D expenditure and δ is the depreciation rate of R&D
capital stock.
Initial R&D capital stock (for base year say at time 0), is defined by
S 0 = R0 / δ .
(8)
Equation (8), indicates that if R&D expenditure is constant over the past, then the
value of the stock is simply defined by the ratio between present R&D
expenditure and the depreciation rate of R&D capital stock. A more realistic way
to define R&D capital stock, consists in taking into account the real R&D
expenditure over the past. Simply using average past growth as a proxy to take
into account the historical R&D expenditure growth can do this.
S 0 = R0 / ( g + δ ) ,
(9)
where g is the average growth of R&D expenditure in the past.
88
Equation (9) leads to heterogeneous R&D capital stocks across countries,
depending on their previous efforts in R&D. Formula (9) gives a ratio of GDP to
R&D capital stock around 5 for the G7 countries and 10 for the rest of the
OECD countries. These ratios are provided for each country in the COE and
HELPMAN paper. As we will see later, we use such statistics in our calibration
step of the model.
Finally, it is important to note here that the depreciation rate used by COE and
HELPMAN is 5%, but different estimations are also proposed for δ = 10% or
δ = 15% . Authors conclude that estimated rates of return are sensitive to the
levels of R&D capital stocks and hence sensitive to the assumption of parameters
g + δ in equation (9). Not surprisingly, our results show the same sensitivity for
the choice of the depreciation rate of R&D capital stocks. This is the reason why
we will propose to test this model for different values of δ.
The modifications of the GEM-E3 model
T H E
C H A N G E S
W H I C H
B E
S H O U L D
N E C E S S A R Y
As the production functions are defined at the sectoral level, it would be necessary
to define sector indexes of total factor productivity and then to estimate the link
between these indexes, the domestic R&D capital stock S d and the foreign stock
of knowledge, S f 19.
In addition, in order to avoid any double counting, the R&D expenditures of each
sector have to be separated into capital expenditures K R , wages corresponding to
an amount LR of labour and intermediate consumption. Finally, each sector
would appear partly as a productive sector which uses K − K R and L − LR and
partly as a research sector which uses K R and LR and buids an innovation stock
S d which influences TFP. Doing so could be more in agreement with the general
equilibrium framework but it would also need a lot of work.
The difficulty would be to describe properly the Research and Development
process in each industry. This task necessitate to define inputs in R&D activity as
well as outputs (patent, publication, soft...), or a correct aggregate of these outputs.
More over, theoretical work points that R&D appropriability is an important
determinant of innovative activities, but integrating it into empirical studies of
innovation has proven difficult. Some qualitative interesting results have been
showed on micro-economic studies, but quantitative results about the link
between productivity and R&D capital stock remains in the macro-econometric
area.
The modeling we propose does not include a complete representation of an R&D
sector in GEM-E3. By considering the complete production function including
identified and specific activities related to innovation and knowledge as a black
box, we assert that R&D affect productivity like an externality effect.
It would also be better, in order to capture the externalities which occur between different sectors, to
differentiate the effect of the own stock of knowledge of the sector and the effect of the stock of
knowledge accumulated by the other domestic sectors (like Bernstein-Nadiri [1988]).
19
89
T H E
P R O P O S E D
S P E C I F I C A T I O N
F O R
G E M - E 3
Practically, our proposal, to include a specification of endogenous growth
mechanisms in the GEM-E3 model, must lead to a new production function
allowing an increase in output proportionally to the value of Total Factor
Productivity (TFP). Then the final output defined by a CES production function
must be equal to:
( σ −1)
( σ −1)
1
1
σ
σ
( KAV ) σ + α LEM
( LEM ) σ 
XD = TFP α KAV


σ
( σ −1)
(10)
where KAV and LEM are the two aggregate production factor defined in the
production function used in GEM-E3.
After presenting the way to compute TFP we will present the new expressions for
the input demand and input prices insuring an increase in total production
proportional to TFP.
The TFP growth is endogenously determined in the model through equation (5)
rewritten for notational convenience as follows,
TFPG = α d DRDSG + α f mi FRDSG
(11)
where TFPG is TFP growth which depends on Domestic R&D capital Stock
Growth (DRDSG) and Foreign R&D capital Stock Growth (FRDSG).
Assuming that R&D expenditures are a constant share of GDP, we have the
following equation,
RDE i = si ⋅ GDP ⋅ ei
(12)
where RDE i and GDPi are respectively R&D expenditures and GDP at current
prices, si is constant other time. ei is the nominal exchange rate for country i.
The evaluation of R&D expenditure and R&D capital stock in a same monetary
unit are necessary to compute the foreign R&D capital stocks as a sum of the
domestic R&D capital stocks.
The index i means country i, it must be explicitly included here for clarity of the
subsequent development.
For each country domestic R&D capital stock ( DRDSGi ) is then defined through
equation (7) using equation (9) for initial values. For a specific country, i, the
foreign R&D capital Stock ( FRDSGi ) is,
FRDS i = ∑ c ji ⋅ DRDS j
(13)
j
90
where c ji are the elements of the matrix of manufactures imports of country i
from industrial country j as a proportion of total manufactures imports of country
i from all industrial countries.
We present now, the new expressions for input demands and input prices
compatible with equation (10) of the production function.
Suppose that the production function is of the CES form, for two production
factor K,L, output q is equal to :
[
q = γ α 1/ ρ K ( ρ −1) / ρ + β 1/ ρ L( ρ −1) / ρ
]
ρ
ρ −1
,
where γ is the efficiency parameter changing output in a similar way as TFP.
The profit maximisation problem is
π = pq − ( p
Max
k
K + pL L)
K,L
where, p, pk , pL represents the prices for output capital and labour respectively.
First order conditions implies that,
∂π
∂q
=p
− pK = 0 and ,
∂K
∂K
∂π
∂q
= p − pL = 0 .
∂L
∂L
Hence at the optimum marginal productivity are such that :
∂q p K
=
and ,
∂K
P
∂q p L
=
∂L
P
Remark that the CES production function is linear homogenous since
[
θq = γ α
1/ ρ
(θK )
( ρ − 1) / ρ
+β
1/ ρ
(θL)
ρ
( ρ − 1) / ρ ρ − 1
By Euler's theorem output q can be expressed as
q=
∂q
∂q
K+
L
∂K
∂L
91
]
Under perfect competition firm's long run profits are zero
π = p(
∂q
∂q
K+
L) − ( pk K + pL L)
∂K
∂L
Substituting for the marginal productivity defined above in the profit equation
shows immediately the zero profit condition at the optimum.
The first order conditions yields
 q
∂π
= pγα 1/ ρ K −1/ ρ  
∂K
γ 
 q
∂π
= pγα 1/ ρ L−1/ ρ  
∂L
γ 
1/ ρ
− pK = 0.
1/ ρ
− p L = 0.
Hence the optimal demand for capital and labour is
ρ
 p
K =   qαγ ρ −1 ,
 pK 
(14)
ρ
 p
L =   qβγ ρ −1 .
 pL 
(15)
At the optimum, marginal productivity is equal to real factor price, so we can
write:
 q
p k = pα  
 K
 q
p L = pβ  
 L
1+ ρ
γ −ρ ,
(16)
γ −ρ .
(17)
1+ ρ
Equations (14), (15) and (16), (17) constitute the changes of the complete system
of inputs demand and prices respectively that must be changed in the model. We
will see later that it is possible to use the actual specification of the model including
a Hicks neutral technical progress.
Extension to the case of a nested CES production function is straightforward, it is
always possible to derive the same equations for any sub-production function
defining aggregate level of inputs.
92
Model Extension 3: Endogenous Energy-Saving
Investments in GEM-E3
20
G E N E R A L
P R E S E N T A T I O N
The purpose of this model extension is to incorporate the additional possibility of
investing in energy-saving technology. In this context economic agents are
assumed to have the possibility to increase the productivity of energy (i.e. consume
less energy inputs per unit of output) by investing some resources to accumulate
an energy-saving technology stock.
The decision whether and how much to invest on energy saving technology is in
this model version an endogenous decision of the economic agents.
Producers in the standard version of the GEM-E3 model demand the costminimising mix of factors needed for production (capital, labour, energy and
intermediate goods). Based on the demand they face their existing production
capacity and their expectation about the future they also invest to increase their
productive capital stock. In the new model variant, there is an additional
production factor, the stock of energy-saving technology, which serves to reduce
the amount of energy needed to produce the same output, in other words it acts
in favour of increasing the productivity of energy.
We use the term “energy-savings” to indicate all technologies that may improve
energy productivity.
Producers compare the benefit of having one more unit of additional energy
saving technology (that will induce lower energy costs for all subsequent time
periods) to the cost of acquiring this additional unit. Through their costminimising behaviour, they decide (as the solution of their inter-temporal problem
of allocating their resources) together with the demand for production factors and
the one for productive investments, the optimal investment in energy saving
technology. This investment does not affect their productive capital stock, but is
an additional demand for goods (which for example may be equipment goods).
In addition, in the extended model version, consumers have the possibility to
choose among two classes of durable goods: “ordinary” ones, and more energy
efficient ones, say “advanced technology”, whose acquisition price is however
higher. A trade-off between higher acquisition costs for durable goods and lower
energy (operation) costs, is thus introduced in the decision making of the
consumer.
The investments related to energy saving accumulate to form an energy-savings
capacity (stock) that of course will have permanent effects on energy productivity.
Similarly, the choice of more efficient durable goods will also have permanent
effects on the use of energy in households. The relationship between the energysaving stock and its effectiveness for energy savings exhibits decreasing marginal
This extension has been developed by NTUA and incorporated in Version 2.1 of GEM-E3. It has
been used for the evaluation of the macroeconomic implications of the EU negotiation position for the
Kyoto Conference, December 1997.
20
93
returns (saturation effect). For example if a constant investment on energy savings
is accumulated per year, the resulting increase to the stock is increasing at
decreasing rates, as illustrated in the figure:
Figure 1: Energy-Saving Stock under a constant investment in energy-saving
technology
energy-saving stock
(base period=1)
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
199
1
100
0.5
time periods
The basic algebraic formulation links the energy-saving expenditure to the stock of
energy-saving capital and the increase of that stock (in other terms its marginal
effectiveness). For example, if the energy use costs increases, the firm may quickly
invest on energy saving as long as the accumulated energy-saving capital remains
low. Beyond a certain level of saturation, the firm may decrease further investment
on energy-saving, as the marginal effectiveness of the capital decreases and the
corresponding expenditure that is necessary to maintain a certain level of
effectiveness increases non-linearly. This is illustrated in the following figure:
Figure 2: Energy Saving Investment and Stock under a continuous 3% increase of energy prices every year
200
1.4
160
Energy saving stock
1
140
Investent in improving energy efficiency
120
0.8
100
0.6
80
60
0.4
Investment in energy-saving
technology (monetary units)
Accumulated energy-saving
stock
180
1.2
40
0.2
20
0
0
1
51
101
151
201
Time periods
251
The following remarks must be added:
•
•
The energy-saving stock acts cumulatively, i.e. energy-saving technology
accumulated by year t continues to be available in all subsequent years at no
additional cost. A stock of energy-saving technology once acquired cannot be
scrapped.
The energy saving technology is depletable, i.e. there is an upper limit to the amount
of energy productivity gains that can be achieved, a limit which depends on the
particular economic agent and country (see Figure 1 above).
94
•
•
The desired amount of energy-saving technology depends mainly on the relative
price of energy compared to the cost of acquiring it (which in its turn depends on
the stock of energy-saving technology already
95
accumulated, see Figure 2 above) and the share of energy inputs in
production costs.
Through this mechanism, the model incorporates an important dynamic
mechanism, which is related to the depletable character of the energy savings
potential. This mechanism involves a trade-off over time, as the firms (or
consumers), may prefer to invest on energy savings (allocating less expenditure to
consumption or investment) expecting to then use energy more productively.
Model Implementation
The production function21 involves an additional production factor Ν t defined
as the cumulative stock of energy saving technology, at the disposal of each sector.
XD
t
δ 1σ ⋅ K σ −1σ + δ 1σ ⋅ Lσ
2
t
t
=  1 1
σ
−
1
 + δ σ ⋅ (N ⋅ E ) σ

3
t
t
−1
σ




σ
σ −1
(25)
The producer decides together with the demand for capital, labour, energy and
materials, the desired amount of capital (which defines investment demand) and
the desired amount of energy technology that he would optimally have (which
defines the investment demand for the acquisition of energy saving technology).
The problem can be defined as an inter-temporal optimisation problem of the
following form:
∞
∫ e (PD
Max
− rt
t
XD
t
− PE t E t − PI t I t − PI t C t
)
(26)
0
•
Kt = It − δ ⋅ Kt
•
N
Nt
t
= f
t =∞
(27)
(N t , C t )
(28)
=ω
(29)
where I t is the amount of investment in productive capital and Ct is the amount
of investment in energy-saving technology. ω is the (exogenous) potential for
energy saving. The point above a variable indicates derivative with respect to time.
The above problem can be solved, by defining the Hamiltonian and taking the
corresponding optimality conditions. The “normal” results for investment and the
other production factors remain as before in the model. For the optimal stock of
energy saving technology the following formula can be derived:
21
For reasons of simplicity, the nesting of the production function is ignored for the time being.
96

∂XD t  PC t
=
 δ ⋅ PD t
∂Ν t

•
•


 r + δ − η  ⋅ e − λt where δ = ∂ N t and
 δ

∂Ct

 
•
∂ N t
η =
∂N t
The optimal demand for energy is derived from
∂H t
= 0 which gives:
∂E t
XD t ⋅ N tσ −1
Et =
 PD t 
⋅δ ⋅ 

 PE t 
σ
(30)
The dual production function (as used in GEM-E3) becomes:
PD
t
 δ 1 ⋅ PK t1 − σ + δ 2 ⋅ PL 1t − σ

1−σ
= 
 PE t 


+ δ 3 ⋅ 

 Nt 






1
1−σ
(31)
To proceed further we need an additional assumption about the shape of the
function f linking consumption in energy-saving technology to the corresponding
stock accumulated. This function has to exhibit two basic properties:
•
∂ N t
• it has to increase with Ct , i.e.
∂Ct
> 0
N = ct
• for the same amount of investment, the change in energy-saving stock
must be inversely related to the currently achieved stock.
A simple function that meets the above requirements is f = a ⋅ N −β ⋅ C . The
coefficient and the exponent can then be calibrated according to engineering
evidence ensuring both zero investments in the base year and a reasonable slope
of the curve. With the above function the steady state solution to the problem can
be obtained defining the optimal demand for investment in energy-saving
technology22:
The derivation follows the same principles as with productive investments: the long run optimal
solution serves to compute the desired return on investment in energy-saving technology, which is then
compared to the real benefit from obtaining an additional unit of energy-saving technology.
22
97

 PE ⋅ r ⋅ E ⋅ N σ −1
1
b +1 
C = ⋅ N ⋅ (1 + stgr ) ⋅ 
 PC ⋅ (r + r )⋅ N β

α
p


σ
 − 1

 − 1 ⋅ e ω − N




(32)
This formula can easily be extended to reflect depreciation of the energy-saving
stock.
In summary, equations are (30), (31) and (32) are calibrated and introduced for all
sectors of the model. Also, similar equations are introduced for the choice of
durable goods in consumption allocation of households. For both producers and
consumers, energy saving expenditure is further split in goods and services that are
demanded to build the energy saving capacity. These act as additional demand to
the economy.
98
Model Extensions 4: Labour market
imperfection and disaggregation
23
T H E
A G G R E G A T E
L A B O U R
M A R K E T
C L O S U R E .
Introduction
In these notes we set out the first stage of implementing the imperfectly
competitive labour market closures outlined in McGregor, Swales and Yin (1996)
within GEM-E3. It should be noted from the outset that, for the moment, we
deal only with the wage-setting function, the "bargained real wage function" or
BRW. The specification of the price-determined-real wage function (PRW) awaits
the decision on the appropriate incorporation of imperfectly competitive
commodity markets into GEM-E3. However, it is important to note that it is the
interaction of these functions, in general, that ties down the behaviour of the
unemployment rate. For example, although a "trend productivity" term enters the
BRW, it also enters the PRW with an equal coefficient, so that labour productivity
growth is neutral in terms of its impact on the equilibrium unemployment rate.
For the present the task is to introduce the BRW function, and use it to replace
the competitive labour supply function: the labour demand functions remain as
before for the aggregate model, and only have to be modified for the
skills-disaggregated variant, on which notes will follow shortly.
We suggest proceeding by creating new versions of GEM-E3, and retaining the
current version as a possible competitive benchmark. We begin by discussing the
specification of the aggregate BRW function per se and then note the implications
for the specification of the rest of the model. We suggest implementation for the
aggregate UK labour market initially. Subsequent notes extend this to: a skill
disaggregated variant for the UK; aggregate versions for other EU countries; skills
disaggregated versions for other EU countries.
The specification of the aggregate BRW function
There remains some uncertainty in our minds about the intended time scale of the
model. Undoubtedly the most straightforward approach would be to replace the
labour supply function in GEM-E3 with the steady-state version of the BRW
function. Conceptually, this is the logical counterpart to the labour supply
function. However, we also allow for a dynamic adjustment variant of the BRW
function in general (although the complete variant of this - with lagged wage
adjustment as well as transitory influences on the adjustment path - is actually not
required in the UK case). Nevertheless, we do not allow for nominal inertia even
in this latter version (although it is present in the estimated versions of the
equations): the nature of the macroeconomic closures of the current version of
GEM-E3 suggest a time scale of sufficient duration to allow all sources of nominal
inertia to be eliminated. (This preserves the "only relative prices matter" feature of
GEM-E3.)
The University of Strathclyde has developed this model extension. Only limited testing has been
performed at present.
23
99
The steady-state version(s) of the aggregate BRW function
The version reported in Layard, Nickell and Jackman (1991, eg p405), is as follows
(suppressing terms that are intended to capture nominal inertia):
w - p = α 0 − α 1 u + α 2 s. c + α 3 (k - l) + α 4 z + α 5U
where: w is the natural logarithm (log) of the nominal wage; p is the (log) of the
price of value-added; u is the log of the unemployment rate; c = p* + e - p is the
log of competitiveness; s the share of imports in GDP, p* is the log of the foreign
currency price of imported goods and e is the log of the nominal exchange rate; k
is the log of the capital stock and 1 is the log of the labour force; z is a vector of
wage push variables including "mismatch" and union power; U is the
unemployment rate (which enters because of the influence of long-term
unemployment on w-p). (In fact the specification of the BRW varies a bit across
EU economies, so this specification is not entirely general, although many of the
same variables enter. Will this create problems?)
(While this is the equation that LNJ argue is supported by the data (and further
evidence for it is offered in Nickell and Bell (1996)), the absence of the tax wedge
in the steady-state version is controversial. At least for tax rate changes, it may be
instructive to at least consider the variant with a lasting tax wedge effect:
w - p = α 0 − α 1 u + α 2 s. c + α 3 (k - l) + α 4 z + α5U + α 6 t
where t = t1 + t2 + t3 is the total tax wedge, reflecting income, expenditure and
payroll tax rates etc.)
The dynamic version of the aggregate BRW function
The dynamic version of the model is, in effect, an ECM variant of the first
equation, and so differs from it in containing the first differences of some of the
arguments and a lagged dependent variable, so with no lasting tax wedge we have:
w - p = β 0 − β 1 u − β 11 ∆U + β 2 s.c
+ β 3 (k - l) + β 4 z + β 5U + β 7 ∆t + β 8 (w − p )t − 1
The first difference of the (log of) the unemployment rate is interpreted as picking
up the influence of "persistence" effects, as may operate through insider and
long-term unemployment rate effects. (LNJ (1991, chpt 9) and Nickell (1995)
offer evidence that the unemployment change term is picking such effects). With
effect we have:
w - p = β 0 − β 1 u − β 11 ∆U + β 2 s.c + β 3 (k - l)
+ β 4 z + β 5U + β 6 t + β 7 ∆t + β 8 ( w − p )t − 1
100
Other changes to the model structure
Where wages are set, as here, through bargaining rather than competition, the
treatment of household labour supply and consumption decisions as fully
integrated makes little sense. The simplest approach here is to treat the labour
supply and consumption decisions as quite distinct. This separability assumption is
motivated by the notion that bargaining first ties down wages and employment
and then households plan their consumption decisions conditional upon
anticipated labour incomes. In effect, this means reverting to the LES system for
consumption, augmented to accommodate durables.
T H E
D I S A G G R E G A T
E D
L A B O U R
M A R K E T
C L O S U R E .
Introduction
This note summarises the skill disaggregated imperfectly competitive labour
market closure as outlined in McGregor, Swales and Yin (1996) within GEM-E3.
It is the second stage of the imperfectly competitive labour market closure
specification, the first stage being the aggregate labour market closure that was
specified in an earlier note. In this version, we deal with separate bargained real
wage functions for the skilled and unskilled labour (i.e., the skill-specific BRW
functions). It has to be noted that in the aggregated imperfectly competitive labour
market closure, there was no change made to the labour demand function in
GEM-E3. For this version, however, we specified different demand functions for
each skill group in such a way that they can be combined through the CES
aggregation function to give the composite demand for labour.
In the short-run (over which the labour force for each skill group is exogenous),
equilibrium real wages and employment rates are determined by the interaction
between the wage setting and the labour demand functions (LNJ (1991), Nickell
and Bell (1996a)). The long run equilibrium, however, is governed by the skill
mobility (migration) function in which the unemployment differentials and wage
differentials between skill groups play a key role in determining net-(migration)
mobility across skill groups.
Skill-specific BRW functions
In line with our proposed modification of the aggregate model, we suggest
allowing for skill-specific bargained-real-wage functions which are specified as
follows:
 US 
 K
WS * = exp[αs0 − αs1 log
 + αs2 log( S * C ) + αs3 log 
 NSUPBS 
 L
 U 
+ αs4 z + αs5 
 + αs6 t ]
 NSUPB 
101
(33)
 UU 
WU * = exp[αu0 − αu1 log
 + αu2 log( S * C )
 NSUPBS 
 K
 U 
+ αu3 log  + αu4 z + αu5 
 + αu6 t ]
 L
 NSUPB 
(2)
where, WS*, WU*, contemporaneous bargained skilled and unskilled real wages;
US,UU, U: number of skilled, unskilled and total unemployment;
NSUPBS, NSUPBU, NSUPB: number of skilled, unskilled, and total
aggregate labour supply;
S: share of imports in GDP;
the
C = P*E/P: is competitiveness (E is nominal (£/$) exchange rate), P* is
foreign price level, and P is domestic price of value-added.
K: capital stock
L: labour force
z: vector of wage push variables including “mismatch” and union power
taxes,
t = t1 + t2 + t3 : total tax wedge reflecting income, expenditure, and payroll
etc.
αs 0, αu 0: intercept term
αs 1... 6, αu1... 6: elasticity of real wages w.r.t. the corresponding variables.
The dynamic version of the disaggregated BRW function
The short-term real wage is given as follows:
 U 
 US 
STWS = exp[ βs0 − βs1 log
 + βs2 log( S * C )
 − βs11 ∆
 NSUPB 
 NSUPBS 
 LHWS * 
 K
 U 
 + βs6 t + βs7 ∆t + βs8 
]
+ βs3 log  + βs4 z + βs5 
 NSUPB 
 L
 CPIL 
(3)
102
 UU 
 U 
STWU = exp[ βu0 − βu1 log
 − βu11 ∆
 + βu2 log( S * C )
 NSUPBS 
 NSUPB 
 LWHU * 
 K
 U 
+ βu3 log  + βu4 z + βu5 
 + βu6 t + βu7 ∆t + βu8 
]
 L
 NSUPB 
 CPIL 
(4)
where, STWS, STWU: short-term skilled and unskilled real wage;
LHWS, LHWU: lagged nominal take-home skilled and unskilled wage;
CPIL: lagged consumer price index;
βs0 , βu0 : intercept terms;
βs1 ... 7 , βu1 ... 7 : elasticity parameters
βs8, βu8: parameter denoting the speed at which the short-term real wage
adjusts to the contemporaneous real wage.
The nominal take-home pay for the skilled and unskilled workers (HWS, HWU) is:
HWS = CPI * STWS, HWU = CPI * STWU
(5)
The demand for labour by skill
The demand side of the labour market also needs to be augmented to include the
skill dimension. The most straightforward treatment here is simply to create
another level of the production hierarchy (below what will now be the composite
labour level in the labour, materials and fuels production function) in which labour
of different skill groups combine through a CES aggregation function to yield the
aggregate labour input which currently enters the model.
The formulation here is based on the specification of cost-minimisation for the
demands for skilled and unskilled labour (assuming competitive commodity
markets). We start with the demand for the composite labour input in each
industry (given the simple K-L CES value-added production function):
SNDEM i = ( δ l i *
PVAi σ
) l i * VAi , i = 1, 2, ..., n
PLi
(6)
where, SNDEM: demand for the composite labour input in each industry;
PVA: price of value added;
PL: price of the composite labour;
VA: value added;
103
δl: CES share parameter;
σl: elasticity of substitution between labour and capital.
The demand for skilled and unskilled labour inputs in each industry is given by::
NS i = ( δ lsi *
PLi σ
) lsi * SNDEM i , i = 1, 2, ..., n
PLS i
NU i = ( δ lui *
(7)
PL i σ
) lsi * SNDEM i , i = 1, 2, ..., n (8)
PLU i
where, NS, NU: demand for skilled labour and unskilled labour in each industry;
PLS, PLU: price of skilled labour and unskilled labour;
δls, δlu: CES share parameters;
σls: elasticity of substitution between skilled and unskilled labour.
The total demands for skilled and unskilled labour are obtained by aggregation
over all industries:
n
NDEMS =
∑ NS i ,
n
NDEMU
i=1
= ∑ NU ,
(9)
i
i=1
Unemployment is defined as follows:
US = NSUPBS - NDEMS, UU = NSUPBU - NDEMU
(10)
The nominal price of labour is given by:
PLSi = θsi HWS (1+t1s)(1+t2s), PLUi = θui HWU (1+t1u)(1+t2u)
(11)
where, PLS, PLU: nominal price of skilled and unskilled labour;
θs, θu: share parameters;
t2s, t2u: average income tax rate;
t1s, t1u: average rate of national insurance contributions.
1
PL i = [ δ lsiσ lsi PLS 1-i σ lsi + δ luσi lsi PLU 1-i σ lsi ] 1-σ lsi (12)
This differs slightly from the approach in LNJ (1991, chapter 6) and Nickell and
Bell (1996a). They start with a CES labour composite, but this is not embedded
104
into a wider production function, and the model is not fully specified on the
demand side. The LNJ and Nickell and Bell (1996a) specification appears to be a
theory of the competitive firm’s demand for labour, although the model is used to
interpret aggregate labour market experience. Here the skill distinction is
embodied in a complete system, where aggregate demands for skilled and unskilled
labour are obtained by summing such demands across all industries. This
therefore seems a preferable approach, in which the impact of various
disturbances is more transparent.
Labour mobility and labour markets in the longer term
In the longer term the labour force for each skill group cannot be treated as
exogenously determined. To close the model over the longer-run once the labour
market is disaggregated we require (as a minimum) net “migration”/mobility
functions describing how labour moves between “segments” of the labour market.
Skill wage and unemployment differentials are likely to be key arguments of the
net migration functions across skill groups. The precise specification of such
migration functions is likely to prove critical in governing the longer-run behaviour
of the model, yet there does not appear to be any generally agreed specification
(and indeed there appears to be little work on this that we could find). We briefly
outline a number of possibilities here, and suggest some simulation experiments.
The Layard, Nickell and Jackman (1991, chapter 6) model essentially adopts a
Harris-Todaro (1970) model (or rather the modified version of it that allows for
different responsiveness to unemployment and wage differentials). When
adjustment through migration is complete, another zero-net-migration equilibrium
is established.
A number of alternative approaches to migration have been adopted in the
regional CGE literature (eg. Morgan, Mutti and Partridge (1989) and Jones and
Whalley (1988)), and these typically run with alternative views about the degree of
labour mobility. However, overall, our preference is to run with comparatively
simple specifications of the net migration function across skill groups. We suggest
taking Harris-Todaro (1970) specifications as one benchmark case (but an
intercept in the net migration function acts to inhibit mobility, to a degree which is
inversely related to the wage and unemployment differential elasticities) :
HWS
HWU
) - log(
)
CPI
CPI
US
UU
+ σ g 1 ( log(
) - log(
)]NSUPBSL
NSUPBS
NSUPBU
(13)
NSM = [ σ g 2 + σ g 0 ( log(
where, NSM: net migration from the unskilled group to the skilled group;
NSUPBSL: lagged supply of skilled labour.
NSUPBSLt+1 = NSUPBSt
(14)
NSUPBSt+1 = NSUPBSt + NSM, NSUPBUt+1 = NSUPBUt - NSM
105
(15)
However, given heterogeneity among potential migrants, including different ability
levels, it seems reasonable to presume a distribution of expected returns to skill
migration. Under such circumstances, a stock-adjustment specification of the net
migration function may be warranted. For constant populations this would imply
that a relative increase in the wages of skilled employees, for example, would
generate a once-and-for all reallocation of labour across skill groups. Continuing
flows would only arise in the presence of growing populations. In such a context,
changes in skill wage or unemployment differentials would generate stock and flow
adjustments. However, zero net migration equilibria would cease to impose the
very tight constraint associated with Harris-Todaro. We would also hope to deal
with the asymmetry problem, namely that it is typically easier for skilled to become
unskilled than vice versa, and does not require a training period.
106
Model Extension 5: The Financial/Monetary
Sector
The design of this sub-model of GEM-E3 is largely inspired from the work of M.
Parkin (1970), Van der Beken W. and Van der Putten R.C.P. (1989), and Van Erp
F.A.M et. al. (1989). The approach avoids reduced-form models of financial
mechanisms and uses relative interest rates as explanatory variables. Depending on
whether liberalised capital markets are represented in the model, these interest
rates can be derived from the equilibrium of financial supply and demand flows. In
addition, different institutional characteristics can be represented, which might
prevail in the financial markets and policy. The financial behaviour of economic
agents is based on a portfolio model which is derived by maximising expected
utility. The model allocates financial wealth among various assets. The allocation is
made using logistic curves that involve relative rates of return of assets.
Figure 3: The matrix of flow-of-funds (simplified)
PRIVATE
BANKS
ASSETS
placemen
t of assets
supply of
credits
and loans
LIABILITIES
credits
and loans
deposits
GOVERNM
ENT
FOREIGN
transfer and
financing of
foreign debt
financing of
deficit
Regarding its accounting structure, the model is based on a matrix of flows of
funds (Figure 10), involving four financial agents, namely private (aggregating
households and firms), government, banks24 and foreign sector.
In the model the foreign and public sectors are represented only with respect to
the financing of their surpluses, while the banking and private sectors are
represented following an “assets-liabilities balance” approach. The model fully
guarantees stock-flow consistency for all transactions. A simplified form of the
flow-of-funds matrix is shown above.
T H E
P R I V A T E
S E C T O R
On the assets side of the private sector, total wealth (W) is evaluated, dynamically,
by private net savings, a variable coming from the real part of the model.
WL = WL−1 + S P + ∆A f + ∆LP
(1)
The allocation of total wealth of the private sector is described as “risk averse
investment behaviour”. Private agents are assumed to maximise the utility of the
return from a portfolio. In this respect future returns are uncertain and the risk
aversion is formalised as diminishing marginal utility. It is also assumed that
The banking system, as defined in this model comprises, beside the central bank, all commercial
banks and specialised credit institutions.
24
107
changes in the composition of the portfolio in relation to the starting point entail
costs.
The basic model, expanded with a number of sector-specific variables, determines
the optimum portfolio composition, in terms of: cash, time deposits, saving
deposits, government bonds, bank bonds and treasury bills. The allocation mainly
depends on the relative rates of return (assimilated to interest rates) from the
above assets. Adjustment costs and dynamic behaviour are incorporated in these
equations.
Asi = As min,i +


⋅  WL − ∑ As min, j  (2)

j
∑ EXP( a j + b j (1 + r j )) 
j
EXP( a i + bi (1 + ri ))
∆Ai ,t = Asi ,t − Asi ,t −1 (3)
Foreign exchange deposits are explained by the evolution of the exchange rate, the
foreign to domestic interest rate differential and the capital and transfer inflow
which enters the country.
The demand of credit by the private sector bears the influence of the real interest
rate, the profit rate and the volume of total investments of the sector.
r 
∆LP = ∑ I *  l 
a
η
(4)
This demand behaviour is important, because it is part of the demand/supply
equilibrium of the capital flows addressed to the private sector, through which, the
private lending interest rate, i.e. rl , is determined. This in turn leads the rates of
both the saving deposits and the time deposits. The assets-liabilities balance in the
banking sector serves to evaluate the capacity of banks to lend the private sector,
i.e. variable ∆B p , which is a supply behaviour. This formulation also is in
accordance with that institutional regime in which prevails a leakage in capital
supply to the private sector induced by the imperative financing of public deficit.
T H E
P U B L I C
S E C T O R
The approach to modelling the public sector behaviour is drawn by the concern
of financing the public deficit. Although in many respects the financing of the
public sector is often a matter of political decision, some behavioural equations are
introduced in the specification of the model to mimic such decisions.
The financing of the public sector's deficit can be effected by borrowing from the
domestic sectors (from the private sector and the commercial banks), the foreign
sector, and from the central bank. The share of public deficit covered by foreign
loans depends mainly on the interest rates differential.
Domestic borrowing of government is divided into two parts: the treasury bills
and the government bonds. Both can be acquired by the private sector and by
108
commercial banks. Concerning the private sector, investment in these two assets
emanates from portfolio allocation.
The government demand for selling bonds ( ∆b pg ), depends on the domestic
public debt of the previous year ( D DOM ,t −1 ) , the lending capacity of the
government ( SU G as computed in the real part of the model) and the relation
between the rate of the government bonds ( rB ) and that of the foreign loans ( rF ).
(
∆b = a ⋅ D DOM ,t −1 + SU G
g
p
)
σ
 1 + rB 
⋅

 1 + rF 
ρ
(5)
The demand/supply equilibrium serves to determine the rate of interest of
government lending, i.e. rg , which further leads the interest rates of bonds and
treasury bills in equations.
The assets-liabilities balance in the banking sector serve to evaluate the capacity of
banks to lend the private sector, which is a supply behaviour. The equilibrium
price is the private lending interest rate, i.e. rl , which is used in both the real and
the monetary sectors of the model.
T H E
F O R E I G N
S E C T O R
Modelling of the foreign sector is oriented towards determining the ways for
covering the current account deficit. Foreign capital inflow ( ∆A f ) is a function of
relative profitability of investment assets.
1 + rB 
∆A f = a ⋅ ∆A f,t-1 ⋅ 

1 + rF 
φ
(6)
In the model, it is assumed that changes in bank reserves are maintained at some
predetermined level.
E Q U I L I B R I U M
C O N D I T I O N S
The financial/monetary sector, can determine endogenously three equilibrium
prices:
1. the private sector lending interest rate,
2. the government lending interest rate and
3. the exchange rate.
The above specification does not exclude, however, the possibility to include
different structural or institutional changes that may occur in the economy. This
may be effected by some other selection of endogenous and exogenous variables.
For example, it is possible is to consider that the exchange rate is exogenously
determined by the authorities. In this case foreign exchange reserves can be
endogenous. In both cases of closure rules, the IS-LM module can evaluate the
level of inflation.
109
Model Extension 6: The engineering oriented
energy sub-model.
I N T R O D U C T I O N
A usual critique of economic models when used to perform analysis of policies
that affect the energy system, is their lack of engineering evidence concerning the
substitution possibilities and costs in production and consumption.
To overcome this shortcoming, a separate engineering-oriented optimisation
model of the energy system is currently tested and will subsequently be
incorporated in the GEM-E3 model. The energy sub-model in GEM-E3 will take
as given the demand of the sectors for energy products and will then determine
energy prices and the fuel mix that meets this demand. This information will then
be used in the optimisation decision of the economic agents defining the energy
demand at the new iteration. At the equilibrium prices and quantities used by both
models will be equal.
D E S C R I P T I O N
O F
T H E
E N E R G Y
The energy system sub-model is a simplified version of the PRIMES energy
model25, involving a much more aggregated representation of technologies, but
using the same design principles. The energy sub-model in GEM-E3 will:
S U B -
• explicitly compute the energy prices of equilibrium;
M O D E L
• have a flexible modularised architecture, in the sense that each agent is
represented by a separate optimisation sub-model;
• cover with engineering detail, both the country-specific energy
systems and the overall energy market clearing at the European
Community;
The sub-model of GEM-E3 will (like PRIMES) belong to the new generation of
energy models at the Commission of the European Communities, since it will be
oriented towards the price-driven equilibrium paradigm. In this sense the model
will:
• consider explicitly and compute the formation of energy prices, so to
be able to study price-related and market-related policy instruments;
• represent market clearing mechanisms and related behaviours as the
main explanatory force in the models, so to be able to make realistic
forecasts given the increasing trend towards liberalisation of markets;
NTUA is the coordinator of the development of the PRIMES energy model. The model is being
built under the auspices of the European Commission DG-XII, JOULE programme.
25
110
• recognise the individual character of agents' behaviours, and abolish
the central planning paradigm, by modularising the model and
decentralising optimisation behaviours;
The model is built around the assumption that producers and consumers both
respond to changes in price. The factors determining the demand for and the
supply of each fuel are analyzed and represented, so they form the demand
and/or supply behaviour of the agents. Through an iterative process, the model
determines the economic equilibrium for each fuel market, which is then
introduced in the economic model.
The fundamental design feature of the model is its modularity. The model is
organised by fuel (oil products, natural gas, coal, electricity, others) for supply and
by end-use sectors for demand (residential and commercial, transports, industrial
sectors). The individual modules vary in the depth of their structural
representation. The modularity feature allows each sector to be represented in a
way considered appropriate, highlighting the particular issues important for the
sector, including the most expedient regional structure. The electricity module
expands over the whole Europe, while representing chronological load curves and
dispatching at the national level. Coal supply, refineries and demand operate at the
national level.
At the global level, that is the market clearing level, the formulation of the model
corresponds to a market equilibrium of the type:
Demand = Function (Price)
Supply = Demand
Price = InverseFunction (Supply)
By considering that the behaviour in the supply side, corresponding to cost
minimisation, is formulated as a set of linear programming models and that the
demand side has the form of a system of (nonlinear) equations, the equilibrium
model can be written:
Solve for x , q , p , u that satisfy:
Supply side:
min c x
s.t. x in the set X
Ax = q
Demand side:
q = Q(p)
Cost Evaluation:
u = f ( c, x and other factors)
Equilibrium Condition:
p = u + taxes
where x and q denote supply and demand quantities, while u and p stand for
producer and consumer prices.
111
The supply side may include more than one mathematical programming problems
which would correspond to the behaviour of several supplying agents (for
example, one for refineries, one for gas and one for electricity). In addition, it is
not excluded that some suppliers of commodities may be, in the same time,
demanders for other commodities (for example, the electricity sector).
Notice that the process of specifying such a model involves the following steps:
1. define which are the agents, the commodities and the markets;
proceed to an activity analysis, i.e. define supplying and demanding
activities of agents for each commodity;
2. choose a mathematical formulation of each agent's behaviour and
specify the corresponding sub-model, while respecting activity analysis
defined in the previous step; a sub-model may be a mathematical
programming model (linear, nonlinear or mixed-integer) or a system
of (nonlinear) equations; all sub-models consider commodity prices
are given; the supply sub-models have to correspond to cost
minimisation and should satisfy demand; the demand sub-models
must relate demand quantities to commodity prices; a supply submodel may include formulations of market allocation among many
suppliers, if necessary (for example between domestic production and
imports);
3. define a price setting mechanism for each commodity; this may be
based on average cost or marginal cost pricing and may include any
other external factors influencing prices (for example world-wide
leading prices); it is interesting to note that this part of the model can
reflect realistic situations concerning price-setting regimes (excluding
artificial price-setting based on shadow prices); the price setting
mechanisms should be related, but not exclusively, to the results of
the supply sub-modules;
4. define the equilibrium conditions for all commodities by equalising
producer prices (from step 3) and consumer prices (used in demand
sub-models in step 2); taxes and subsidies may be included in these
equilibrium conditions, such as excise taxes, VAT, carbon-tax and so
on (other types of regulations must be incorporated in the
corresponding submodels at the agent level).
Normally the solution of this model would involve an iteration procedure. starting
from an initial guess of the vector of commodity prices, demand quantities are
computed from sub-models corresponding to demanders; mathematical
programming models for supplying agents are then solved constrained to demand
quantities computed before; based on the results of the supply sub-models, the
cost evaluation equations compute produced prices, which augmented with taxes
are used to evaluate a new approximation to consumer prices; these are compared
to the ones used in the previous iteration and if they are found close enough the
process is terminated, otherwise the process restarts by re-computing demand.
112
Obviously, such a solution algorithm is not only time consuming (especially since
the results of this model must be used as input to GEM-E3, which is in itself a
very large scale model), but also due to the non-convexities present in the submodules no guarantee of convergence exists.
T H E
E N E R G Y
S U B - M O D E L
A
A S
M I X E D
C O M P L E M E N T A
R I T Y
P R O B L E M
The solution of this model (and its link with GEM-E3) is facilitated by recent
developments in the development of powerful software for solving mixed
complementarity problems26. In the complementarity approach, this problem can
be re-written as a single system of inequalities in which the objective functions are
replaced by the appropriate KKT (Karush-Kuhn-Tucker) optimality conditions
and all constraints of all subproblems and the demand-supply constraints relating
agents are included. Under certain conditions it can be proved27 that this approach
is mathematically equivalent to solving the sequential problem described above.
To exemplify the complementarity approach considers the following formal
presentation of the energy sub-model: the model comprises of n non-linear
optimisation (NLP) or simulation modules, each representing one individual
decision maker (agent).
Let us consider the i − th of these modules. This takes as given an input vector of
prices and quantities denoted respectively pi and qi . The solution to this subproblem is the vector x i . The sub-problem includes a number of demand and
non-demand constraints. A dual value (or shadow cost) is associated with each of
these constraints. These are denoted by the vectors ui and v i respectively. The
objective function of each NLP involves minimising a non-linear cost function
θ ( x i , pi ) .
The general form28 of the i − th NLP problem is then:
min θ ( x i , pi )
s. t.
(7)
− g i ( x i ) ≥ N i ( qi )
− hi ( x i ) ≥ 0
xi ≥ 0
where the first set of constraints represent demand limitations (i.e. production
must meet demand), while the second is the set of engineering constraints
imposed by the nature of the agent29.
26
The same approach is also followed in the PRIMES model.
27
See Gabriel and Kydes (1995), also Ferris and Pang (1997).
28
The simulation modules do not need any modification.
Note that strict equality constraints can also be introduced. In this case the associated dual price is
unconstrained in sign.
29
113
Assuming that all functions in the above are convex and twice continuously
differentiable, then the KKT conditions are sufficient for solving the above NLP.
Defining the Lagrangian function:
(8)
[
]
L( x i , ui , v i ) = θ ( x i ) + uiT ⋅ g i ( x i ) + N i (qi ) + v iT ⋅ H i ( qi )
The solution of the NLP problem described above is then identical to solving the
following mixed complementarity problem (MCP):
∇L( x i , ui , v i ) ≥ 0
(9)
∇L( x i , ui , v i ) ⋅ x i = 0
T
xi ≥ 0
(
⋅ (− h ( x )) = 0
)
− gi ( x i ) − N i ( qi ) ≥ 0
ui ≥ 0
uiT ⋅ − gi ( x i ) − N i ( qi ) = 0
− hi ( x i ) ≥ 0
vi ≥ 0
v iT
i
i
It should be stressed that for each NLP pi and qi are exogenous parameters and
so not considered as variables in the MCP problem.
The sub-problems communicate via constraints that link demanded and supplied
quantities of fuels. The equilibrium fuel prices pi are affine transformations of the
dual prices associated with the demand constraints of the subproblem(s) in which
they appear. So the price of fuel k produced by agent i is a function f k ( ui )
reflecting the price setting behaviour of the agent. This way a number of
alternative pricing mechanisms (marginal cost, average cost, Ramsey pricing etc.)
can be accomodated.
The incorporation of other constraints, such as for example those relating to the
environment is straightforward: suppose for example that an emission reduction
target is imposed. This represents an additional constraint for the model. If this
constraint is binding at the optimal solution, then the associated dual value of the
constraint will be positive. This represents an additional cost for all agents that
produce emissions, a cost entering their objective functions. In the MCP format
the dual price of the environmental constraint will appear in the Lagrangian.
The full then structure of the energy sub-model is then:
114
Table 4: Structure of the energy sub-model in GEM-E3
NLP1 ( x1 , u1 , v1 , p1 , q1 )
NLP2 ( x 2 , u2 , v 2 , p2 , q2 )
...
NLP transformed in MCP format as in (9)
NLPn ( x n , un , v n , pn , qn )
p1 = f ( ui )
p1 = f ( ui )
...
Fuel prices derived from demand constraints
p1 = f ( ui )
( )
l( x i ) = m q j
M O D E L
I M P L E M E N T A T
I O N
Demand for a fuel must be satisfied by suppliers
Thus, the GEM-E3 model will be expanded by the equations and inequalities of
this single energy model and written in complementarity format. The software that
will be used to solve this model will be PATH in GAMS. GEM-E3 has already
been solved in PATH with full success (see chapter on model implementation),
while a prototype version of the energy sub-model has also run as a stand-alone in
PATH. The first tests of linking the two show that no major technical obstacle for
their integration exists (for example model size), so it is foreseen that in the next
months an operational version of GEM-E3 including an energy sub-model will be
operational.
115
5
Chapter
Data and Nomenclature
The regional, sectoral and other coverage of the model is presented in this
chapter. The data sources and their processing is also presented. The model
parameters and variables are explained at the end of the chapter.
Data Sources for main model
The main sources of the data
are:
• the Input-Output tables in
producer’s prices, per
member-state, compiled by
Eurostat from national
sources.
• Consumption matrix,
There does not exist a complete data set for each of the 14 EU
countries for 1985, the calibration year of GEM-E3, therefore
though a general procedure has been constructed, it was always
necessary to adapt it to the specific data set of each country.
The GEM-E3 model identifies the following products/sectors:
No
Sector Name
1
Agriculture
investment matrix and
2
Solid Fuels
also compiled by Eurostat.
• the Eurostat Energy
Balances.
• National accounts by
sector and by branch from
Cronos of Eurostat, that
(after aggregation) have
been used to complete the
income distribution part of
the Social Accounting
Matrix by country.
• the Trade Data of bilateral
trade flows as in
COMEXT.
3
Liquid Fuels
4
Natural Gas
5
Electricity
6
Ferrous & Non-Ferrous, Metals
7
Chemical Products
8
Other Energy-Intensive Industries
9
Electrical Goods
10
Transport Equipment
employment by sector,
116
11
Other Equipment Goods Industries
12
Consumer Goods Industries
13
Building And Construction
14
Telecommunication Services
15
Transports
16
Services Of Credit And Insurance
17
Other Market Services
18
Non-Market Services
The classification of the consumption of households by purpose is as in the
following table (ND stands for non durables and D for durables):
No
Purpose Name
Status
1
Food, Beverages and Tobacco
ND
2
Clothing and Footwear
ND
3
Housing and Water
ND
4
Fuels and Power
ND
5
Housing Furniture and Operation
ND
6
Heating and Cooking Appliances
D
7
Medical Care and Health Expenses
ND
8
Transport Equipment
D
9
Operation of Transport Equipment
ND
10
Purchased Transport
ND
11
Telecommunication services
ND
12
Recreation, Entertainment, Culture, etc.
ND
13
Other Services
ND
117
General Procedure
The general procedure consist in combining the different data sources in a
consistent way to arrive at a Social Accounting Matrix for each country, with the
disaggregation level needed in GEM-E3. The steps of this procedure are the
following:
• Aggregation of the IO table in producer’s prices into GEM-E3
nomenclature
• Transformation of the IO table in producer’s prices into IO table in
consumer’s prices. This means adding the VAT to the delivery of the
branches to final demand (except exports and part of investment) and
to the payments of the branches to the public sector.
• Construction of investment and consumption matrix, if not available
• Allocating the revenues generated by the economic activity to the
different economic sectors, as disaggregated in GEM-E3 based on the
IO table and the National Account data disaggregated by branches.
The IO table in GEM-E3 nomenclature
The aggregation of Nace-Clio R59 has been used for the initial Input-Output
table. For some of the countries where this aggregation was not available, the
Nace-Clio R25 aggregation was used instead. The procedure that has been
followed to convert the table of 59 branches into the specific one of 18 branches
for the GEM-E3 model, is showed in the following structure:
118
Nace-Clio
R59
010
031
033
050
071
073
075
095
Branch
097
098
099
Electric power
Manufactured gases
Steam, hot water, compressed air
9
10
11
110
Nuclear fuels
12
Electrical goods
Transport equipment
Other equipment goods
industries
Consumer goods industries
135
136
137
151
153
Iron ore & ECSC iron & steel products
Non-ECSC iron & steel products
Non-ferrous metal ores,non-ferrous metals
Cement, lime, plaster
Glass
13
14
15
16
17
Building and construction
Telecommunication services
Transports
Services of credit and insurance
Other market services
155
157
170
190
210
230
250
270
290
310
330
350
370
390
410
430
450
471
473
490
510
530
550
570
590
611
613
617
631
633
650
670
690
710
730
750
770
790
810
850
Earthenware & ceramic products
Other minerals & derived products
Chemical products
Metal products
Agricultural & industrial machinery
Office machines
Electrical goods
Motor vehicles & engines
Other transport equipment
Meat & meat products
Milk & dairy products
Other food products
Beverages
Tobacco products
Textiles & clothing
Leather & footwear
Timber & wooden furniture
Pulp, paper, board
Paper goods, products of printing
Rubber & plastic products
Other manufacturing products
Building & civil engineering works
Recovery & repair services
Wholesale & retail trade
Lodging & catering services
Railway transport services
Road & transport services
Inland waterway services
Maritime & coastal transport services
Air transport services
Auxiliary transport services
Communications
Credit & insurance
Business services provided to enterprises
Renting of immovable goods
Market services of education & research
Market services of health
Market services n.e.c.
General public services
Non-market services of education &
research
Non-market services of health
Non-market services n.e.c.
18
Non-market services
890
930
Agricultural, forestry & fishery products
Coal & coal Briquettes
Lignite & lignite briquettes
Products of coking
Crude petroleum
Refined petroleum products
Natural gas
Water (collection, purification, distribution)
No
1
2
3
4
5
6
7
8
GEM-E3
Aggregation
Agriculture
Solid fuels
Liquid fuels
Natural gas
Electricity
Ferrous & non-ferrous metals
Chemical products
Other energy intensive industries
010
031+033+050
071+073
075+098
097+099+110
135+136+137
170
151+153+155+157+190+471+
473
250
270+290
210+230
119
310+330+350+370+390+410+
430+450+490+510
530
670
611+613+617+631+633+650
690
550+570+590+710+730+750+
770+790+095
810+850+890+930
As far as the Nace-Clio R25 aggregation is concerned there were no significant
problems in the transformation on account of the usage of the Energy Balance
Sheets provided by the Eurostat. In the example below we can see the way that
No
GEM-E3 Sector Name
NACE-CLIO R25
AGGREGATION
1
Agriculture
010
2
Solid Fuels
Part of 060
3
Liquid Fuels
Part of 060
4
Natural Gas
Part of 060
5
Electricity
Part of 060
6
Ferrous And Non-Ferrous Ore And Metals
130
7
Chemical Products
170
8
Other Energy-Intensive Industries
150+190+470
9
Electrical Goods
250
10
Transport Equipment
280
11
Other Equipment Goods Industries
210+230
12
Consumer Goods Industries
360+420+490+48
0
13
Building And Construction
530
14
Telecommunication Services
670
15
Transports
610+630+650
16
Services Of Credit And Insurance
690
17
Other Market Services
560+590+740
18
Non-Market Services
860
this conversion took place.
Due to the fact that the energy sectors of the GEM-E3 model are included in one
single sector of the R25 aggregation the disaggregation has been successfully
achieved by taking into account the appropriate information provided by the
Energy Balance Sheets of the specific countries.
For the case of the imputed output of bank services we isolate it by using the
figures given in the National Accounts by sector.
For countries where no Eurostat IO table for 1985 exists, the data from Beutel
were used, complemented with the National Accounts data by sector to ensure
the compatibility between both sources.
120
The IO table in market prices
In order to create the IO table in market prices a procedure divided in three basic
levels has been followed.
the total VAT income are taken from the NA by sector and distributed between
investment, private consumption and public consumption, based on the
differences between data in producers prices (from IO tables) and data in
consumers prices (from NA by branches).
• the allocation of the VAT by branches was based on the consumption
matrix or on the NA by branches.
• the computation of the IO table in consumer’s prices has been made.
The IO table has to be translated from the domestic concept into the national
concept, to be able to combine it with the NA data into a social accounting
matrix. The expenditure by tourist (abroad and on the national territory), added to
the IO imports and exports when necessary, were allocated between branch as the
private consumption deliveries.
The investment matrix translates the demand of investment goods by the
branches into deliveries by branches.
C O N S T R U C T I O
N
O F
T H E
The matrix which has been constructed to portray the investment transactions
between sectors of the French Economy is showed in the following example:
I N V E S T M E N T
M A T R I X
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
Total
01
2584
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
33
2616
02
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
03
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
04
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
05
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
06
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
07
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
08
983
156
414
778
5648
2975
2965
7428
3360
3871
3958
10630
2023
467
3847
391
11434
2887
64213
09
0
136
362
681
4940
2581
1600
2383
1535
1013
1533
2250
659
13791
2071
360
14188
9434
59515
10
1646
32
84
159
1152
180
592
1434
621
159
555
3725
6707
973
20761
805
15792
3393
58771
11
16619
227
604
1135
8239
5536
5048
9129
5657
3719
5684
14098
7346
1839
3667
3858
37735
4242 134383
164
1595
12
0
14
38
71
512
210
174
273
146
302
159
454
164
228
71
13
6901
803
2136
4016
29152
1403
2370
3581
1852
5978
1926
7629
5311
10798
16716
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17
2042
38
101
190
1379
423
408
701
442
288
425
1214
1133
952
2445
1110
48457
2577
64326
0
0
0
0
18
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Total
30775
1405
3738
7029
51022
13307
13157
24929
13613
15331
14240
40000
23342
29047
49579
3753
8326
13147 294770 104654 513142
19834 423971 130972 905291
As we can see in the previous example it is clear that the deliveries were basically
made by the branch of other energy intensive industries (number 08), the branch
of Electrical Goods (number 09), the “Transport Equipment” branch (number
121
10), the “Other Equipment Goods Industries” branch (number 11), the “Building
& Construction” (number 13) which appear to have the more considerable
contribution and finally the branch which represents the related market services
(number 17).
As long as no such matrix exists, which is a fact for some countries, the procedure
which is described below was followed in order to build such a matrix:
• The demand of investment goods by branch is taken from the
National Accounts by branches (Gross fixed capital formation, by
ownership branch),
• The total deliveries by branch are taken from the Input-Output table,
• Finally these figures were used and appropriate assumptions were
made for every country individually to fill the matrix.
C O N S T R U C T I O N
O F
T H E
C O N S U M P T I O N
M A T R I X
The consumption matrix translates the demand per consumer categories into
deliveries by branch. For countries where such a matrix exists, they are usually
expressed in consumer’s prices, i.e. they include the VAT and the margins are
included in the price of the delivery and not considered as a separate delivery by a
service branch. For the use in the model, the matrix has to be in producer’s prices
and with explicit delivery by service branches. Therefore, the following corrections
were made :
• given VAT rates for the different consumer categories, a consumption
matrix without VAT is computed,
• the margins included in the deliveries by branch are evaluated as the
difference between the consumption matrix deliveries (without VAT)
and the IO deliveries.
• these margins are allocated between the services branches based on
exogenous parameter compatible with the Input-Output deliveries of
these branches.
122
01
02
03
04
05
06
07
08
09
10
11
12
13
Total
01
15893
0
0
261
0
0
0
0
0
0
0
6054
164
02
0
0
0
1588
0
0
0
0
0
0
0
0
0
1588
03
0
0
0
19369
0
0
0
0
30126
0
0
0
0
49495
04
163
77
0
11805
65
12
15
19
24
0
0
62
24
12266
05
0
0
0
25123
0
0
0
0
0
0
0
0
0
25123
06
0
0
0
0
0
0
0
4
10
3
0
344
0
360
07
40
0
0
5
3002
548
6394
24
58
15
0
1899
3253
15239
08
126
50
0
3
8442
1540
47
19
46
12
0
14397
4332
29013
09
0
0
0
0
6405
1168
42
97
239
61
0
9976
265
18255
10
0
0
0
0
124
23
7
26646
13411
0
0
822
0
41033
11
0
0
0
0
330
60
1494
0
0
0
0
2432
1879
6196
12
125120
61042
0
229
28793
5253
225
0
2031
0
0
9234
6160
238087
22372
13
0
0
0
0
2481
453
0
0
0
0
0
0
0
2934
14
455
214
0
45
180
33
42
53
68
0
18670
173
67
20000
15
1374
648
0
136
545
99
126
160
2194
16362
0
522
1831
23998
16
839
395
0
83
333
61
77
98
125
1
0
319
33453
35784
17
52899
24923
159062
5248
24152
4406
17567
6160
37300
49
0
45377
63888
441031
18
4479
2110
278
444
3097
565
6842
776
1295
164
0
7369
132895
160314
Total
201390
89460
159340
64340
77950
14220
32880
34056
86929
16665
18670
98980
248210
1143090
The example of the consumption matrix of Germany is contrasted above:
The previous table represent the demand of every one of the 18 branches divided
into 13 consumption categories.
For the countries where no such matrix exist, the matrix was computed using the
following procedure:
• The consumption per consumer category is taken from the NationalAccounts (final consumption of households on the economic
territory, by purpose) and corrected for the consumption by tourist.
• Given VAT rates for the different consumer categories, the total per
category without VAT is computed
• The total deliveries are taken from the Input-Output tables and
appropriate assumptions were made to allocate the total per categories
to the delivery branch.
Construction of the Social Accounting Matrix
The construction of the SAM is the starting point of the model building work. In
the base year, the definition of the set of prices is such that the balance of flows in
the SAM is satisfied in both constant and current currency. The balance is
conceived as the
equality between the sum by row and the sum by column. In addition, a SAM
ensures the fulfilment of the Walras law in the base year, since by construction the
algebraic sum of surplus or deficits of agents is equal to zero. To understand the
notation used, figure 6 gives a more detailed presentation of the SAM framework,
as used in GEM-E3.
123
The SAM of GEM-E3 represents flows between production sectors, production
factors and economic agents. The production sectors produce an equal number of
distinct goods (or services), as in an Input-Output table. Production factors
include, in the SAM, only primary factors, namely labour and capital. These are
rewarded by sharing sectoral value added. The economic agents, namely
households, firms, government and the foreign sector, are owners of primary
factors, so they receive income from labour and capital rewarding. In addition,
there exist transactions between the agents, due to taxes, subsidies and transfers.
The agents partly use their income for consumption and investment, and form
final domestic demand. The foreign sector also makes transactions with each other
sector. These transactions represent imports (as a row) and exports (as a column)
of goods and services. The difference between income and spending (in
consumption and investment) by an economic agent determines his surplus of
deficit.
Combining the Input-Output data, adapted to market prices and to national
concept (instead of domestic concept), and the data of the National Accounts by
sector allows to build the Social Accounting Matrix for each country. The
allocation of the adapted Input-Output totals to the different sectors, household,
government, firms and rest of the world is rather straightforward from the NA
data, and can be summarised as follows :
• the total labour value added is allocated to the households except for
the part going to the ROW
• the capital income is distributed between household, firms and
government as in the NA
• the transfers of income by the government (interest payments, social
security and other welfare transfers) are all paid to the household, with
the exception of the amount received by the ROW, the same for the
income/transfer payments by firms
• the social security contributions are paid by the household to the
government and to the firms
• households and firms pay the direct taxes to the government
• the transfers received by the ROW are all coming from the
government and the ROW payments are allocated to the government
The general form of the Social Accounting Matrix is as followed:
124
REVENUES
EXPENDITURES
→
↓
Sectors
Factors
Agents
Investment
& Stocks
Total
expend.
intermediate
consumption
0
demand for goods
for consumption
and exports
demand for
goods for
investment
total demand of
goods
rewarding of factors
from value added by
sector
0
income transfers
from foreign
0
indirect taxes,
VAT, subsidies,
duties and
imports
0
factor payments to
agents according
ownership
income transfers
between agents
0
0
0
Total
Revenues
total supply of goods
total payments of
factors
total revenues
minus investment
and stocks
total spending of
agents
Surplus or
Deficit
0
0
lending (+ or -)
capacity by sector
(Sum = 0)
0
Goods
from
Sectors
Factors
(labour
and
capital)
Agents
Gross
Savings
total factor
revenues
total income of
agents
0
The Social Accounting Matrix can be faced as a table consisted of four main
divisions. These specific divisions represent the Intermediate Consumption, the
Final Demand, the Revenues from Sectors and finally the Transfers between
Sectors.
Each of these four tables are showed separately in the following figures and they
Intermediate Consumption
01
01
02
03
02
81327
03
04
05
06
07
10
11
12
0
27
11
802
1480
0
4
0 7051
0
0 6201
8391
453
1597
3
80
10
259 145277
70 3763
1439 23888
7581
816
1681
1081
10783
04
254
570
1528 31345
1743
733
1022
0
0
8330
3055
427
12
10
40
26
279
430
25010
8696
8994
674 34861
802
21477 10944
283088
4751
412
991
300
3168
114
109
169
150
7845
1343
2447
1398
9967
1837
728
4235
824
271
6492
08
2396
449
2223
146 1612
09
67
91
1269
73 2575
0 1317 67907
0
436
3253 35126
3399 75804 14139
10971 13975 12201
2482
4176
461
0
40
11
83
49
11
6310
591
616
125
870
1340
12
41222
481
780
0
129
13
1095
218
2877 1296
14
73
47
15
2689
335
16
3821
4
769
8160 21262 19960
142
1071
1440 10481
388 17081
111 61754
2300
4876 11307
441
0
0
28831 75858
893
1676
5881
69662 14682
416007
324 18590 2529
572
0
10008 12688
108441
5829 25633
104162
8415
151
648
7458
0
18
624
108
15782
2037
93594
5745 188772 28386
719
2782
387
45741 25654
401558
462
607
261
631
326
599
1996
4582
1270
1424
1953
3634
4360 1529
1888
0
0
245
166
2278 3063
540 10310
1661
7429
1460
6534 24032
70650
7933
210372
19073
1814
94441
84522 90824 5974 26237 54607 277027 66129
849969
5807
4555
4697 10693 15554 1780 34521
2304
2743
2533
0
0
0
0
6745 13859
0
0
0
0
0
0
0
35609
56237
76505
4400 10394 27129
24512 38696 33467
6429 26254
9310
1029
0
162323
205507
216
203
11408 2189 11173 12875 29532 51852
50
506
784
5133
10
7641 12163
5213 12937
940
3282
63204
118531
227
3718
674
3140
17335 11208
0
195
21
305836
0
8455 24348
9869 12656 20767
4498
Total
5316
1986 40075
2905 18455 113773 17947 34867 23750
1089
10
0
16
7444
95
841
15
5429
343
0
18
1
2963
525
258
14
5339
30828
0
17
0
1299
06
27210 1734
13
82 210625
276 44821
07
18
09
0
05
17
08
91
0
0
0
Total 210803 13094 179261 37274 81527 114510 200625 305175 104457 217205 122440 607815 286619 16880 122579 106015 615421 233084 3574785
stand for the Social Accounting Matrix of France.
125
Final Demand
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
Total
Consumption
Investments
Change
FIRMS Total
Labour Capital Total Househ. Govern. Banks
Exports Househ. Private Govern. Total
in Stocks
0
0
0
76221
0
0
0
65419
0
2584
33
2616
1610
0
0
0
2860
0
0
0
1570
0
0
0
0
-652
0
0
0 138610
0
0
0
33378
0
0
0
0
-6677
0
0
0
29931
0
0
0
1119
0
0
0
0
504
0
0
0
68767
0
0
0
20740
0
0
0
0
-2378
0
0
0
620
0
0
0
66223
0
0
0
0
-2105
0
0
0
68343
0
0
0
116845
0
0
0
0
192
0
0
0
53757
0
0
0
76235
6951 54375
2887 64213
-5322
0
0
0
36205
0
0
0
67230
8626 41456
9434 59515
375
0
0
0 102172
0
0
0
160008
9601 45777
3393 58771
-2942
0
0
0
15606
0
0
0
100047 22941 107200
4242 134383
1015
0
0
0 550290
0
0
0
190622
969
3604
3753
8326
4070
0
0
0
27173
0
0
0
677 179202 229285 104654 513142
-5549
0
0
0
53880
0
0
0
2649
0
0
0
0
0
0
0
0
78774
0
0
0
56478
0
0
0
0
0
0
0
0
63242
0 192340
0
8705
0
0
0
0
0
0
0
0 1408200
0
0
0
153584 29459 32290
2577 64326
0
0
0
0
96446 910323
0
0
2402
0
0
0
0
0
0
0
0 2871097 910323 192340
0 1123930 257749 516570 130972 905291
-17859
Total
451703
28789
448399
94758
205661
227062
390887
604889
271766
422171
344644
1154866
591680
133034
345624
358728
2476079
1009170
9559907
Revenues from Sectors
01
Wages+SSC
02
03
04
05
06
07
08
09
10
11
12
30038 9384 11306 8511 31317 33397 56660 157191 71473 92796 70420
Capital
154346 1521 3940 14180 61842 11816 25802 52592 22393 9884 27176
Tot Val. Add. 184384 10905 15246 22691 93159 45213 82462 209783 93866 102681 97596
Act. Output
395187 23999 194507 59965 174686 159723 283087 514958 198323 319886 220036
13
14
15
16
17
18
Total
194243 168612 54611 126058 118147 696477 651805 2582446
103042 71352 50252 74076 91734 869670
64524 1710141
297285 239965 104862 200133 209881 1566147 716329 4292587
905100 526584 121742 322712 315896 2181568 949413 7867372
HHS
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
FIRMS
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
751 10282
2391
5297 10505
4055 11255 53559 139768
Indir. Taxes
8501
3975
7424
4089
49191
412485
Direct Taxes
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Soc. Security
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Subsidies
-8440 -7123
-20
-12
-482
-474
-405
-2883
-1606
-7828
-1541
-17565
-3010
-18 -23178 -24665
-43339
VAT taxes
3579
279 13538 2923
6716
61
6654
6866
6765 12602
7257
37023 57258
5149
7629
9175
321279
Duties
1175
1
51
1
1
156
599
384
1464
996
1442
2470
0
0
0
0
1
0
8741
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50145 64704
9186
-4294 34931 228198
58366
599916
Gov. Foreign
Gov. firms
Total Taxes
Distr. Output
391 62378
4815 -6452 75947 3663 16517
2134 12145 14872 10598 13194 11247
400002 17547 270454 63628 191203 161857 295232 529830 208921 333080 231283
28217 10456
6037 131768
955245 591288 130928 318418 350827 2409766 1007779 8467288
EC
14026 4159 46550 9063
6128 36199 65776 45876 29857 47096 60775
116581
0
568 12090
2799
19330
NON-EC
Total Imports
36575 7041 129395 21635 7337 28997 28893 28407 32465 40521 52361
51701 11241 177945 31130 14457 65205 95655 75059 62844 89091 113361
75101
199621
0
392
761 13979
2106 27205
4190
7901
26667
66313
0
0
0
0
Savings
0
0
0
0
0
0
0
0
0
0
0
0 -142589
0
0
0
516873
0 534325
1391 1092619
0
0
Total Resour. 451703 28789 448399 94758 205661 227062 390887 604889 271766 422171 344644 1154866 591680 133034 345624 358728 2476079 1009170 9559907
126
Transfers between Sectors
Consumption
Labour
Capital
Total
Househ.
Govern.
Total
FIRMS
Banks
Investments
Exports
Househ.
Private
Total
Change
Govern.
Total
in Stocks
Wages+SSC
0
0
0
0
0
0
0
10350
0
0
0
0
0
2592796
Capital
0
0
0
0
0 -192340
0
0
0
0
0
0
0
1517801
Tot. Val. Added
Actual Output
0
0
0
0
0
0
0
0
0 -192340
0
0
0
0
10350
0
0
0
0
0
0
0
0
0
0
0
4110597
7867372
0 171798
-13955
0
0
0
0
0
4719136
0
0
0
0
0
0
677182
0
0
0
0
0
0
412485
1416
0
0
0
0
0
426475
7441
0
0
0
0
0
992933
32898
0
0
0
0
0
163
0
0
0
0
0
0
321279
HHS
2573107
FIRMS
838188 3411295
600203
600203
0
1149998
76979
Indirect Taxes
0
0
0
Direct Taxes
0
0
0
311356
Social Security
Subsidies
0
0
0
985492
0
0
0
VAT taxes
0
0
0
0
113703
109854
Duties
0
0
0
0
0
0
0
0
0
8741
Gov. Foreign
Gov. firms
0
0
0
79410
0
79410
0
0
0
0
0
0
0
0
0
0
0
0
0
79410
Total Taxes
0
79410
79410
Distr. Output
0
0
0
Total Imports
19689
0
19689
0
47459
0
0
0
0
474212
23852
2592796 1517801 4110597
4719136
2241486
SAVINGS
Total Resources
1296848
109854
0 113703
41755
0
0
0
0
0
2241486
0
0
0
0
0
0
8467288
0
0
0
0
0
0
0
1159767
0 391681
-2313
0
0
0
0
0
1201188
0 677182 1159767
257749 516570
130972 905291
-17859 23355507
Foreign Trade Data
The Comext data have been used to compute a bilateral trade matrix for the
GEM-E3 branches for 1985, but no evaluation of the evolution in the trade
matrix has been possible.
Different problems have been encountered :
1. Quality of the data: though trade matrix computed from the imports
and from the exports data (that are separate), it seems impossible to
make a clear link between both type of data and the differences can be
sometimes very large (up to 25%) without any clear explanation. It has
therefore been impossible to derive CIF/FOB relations from these
data. Also from 1993 the discrepancies increase, partly explained by
the new procedure implemented (due to the IM) for collecting the
data.
2. Nimexe-Nace classification : the data for 1985 were in Nimexe
classification and had to be aggregated in the new NACE classification
of GEM-E3. After 1988 the classification changed implying a break of
continuity of the time series. This is the reason for the impossibility to
build a time-series of trade matrices.
3. The Comext data only concern trade of goods and there are no other
sources for the disaggregation by country of the external trade in
services of one country. A special Eurostat publication, used for this
matter, published only aggregate data of service trade. We had to
assume the allocation of services trade by country.
127
4. The Comext data are very different from the Input-Output exports
and imports data by branch and we have not yet been able to receive a
clear explanation. The national account data for exports and imports
by branch (in new Cronos) are too bad to be used (Eurostat is
currently modifying them).
The 1985 trade matrix has been used to calibrate costs of services and transports
associated to trade of other goods.
In the following example it is showed the Trade Matrix for Agriculture
Importer
Exporter
AU
BE
DE
DK
FI
FR
GR
IR
IT
NL
PL
SP
SV
UK
RW
AU
0
16018
258019
20634
106
38363
10600
145
155061
176896
572
28447
5098
3313
810474
BE
15562
0
158246
42115
1398
1342552
10348
4700
89138
508526
8082
71935
24027 110728
2294336
DE 131446
611269
0 426624
18116
30840 1126883
2900127
10271
500749
69137 158394
8548802
1515941 129519
DK
893
16061
73091
0
2641
104209
2104
1298
31900
83340
6243
27738
96507
21130
785916
FI
467
6209
20214
16052
0
15274
233
562
8385
37000
538
10111
35719
2417
348423
96329 499041
4301291
FR
6157
527120
791
0
23897
75367
424962
717132
23627
490015
GR
6067
5413
225794 197106
30025
24542
2323
148562
0
214
57952
42217
1598
9547
2302
IR
28
7180
8569
5901
998
64050
2103
0
7060
45672
662
6394
1015 313146
160055
IT 437344
NL
9487
116011
449075
243965 160981
399482 75928
7710
700
1870800 275038
823116 22088
29422
8255
0
84378
378165
0
15007
9237
232470
150733
27828 278903
24390 154795
4971499
4173871
PL
198
6436
6649
24913
0
168312
5965
595
14801
33810
0
124900
SP
1492
20737
71885
37718
175
447933
32352
25001
75326
92038 48386
0
SV
UK
8428
3921
10570
129023
67789 101730
163166 66028
9418
5275
41603
950112
2743
30357
1835
187490
36286
200537
135065
528430
3144
23104
39610
210477
RW 282434
120622
941164 340826 117054
2096702 219401
140643
663589
1067905
68787
3269
38618
395690
50947
967600
11654 216561
1880860
0
20575
14971
0
925734
3498108
311397 219094 576129
0
Time series for dynamic calibration
Time-Series for Dynamic Calibration
In the absence of SAMs for years other than 1985, we were obliged to only use
sectoral time-series as provided by Cronos database of Eurostat. We have
collected the following time-series, that have been aggregated to model’s
classification:
• value added per sector (volume, value), factor prices (gaps exist)
and market prices
• exports and imports per sector (volume and value)
• actual output (available for a few countries)
• investment by ownership branch (gaps exist)
• consumption of households by purpose (volume and value)
• employment per sector (gaps exist)
• National Accounts per sector
128
It was however not possible to build a complete benchmark data set for 1993 or
1994, as a complete set of data for each country and with the sectoral
disaggregation needed, only exist up to 1991.
The available data have therefore been used to ensure an evolution in the dynamic
simulations with GEM-E3 which is compatible with this statistical information.
They have served as targets for the dynamic calibration. Practically, the time-series
concern some of the margins of the Input-Output tables and the income
distribution structure.
Social Accounting Matrix for the post-1985 years
Eurostat does not provide new observed Input-Output tables for after 1985. For a
few countries post 1985 I-O tables, following the national methodology are
available, but it was not possible, with the resources within this project, to make
them compatible with Eurostat 1985 tables. We had access only to a time-series of
French Input-Output table, that were used to compute technical progress.
The Input-Output tables of 1991, as prepared by J.Beutel and al., were evaluated,
but were found inappropriate to serve as database for the model for two main
reasons :
1. the structure of the intermediate consumption is created artificially
(i.e. not through real data), using a type of advanced RAS method.
2. the I-O tables are in current prices, and the appropriate deflators
are not available. Thus, it is very difficult to assess volume changes.
129
6
Chapter
Calibration of model
extensions
Data requirements and objectives for
calibrating the environmental module
Since there are no end-of-pipe-technologies for reducing greenhouse gases at
reasonable costs, the end-of-pipe abatement technologies considered in GEM-E3
are limited to the primary pollutants SO2, NOx, VOC and particulates. The
purpose of this Appendix is the parameterization of abatement cost function for
SO2 and NOx.
The estimation of these cost functions is based on data of a survey undertaken by
the Institute for Energy Economics and the Rational Use of Energy (IER,
Stuttgart) in 1985 for the German state Baden-Württemberg.1 Its objective was to
calculate the minimal costs of abatement in the year 2000 under varying technical,
political and economic assumptions. Therefore the emission structure of 1985 was
projected up to the year 2000 without any additional environmental regulations
(i.e. no change in the rate of abatement in this matter up to the year 2000).
For this projection several assumptions have been made:2
1. population decrease:: 0.7 percent (1985-2000)
2. annual GNP growth: 2.2 percent
3. decrease in the energy-intensity of the manufacturing sector: 17.5 %
4. increase of transportation services:
cars
20.7 percent
trucks
26.7 percent
5. increase of specific fuel use for petrol-driven cars from 9.8 to 7.91 liter
per km and for diesel-driven cars from 8.9 to 6.61 liter per km
There are a few other assumption of minor importance. For more detail see Friedrich, R.,
Umweltpolitische Instrumente zur Luftreinhaltung - Analyse und Bewertung, 1993.
1
130
For the consideration of the abatement cost functions these assumptions are not
very restrictive.
• a growth in GNP or in the transport sector will influence the emission
structure. The affected industries may vary their rate of abatement and
therefore the industry-specific costs of abatement could rise or fall.
But the basis of their abatement behavior, the marginal cost function,
won't alter.
• a decrease in energy-intensity (see assumption 2) and 5) ) will reduce
the energy input per unit of output. Hence there will be an emission
reduction which is related to the saving of energy: The emissions will
fall in the same way as energy is saved. The emission intensity per unit
of energy input is not influenced.
• it is the technical progress which will induce a change in the marginal
cost function and subsequently in the abatement behaviour.
Based on the projection up to the year 2000, the author of the study computed
the costs and the abatement rates of present abatement measures in a bottom-up
analysis. Five aggregated groups of emittants were taken into consideration, i.e. (1)
power stations, (2) combustion systems requiring official approval (without
refineries), (3) refineries, (4) combustion systems that do not require official
approval and (5) traffic. The license requirement for a plant depends on type and
size of the inherent combustion process3. Roughly we can say, that huge
combustion plants do require a license while the smaller heating systems of small
and middle scale industries do not.
The abatement data of these five groups of emittants do not fit exactly in type and
size to the classification of the sectors of GEM-E3. In GEM-E3 we distinct
twenty emission relevant sectors (firms) or uses (households):
agriculture/fishery/forestry, coal, crude oil/oil products, natural gas, electricity,
ferrous/non-ferrous/metal products, chemical products, other energy intensive
industries, electrical goods, transport equipment, other equipment goods,
consumer goods, building/construction, telecommunication services, transport
services, services of credit and insurance institutions, other market services, nonmarket services, heating systems of households and private traffic. As already
mentioned, the available data is collected under the criterias "type" and "size" of
the combustion systems. If we aggregate some GEM-E3 industries, we can keep
the consistency of the data.
2see
footnote 1
see 'Verordnung über genehmigungsbedürftige Anlagen', 4. Bundesimmissionsschutzverordnung
(BImSchV)
3
131
Table 1: Grouping of sectors
group of emittants
GEM-E3 industries
1
electric power
2a
ferrous/non-ferrous/metal products, chemical
products, other energy intensive industries,
2b
coal, electrical goods, transport equipment, other
equipment goods
3
crude oil/oil products (refineries)
4a
natural gas, consumer goods, building and
construction, agriculture/fishery/forestry
4b
telecommunication services, services of credit and
insurance institutions, other market services, nonmarket services, heating systems of the households
5
transport and private traffic (households)
Using these cost functions for all countries, implies the following assumptions:
1. availability of the considered abatement technology all over EU-15
2. the installation of this technology is feasible in all countries
3. equal installation costs for all countries
4. abatement before 1985 is not considered. Hence, for this year the
degree of abatement is zero for all countries.
132
Figure 1: Marginal abatement costs of group 1 of emittants (survey)
e le c t ric p o w e r SO 2
c '(a )
12.00
10.00
8.00
6.00
4.00
2.00
0.00
0.00
a
0.20
0.40
0.60
0.80
1.00
e le c t ric p o w e r NO x
c '(a )
12.00
10.00
8.00
6.00
4.00
2.00
0.00
0.00
a
0.20
0.40
0.60
0.80
1.00
Sector specific abatement cost functions
Based on this data a uniform specification of a marginal cost function was
estimated for each group of emittants. This specification assumes CRTS in
abatement emissions for a firm's aggregated abatement technology but the costs
per unit of abated emissions are convex in the degree of abated emissions.
marginal cost function c ′(a ) = β (1 − a )
γ
We derive the unit cost function from the integration of the marginal cost
function.
unit cost function
c(a ) = δ (1 − a ) + κ
where δ =
λ
−β
γ +1
133
λ = γ +1
Econometric estimation yields the following parameterization for NOx and SO2.
Table 2: Unit abatement costs for NOx in ECU per reduced kg of NOx
δ
λ
κ
group 1
4.240
-0.294
-3.189
group 2a
5.39E-03
-7.473
0.943
group 2b
5.39E-03
-7.474
0.741
group 3
2.01E-10
-29.000
7.55E-09
group 4a
1.35E-03
-14.300
0.741
group 4b
1.35E-03
-14.300
0.334
group 5
2.017
-0.734
-0.194
Table 3: Unit abatement costs for SO2 in ECU per reduced kg of SO2
δ
λ
κ
group 1
-1.890
0.408
2.560
group 2a
0.387
-0.586
0.539
group 2b
0.265
-0.612
0.539
group 3
7.35E-07
-14.000
1.11E-05
group 4a
0.078
-2.668
0.134
group 4b
0.078
-2.668
0.134
group 5
0.105
-4.380
0.578
Based on some further information for group 2, the following deliveries of
abatement expenditures are used troughout all sectors and pollutants.
Table 4: Break down of deliveries of abatement technologies (in % of total costs)
cost type
%
assignment to GEM-E3 classification
investment costs
77
equipment goods industries
labour costs
3
labour
waste costs and other
variable costs
12
services
fuel costs
8
main energetic input of the sector
Emission Coefficients and related parameters
for GEM-E3
The following exogenous data were used:
1. EUROSTAT energy balance sheets
2. baseline emission coefficients, from COHERENCE, EUROSTAT
and CORINAIR
134
3. some ratio's needed for the calculation of the input-output table (own
calculations).
The energy data
Energy consumption, by country, sector and fuel, are taken from the Eurostat
energy balances in TOE. The procedure to construct the country excel-workbook
is the following. The energy balance 1985 for each country is copied in the first
worksheet of the general template, it has to be corrected for the fuels and the
energy sectors not available in that country compared to the general template and
then the energy balance is converted into PJ in the 2nd worksheet. In a third
worksheet, a synthetic balance sheet is constructed, aggregating the EUROSTAT
balance sheet and considering only the data needed for the computations of the
data for GEM-E3 (i.e. not import, exports and primary production). The fuel
disaggregation has been kept as in the original energy balance with the exception
of other solid fuels, which aggregates total lignite and tar and with biomass as the
only renewable. The disaggregation takes into account the distinction to be made
between relevant energy input, which causes emissions, and non-relevant energy
input, which does not cause emissions. The following categories are for relevant
energy use:
ELE: energy use in conventional thermal power stations
ENE: own consumption of the energy sector
IND: industrial use for combustion
TRA: energy use for transportation
HEA: energy use by households, commerce, agriculture, fishery
The non-relevant energy use are non-energetic final consumption, transformation
input (except power) and bunkering.
In terms of the energy balance categories, the following disaggregation has been
used, with the non relevant use in italic:
Bunkers
ELE, electricity sector consumption and district heating
NENE, energy sector consumption, which does not give emissions
CKO, coke-ovens
BFG, blast furnace
GAS, gas sector
135
REF, refinery
ENE, energy sector consumption with emission, each sector consuming its own
type of fuel
ENE-SOL
ENE-LIQ
ENE-GAS
ENE-ELEC
Non Ener, non energy consumption of energy
chemical
other
IND, industry energy consumption
I&S
non-ferro
chemical
building-mat
food, drink & tobacco
textile
paper
engineering
other industry
TRA, transport energy consumption
rail
road
air
inland navigation
HEA, energy use for heating
136
household
agriculture/fisheries
tertiary
For the GEM-E3 model, several assumptions have been made to allocate the
EUROSTAT energy balance sheet values to the branches and products of the IO
table:
1. energy consumption by energy branches : combustion of solid fuels
are allocated to branch '2'. Combustion of liquid fuels are allocated to
branch '3'. Combustion of natural gas is allocated to branch '4'.
2. energy consumption by tertiary sector : the total energy inputs are
allocated to the tertiary branches on the basis of ratios derived from
the IO tables.
3. transportation : only LPG, gasoline and diesel oil are used for road
transport. The total road transportation input figures are allocated to
the different branches and households on the basis of 1980 ratios for
Belgium which were extrapolated to 1985. For the computation of the
emission coefficient, product '3' is explicitly specified into a fraction
used for road transport purposes and a fraction used for other
purposes. The energy inputs for non-road transport are allocated to
the branch transportation services.
4. manufactured gases : since the GEM-E3 IO-table do not include
transfers between branches, the manufactured gases have to be
handled as a delivery of solid fuels '2'. Total blast furnace gas
consumption is allocated as a delivery of product '2' to branch iron
and steel. A correction is made for the demand of electricity of this
branch (efficiency=0.4). Coke oven gas used for 'power generation'
and 'own consumption' is allocated as a delivery of product '2' to
branch '2'. A correction is made for the demand for electricity '5' of
the branch '2' (efficiency=0.4). Coke oven gas used by 'I&S' is
allocated as a delivery of product '2' to branch iron and steel.
5. non energy use : the bunkers are allocated as a delivery of product '3'
to branch transportation services. The transformation input are
allocated to their respective branch, with the exception of blast
furnace gas which is already handled as relevant energy use. For the
non-energetic final input, the chem goes to branch chemical and the
other is allocated to the other branches on the basis of 1980 ratios
which are extrapolated to 1985.
With these computations, one obtains, for GEM-E3, one sheet with the relevant
deliveries of the energy branches to all branches and one sheet with total
137
deliveries. This allows to compute the relevant fraction of total input, i.e. the µ
parameter in GEM-E3, which are needed to compute emissions in GEM-E3.
The baseline emission coefficients
CO2 emission coefficients
The CO2 emission coefficients are those used by EUROSTAT, in ‘Environment
Statistics’, if no country specific information available.
NOx and SO2 emission coefficients
The SO2 emission coefficients are computed taking into account the sulphur
content in the fuel, the fraction of sulphur retained and the net heating value of
the fuel. The NOx emission coefficients are those computed by Coherence in the
HECTOR model (1993). The NOx coefficients are fixed on the basis of
technological assumptions. Some corrections were made when more complete
information was available.
VOC emission coefficients
Emission coefficients for VOC were added to the database and were considered
equal across countries. The basic data, with their sources, are given in Table 5 and
in Table 6.
Table 5 : VOC emission factors for stationary sources
NMVOC emission
factor
nomenclature in
GEM-E3
(g/GJ)
Large Boilers
Hard coal or brown coal
P>50MW
1.5
ELE
P<50MW
15
IND
Peat
15
IND
Residual oil
3
IND
Gas oil
1.5
IND
P>50MW
2.5
ELE
P<50MW
4
IND
Oil refinery gas
2.5
IND
Coke oven gas
2,5
IND
Petrocoke
1.5
IND
Wood
48
IND
Natural gas
HEA
Residential space heating
138
Anthracite
10
HEA
Briquettes
200
HEA
Bituminous coal
200
HEA
Brown Coal
200
HEA
Peat
200
HEA
Gas coke
5
HEA
Wood
600
HEA
Gas Oil
3
HEA
Kerosene
3
HEA
LPG
2
HEA
Natural gas
5
HEA
Manufactured gas
5
HEA
Oil refinery (1)
0.23
ENE
Note: Figures in italic were included in the models.
(1) kg/t of material input in the refinery (crude oil as well as heavy residual products to be
transformed);75%
dueInventory,
to storageJuly
and1991
handling
Source:
CORINAIR
Table 6 : VOC emission factors for mobile sources
Road Transport
gVOC/GJ
Gasoline vehicles <2.5t conventional (1)
290.2
Diesel vehicles <2.5t (2)
35.3
LPG vehicles <2.5t (3)
335.4
Gasoline Light Duty vehicles<3.5t
Urban
682.5
Rural
573.0
Highway
356.9
Diesel Light Duty vehicles<3.5t
Urban
89.0
Rural
87.0
Highway
48.2
Gasoline Heavy Duty vehicles>3.5t
Urban
707.8
Rural
834.2
Highway
482.6
Diesel Heavy Duty vehicles 3.5-16t
Urban
139
283.8
Rural
94.6
Highway
94.6
Diesel Heavy Duty vehicles >16t
Urban
378.4
Rural
189.2
Highway
189.2
Motor cycles
<50 cc
7583.9
>50 cc 2 stroke
11375.8
>50 cc 4 stroke
1796.2
Source: Part 3, Default Emission Factors Handbook, CORINAIR Inventory, 1992
(1) 1.999-0.034*V+0.000214*V^2;
(2) 4.61*V^(-0.973); (3)26.3*V^(-0.865) with V=60km/h
The VOC emission coefficients for mobile sources used in the model are given in
Table 7. The average between the two diesel truck categories was computed
(141.9g/GJ) and then between diesel cars and trucks with as weight for diesel cars
the share of household in total diesel consumption, used for the computation of
the energy IO table.
Table 7 : Model VOC emission coefficients
Category
Gasoline vehicles
Coefficient (g/GJ)
290
290
290
Diesel cars
35.3
35.3
Diesel trucks
94.6
141.9
Diesel big trucks
189.2
PM10 emission coefficients
132.8
Particulate matter, and in particular PM10, is considered in several studies as
responsible for important impacts on human health. Its emissions are mainly
related to energy use in the transport sector, electricity generation and refineries.
Information about the contribution of each sector to the emission of PM10 is
coming from ExternE project (stationary sources ), VIA, RWTH (1995) and
TRENEN project (mobile sources). Data from ExternE are presented in Table 8.
ExternE distinguishes the main sources of PM10 for each activity within the fuel
cycle (mining, transport, electricity generation, etc.), however given the structure of
GEM-E3 and PRIMES models, only the data for electricity generation (coal,
lignite, oil and gas) was considered. We assumed the same emission coefficient for
the industry sector. For the conversion from g/MWh to ton/PJ (stationary
sources), we used the efficiency of the power plant considered and the conversion
factor 3600KJ/kWh. As for VOC, the emission coefficients are assumed to be
equal across countries.
140
Table 8 : PM10 emission coefficients for stationary sources
PM10 (g/MWhel)
PM10
(g/GJ)
Coal power plant in Lauffen (efficiency = 37.6%)
200
20.9
Lignite power plant (efficiency = 36.2%)
167
16.8
Oil peak load plant (efficiency = 31%)
18
1.6
Oil combined cycle base load plant
(efficiency=47.5%)
12
1.6
Source: ExternE
Emission coefficients for mobile sources are given in Table 9. An average speed of
60km/h, a diesel density of 0.842 kg/l4 and a net heating value of 42.3 MJ/kg were
assumed.
Table 9 : PM10 emissions from vehicles
Emission
Energy consumption
Emission
Category
( g/Veh km)
(ton diesel/km)
(g/ton diesel)
Normal diesel car
0.0284
4.73574E-05
600.2
Normal diesel bus
0.2324
0.000209005
1111.9
Small lorry (4.37t, diesel)
0.1950
0.000102771
1897.4
Diesel car improved engine with
particule filter
0.0043
4.09845E-05
105.3
Diesel car improved engine
without particule filter
0.0072
4.05346E-05
177.5
Lorry (diesel)*
0.24
0.000238286
1007.2
Lorry + payload (diesel)*
0.46
0.000358692
1282.4
Source: VIA, RWTH (1995), Emission Calculations for TRENEN
*Assumptions for lorry and lorry + trailer:
80%
Utilisation
rate:9.86t, diesel engine for lorries overcharged, intercooler,
Lorry,
payload
16 speed gear box, 28.3l/100km, 0.24gPM10/km
Lorry + trailer, payload 25.8t, diesel engine for lorries overcharged, intercooler,
16 speed gear box, 42.6l/100km, 0.46gPM10/km
The final figures to be used in the model and derived from the table above, are
given in Table 10.
4
Statistisch Vademecum. Simulatie Transport. Christian Cuijpers, KUL, Werkdocument, April 1992)
141
Table 10 : PM10 Emissions from vehicles
Category
Emission(ton/PJ)
Normal diesel car
14.2
Normal diesel bus
26.3
Lorry (diesel)
23.8
Lorry+payload (diesel)
30.3
16.6
26
27
A weighted average was done to calculate the emission coefficients for cars and
buses (80% and 20% respectively). The emission coefficient for diesel vehicles was
computed considering the share of fuel use in each category and the average value
is 26 ton/PJ.
The different emission coefficients are put all in an excel file emiss&share.xls,
which is referred to in the excel file for the computation of GEM-E3 data.
Default coefficients are used when no national data are available.
General data framework
All the data are assembled in an excel file, which structure is given in Table 11.
Table 11 : Content of the country file with energy and emission data
Worksheet
Notes
eurostat-toe
EUROSTAT energy balance in toe, to insert in B4 with
copy/paste special
to be adjusted for all columns and lines not present for one
country
eurostat-pj
eurostat-toe*0.04186, copy B5 to all cells again
Synthesis-pj
Energy balance sheet, aggregated to some main sectors +
correction of adjustment.
It's a simplified version of the previous table, useful for
further computations.
relevant-io-gem-pj-85
Input-output table in PJ, with the relevant energy
consumption
Contains energy consumption that contributes to emissions.
Contains information regarding road transport and service
branch disaggregation.
Coming from the file emiss&share.xls
Total-io-gem-pj-85
Relevant + non-relevant energy consumption from
synthesis-pj
Total-io table-pj-gem-e3
Relevant + non-relevant energy consumption in GEM-E3
format, country indices to change
%relev-io-gem-pj-85
Fraction of relevant energy consumption.
142
%relev.table--gem-e3 Fraction of relevant energy consumption in GEM-E3 format,
country indices to change
Baseline emission factors (SO2, NOx, CO2, VOC, PM10),
country name to change
bec-primes
in kton/PJ
bem-primes
bec*synthesis in kton
bem-SO2-gem-85
Baseline emission calculation on the basis of the relevant
input-output table and
bem-NOx-gem-85
the Hector baseline emission coefficients.
bem-CO2-gem-85 As the file 'relevant-io-gem-pj-85' has total values, we used
the figures from
bem-VOC-gem-85
bem-PM10-gem-85
the file 'synthesis-PJ' that contribute to relevant emissions.
bec-SO2-gem-85
Calculation of the GEM-E3 baseline emission coefficients
through a division
bec-NOx-gem-85 of the baseline emissions by the relevant input-output table
in kton/PJ
bec-CO2-gem-85
bec-VOC-gem-85
bec-PM10-gem-85
Information from three previous worksheets, in GEM-E3
format, country indices to change
bec-gem-E3
Transport and Transformation Coefficients
EMEP Transport Coefficients (NOx and SO2)
Units: % of total emissions
Columns: Emitters
Rows: Receivers
AU
BE
DE
DK
FI
FR
GR
IR
IT
LX
NL
PL
SV
SP
UK
NOX.AU
0.044
0.022
0.024
0.003
0.000
0.016
0.001
0.004
0.014
0.035
0.013
0.000
0.002
0.002
0.007
NOX.BE
0.000
0.026
0.006
0.002
0.000
0.008
0.000
0.004
0.000
0.017
0.013
0.000
0.001
0.001
0.009
NOX.DE
0.023
0.144
0.133
0.044
0.004
0.071
0.001
0.032
0.009
0.173
0.126
0.003
0.015
0.012
0.056
NOX.D
K
NOX.FI
0.000
0.007
0.006
0.028
0.001
0.002
0.000
0.004
0.000
0.000
0.011
0.000
0.006
0.000
0.010
0.001
0.005
0.007
0.025
0.107
0.002
0.000
0.004
0.000
0.000
0.008
0.000
0.046
0.000
0.006
NOX.FR
0.013
0.088
0.045
0.013
0.001
0.152
0.001
0.036
0.026
0.121
0.050
0.027
0.005
0.046
0.047
NOX.GR
0.003
0.001
0.002
0.001
0.000
0.002
0.043
0.000
0.005
0.000
0.001
0.000
0.001
0.001
0.001
NOX.IR
0.000
0.003
0.002
0.001
0.000
0.002
0.000
0.043
0.000
0.000
0.003
0.000
0.001
0.000
0.009
NOX.IT
0.031
0.014
0.017
0.003
0.001
0.032
0.012
0.004
0.113
0.017
0.009
0.003
0.002
0.006
0.005
NOX.LX
0.000
0.002
0.001
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.001
NOX.NL
0.000
0.017
0.006
0.003
0.000
0.005
0.000
0.007
0.000
0.000
0.026
0.000
0.001
0.001
0.012
NOX.PL
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.001
0.068
0.000
0.013
0.000
NOX.SV
0.003
0.022
0.020
0.070
0.068
0.007
0.000
0.011
0.000
0.017
0.026
0.000
0.120
0.001
0.020
NOX.SP
0.003
0.007
0.006
0.002
0.000
0.022
0.000
0.004
0.005
0.017
0.006
0.099
0.001
0.135
0.007
NOX.UK
0.003
0.019
0.011
0.012
0.003
0.011
0.000
0.072
0.001
0.017
0.025
0.003
0.006
0.002
0.074
143
AU
BE
DE
DK
FI
FR
GR
IR
IT
LX
NL
PL
SV
SP
UK
SO2.AU
0.125
0.014
0.018
0.002
0.001
0.012
0.001
0.003
0.008
0.025
0.008
0.000
0.001
0.00
0.00
SO2.BE
0.000
0.107
0.007
0.002
0.000
0.016
0.000
0.003
0.000
0.025
0.033
0.000
0.001
0.00
0.01
SO2.DE
0.031
0.155
0.220
0.055
0.003
0.073
0.000
0.019
0.005
0.213
0.136
0.002
0.012
0.01
0.04
SO2.DK
0.001
0.006
0.005
0.086
0.001
0.002
0.000
0.003
0.000
0.000
0.008
0.000
0.009
0.00
0.01
SO2.FI
0.001
0.003
0.006
0.014
0.216
0.001
0.000
0.001
0.000
0.000
0.004
0.000
0.040
0.00
0.00
SO2.FR
0.012
0.111
0.030
0.009
0.001
0.244
0.001
0.024
0.017
0.163
0.057
0.014
0.003
0.04
0.03
SO2.GR
0.002
0.001
0.001
0.001
0.000
0.001
0.074
0.000
0.006
0.000
0.001
0.000
0.000
0.00
0.00
SO2.IR
0.000
0.003
0.001
0.001
0.000
0.002
0.000
0.123
0.000
0.000
0.002
0.000
0.000
0.00
0.01
SO2.IT
0.035
0.008
0.012
0.002
0.001
0.025
0.009
0.001
0.148
0.013
0.005
0.001
0.001
0.00
0.00
SO2.LX
0.000
0.002
0.001
0.000
0.000
0.002
0.000
0.000
0.000
0.038
0.001
0.000
0.000
0.00
0.00
SO2.NL
0.001
0.041
0.009
0.004
0.001
0.008
0.000
0.004
0.000
0.000
0.113
0.001
0.001
0.00
0.01
SO2.PL
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.121
0.000
0.01
0.00
SO2.SV
0.002
0.014
0.015
0.089
0.065
0.005
0.000
0.007
0.000
0.013
0.015
0.001
0.231
0.00
0.01
SO2.SP
0.002
0.006
0.003
0.001
0.000
0.019
0.000
0.003
0.003
0.013
0.004
0.083
0.000
0.17
0.00
SO2.UK
0.001
0.026
0.009
0.009
0.001
0.013
0.000
0.074
0.000
0.013
0.032
0.001
0.004
0.00
0.19
EMEP Transport Coefficients
(NOx, VOC and Ozone)
change in yearly
average change in ozone concentrations (ppb)
if 1000kt VOC is increased in the country in the column :
TPCC (VOC,O3)
AU
BE
DE
DK
FR
GR
LU
NL
PL
SP
SV
UK
AU
0.260
0.136
0.288
0.080
0.011
0.104
0.000
0.038
0.193
0.219
0.142
0.000
0.007
0.026
0.063
BE
0.023
1.105
0.503
0.080
0.006
0.197
0.000
0.188
0.005
0.563
1.049
0.002
0.010
0.030
0.388
DE
0.063
0.444
0.475
0.154
0.011
0.158
0.000
0.119
0.018
0.507
0.451
0.000
0.009
0.037
0.200
DK
0.014
0.145
0.118
0.350
0.021
0.057
0.000
0.093
0.001
0.102
0.150
0.001
0.001
0.062
0.138
FI
0.001
0.016
0.012
0.054
0.048
0.004
0.000
0.010
0.001
0.009
0.015
0.000
0.000
0.029
0.017
FR
0.041
0.462
0.281
0.037
0.002
0.265
0.000
0.070
0.039
0.457
0.420
0.014
0.064
0.015
0.123
GR
0.020
0.011
0.020
0.008
0.002
0.008
0.547
0.001
0.075
0.010
0.005
0.002
0.003
0.004
0.002
IR
0.003
0.194
0.084
0.032
0.000
0.043
0.000
0.445
0.002
0.040
0.214
0.003
0.002
0.004
0.360
IT
0.124
0.085
0.099
0.022
0.005
0.145
0.007
0.016
0.418
0.114
0.069
0.006
0.024
0.009
0.023
LU
0.052
0.842
0.713
0.147
0.017
0.218
0.000
0.134
0.015
1.405
0.904
0.003
0.018
0.054
0.212
NL
0.008
0.786
0.359
0.101
0.004
0.146
0.000
0.227
0.002
0.281
0.944
0.002
0.006
0.029
0.445
PL
0.000
0.011
0.003
0.005
0.000
0.015
0.000
0.005
0.002
0.010
0.009
1.739
0.341
0.001
0.011
SP
0.004
0.036
0.017
0.005
0.000
0.049
0.000
0.007
0.007
0.041
0.031
0.409
0.296
0.002
0.014
SV
0.003
0.038
0.037
0.105
0.033
0.011
0.000
0.022
0.001
0.025
0.047
0.000
0.000
0.047
0.048
UK
0.002
0.197
0.100
0.046
0.002
0.045
0.000
0.266
0.002
0.068
0.097
0.003
0.001
0.011
0.630
RW
0.079
0.086
0.148
0.066
0.013
0.050
0.050
0.023
0.075
0.108
0.088
0.000
0.004
0.021
0.133
FI
IR
144
IT
change in yearly
average change in ozone concentrations (ppb) if
1000kt NOx is increased in in the country in the column :
TPCC(NOX,O3)
AU
BE
DE
DK
FI
FR
GR
IR
IT
LU
NL
PL
SP
SV
UK
AU
1.173
0.142 -0.085
0.046
0.035
0.076
0.000
0.024
0.077 -0.096 -0.155
0.001
0.008
0.055 -0.041
BE
0.017 -1.916 -0.699
0.027
0.012
0.192
0.000
0.296
0.001 -0.322 -1.353
0.000
0.014
0.044 -0.387
DE
0.147 -0.479 -0.353
0.162
0.029
0.130
0.000
0.142 -0.004 -0.096 -0.453
0.000
0.011
0.106 -0.137
DK
0.002 -0.044
0.021
0.951
0.093
0.019
0.000
0.135
0.001
0.000
0.001
0.474
0.038
FI
0.001 -0.009
0.001
0.130
1.779
0.000
0.000
0.015
0.000 -0.004
0.003
0.000
0.000
0.636
0.007
FR
0.030 -0.409 -0.207
0.008
0.002
0.682
0.000
0.187
0.034 -0.352 -0.318
0.018
0.164
0.011 -0.066
GR
0.038 -0.001
0.001
0.007
0.019
0.874
0.002
0.122
0.000
0.003
0.012
0.008
-0.002 -0.206 -0.095 -0.002
IR
0.002
0.020 -0.010
0.000
0.000
0.003
0.010
0.000
2.287 -0.002 -0.031 -0.200
0.006
0.003
0.026 -0.267
IT
0.172 -0.035 -0.034
0.011
0.011
0.305
0.020
0.020
0.266 -0.044 -0.038
0.013
0.069
0.014 -0.011
LU
0.003 -1.070 -0.920 -0.029
0.009
0.373
0.000
0.178 -0.002 -1.703 -0.909
0.000
0.031
0.038 -0.163
NL
0.001 -0.969 -0.466
0.074
0.014
0.097
0.000
0.343
0.001
0.001
0.005
0.061 -0.365
PL
0.000
0.000
0.000
0.006
0.000
0.029
0.000
0.020
0.008 -0.001
0.002
2.023
0.465
0.004
0.005
SP
0.005
0.004 -0.004
0.008
0.000
0.154
0.000
0.027
0.022
0.010
0.001
1.051
1.279
0.004
0.005
SV
0.005 -0.010
0.006
0.302
0.702
0.002
0.000
0.042
0.000 -0.003
0.003
0.000
0.000
1.287
0.020
UK
0.000 -0.193 -0.081
0.092
0.007
0.017
0.000
1.091 -0.001 -0.020 -0.229
0.002
0.004
0.054 -0.872
RW
0.238 -0.066 -0.042
0.081
0.094
0.053
0.096
0.027
0.001
0.007
0.151 -0.018
0.040 -1.336
0.044 -0.063 -0.062
ETSU Transport Coefficients for Particulates
change in yearly particulate concentration in µg m-3 from 1000t/y of emission in country in
column
TPCC
PM10
PM10.AU
AU
BE
DE
DK
FI
FR
GR
IR
IT
1.66E-02 8.92E-04 1.52E-03 7.29E-04 3.36E-04 7.77E-04 6.10E-04 3.49E-04 1.70E-03 8.31E-04 2.69E-04 4.31E-04 3.63E-04 5.21E-04
PM10.BE
8.92E-04 2.79E-02 2.24E-03 1.13E-03 3.11E-04 1.94E-03 3.11E-04 7.77E-04 7.77E-04 5.44E-03 3.79E-04 5.21E-04 4.96E-04 1.52E-03
PM10.DE
1.52E-03 2.24E-03 5.44E-03 1.37E-03 3.63E-04 1.13E-03 3.79E-04 5.21E-04 9.62E-04 2.64E-03 3.11E-04 5.78E-04 4.12E-04 8.31E-04
PM10.DK
7.29E-04 1.13E-03 1.37E-03 8.24E-03 5.78E-04 6.10E-04 2.79E-04 5.48E-04 4.96E-04 1.70E-03 2.52E-04 1.24E-03 2.89E-04 8.31E-04
PM10.FI
3.36E-04 3.11E-04 3.63E-04 5.78E-04 5.44E-03 2.52E-04 1.96E-04 2.52E-04 2.44E-04 3.49E-04 1.26E-04 1.24E-03 1.44E-04 3.00E-04
PM10.FR
7.77E-04 1.94E-03 1.13E-03 6.10E-04 2.52E-04 5.44E-03 3.23E-04 6.46E-04 9.62E-04 1.24E-03 5.78E-04 3.49E-04 8.31E-04 9.62E-04
PM10.GR
6.10E-04 3.11E-04 3.79E-04 2.79E-04 1.96E-04 3.23E-04 5.44E-03 3.49E-04 6.46E-04 3.00E-04 1.96E-04 2.14E-04 2.52E-04 2.28E-04
PM10.IR
3.49E-04 7.77E-04 5.21E-04 5.48E-04 2.52E-04 6.46E-04 3.49E-04 1.66E-02 3.36E-04 7.77E-04 4.12E-04 3.79E-04 4.31E-04 1.94E-03
PM10.IT
1.70E-03 7.77E-04 9.62E-04 4.96E-04 2.44E-04 9.62E-04 6.46E-04 3.36E-04 4.04E-03 6.46E-04 3.49E-04 3.11E-04 4.96E-04 4.51E-04
PM10.NL
8.31E-04 5.44E-03 2.64E-03 1.70E-03 3.49E-04 1.24E-03 3.00E-04 7.77E-04 6.46E-04 1.66E-02 3.49E-04 6.10E-04 4.31E-04 1.52E-03
PM10.PL
2.69E-04 3.79E-04 3.11E-04 2.52E-04 1.26E-04 5.78E-04 1.96E-04 4.12E-04 3.49E-04 3.49E-04 8.24E-03 1.74E-04 2.24E-03 4.12E-04
PM10.SV
4.31E-04 5.21E-04 5.78E-04 1.24E-03 1.24E-03 3.49E-04 2.14E-04 3.79E-04 3.11E-04 6.10E-04 1.74E-04 3.20E-03 1.96E-04 4.96E-04
PM10.SP
3.63E-04 4.96E-04 4.12E-04 2.89E-04 1.44E-04 8.31E-04 2.52E-04 4.31E-04 4.96E-04 4.31E-04 2.24E-03 1.96E-04 5.44E-03 4.72E-04
PM10.UK
5.21E-04 1.52E-03 8.31E-04 8.31E-04 3.00E-04 9.62E-04 2.28E-04 1.94E-03 4.51E-04 1.52E-03 4.12E-04 4.96E-04 4.72E-04 5.44E-03
PM10.RW
1.40E-03 5.43E-04 7.67E-04 5.93E-04 5.18E-04 5.01E-04 8.78E-04 2.72E-04 8.54E-04 5.41E-04 2.06E-04 5.50E-04 2.62E-04 3.63E-04
Concentration/Deposition Relations
N deposition to nitrate concentration
NO3- [µg m-3] = 9.98 * N deposition [t km-2] + 1.88
145
NL
PL
SV
SP
UK
S deposition to sulphate concentration
SO4-- [µg m-3] = 2.09 * S deposition [t km-2] + 2.06
S deposition to SO2 concentration
SO2 [µg m-3] = 5.74 * S deposition [t km-2] + 2.37
146
7
Chapter
Model Calibration
This chapter presents the calibration decisions adopted in GEM-E3 and
the values assigned to elasticities and other exogenous parameters. The
equations of the calibration module conclude the chapter.
Calibration structure and data
The first step for running the calibration procedure of the GEM-E3 model, is to
guess-estimate values for the elasticities that determine all coefficients that do not
correspond to directly observable variables and then to run the calibration
procedure.
This is written as a separate model and has a recursive structure (except for the IC
sectors). The base-year data, used for calibration, correspond to monetary terms,
therefore appropriate price indices are chosen to compute the corresponding
volumes (quantities).
Once the model is calibrated, the next step is to define a baseline scenario that
starts from 1985, tries to reproduce as accurately as possible the last year for which
observations are available (1994) and then gives some projections up to a future
year which is the final year of the model simulation (usually 2010 or beyond). This
simulation defines the model baseline projection against which the policy
simulations can be evaluated.
The “counterfactual” equilibria can be computed by running the model under
assumptions that diverge from those of the baseline. This corresponds to scenario
building. In this case, a scenario is defined as a set of changes of exogenous
variables, for example a change in the tax rates. Changes of institutional regimes,
that are expected to occur in the future, may be reflected by changing values of
the appropriate elasticities and other model parameters that allow structural shifts
(e.g. market regime). These changes are imposed in the baseline scenario thereby
modifying it. To perform a counterfactual simulation it is not necessary to recalibrate the model. The exact process of calibrating and running GEM-E3 is
illustrated in the following figure:
147
Figure 2: Using the GEM-E3 model
Elasticities
(econometrically
estimated)
Benchmark Equilibrium
Data Set
Static Calibration to reproduce
observed equilibrium
Baseline Scenario to reflect
the main changes observed
between 1985-94, and
projections for the future
Specification of counterfactual
scenario modifying
assumptions of the baseline to
reflect:
• Policy change
• Institutional regime
Counterfactual simulation
Reference (baseline)
Simulation
Policy appraisal, based on
comparison between reference and
counterfactual scenarios
Static calibration of the CGE model follows a standard procedure, as in most
CGE models. The starting data set includes the following:
• values of production, consumption, investment, imports and exports
per sector, which are available from the Social Accounting Matrix
tables, that include the Input-Output tables and the National
Accounts;
• bilateral sectoral trade tables for the EU member states and the restof-the-world.
The calibration procedure is a model run, that assumes unit values for the export
price and the price of absorption and a complete set of elasticity parameters. The
calibration computes volumes, effective fiscal policy rates and a number of share
parameters in production and consumption functions.
Values of elasticities and other exogenous
model parameters
Three main sets of elasticities are used in the GEM-E3 model:
148
• Demand function elasticities following the Armington assumption
adopted in the model (substitutability of domestic/imported goods
and across imported goods, by country of origin).
• Elasticities of substitution in production (substitution among
production factors).
• Consumer preferences (price or income elasticities in households
demand for commodities).
L I T E R A T U R E
S U R V E Y
O N
E M P I R I C A L
S T U D I E S
F O R
T H E
A R M I N G T O N
E L A S T I C I T I E S
Despite of the popularity of the Armington concept, only few studies on direct
econometric estimates of substitution elasticities have been published. Elasticities
of upper-level substitution between imported and domestic goods have been
estimated, for example, by Reinert and Roland-Holst (1992), Shiells et al. (1986)
and Lächler (1985). Shiells and Reinert (1993) have estimated lower-level elasticities
and non-nested elasticities, as well as Sobarzo (1994), and Roland-Holst et al
(1994). Unfortunately, the estimated values from the literature are difficult to
compare, as the sectoral aggregation levels differ according to the statistical data
base used.
A study for Germany was conducted by Lächler (1985). Lächler estimated
disaggregated elasticities of substitution between demand for imports and
domestic substitutes in Germany. He found that the primary goods industry
which consists of relatively homogeneous and easily replaceable goods and which
is under high pressure in terms of international competitiveness is the one with the
highest elasticity ranking: Apart from two exceptions, elasticity values range from
0.233 to 2.251. In contrast, in the case of the investment goods sector, and
particularly in the case of capital goods in the short run, technological rigidities
restrict the substitutability; thus, elasticity values are rather low and between the
range of -2.283 to 1.209. Finally, the sectors that are classified as belonging to the
consumption goods industry differ with respect to the degree of international
competitive pressure, reflected by wide differences in measured substitution
elasticities (-0.697 to 1.092).
Likewise, Reinert and Roland-Holst (1992) have estimated elasticities of
substitution between imported and domestic goods for 163 U.S. mining and
manufacturing sectors, based on U.S. trade data time series of both prices of
domestic and imported goods, and real values of domestic sales of domestic goods
and imports. In about two-thirds of the cases Reinert and Roland-Holst obtained
positive and statistically significant estimates ranging from 0.14 to 3.49. Their
results allow the conclusion that at the level of aggregation chosen imports and
U.S. domestic products are far away from being perfect substitutes.
Furthermore, Shiells et al. (1986) have published estimations on disaggregated
own-price elasticities of import demand for 122 3-digit SIC U.S. industries
(covering mainly mining and manufacturing sectors) which serve as a basis for
inferring upper-level substitution elasticities. The estimations are based on annual
data for period 1962-1978. In 48 cases positive and statistically significant
149
elasticities of substitution were obtained, ranging from 0.454 for SIC 208
(beverages) to 32.132 for SIC 373 (yachts).
Shiells and Reinert (1993) estimated both lower-level nested and non-nested
elasticities of substitution among U.S. imports from Mexico, Canada, RoW, and
competing domestic production, for 22 mining and manufacturing sectors, based
on quarterly data for 1980-88. In the non-nested specification, U.S. imports from
Mexico, Canada, and RoW as well as domestic substitutes enter a single CES
function. The estimates of the non-nested elasticities of substitution range from
0.101 (sector primary lead, zink, and non-ferrous metals, n.e.c.) to 1.49 (sector
primary aluminium). The nested specification is composed of an upper-level CES
aggregation function for U.S. imports as a whole and a lower-level CES aggregate
function for the various import sources, i.e. lower-level substitution elasticities are
among U.S. imports from Mexico, Canada, and RoW. Estimates range from 0.04
(sector clay, ceramic, and non-metallic minerals) to 2.97 (sector iron, and ferroalloy
ores mining).
A comparison of estimates for non-nested, lower-level and upper-level elasticities
for selected sectors taken from Shiells and Reinert (1993) and Reinert and RolandHolst (1992) show that values differ. While the non-nested estimates lie mainly
above the upper-level estimates, they are in half of the cases lower and in half of
the cases higher than the lower-level estimates. As already mentioned in Section 0,
lower-level elasticities are not generally higher than upper-level elasticities, but only
in about two thirds of the sectoral cases considered in the table. However, lowerlevel estimates show that the range of positive values (0.04 - 2.97) is larger, as in
the case of the non-nested specification (0.1 - 1.49) and in the case of upper-tier
estimates (0.02 - 1.22).
All in all,
the sectoral values used in the GEM-E3 model are close to the
typical values found in the literature. In most cases the estimates arise from
U.S. data whereas for EU countries no estimates are available in the literature.
S P E C I F I C A T I O
N
O F
Table 12 contains upper- and lower-level Armington elasticity values actually used
in the GEM-E3 model in EU and RoW import demand. Elasticities differ among
sectors, but values for each sector are identical for all EU countries.
A R M I N G T O N
E L A S T I C I T I E S
For EU countries upper-level elasticity values are greater than 1 for sectors with a
relatively high degree of international competition, such as energy-intensive or
consumer goods industry, while values of service sectors or sectors with relatively
homogeneous goods (e.g. sector crude oil and oil products) are set below 1.
Basically, lower-level elasticity values are set higher than upper-level elasticities. As
Shiells and Reinert (1993) - with reference to Brown (1987) - have noted, the twolevel nested Armington approach may imply large terms-of-trade effects that are
the greater the larger the upper-level elasticities are relative to the lower-level
elasticities. Thus, in order to avoid large terms-of-trade effects, lower-level
elasticities take often higher values than upper-level elasticities in empirical trade
models. However, as empirical studies indicate, this pattern is not absolutely
evident. For instance, a comparison of U.S. upper-level elasticities estimated by
Reinert and Roland-Holst (1992), with U.S. lower-level elasticities estimated by
150
Shiells and Reinert (1993) shows that for some sectors lower-level elasticities are
higher than upper-level elasticities5.
The last column of Table 12 presents values of substitution elasticities used in
RoW's import demand. Lower-level elasticity values are set equal to upper-level
elasticity values. With regard to relative sectoral degrees of substitutability RoW's
elasticities are specified nearly comparable to EU elasticities.
Table 12: Armington elasticity values in the standard version of the GEM-E3
model
EU-14
σx
σm
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Agriculture
Coal
Crude oil and oil products
Natural gas
Electricity
Ferrous, non-ferrous ore and metals
Chemical products
Other energy intensive industries
Electrical goods
Transport equipment
Other equipment goods industries
Consumer goods industries
Building and construction
Telecommunication services
Transports
Credit and insurance
Other market services
Non-market services
1.2
0.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
0.6
1.2
0.6
0.6
-
1.6
0.8
2.4
2.4
2.4
2.4
2.4
2.4
2.8
1.6
2.4
1.6
1.6
-
RoW
σ xr o w = σ m r o w
1.4
0.6
0.6
0.6
0.6
2.2
2.2
2.2
2.2
2.2
2.2
2.5
1.4
1.4
2.2
1.4
1.4
0.6
No econometric estimates of sector- and country-specific substitution elasticities
for EU countries are available in the literature. Thus, in this section the required
set of Armington elasticities for the 14 EU countries is generated following a
procedure proposed by Harrison et al. (1991, p. 100). The procedure takes place in
three steps:
1. Starting point are sector-specific ‘best guess’ upper-level Armington
elasticities for the U.S. presented in Shiells et al. (1986). Using countryspecific import weights (drawn from 1993 data6) for each country an
average Armington elasticity of substitution σ av
x is calculated. The countryav
specific import weighted elasticities σ x are reported in Table 16.
2. The country-specific elasticities σ av
x are then compared with country-
specific Armington elasticities ( σ inf
x ) that are inferred from countryWhalley (1985, p. 109), for example, in his seven region model uses upper-level elasticity values, that
are based on literature values of import-price elasticities. The lower-level elasticity values are set for all
sectors and regions on a common value of 1.5, which roughly approximate literature estimates of
export price elasticities.
5
6
1993 International Trade Statistics Yearbook. Vol. 1. Trade by Country. United Nations. New York.
151
specific import price elasticities ( ε ) and from import shares. Whereas
the national import price elasticities are taken from the empirical trade
literature (Stern et al. 1976), the import shares are calculated from the
equilibrium benchmark data set.
3. Finally, we re-scale for each country the sector-specific elasticities so
that the aggregated, import-weighted elasticity σ av
is equal to the
x
inf
country-specific elasticity σ x which is derived from the national
import price elasticity. The results of the sectorally and nationally
disaggregated substitution elasticities are reported in
4.
Case 0:
Case 1:
Case 2:
Standard version
of GEM-E3
Halved
values
Doubled
values
1.2
0.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
0.6
1.2
0.6
0.6
0.60
0.30
0.75
0.75
0.75
0.75
0.75
0.75
0.85
0.30
0.60
0.30
0.30
2.40
1.20
3.00
3.00
3.00
3.00
3.00
3.00
3.40
1.20
2.40
1.20
1.20
Agriculture
Crude oil and oil products
Ferrous, non-ferrous ore and metals
Chemical products
Other energy intensive industries
Electrical goods
Transport equipment
Other equipment goods industries
Consumer goods industries
Telecommunication services
Transports
Credit and insurance
Other market services
5. Table 17.
Table 13: Sectoral values of upper-level Armington elasticities
in RoW’s import demand
Agriculture
Crude oil and oil products
Ferrous, non-ferrous ore and metals
Chemical products
Other energy intensive industries
Electrical goods
Transport equipment
Other equipment goods industries
Consumer goods industries
Telecommunication services
Transports
Credit and insurance
Other market services
Case 0:
Case 1:
Case 2:
Case 3:
Standard version
of GEM-E3
Halved
values
Doubled
values
U.S. 'best guess' estimates
1.2
0.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
0.6
1.2
0.6
0.6
0.60
0.30
0.75
0.75
0.75
0.75
0.75
0.75
0.85
0.30
0.60
0.30
0.30
2.40
1.20
3.00
3.00
3.00
3.00
3.00
3.00
3.40
1.20
2.40
1.20
1.20
Country- and sectorspecific values
(for sector 3, 7- 10:
values as calculated from
'best guess' estimates
presented in Shiells et al. (1986);
for sector 1, 6, 11-17:
values as in standard version)
While step 1 and step 3 are more or less self-evident, some comments should be
made on the derivation of the national Armington elasticities from literature-based
import price elasticities (step 2).
152
U.S. 'best g
Country
speci
(for sec
values as
'best gue
presented in S
for secto
values as in
Obviously, the procedure proposed is faced with some problems which arise from
the existence of non-tradable sectors and non-competitive imports. Both import
demand of non-traded and non-competitive commodities are excluded from the
Armington assumption. It is assumed that they are determined not by price
relations but by the domestic production level and institutional settings, such as
supply contracts. As national import price elasticities, taken from the literature,
normally refer to the national aggregate of import demand (aggregating all sectors),
they may provide a distorted picture of Armington elasticities. However, this
problem is less important here. Fortunately, in the GEM-E3 model the national
shares of imports of non-tradable goods in total imports are low and by a majority
below 5% (see Table 14). Thus, the literature-based import price elasticity values
are reasonable approximates for the price elasticity of import demand of tradable
goods in the GEM-E3 model.
Table 14: Import shares of non-tradable commodities in the GEM-E3 model
Share of imports of nontradeables goods in all imports
(base year)
Austria
Belgium
Germany
Denmark
Finland
France
Greece
Ireland
Italy
Netherlands
Portugal
Spain
Sweden
Un. Kingdom
4.14%
4.02%
5.70%
3.48%
10.34%
5.36%
0.44%
2.29%
4.87%
1.90%
0.41%
2.92%
1.00%
3.26%
More importance should be attached to the problem arising from noncompetitive imports. Given the same import price elasticity value, the share of
non-competitive imports assumed influences the inferred Armington elasticity
values σ inf
decisively. This can be demonstrated by using equation (27) and
x
equation (28) alternatively for the derivation of the Armington elasticities. As can
be shown easily, in the GEM-E3 model the price elasticity of the aggregate import
demand ε in terms of upper-level Armington elasticity σ x and empirically
measurable parameters (import shares) is given by
(27)
ε c = σ x ⋅ (ω − 1) ,
when all imports are competitive, and by
(28)
IMC
IMNC
ε nc = σ x ⋅ 
⋅ (ω − 1) +
⋅ (ω − ω nc )
IM
 IM

153
when non-competitive imports exist7. IM are total imports of tradable goods.
IMC represent the competitive and IMNC the non-competitive part. ω denotes
the share of expenditure on imports in expenditure on domestically supplied
goods and ω nc denotes the ratio of expenditure on non-competitive imports to
expenditure on domestically produced and demanded goods, i.e.
ω=
PIM ⋅ IM
PIM ⋅ IMNC
and ω nc =
.
PY ⋅ Y
PXD ⋅ XXD
When IMC = IM and IMNC = 0 , then equation (28) is the same as equation (27).
Table 15: Sector- and country specific upper-level Armington elasticities for EU14
Sector
Austria
Belgium Germany
Denmark Finland
France
Greece Ireland Italy Netherlands
Portugal Spain Sweden
Un. Kingdom
3 Crude oil and oil products
5.1
5.6
3.2
3.1
3.0
3.4
2.3
3.2
7.5
3.9
3.8
3.1
1.6
1.4
3.1
5.6
3.4
6.2
2.0
3.6
1.9
3.4
1.8
3.3
2.1
3.8
1.4
2.5
2.0
3.5
4.6
8.3
2.4
4.3
2.3
4.2
1.9
3.4
1.0
1.7
0.9
1.6
6.2
6.5
3.7
3.3
3.5
3.8
2.4
3.5
8.3
4.2
3.8
3.4
1.9
1.5
4.5
5.0
2.9
2.8
2.6
3.1
2.1
2.9
6.7
3.5
3.4
2.7
1.4
1.3
10 Transport equipment
7.7
8.5
4.9
4.7
4.5
5.2
3.5
4.9
11.4
5.9
5.7
4.6
2.4
2.2
11 Other equipment goods
industries
2.3
2.5
1.4
1.4
1.6
1.5
1.0
1.4
3.4
1.7
1.7
1.4
0.7
0.6
12 Consumer goods
industries
5.2
4.9
3.2
2.6
2.7
2.0
1.9
2.8
5.9
3.4
2.5
2.5
1.5
1.2
6 Ferrous, non-ferrous ore
and metals
7 Chemical products
8 Other energy intensive
industries
9 Electrical goods
As Table 16 shows, a variation of the share of non-competitive imports in total
imports of tradable goods leads to different values of Armington elasticities. In
summary, one can say that the higher the share of non-competitive imports, the
higher the Armington elasticity which corresponds to a given import price
elasticity. In the GEM-E3 model the shares of non-competitive imports are set
equal to 0.5 for all countries and all sectors. Thus, the country-specific upper-level
Armington elasticities σ inf
depicted in the fourth column of Table 16 are applied.
x
Keeping in mind that values of own import price elasticities vary widely between
alternative import demand specifications (see Kohli 1982), the Armington
elasticities derived from the import price elasticities must be interpreted as crude
approximations. However, Whalley (1985, p. 103) states that import price elasticity
values in the neighbourhood of unity still reflect the current consensus on import
price elasticities.
The own-price elasticity of the import aggregate demand is defined as ε
=(∂IM/∂PIM)∗(PIM/IM), whereas domestic supply Y is kept constant. If all imports of tradable goods
are competitive (i.e. IM=IMC) the import price elasticity εc is derived from equation (12) which
expresses the upper-level import demand for tradable goods. If a positive share of total imports of
tradable goods is non-competitive (i.e. IM=IMC+IMNC) the derivation of εnc must consider that the
specification of non-competitive imports in the GEM-E3 model includes two further equations:
PXD=PD+RTNC∗PIM and IMNC=XXD∗RTNC, where RTNC is calibrated. Thus, the price for
domestically produced and demanded goods, PXD, entering the unit cost function of domestic supply
(equation (11)), is no longer independent from PIM.
7
154
Finally, re-scaling the average Armington elasticity values σ av
x according to step 3
leads to the final values which are reported in
Case 0:
Case 1:
Case 2:
Standard version
of GEM-E3
Halved
values
Doubled
values
1.2
0.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
0.6
1.2
0.6
0.6
0.60
0.30
0.75
0.75
0.75
0.75
0.75
0.75
0.85
0.30
0.60
0.30
0.30
2.40
1.20
3.00
3.00
3.00
3.00
3.00
3.00
3.40
1.20
2.40
1.20
1.20
Agriculture
Crude oil and oil products
Ferrous, non-ferrous ore and metals
Chemical products
Other energy intensive industries
Electrical goods
Transport equipment
Other equipment goods industries
Consumer goods industries
Telecommunication services
Transports
Credit and insurance
Other market services
Case 3:
U.S. 'best guess' es
Country- and sec
specific values
(for sector 3, 7values as calculate
'best guess' estim
presented in Shiells et a
for sector 1, 6, 11
values as in standard
Table 17.
Table 16: Country-specific price and substitution elasticities of import demand for
different shares of non-competitive imports
Austria
Belgium
Germany
Denmark
Finland
France
Greece
Ireland
Italy
Netherlands
Portugal
Spain
Sweden
Un. Kingdom
ε*
σxav **
-1.32
-0.83
-0.88
-1.05
-0.50
-1.08
-1.03
-1.37
-1.03
-0.68
-1.03
-1.03
-0.79
-0.65
2.13
2.13
2.12
1.99
2.37
1.63
2.15
1.95
2.01
2.03
1.92
2.03
2.06
1.93
σxinf ***
(IMNC/IM=0)
(IMNC/IM=0.5)
(IMNC/IM=0.8)
1.88
1.67
1.09
1.53
0.62
1.31
1.04
1.62
1.77
1.20
1.33
1.21
0.80
0.66
4.57
5.03
2.90
2.61
2.97
2.36
2.10
2.65
6.39
3.32
3.05
2.63
1.38
1.17
10.48
6.53
6.09
-10.31
3.46
7.31
5.24
8.94
8.57
5.63
7.52
6.68
1.99
1.83
* ‘Best guess’ estimates of uncompensated import price elasticities suggested by Stern et
al. (1976, p. 20), constructed as point estimates for several countries according to the
three-digit International Standard Industrial Classification (ISIC). As for Greece, Spain
and Portugal no data were available, we used Italian data.
** Based on Shiells et al. (1986).
*** Elasticities are inferred from equation (27) for IMNC/IM=0 and from equation (28)
for IMNC/IM>0. Import shares ω and ω nc are based on observed data of the benchmark
equilibrium.
155
Table 17: Sector- and country specific upper-level Armington elasticities for EU14
Agriculture
Crude oil and oil products
Ferrous, non-ferrous ore and metals
Chemical products
Other energy intensive industries
Electrical goods
Transport equipment
Other equipment goods industries
Consumer goods industries
Telecommunication services
Transports
Credit and insurance
Other market services
Case 0:
Case 1:
Case 2:
Case 3:
Standard version
of GEM-E3
Halved
values
Doubled
values
U.S. 'best guess' estimates
1.2
0.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
0.6
1.2
0.6
0.6
0.60
0.30
0.75
0.75
0.75
0.75
0.75
0.75
0.85
0.30
0.60
0.30
0.30
2.40
1.20
3.00
3.00
3.00
3.00
3.00
3.00
3.40
1.20
2.40
1.20
1.20
Country- and sectorspecific values
(for sector 3, 7- 10:
values as calculated from
'best guess' estimates
presented in Shiells et al. (1986);
for sector 1, 6, 11-17:
values as in standard version)
Case 0:
Case 1:
Case 2:
Standard version
of GEM-E3
Halved
values
Doubled
values
1.2
0.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
0.6
1.2
0.6
0.6
0.60
0.30
0.75
0.75
0.75
0.75
0.75
0.75
0.85
0.30
0.60
0.30
0.30
2.40
1.20
3.00
3.00
3.00
3.00
3.00
3.00
3.40
1.20
2.40
1.20
1.20
Agriculture
Crude oil and oil products
Ferrous, non-ferrous ore and metals
Chemical products
Other energy intensive industries
Electrical goods
Transport equipment
Other equipment goods industries
Consumer goods industries
Telecommunication services
Transports
Credit and insurance
Other market services
Case 3:
U.S. 'best guess' es
Country- and sec
specific values
(for sector 3, 7values as calculate
'best guess' estim
presented in Shiells et
for sector 1, 6, 11
values as in standard
Table 18 reports the values of the upper-level Armington elasticity for which
sensitivity analysis is performed. As in the previous section, the case of doubled
and halved elasticity values are tested. Additionally, the calculated sector- and
country-specific values from
Case 0:
Case 1:
Case 2:
Standard version
of GEM-E3
Halved
values
Doubled
values
1.2
0.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
0.6
1.2
0.6
0.6
0.60
0.30
0.75
0.75
0.75
0.75
0.75
0.75
0.85
0.30
0.60
0.30
0.30
2.40
1.20
3.00
3.00
3.00
3.00
3.00
3.00
3.40
1.20
2.40
1.20
1.20
Agriculture
Crude oil and oil products
Ferrous, non-ferrous ore and metals
Chemical products
Other energy intensive industries
Electrical goods
Transport equipment
Other equipment goods industries
Consumer goods industries
Telecommunication services
Transports
Credit and insurance
Other market services
156
Case 3:
U.S. 'best guess' es
Country- and sec
specific values
(for sector 3, 7values as calculate
'best guess' estim
presented in Shiells et a
for sector 1, 6, 11
values as in standard
Table 17 are applied.
Table 18: Sectoral values of upper-level Armington elasticities in RoW’s import
demand
Agriculture
Crude oil and oil products
Ferrous, non-ferrous ore and metals
Chemical products
Other energy intensive industries
Electrical goods
Transport equipment
Other equipment goods industries
Consumer goods industries
Telecommunication services
Transports
Credit and insurance
Other market services
S E N S I T I V I T Y
O F
M O D E L
R E S U L T S
W I T H
R E S P E C T
T H E
O F
T O
C H O I C E
T H E
A R M I N G T O N
E L A S T I C I T I E S
Case 0:
Case 1:
Case 2:
Case 3:
Standard version
of GEM-E3
Halved
values
Doubled
values
U.S. 'best guess' estimates
1.2
0.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
0.6
1.2
0.6
0.6
0.60
0.30
0.75
0.75
0.75
0.75
0.75
0.75
0.85
0.30
0.60
0.30
0.30
2.40
1.20
3.00
3.00
3.00
3.00
3.00
3.00
3.40
1.20
2.40
1.20
1.20
Country- and sectorspecific values
(for sector 3, 7- 10:
values as calculated from
'best guess' estimates
presented in Shiells et al. (1986);
for sector 1, 6, 11-17:
values as in standard version)
As Table 19 indicates, the four cases of parameter choice differ only slightly with
respect to macroeconomic impacts. Differences arise mainly in trade flows and
price indices. All other macroeconomic variables show only marginal changes. As
consumption and employment, or leisure respectively, remain nearly constant,
economic welfare also varies scarcely. Sectoral trade flows between EU-14 and
RoW are given in Error! Reference source not found..
The interpretation of results starts with examining the pure effects of a variation
of Armington elasticities.
In Case 1, Armington elasticity values in the aggregate import demand of all EU
countries are halved, i.e. substitution possibilities between domestic production
and imports are more restricted for all EU countries. For instance, in Case 1 a
policy-induced price increase in European domestic supply will induce a lower
substitution effect than in the standard version, i.e. import demand for tradable
goods will be expanded to a lower extent than in the standard case. This, however,
implies that in Case 1 (relatively expensive) domestic production has a relatively
bigger share in overall EU domestic supply. The pure substitution effect leads, in
Case 1, to relatively higher prices. The latter is expressed by a decrease of the
GDP deflator by -0.72% (compared to -0.74% in Case 0).
In Case 2, we have to argue the other way round. Doubling the Armington
elasticities increases the substitution effect, i.e. a shift in the price relation of
domestic supply and imports results in a comparatively higher demand for
imports. Now, domestic production constitutes a lower part in domestic supply
compared with both Case 0 and Case 1. This, in turn, results in a decrease in
domestic prices. To conclude, the price level is at its highest in Case 1 and at its
lowest in Case 2. Case 0 lies in between.
157
Let us recall the main mechanisms running in the standard version which have
already been described. In the standard model, the double dividend policy results
in a decrease in exports and imports and in a drop in the GDP deflator (resulting
from a decrease in aggregate demand).
As just mentioned, in the case of halved Armington elasticity values (Case 1) the
drop in the GDP deflator is less significant, i.e. prices are higher. This exactly
reflects the cost effects of a lower degree of substitution of European producers
and consumers. Due to comparably higher prices, EU exports are reduced to a
greater extent. Whereas exports fall by -1.02% in the standard version, they fall by
-1.05% in Case 1. The greater percentage reduction of imports can be explained
by reduced substitution possibilities in Case 1, i.e. import demand increases less in
response to an increase in domestic production prices.
In the case of doubled Armington elasticities (Case 2) domestic prices are lower.
Thus, exports are reduced to a lower extent (by -0.97% compared to -1.02% in
Case 0). Imports decrease to a lower extent as well (by -1.42% compared to 1.46% in Case 0) due to the higher substitution possibilities given by doubled
elasticity values.
A variation of Armington elasticities according to the calculated set of countryand sector-specific parameter values given in
Case 0:
Case 1:
Case 2:
Standard version
of GEM-E3
Halved
values
Doubled
values
1.2
0.6
1.5
1.5
1.5
1.5
1.5
1.5
1.7
0.6
1.2
0.6
0.6
0.60
0.30
0.75
0.75
0.75
0.75
0.75
0.75
0.85
0.30
0.60
0.30
0.30
2.40
1.20
3.00
3.00
3.00
3.00
3.00
3.00
3.40
1.20
2.40
1.20
1.20
Agriculture
Crude oil and oil products
Ferrous, non-ferrous ore and metals
Chemical products
Other energy intensive industries
Electrical goods
Transport equipment
Other equipment goods industries
Consumer goods industries
Telecommunication services
Transports
Credit and insurance
Other market services
Case 3:
U.S. 'best guess' es
Country- and sec
specific values
(for sector 3, 7values as calculate
'best guess' estim
presented in Shiells et a
for sector 1, 6, 11
values as in standard
Table 17 (Case 3) show that impacts lie between those of Case 1 and Case 2. Table
A-2 and Table A-3 in the Appendix depict the impacts of the double dividend
policy at a national level for the standard case and for Case 3. Obviously, mostly
affected in terms of economic welfare are Belgium, Ireland and United Kingdom.
158
Table 19: Coordinated Double Dividend Policy. Variation of upper-level
Armington elasticities in import demand of EU countries (numbers indicate percent
changes from baseline except if defined otherwise)
Macroeconomic Aggregates for EU-14
Case 0:
Case 1:
Case 2:
Case 3:
Standard version
of GEM-E3
Halved
values
Doubled
values
U.S. 'best guess'
estimates
Gross Domestic Product
Employment*
Production
Private Investment
Private Consumption
Domestic Demand
Exports in volume
Imports in volume
Intra trade in the EU
-0.04%
780
-0.57%
-0.18%
0.21%
-0.56%
-1.02%
-1.46%
-1.20%
-0.04%
784
-0.57%
-0.17%
0.21%
-0.55%
-1.05%
-1.48%
-1.25%
-0.04%
774
-0.58%
-0.18%
0.20%
-0.56%
-0.97%
-1.42%
-1.11%
-0.04%
775
-0.58%
-0.18%
0.20%
-0.56%
-1.02%
-1.45%
-1.14%
Energy consumption in volume
Consumers’ price index
GDP deflator in factor prices
Current account as % of GDP***
-6.21%
1.19%
-0.74%
-6.21%
1.21%
-0.72%
-6.22%
1.16%
-0.77%
-6.25%
1.18%
-0.73%
0.08
0.08
0.08
0.08
0.23%
0.23%
0.22%
0.23%
Equivalent Variation of total welfare
Economic welfare**
* in thousand employed persons
** as percent of GDP
*** absolute difference from baseline
Elasticities of substitution in production
In the derived factor demand of the industrial sectors, the assumptions regarding
the substitution elasticities are crucial parameters for the results obtained. Many
econometric studies have tried to evaluate the substitution possibilities between
the production factors within an integrated production model. They point out to
the importance of the number of productions factors specified and of the
specification of technical progress. The distinction between electricity and other
fuels is necessary because the substitution mechanism and possibilities between
these energy factors and the other production factors are different. The
specification of the technical progress has a clear impact on the estimated
substitution elasticities.
The nested CES structure and the substitution elasticities in GEM-E3 are
based on the econometric study by CES and the Belgian Planning Office on
the substitution possibilities in 10 Belgian industrial sectors, as this study was
available and took into account the main findings on the specification needed for
the modelling of factor demand. Production factors demand equations derived
from CRESH production function have been jointly estimated for 10 industrial
sectors in Belgium and 5 factors (capital, labour, electricity, fuels and other
intermediate inputs) over the period 1966-1986, taking into account the within and
across equation constraints imposed on the parameters by the CRESH production
function and with factor specific technical progress. The CRESH function
159
imposes substitutability between factors, but estimation results with other
functional forms allowing for both complementarity and substitutability were
worse. The long run substitution elasticities are rather low for all factors (i.e. below
1) and especially between capital and the other factors. Electricity is also a rather
poor substitute. The highest substitution possibilities are between labour, materials
and fuels.
Based on these results, the following nesting structure and substitution elasticities
were applied in GEM-E3. The nesting structure is the same for all branches in
GEM-E3 as shown in the following figure (repeated here from previous chapter) :
Production (output)
Level 1
Labour
Energy
Materials bundle
Capital
Agriculture
Ferrous, ore, metals
Level 2
Electricity
chemicals
Other en. intensive
Electrical goods
Transport equip.
Other equipment
Labour
Materails
Fuels bundle
Coal
Oil
Fuels
Gas
Consumer goods
Labour
Level 3
Building/Constr.
Telecommunication
Credit & insurance
Materials
Credit & insurance
Market services
Non-market services
Level 4
The substitution elasticities can vary between sectors and is reproduced in the
next table.
Table 20: Elasticities of substitution in GEM-E3
level 1
level 2
level 3
level 4
Energy Intensive sectors
0.4
0.5
0.5
0.9
Equipment goods sectors
0.4
0.5
0.3
0.6
160
Consumer Good
0.4
0.5
0.1
0.4
Services
0.3
0.5
0.3
0.6
Calibration of sectors with imperfect
competition
C A L I B R A T I O N
F O R
S E C T O R S
W I T H
I M P E R F E C T
C O M P E T I T I O N
The choice of imperfectly competitive sectors is based on the results by Pratten
(1988) who identified the sectors with significant unexploited potential of
economies of scale and the ex-ante evaluations of the Single Market Programme,
as surveyed in the literature.
The table below shows the sectors of the model in which oligopolistic
competition is assumed to prevail:
The above statistics have been complemented with specific information to
calibrate the imperfect market formulations. We have been based on:
• The Pratten (1988) study regarding the engineering estimation of the
Minimum Efficient Scales per sector and the cost increase gradient
(related to the number of firms).
• Herfindahl indices computed for 1985 and 1992; these have been
compared to similar information available by Bruce Lyons (East
Anglia University) who provided such an index for the whole
European Union and 1988; statistical rank correlation analysis showed
for example that the UK numbers were close to those of the whole
EU.
The starting data set includes the following:
• values of production, absorption, imports and exports per sector,
which are available from the SAM tables;
• the Minimum Efficiency Scale per unit of domestic production,
computed from the engineering data of Pratten;
• the cost gradient, that is the percent increase of average cost of the
firm when it produces 1/3 of the Minimum Efficiency Scale; (available
from Pratten)
• the number of firms per sector, computed as the inverse of a sectoral
Herfindahl index.
161
The calibration procedure starts from the computation of the fixed cost per firm.
This computation assumes that the firm operates at zero profit in the base year.
The formula is derived as follows. The cost gradient is defined as the increase in
average cost AC when production of a firm is reduced from the MES to 1/3 of
AC( 13 ⋅ MES ) − AC( MES ) MC +
=
Cost _ gradient =
AC( MES )
3Fixed _ Cost
Fixed _ Cost
MES − MC −
MES
Fixed _ Cost
MC +
MES
the MES.
or
2 Fixed _ Cost
MES
Fixed _ Cost
MC +
MES
Cost _ gadient =
marginal cost.
Assuming now zero-profits AC = MC +
(1) where MC is the
Fixed _ Cost
(2)
XD Firm
2 ⋅ Fixed _ Cost
2 ⋅ Fixed _ Cost
MES
MES
Cost _ gradient =
=
N ⋅ Fixed _ Cost Fixed _ Cost
Fixed _ Cost Fixed _ Cost
AC −
AC −
+
+
XDValue
MES
XD Firm
MES
Combining the two above equations, and letting N be the number of firms.
Cost _ gradient =
XD Branch
2 ⋅ Fixed _ Cost
MES XD Branch
Fixed _ Cost
+
− N ⋅ Fixed _ Cost
MES XD Branch
from which the fixed cost can be derived
Fixed _ Cost =
 MES

XDbranch  ⋅ ( Cost _ gradient ) ⋅ XDbranch

(
)
2 − ( Cost _ gradient ) ⋅  N ⋅ MES XD branch − 1


The calibration procedure runs, then, a simultaneous system of equations per
sector involving:
162
• unit price assumption for the export price and the price of absorption
• the relationship between marginal costs and selling prices to domestic,
exports to EU and exports to the rest-of-the-world (RW), involving
the mark-ups under a segmentation hypothesis
• the analytical formulas of the mark-ups, including the elasticities of
substitution in the love of variety of domestic, EU and RW
consumption, the number of firms and the value shares (known from
the SAM)
• a zero profit condition per sector
• a domestic production equilibrium condition for volumes.
This system is iteratively solved for the elasticities of substitution in the love of
variety of domestic consumption, the mark-ups, the selling prices and the volumes
of production and exports. Once this completed, a set of recursive equations
compute the rest of the calibration as in any CGE model (there we use the code
from the original GEM-E3 model).
The following table illustrates the calibration of IM sectors:
163
Calibration for IM sectors (1985)
Sectors
MES as % of Cost Gradient Herfindahl
production at 1/3 of MES
Index
Fixed cost as
percent of dom.
production
Mark-ups in %
Variety
Domestic EU Exports
Belgium
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
53.2%
31.6%
6.1%
132.6%
83.2%
21.4%
165.5%
68.2%
8%
7%
7%
7%
9%
7%
9%
10%
0.167
0.143
0.056
0.333
0.250
0.111
0.250
0.167
11.1%
7.4%
4.0%
12.6%
13.7%
6.3%
23.8%
17.7%
18.7%
13.4%
5.7%
28.3%
27.0%
11.3%
33.3%
21.8%
9.8%
6.4%
2.9%
11.3%
12.3%
5.7%
10.6%
6.1%
36.0
49.0
72.0
45.0
32.0
45.0
240.0
60.0
9.7%
3.9%
0.6%
2.0%
29.9%
0.7%
93.0%
33.6%
8%
10%
7%
7%
9%
7%
10%
7%
0.056
0.045
0.011
0.025
0.125
0.013
0.200
0.100
6.4%
4.4%
2.0%
2.8%
10.2%
1.8%
19.7%
10.9%
7.7%
5.7%
2.1%
3.4%
15.8%
2.2%
25.2%
12.2%
4.7%
3.4%
1.5%
2.3%
9.2%
1.7%
11.4%
3.6%
45.0
66.0
92.0
80.0
40.0
96.0
300.0
100.0
161.5%
112.5%
8.5%
95.7%
130.5%
4.8%
298.2%
93.6%
8%
10%
7%
7%
9%
7%
10%
7%
0.333
0.333
0.056
0.250
0.333
0.042
0.333
0.167
15.9%
15.1%
5.6%
12.2%
15.7%
3.9%
32.0%
16.9%
34.5%
32.4%
6.8%
22.5%
34.7%
5.5%
50.1%
21.3%
13.1%
11.3%
3.1%
8.3%
13.2%
3.3%
13.7%
6.0%
30.0
39.0
54.0
40.0
30.0
48.0
180.0
60.0
13.7%
6.7%
0.8%
13.1%
17.9%
2.7%
106.7%
22.6%
8%
7%
7%
7%
9%
7%
9%
10%
0.071
0.050
0.013
0.071
0.100
0.026
0.200
0.100
6.9%
4.7%
2.4%
6.2%
7.9%
3.6%
20.1%
10.6%
9.3%
6.1%
2.5%
8.3%
11.8%
4.4%
25.4%
12.1%
5.3%
3.3%
1.7%
3.9%
6.1%
3.1%
8.4%
4.3%
39.2
60.0
77.0
56.0
50.0
46.8
300.0
100.0
71.9%
35.9%
7.8%
85.9%
132.3%
30.9%
321.8%
101.0%
8%
10%
7%
7%
9%
7%
10%
7%
0.200
0.167
0.056
0.200
0.250
0.100
0.333
0.167
12.3%
10.2%
5.2%
13.5%
20.1%
9.8%
33.7%
18.0%
22.4%
16.2%
6.3%
19.1%
26.8%
11.4%
50.8%
22.0%
8.6%
7.0%
2.6%
7.4%
10.6%
6.1%
13.0%
5.9%
35.0
36.0
72.0
35.0
28.0
30.0
180.0
60.0
39.1%
4.9%
1.0%
19.3%
13.9%
1.4%
157.3%
32.0%
8%
10%
7%
7%
9%
7%
10%
7%
0.111
0.048
0.014
0.083
0.083
0.018
0.250
0.100
12.0%
5.1%
2.7%
7.7%
7.4%
2.7%
24.9%
10.4%
15.3%
6.0%
2.9%
10.0%
9.8%
3.2%
33.8%
12.0%
7.3%
2.9%
1.9%
4.4%
4.4%
2.2%
10.5%
4.3%
27.0
63.0
69.0
48.0
60.0
66.0
240.0
100.0
Germany
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
Denmark
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
France
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
Greece
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
Italy
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
164
Calibration for IM sectors (1985) (continued)
Sectors
MES as % of Cost Gradient Herfindahl
production at 1/3 of MES
Index
Fixed cost as
percent of dom.
production
Mark-ups in %
Variety
Domestic EU Exports
Netherlands
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
98.0%
3.4%
15.8%
73.6%
36.9%
21.0%
149.6%
95.7%
8%
10%
7%
7%
9%
7%
10%
7%
0.250
0.050
0.083
0.250
0.167
0.111
0.250
0.167
13.2%
3.5%
6.8%
9.6%
9.5%
6.2%
24.0%
17.2%
26.7%
5.2%
9.1%
19.9%
16.5%
11.0%
32.8%
21.8%
11.3%
3.1%
3.9%
8.6%
7.1%
5.7%
11.1%
6.8%
32.0
70.0
60.0
48.0
48.0
45.0
240.0
60.0
149.9%
23.6%
17.2%
185.3%
173.7%
34.2%
317.1%
100.0%
8%
10%
7%
7%
9%
7%
10%
7%
0.250
0.111
0.083
0.333
0.333
0.111
0.333
0.167
18.9%
10.1%
7.4%
16.8%
19.9%
9.7%
33.4%
17.9%
30.2%
13.1%
10.3%
33.1%
39.0%
13.3%
50.7%
22.0%
10.7%
5.6%
4.0%
11.5%
13.5%
6.8%
13.0%
5.9%
28.0
36.0
48.0
27.0
27.0
27.0
180.0
60.0
111.2%
14.3%
4.0%
29.5%
24.2%
7.1%
152.3%
41.8%
8%
10%
7%
7%
9%
7%
10%
7%
0.200
0.083
0.033
0.100
0.111
0.050
0.250
0.111
17.8%
8.3%
4.4%
9.7%
9.4%
4.7%
24.3%
12.0%
26.4%
10.4%
5.0%
12.0%
13.3%
6.0%
33.7%
13.7%
9.1%
4.5%
2.5%
4.8%
5.4%
3.2%
10.5%
4.0%
35.0
42.0
60.0
40.0
54.0
60.0
240.0
90.0
7.5%
2.4%
0.7%
5.8%
8.0%
0.5%
91.0%
21.3%
8%
10%
7%
7%
9%
7%
10%
7%
0.050
0.037
0.012
0.043
0.067
0.011
0.200
0.083
5.5%
3.3%
2.2%
4.6%
5.4%
1.6%
19.3%
8.5%
7.1%
4.4%
2.4%
5.8%
7.4%
1.9%
25.0%
9.9%
4.2%
2.4%
1.5%
3.4%
3.5%
1.3%
11.6%
5.0%
40.0
81.0
83.0
46.0
75.0
108.0
300.0
120.0
95.3%
27.7%
92.0%
19.6%
72.7%
9.3%
309.2%
96.4%
8%
10%
7%
7%
9%
7%
10%
7%
0.250
0.167
0.200
0.125
0.250
0.067
0.333
0.167
12.9%
8.1%
15.1%
5.4%
12.2%
4.6%
32.8%
17.3%
26.1%
15.8%
23.7%
9.8%
25.0%
7.6%
50.6%
21.5%
10.7%
7.1%
8.5%
4.7%
10.7%
4.3%
13.3%
6.0%
28.0
36.0
25.0
56.0
28.0
45.0
180.0
60.0
Portugal
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
Spain
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
Un. Kingdom
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
Ireland
Metallic
Chemical
Non metallic
Electrical Goods
Transport Equipment
Other Equipment
Telecomms
Banks
165
I N D U S T R I A L
C O N C E N T R A T I
O N :
C O M P U T A T I O N
O F
H E R F I N D A H L
I N D E X
Information on the firm size distribution in all three-digit industries:
• No of firms in each firm size class
• Total output value in each size class
The computation of model firm numbers proceeds as follows:
1. Compute Herfindahl index Hi for each three digit industry (as
explained below)
2. Compute the implied number of symmetric firms ni in each three
digit industry simply by taking the reciprocal value of Hi : ni =
1
Hi
3. Compute the firms number used in the model as output-weighted
average of the three digit level ni figures: n = ∑ Wi ⋅ ni
i
i : index over three-digit industries in a model sector
Wi : Output (gross production value) of sub-industry i divided by the Output of
model industry
n : Firm no used in the model
The Herfindahl index Hi in step 1 is computed as follows.
In general, the Herfindahl index is defined as:
H = ∑ MS 2j
j
i.e. sum of the squared market shares of each firm, where j index over all firms in
an industry and MS j is the market share (output share) of firm j.
In practice, Census of Production data provide numbers of firms by size class and
one has to assume for the computation that all firms within a discrete size class are
equal sized.
A practical example for the UK 1985 may be helpful.
166
Size
Class k
Enterprise size by number
of employees (1)
No of enterprises
nk (2)
Gross Output per size
class (£ million) X k (3)
1
2
3
4
5
6
1-99
100-199
200-499
500-999
1000-1499
1500 and over
935
34
35
12
7
8
1065
600
1523
1184
1299
6767
12439
6
= ∑ Xk
k =1
Let us take “Chemicals” (model sector 4). According to the UK SIC classification,
the sector consists of 7 three digit industries (251, 255, 256, 257, 258, 259, 260). Let
us take sector 251 (basic industrial chemicals) as example. The UK 1985 Census of
Production gives the information presented in the table.
The output share of a typical firm is size class k is then
(X
k
/ nk )
∑X
: = MS k
k
(e.g. MS1=(1065/935)/12439)
and Hi = ∑ n k ⋅ ( MS k ) = 0.039822
6
2
k =1
⇒ ni =
1
= 251
.
Hi
The same procedure is then repeated for the other six sub-industries and the n
for model sector 4 is computed as an output-weighted average over the 7 subindustries.
167
8
5
Chapter
Model Implementation
The GEM-E3 model can be solved either by its dedicated software,
SOLVER/NTUA, or recently in GAMS/PATH. The two solvers
are compared in terms of speed and efficiency.
Model implementation in SOLVER/NTUA
The latest version of the GEM-E3 model is involves a system of about 60,000
non-linear equations per time period. The model is operated and solved using
SOLVER/NTUA software in MS-WINDOWS.
The user interface involves a number of EXCEL spreadsheets that automate
scenario preparation and reporting of results. These interfaces work in
conjunction with SOLVER/NTUA and comprise a whole environment for the
GEM-E3 model.
SOLVER/NTUA has been used since the development of the first operational
model version (in 1993).
For more information on SOLVER/NTUA a separate software manual is
provided, while a description of the use of GEM-E3 in conjunction with
SOLVER/NTUA is provided in the user’s manual of the model.
Model implementation in GAMS/PATH.
Comparisons
Recently the GEM-E3 model has been successfully transformed as a mixed
complementarity model and solved in GAMS using the PATH solver.
Previous attempts to solve the model in other solution algorithms (as with
MINOS and CONOPT) have been unsuccessful mainly due to the model’s large
size and complexity. As a matter of fact these early failures incited the
development of SOLVER/NTUA the specialised software that manipulates and
solves the GEM-E3 model.
The PATH solver on the other hand, has been successful in solving very large
scale models and through the complemenetarity approach that it uses, enables the
168
expansion of GEM-E3 to include inequalities and a separate optimisation energy
sub-module (an on-going effort). Indeed, the model was successfully transformed
into the mixed complementarity formulation and solved with GAMS/PATH.
A comparison of solution times shows that GAMS/PATH is many times quicker
than SOLVER/NTUA in performing the model calibration. However, solution
times are in favour of SOLVER (if one takes into account the difference in
computing power of the two computers). Due to its memory requirements PATH
solution times have only been tested on an ALPHA machine (sample tests show
that on a PENTIUM PC the solution times would more than double).
SOLVER: Pentium 200 MHz
PC, 32 MB RAM, SCSI harddisk
GAMS/PATH: Alpha 500
MHz, 64 MB RAM, SCSI
hard disk
Model Calibration
3:30’
60”
Base year run
25”
5’54”
Baseline scenario for 10
years
60’
42’
Also, partly due to the fact that SOLVER takes into account the structure of the
model and derives an optimal ordering of the equations that minimises the
number of simultaneous variables, its solution algorithm benefits from a higher
stability in solving scenarios that considerably depart from the baseline.
Conceivably the performance of PATH would be enhanced if the model structure
would be simplified. This task is already under way.
The GEM-E3 team is in continuous contact with the team that built the PATH
solver, so improvements can be expected to occur in the next future.
169
9
Chapter
Direction of future
model developments
A brief overview of on-going and projected further model developments are
presented in this chapter.
GEM-E3 has been continually expanded and updated since its development in
late 1993. The main steps of the progress until the present period has been
reflected in the main model versions that have been delivered. These are:
Model Version
Date of completion
Main Characteristics
GEM-E3 ver. 1.0
end 1993
First linked model version for EU12. 11 sectors covered.
Incorporation of IS/LM closure
GEM-E3 ver. 1.6
1995
Revised model database;
incorporation of environmental
module; representation of durable
goods
GEM-E3-SM
1996
Imperfect markets. 15 sectors. No
environmental module.
GEM-E3 ver. 2.0
1997
Linked model version for EU-14.
18 sectors. Full environmental
module but perfect competition in
all goods markets.
In the next months, the GEM-E3 model will be used in the studies conducted
within the new research project (starting beginning 1998) “European emission
mitigation policy and technological evolution: economic evaluation with the
GEM-E3-EG model. Acronym: GEM-E3-ELITE” of DG-XII, JOULE-III
programme.
The modelling research work component of the project, concerns extending the
GEM-E3 model in the areas that are in the core of the climate debate, and that
are inadequately covered by current empirical approaches:
170
•
Endogenous representation of dynamics of innovation and
technological progress and their role in economic growth; two
prototype attempts have already been implemented in this respect.
The specification for the full incorporation of endogenous growth
mechanisms in the model is currently being specified.
•
Representation of QELROs8 targets,
their internalisation in the
economy through total value of damages and the time-path for their
implementation; the environmental module of the model already
incorporates the computation of external damages (as valuated by the
EXTERNE project, see the previous chapter describing the
environmental module), there is currently however no feedback from
these to the economic system.
• Aggregate, but engineering oriented representation of the energy
through a separate sub-module; A prototype version of this
module has already been specified and written a a mixed
complementarity problem. Linking this sub-module to the full GEME3 model is currently under way.
system
• Representation of the
links between policy measures and RTD
orientation;
Public policy can help shape the evolution of new
technologies by giving incentives towards some technological options.
Such mechanisms including property rights etc. will be incorporated in
the model.
• to address more specifically burden-sharing issues among social classes
and labour skills the current represntation of the labour market will be
modified to incorporate:
1. specification of labour market imperfections (both in labour
demand and in labour supply) and
2. disaggregation of labour into several skills;
• finally the
and baseline scenario will be updated
when the new Input-Output tables are available from EUROSTAT.
8
model database
Quantitative Emission Limitation and Reduction Objective.
171
Chapter
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