Ministry of Economy and Finance
Department of the Treasury
Working Papers
N°4 - October 2016
ISSN 1972-411X
IGEM II: a New Variant of the
Italian General Equilibrium Model
Barbara Annicchiarico, Fabio Di Dio, Francesco Felici
Working Papers
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© Copyright:
2016, Barbara Annicchiarico, Fabio Di Dio, Francesco Felici.
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used, providing that its source and author(s) are quoted.
Editorial Board: Riccardo Barbieri Hermitte, Mauro Marè, Libero Monteforte, Francesco Nucci
Organizational coordination: Cristina Gambini
CONTENTS
1
INTRODUCTION ............................................................................................................ 2
2
AN OVERVIEW OF IGEM .............................................................................................. 3
3
THE MODEL ................................................................................................................... 6
3.1
3.2
3.3
3.4
3.5
POPULATION STRUCTURE AND HOUSEHOLDS .................................................................. 6
W AGE SETTING, W ILLINGNESS TO W ORK AND UNEMPLOYMENT ....................................... 9
FIRMS .......................................................................................................................... 13
FISCAL AND MONETARY AUTHORITIES ........................................................................... 19
AGGREGATION AND FOREIGN ASSET POSITION ............................................................. 20
4
PARAMETRIZATION AND MODEL SOLUTION ........................................................ 21
5
SIMULATION EXERCISES .......................................................................................... 24
5.1
6
FINAL-GOOD PRODUCERS ............................................................................................. 24
CONCLUSIONS ........................................................................................................... 26
REFERENCES .......................................................................................................................... 26
Appendix A ............................................................................................................................... 29
Appendix B ............................................................................................................................... 33
Tables
................................................................................................................................ 48
IGEM II: a New Variant of the
Italian General Equilibrium Model
‡
*
Barbara Annicchiarico , Fabio Di Dio , Francesco Felici
§
Abstract
This paper provides a full technical description of a variant of the Italian General
Equilibrium Model (IGEM), a dynamic general equilibrium model used as a laboratory
for policy analysis at the Department of the Italian Treasury. This version of IGEM
presents four specific key features: (i) imperfectly competitive final good sector; (ii)
involuntary unemployment; (iii) a business tax bearing on firms; (iv) market frictions in
the labor market of atypical workers.
The paper presents some simulation scenarios of structural and fiscal reforms.
JEL Classification: E27, E30, E60.
Keywords: Dynamic General Equilibrium Model, Quantitative Policy Analysis,
Simulation Analysis, Italy.
*
Università degli Studi di Roma Tor Vergata, Dipartimento di Economia e Finanza, Via Columbia 2, 00133 Roma Italy. E-mail: [email protected]
‡
Sogei S.p.A. - IT Economia - Modelli di Previsione ed Analisi Statistiche - Via Isonzo 19/E - 00198 – Roma - Italy.
E-mail: [email protected]
§
Dipartimento del Tesoro - Ministero dell.Economia e delle Finanze Direzione I . Analisi Economico-Finanziaria Via
XX Settembre 97 .00187 - Roma -Italy. E-mail: [email protected]
1
1
Introduction
In this paper we present an extension of IGEM, the dynamic general equilibrium (DGE) model
for the Italian economy, entirely developed at the Department of Treasury of the Italian Ministry of the Economy and Finance (see Annicchiarico et al. 2013a, 2015). The present paper
incorporates several parts of Annicchiarico et al. (2013a) and amends the original paper only
in those parts presenting the extensions and the simulation results.
Notably, IGEM has been designed to study the impact and the propagation mechanism of
temporary shocks, evaluate the impact of alternative structural reform scenarios and analyze
the e¤ects of single policy interventions and …scal consolidation packages in Italy. In particular,
this extension of the model has four key features: (i) imperfectly competitive …nal good sector;
(ii) involuntary unemployment; (iii) a business tax bearing on …rms;1 (iv) market frictions in
the labor market of atypical workers.
IGEM belongs to the class of large scale DGE models used for policy analysis and the
construction of complex reform scenarios. These models, indeed, represent a useful tool of
analysis for the study of the macroeconomic of structural reforms, since they embody several
market imperfections and sources of ine¢ ciencies that reforms aim to reduce and alleviate. In
addition, the explicit modelling of real and nominal rigidities and of delayed adjustments allow
to study the potential e¤ects of policy interventions from a dynamic perspective, distinguishing
between impact e¤ects, short and medium run dynamics and long run impact. However, it is not
until recently that these models have been used for the analysis of the macroeconomic impact
of structural reforms. Earlier contributions in this direction include Bayoumi et al. (2004)
and Everaert and Schule (2006) who employ variants of the International Monetary Fund’s
Global Economy Model, Roeger et al. (2008, 2009), D’Auria et al. (2009), Varga et al. (2014)
who use QUEST III as a laboratory for several policy experiments for the EU countries, Forni
et al. (2010) who analyze the e¤ects of increasing competition in the service sector in Italy,
employing a two-region currency union DGE model, Lusinyan and Muir (2013) who in a variant
of the IMF‘s Global Integrated Monetary and Fiscal model (GIMF) analyze the macroeconomic
impact of a comprehensive package of reforms in the labor and in the goods markets for the
Italian economy, Annicchiarico et al. (2013b) who study the e¤ects of structural reforms in the
labor and in the product markets using the European Commission’s model QUEST III in the
version adapted for the Italian economy.
Consistently with the so called "New Neoclassical Synthesis" (see Goodfriend and King
1997) IGEM presents a large variety of nominal and real frictions in‡uencing the short and
the medium term behavior of the economy, while neoclassical features prevail in the long run,
where output is determined by technology, preferences and the supply of factor inputs (capital
and labor). What distinguishes IGEM from other large scale DGE models is the presence
of a labor market where di¤erent contract types coexist,2 so to better describe the Italian
1
2
This tax on business is meant to map the IRAP (Imposta regionale sulle attività produttive).
On the structure of the Italian labor market, see Boeri and Garibaldi (2007), Duranti (2009), Ichino et al.
2
economy, whose labor market is strongly heterogeneous. Notably, the dualism of the Italian
labor market consists in its separation into a primary sector and a secondary sector.3 The
former is characterized by union coverage, strong job security protection, high …ring costs,
while the latter is dominated by little or no union coverage, weak security protection and low
…ring costs. In IGEM, households with no access to …nancial markets are mainly identi…ed with
workers belonging to this secondary labor market, while the remaining households supply labor
inputs into the primary market. Self-employed workers, instead, are modeled as an additional
category which is somehow transversal to both markets. The main parameters governing the
supply of labor inputs have been estimated using a microsimulation model named EconLav, in
which the behavioral responses of workers are explicitly modeled making use of the information
gathered from di¤erent statistical sources.4 Clearly, when exploring the dynamic properties
of the model, this heterogeneity in the labor market, coupled with a high degree of real and
nominal rigidities, will reveal to be essential in explaining the transmission mechanisms and the
e¤ects on employment and income of the business cycle and of di¤erent policy interventions.
In this paper we construct various reform scenarios, recently advocated in economic and
policy circles as a means to promote growth, such as product market reforms, mapped onto the
model by decreasing the markups and (ex ante) budget neutral tax shifts from business and
labor to consumption.
The remainder of this paper is as follows. Section 2 provides a non-technical overview of
IGEM and discusses the general structure, some key model properties and the updates. In
Section 3 we present a detailed and technical description of the new structure of the model.
Section 4 describes the parametrization and the solution strategy. Section 5 considers several
applications and presents some simulation scenarios of structural reforms designed to illustrate
some speci…c features of IGEM. Section six concludes.
2
An Overview of IGEM
The skeleton of the model consists of an open economy taking as given the world interest rate,
world prices and world demand with six types of economic agents: …rms, households, unions,
a foreign sector and monetary and …scal authorities adopting rule-based stabilization policies.
Several adjustment costs on nominal and real variables enable IGEM to capture the typical
persistence of macroeconomic variables and mimic their empirical dynamics in response to
shocks. Speci…cally, the model features two nominal frictions, convex costs on price and wage
adjustment à la Rotemberg (1982), and …ve sources of real rigidities, investment and labor
(2005), Lucidi and Kleinknecht (2010).
3
This feature of the models has been fruitfully used in simulating the impact of the recent Jobs Act. See the
National Reform Programme 2015, available for download at: http://ec.europa.eu/europe2020/europe-2020-inyour-country/italia/national-reform-programme/index_en.htm
4
EconLav is one of the microsimulation tools available at the Department of Treasury of the Italian Ministry
of the Economy and Finance. Starting from a detailed description of the …scal rules and bene…t schemes,
EconLav is able to represent the behavioral responses of agents to several policy changes. For details see
http://www.dt.tesoro.it/en/analisi_programmazione_economico_…nanziaria/modellistica/
3
adjustment costs, variable capital utilization, external habit in consumption, and imperfect
competition in product and labor markets. All these frictions are necessary to create plausible
short-run dynamics, consistently with what it is observed in the data.
The economy presents four types of …rms: (i) a continuum of monopolistically competitive …rms each of which producing a single tradable di¤erentiated intermediate goods by using
labor and physical capital as factor inputs; (ii) a continuum of monopolistically competitive
exporting …rms transforming domestic intermediate goods into exportable goods using a linear
technology; (iii) a continuum of monopolistically competitive importing …rms transforming foreign intermediate goods into importable goods using a linear technology; (iv) a continuum of
monopolistically competitive …rms combining domestically produced intermediate goods with
imported intermediate goods into a …nal non-tradable good. Domestic producers of intermediate tradeable goods face competition from importers and have to price their products in the
domestic market, so as to achieve maximum pro…ts. Similarly, exporters and importers seek to
maximize pro…ts by setting prices.
As already emphasized, one of the key features of IGEM consists in a detailed representation of the labor market, designed to capture the main dualism of the Italian labor market
characterized by a primary sector with higher protection, better working conditions, superior
opportunities for promotion, higher pays, and a secondary sector with poor protection, limited
promotion opportunities, lower pays. The labor force of the model, in fact, is divided in three
di¤erent categories: (i) employees (skilled and unskilled) with a stable contract of employment
and strong protection; (ii) atypical workers who have ‡exible working patterns and weak employment protection; (iii) self-employed workers and professionals who may supply work under
contracts for services. Hiring and …ring those who are quali…ed as employees entail high adjustment costs.5 Similarly, the degree of nominal wage stickiness is much higher for employees,
as well as their market power. By contrast, atypical workers who often fail to qualify for employment protection rights, have low hiring and …ring costs and weak market power.6 Together
with self-employed workers, they represent the more volatile component of the workforce, more
subject to the e¤ects of the business cycle ‡uctuations. In our model, this heterogeneity in
the labor market allows us to include a large set of …scal instruments into the model, opening
up to the possibility of exploring the e¤ects of several …scal and structural reforms aimed at
increasing employment, favoring social inclusion and reducing inequalities.
This new version of IGEM is extended to allow for unemployment, as proposed by Galí
(2011a, b). Notably this approach represents a parsimonious way of introducing unemployment
into a dynamic general equilibrium model. Yet with this simple extension the model is now
able to determine the behavior of unemployment conditional on the shocks and on the policy
5
It should be noted that IGEM does not break down the economy into a shadow and an o¢ cial economy. As
a matter of fact, the dualism of the labor market characterizes the o¢ cial Italian economy itself. For a study
on the e¤ects of …scal reforms on the Italian economy, accounting for the presence of an undeground sector with
irregular labor, see Annicchiarico and Cesaroni (2016).
6
In the previous version of IGEM atypical workers supplied their labor services in a perfectly competitive
market.
4
interventions put in place.
Households consume the …nal non-tradeable goods supplied by perfectly competitive …rms,
supply labor and rent out capital to …rms. As in Galí et al. (2007) and Forni et al. (2009)
IGEM incorporates two types of households: the Ricardian households who have access to
…nancial markets, accumulate physical capital and …nancial assets and are so able to smooth
out their consumption pro…le in response to shocks (i.e. they manage to keep their lifetime
consumption as smooth as possible) and the non Ricardian households who cannot trade in
…nancial markets and accumulate capital, so that as in Campbell and Mankiw (1989), they
simply consume their after-tax disposable income (the so called “hand to mouth” consumers).
In our model this heterogeneity of households is strictly related to that considered in the labor
market. In fact, it is assumed that Ricardian households supply labor services as employees
and as self-employed workers, while non Ricardian consumers supply labor services as atypical
workers and as unskilled employees.7 Intuitively, workers with stable contracts have an easy
access to credit, while atypical workers with ‡exible labor patterns are more likely to be liquidity
constrained. Similarly, some low income workers are likely to be liquidity constrained.
Monopolistic trade unions set wages of skilled and unskilled subordinate workers, so as to
maximize households’ expected utility. Market power introduces a wedge between the real
wage rate and the marginal rate of substitution between leisure and consumption. Further,
self-employed and professionals are assumed to work on their own under the tutelage of the
professional orders (or registers). Hence, despite this category of workers are not covered by
the legal and trade-union protections a¤orded to employees and are paid by their clients or
customers, they have some market power in setting their remuneration.
The monetary authority controls the nominal interest rate and responds to in‡ation and output variations. The model allows for a variety of di¤erent reaction functions to be incorporated
(active v. passive interest rate rules, current, backward or forward rules).
The government issues nominal debt in the form of interest-bearing bonds. Public consumption and investments, interest payments on outstanding public debt, transfers to households and
subsidies to …rms are …nanced by taxes on capital, labor, consumption and business, by social
security contributions and/or by issuance of new bonds. To ensure that the …scal budget constraint is met, the …scal authority is assumed to adopt a …scal rule responding to public debt.
The foreign sector is modeled as exogenous. In details, Italy faces an exogenous world rate
and takes as given world demand and world prices on tradeable goods. The development of the
net foreign asset position depends on the current account surplus and so on the decisions of …rms,
households and government. Finally, the transmission mechanism from internal to external
variables is further complicated by the assumption that Italian exporting and importing …rms
have some market power in the prices they set, so that the net external position will depend on
conditions in both …nancial and goods markets.
7
More precisely, in this model, the category of workers labeled as “atypical” also includes a small fraction of
self-employed workers (the young) who may be little di¤erent, as no less dependent economically on their work
for subsistence than strictly speaking atypical workers. This is also meant to capture the phenomenon of the
false independent work.
5
3
The Model
The economy is populated by households, unions, …nal and intermediate goods producing …rms,
a foreign sector and a monetary and a …scal authority. As already emphasize, the core of
the model consists in neoclassical model, augmented to include a large assortment of real and
nominal frictions in the spirit of the so called "New Neoclassical Synthesis", several market
imperfections, a dual labor market and a foreign sector. In what follows we outline in detail
the behavior of the di¤erent types of agents and characterize the decentralized equilibrium and
the aggregate resource constraint of economy.
3.1
Population Structure and Households
There is a continuum of households in the space [0; 1] : There are two types of households di¤ering
in their ability to access …nancial markets: the non Ricardian households in the interval [0; sN R ] ;
who simply consume their disposable income (i.e. the hand to mouth consumers) and supply
di¤erentiated labor services as atypical workers and unskilled employees, and the Ricardian
households in the interval [1
sN R ; 1] ; who are able to smooth consumption over time and
supply di¤erentiated labor services as skilled and unskilled employees and as self-employed. For
the sake of simplicity it is assumed that each type of household provides all di¤erentiated labor
inputs within each category it supplies. It follows that by denoting sNA , sNS , sLL and sLH ;
respectively, the population shares of atypical workers, self-employed workers, unskilled and
skilled employees, we have that the following identities must hold:
sN R = sNA +
1
LL sLL ;
sN R = sNS + sLH + (1
where
LL
3.1.1
Ricardian Households
(1)
LL ) sLL ;
(2)
is the share of unskilled labor inputs supplied by non Ricardian households.
The representative Ricardian household derives utility from consumption C R of the …nal good
(where the superscript R stands for “Ricardian") and experiences disutility from supplying
labor inputs as unskilled employees LL ; skilled employees LH and self-employed NS :
E0
1
X
t=0
t
"
U (CtR
R
hC R C t 1 )
X
`R
#
V`R (`R
t ) ;
(3)
where E0 is the expectations operator conditional on information available at time 0, and
2 (0; 1) represents the subjective discount factor and `R 2 fLL ; LH ; NS g the index denoting
the three di¤erent categories of workers. Preferences described by the period utility function
U displays external habit formation (i.e. “catching up with the Joneses” preferences. See Abel
R
1990), with hC R 2 [0; 1) being the habit coe¢ cient and C t
6
1
the lagged aggregate consumption
of Ricardian households (taken as given by each household). The typical household derives
disutility from labor according to the period utility functions V`R .
In what follows we adopt the following standard functional forms:
R
u(CtR
hC R C t
R
= log CtR
1)
hC R C t
1
;
(4)
1+v
V`R (`R
~`R
t ) = ! `R s
`R
`R
t
;
1 + v` R
(5)
where ! `R is a scale parameter measuring the disutility of labor, v`R is the inverse of the Frisch
elasticity of labor supply and s~`R denotes the share of time devoted by the typical Ricardian
household to the working activity of kind `R :8 Being each household endowed with one unit of
X
s~`R = 1:9
time we have
`R
Ricardian households are assumed to own three assets: government bonds, B R ; paying a
gross nominal interest rate equal to R; foreign …nancial assets, BFR ; paying a gross rate equal
to R adjusted for a risk premium
physical capital,
K R;
F
(increasing in the aggregate level of foreign debt), and
which accumulates according to:
R
Kt+1
= (1
where 0 <
R
K )Kt
+ ItR ;
(6)
< 1 denotes the depreciation rate of physical capital and I R investments. Invest-
K
ment decisions are subject to a convex adjustment cost of
where
I
ItR =
2
ItR KtR units of the …nal good,
2
ItR
KtR
I
I
K
,
I
> 0:
(7)
Owners of physical capital are also assumed to control the rate of utilization at which this factor
K
is utilized, uK
t : As in Christiano et al. (2005), using the stock of capital at a rate ut entails a
cost in terms of the …nal good equal to
uK
uK
=
t
uK
1
uK
t
uK
uK
KtR , where
t
1 +
uK
2
2
uK
t
1
2
;
;
uK
1
uK
2
> 0:
(8)
Households rent out their capital stock to the intermediate goods producing …rms and receive
a competitive rental price, rtK , per unit of capital. Given the degree of capital utilization uK
t ,
R
total gross income stemming from the rental amounts to rtK uK
t Kt .
X
R
Households earn a gross labor income equal to
s~`R Wt` `R
t and wage decisions are made
`R
by unions which supply labor in monopolistic competitive markets and face Rotemberg-type
8
In the previous version of IGEM preferences where such that the Frisch elasticity of labor supply was decreasing in the level of hours worked.
sL
(1 LL )sLL
9
It should be noted that from the economy’s population structure we have: s~LL =
; s~LH = 1 sH
1 sN
N
and s~NS =
sNs
1 sN
sNS + sLH + (1
R
; so that on aggregate the labor force supplied by Ricardian households is exactly 1
R
LL ) sLL :
7
R
sN R =
quadratic adjustment costs in terms of domestic production, Yt ; on nominal wage changes speR
ci…c for each category of represented workers,
function of
W`
R
R
Wt` =Wt` 1 :
R
R
(Wt` =Wt` 1 )Yt ,
W`
R
( ) being a quadratic
Finally, households receive dividends, P ROR ; from the intermediate goods …rms, transfers
from the government, T rR ; and pay lump-sum taxes, T AX R ; consumption taxes (at a rate
`R
wage income taxes (at rates
and tax credit
(tcrK ).
K ),
) and capital income taxes (
t
C ),
less depreciation allowances
Finally, we also assume that households pay contributions to social
R
security (at rates
W`
h;t
).
The period-by-period budget constraint for the typical Ricardian agent in nominal terms
reads as:
(1 +
C
R
t )PC;t Ct
R
+ BtR + St BF;t
+ PI;t ItR =
`R
t
1
W`
h;t
R
X
R
s~`R Wt` `R
t +
(9)
`R
+Rt
R
1 Bt 1
+ (Rt
1
+
+ P ROtR + T rtR
+
+(1
PI;t
uK
K
K R
t K PI;t ut Kt
T AXtR Pt
+ tcrtK PI;t ItR +
K K
K R
t )rt PI;t ut Kt
uK
KtR
t
Pt
X
F
R
t 1 )St BF;t 1 +
PI;t
s~`R
I
ItR KtR +
R
W `R
R
(Wt` =Wt` 1 )Yt ;
`R
where PC denotes the price of a unit of the consumption good, PI the price of a unit of the
investment good, St is the nominal exchange rate de…ned as units of domestic currency per unit
of foreign currency, Pt is the price level. The solution to the Ricardian household problem is
summarized in Appendix A.
3.1.2
Non Ricardian Households
The representative non Ricardian household faces a periodic utility function of the form:
U (CtN R
NR
1)
hC N R C t
+
X
R
V`N R (`N
t );
(10)
`N R
where all variables are as in the previous section and the superscript N R stands for “non
Ricardian". As already mentioned, non Ricardian households only supply labor services as
atypical workers and as unskilled employees (represented by trade unions), hence `N R 2 fLL ;
NA g: We assume that functional forms of U ( ) and V ( ) are as in (4) and (5). By assumption,
non Ricardian households have no access to …nancial markets and do not own physical capital
(i.e. non Ricardian households can neither save nor borrow), hence they derive income only
from labor activities, adjusted for taxation. The ‡ow budget constraint in nominal terms reads
8
as:
C
NR
t )PC;t Ct
(1 +
=
`N R
t
1
X
W`
h;t
NR
X
s~`N R Wt`
NR
R
`N
+
t
(11)
`N R
s~`N R
W `N R
(Wt`
NR
=Wt`
NR
1
)Yt + Pt T rN R
T AXtN R ;
`N R
where T rN R and T AX N R denote government transfers and lump-sum taxes and
W `N R
(Wt`
NR
=Wt`
denotes the nominal wage adjustment costs faced by non-Ricardian individuals in changing nominal wages, with
NR
W`
( ) being a quadratic function of Wt`
NR
=Wt`
NR
1
:. See Appendix A for
details.
3.2
Wage Setting, Willingness to Work and Unemployment
We assume that wage decisions for each labor type are by central authorities external to the
households: a professional order will act in the interest of each variety of labor services supplied
as self-employed and a union will represent each variety of labor services supplied as employee
and atypical workers. The corresponding aggregate employment levels for each of the four
category of workers is determined by …rms labor demand decisions. In this sense, households
take employment and wage as given.10 See Appendix A for details.
3.2.1
Self-Employed Workers
For the self-employed labor decisions are taken under the tutelage of professional orders which
supply labor services monopolistically to a continuum of labor markets of measure 1 indexed
by hNS 2 [0; 1] : It is assumed that in each market hNS the professional order faces a demand
for labor given by NS;t (hNS;t ) =
NS
(hNS )
NS
Wt
NS
Wt
NS;t ; where
NS
> 1 is the elasticity of
substitution between labor inputs, WtNS (hNS ) is the market-speci…c nominal retribution, WtNS
Z1
is the wage index and NS;t = NS;t (hNS )dhNS so to satisfy the time resource constraint.
0
The monopolistic professional order sets WtNS (hNS;t ) in order to maximize households’expected utility (3), given the demand for its di¤erentiated labor services and subject to a convex
adjustment costs function:
NS
NS
W NS (Wt (hNS )=Wt 1 (hNS ))
where
W NS
> 0 and
W
t 1
1
W
=
2
WtNS (hNS )
1
W NS
W
t 1
1
W
WtNS1 (hNS )
1
!2
Yt ;
(12)
is a geometric average of past (gross) and long-run in‡ation,
where the weight of past in‡ation is determined by the indexation parameter
10
W
2 [0; 1].
In the former version of IGEM atypical workers were assumed to have no market power and supplied labor
services taking wage as given.
9
NR
1
)Yt
In the symmetric steady-state equilibrium the wage equation, NS;t reads as:
W NS
=
P
where
R
NS
! NS (Ns )vNS
1
NS
11
NS
R
W NS
h
;
(13)
is the Lagrange multiplier associated to the budget constraint (9) expressed in real
terms. Notice that market power in the labor market introduces a wedge between the real remuneration of self-employed workers, W NS =P; and the marginal rate of substitution between leisure
and consumption adjusted for direct and indirect taxation. This markup
the elasticity of substitution between di¤erentiated labor services,
NS ,
NS
NS
1
is decreasing in
and re‡ects the degree
of imperfect competition characterizing the labor market. The impact of structural reforms
aimed at increasing the degree of competition among self-employed, such as the liberalization of
professional orders, can be simulated by permanently modifying the elasticity parameter
NS .
We are now ready to introduce a measure of involuntary employment. Following Galí (2011a,
2011b) we assume that a household is willing to work as a self-employed if the following condition
holds:
NS
t
1
WtNS
Pt
W NS
t;h
! Ns
s
Ns;t
vNs
;
R
t
(14)
where Nss denotes the supply of labor-type Ns : The above conditions implies that individuals will participate to this labor market provided that the net real remuneration exceeds the
corresponding marginal disutility of labor. A measure of unemployment immediately follows:
u
Ns;t
=
s
Ns;t
Ns;t
;
s
Ns;t
(15)
u is to be interpreted as the unemployment rate.
where Ns;t
From the above results it clear that the level of unemployment will be lower as a result of a
reform able to reduce the wage markup.
3.2.2
Skilled Employees
Within each Ricardian household, a union is assumed to supply labor inputs as skilled employee
monopolistically to a continuum of labor markets of measure 1 indexed by hLH 2 [0; 1] : In each
LH
(hLH )
L
Wt H
Wt
market, the union faces a demand for labor given by LH;t (hLH ) =
LH
LH;t where
> 1 is the elasticity of substitution between di¤erentiated labor services, WtLH (hLH ) is the
Z1
LH
market-speci…c nominal wage, Wt is the wage index and LH;t = LH;t (hLH )dhLH . We also asLH
0
sume for employees costly nominal wages adjustment of the form
W LH
2
1
W
t 1
1
L
Wt H (hLH )
W W LH (h
LH )
t 1
2
1
Yt ; where
W LH
LH
LH
W LH (Wt (hLH )=Wt 1 (hLH ))
> 0:
In steady state and imposing symmetry across di¤erentiated skilled labor services, the wage
10
=
equation boils down to
W LH
=
P
1
LH
11
LH
R
W LH
h
LH
! LH
:
(1 LH )vLH
(16)
It follows that reforms, aimed at reducing the bargaining power of insiders and align wages
to productivity trends, are simply mapped onto the model by increasing the elasticity of substitution between pairs of di¤erentiated skilled labor inputs so to reduce the wage markup
LH
LH
1:
Also in this case, we assume that a household is willing to work as a skilled-employee provided
that the following condition holds:
1
WtLH
Pt
WH
h;t
LH
t
! LH
vLH
LsH ;t
R
t
;
(17)
where LsH ;t denotes the supply of labor-type LH ;t : The above conditions implies that individuals will participate to this labor market provided that the net real remuneration exceeds the
corresponding marginal disutility of labor. A measure of unemployment immediately follows:
LuH;t
=
LsH;t
LH;t
LsH;t
;
(18)
where LuH;t is to be interpreted as the unemployment rate of skilled employees.
3.2.3
Unskilled Employees
Unskilled labor services are assumed to be supplied by both Ricardian and non Ricardian
households. As for skilled employees, we assume a continuum of di¤erentiated labor inputs
indexed by hLL 2 [0; 1] supplied monopolistically by unions. For simplicity we assume that
households are distributed uniformly across unions, hence aggregate demand of labor type
hLL , that is LL;t (hLL ) =
LL >
LL
Wt (hLL ) is
Z1
LL
(h
Wt
LL )
L
Wt L
LL
LL;t ; is evenly distributed between all households,
1 denoting the elasticity of substitution between di¤erentiated labor services,
with
the nominal wage of type hLL , WtLL is the wage index of the category and LL;t =
LL;t (hLL )dhLL . It follows that a share
LL
of the associates are non Ricardian consumers,
0
while the remaining share is composed by Ricardian agents. The union will set the nominal
wage WtLL (hLL ); so as to maximize a weighted average of agents’lifetime utilities. Adjustment
costs on nominal wages are given by a quadratic cost function,
W LL
2
1
W
t 1
1
L
Wt L (hLL )
L
W W L (h
t 1 LL )
2
1
Yt ; where
W LL
LL
LL
W LL (Wt (hLL )=Wt 1 (hLL ))
=
> 0:
In steady state the …rst-order condition for wage setting, after having imposed symmetry
11
across di¤erentiated unskilled labor services, reads as follows:
W LL
=
P
11
LL
! LL LvLLL
LL R
) + LL
1
LL
W LL
h
LL
[(1
NR
]
;
(19)
where we have used the fact that given the population structure the weights attached by the
union to Ricardian and non Ricardian households are given by (1
sN R ) and sN R , respectively,
and that given the allocation of time within each household, the e¤ective weights boil down to
(1
LL )
and
LL ,
respectively.11 By permanently modifying the elasticity parameter
LL
we
are able to alter the market power of the trade unions representing unskilled labor workers.
As done for the skilled workers, we can de…ne the willingness to work as an unskilled worker
for both categories of households and then …nd a measure of unemployment:
LuL;t
=
LsL;t
LL;t
LsL;t
;
(20)
where LuL;t is to be interpreted as the unemployment rate of unskilled-employees and LsL;t the
corresponding supply.
3.2.4
Atypical Workers
As already mentioned, in this new version of IGEM, also for atypical workers we assume the
existence of a continuum of di¤erentiated labor inputs indexed by hNA 2 [0; 1] supplied monopolistically by unions. For simplicity we assume that households are distributed uniformly across
unions, hence aggregate demand of labor type NA;t (hNA;t ) =
NA
(hNA )
N
Wt A
Wt
NA
NA;t ; where
> 1 is the elasticity of substitution between labor inputs, WtNA (hNA ) is the market-speci…c
Z1
NA
nominal retribution, Wt is the wage index and NA;t = NA;t (hNA )dhNA so to satisfy the
NA
0
time resource constraint.
The union sets WtNA (hNA;t ) in order to maximize households’expected utility (10), given the
demand for its di¤erentiated labor services and subject to a convex adjustment costs function:
NA
NA
W NA (Wt (hNA )=Wt 1 (hNA ))
where
W NA
> 0 and
W
t 1
1
W
=
2
WtNA (hNA )
1
W NA
W
t 1
1
W
WtNA1 (hNA )
!2
1
Yt ;
(21)
is a geometric average of past (gross) and long-run in‡ation,
where the weight of past in‡ation is determined by the indexation parameter
W
2 [0; 1].
Proceeding as in the previous sections and recalling that by assumption only non Ricardian
households supply labor services as atypical workers, we obtain the following wage equation for
11
Given the population structure and the allocation of time within each household, the weights attached by the
1
L
L
union to Ricardian and non Ricardian households are, in fact, given by (1 sN R ) 1 sN L
sLL and sN R sN L
sLL :
R
R
12
the symmetric steady state:
W NA
=
P
where
NA
NA
vNA
! NA NA
1
NA
11
W NA
h
NA
NR
:
(22)
> 1 denoting the elasticity of substitution between di¤erentiated labor services.
From the willingness to work we also obtain a measure of involuntary unemployment:
u
NA;t
=
s
NA;t
NA;t
s
NA;t
;
(23)
u is to be interpreted as the unemployment rate and N s the labor supply.
where NA;t
A;t
3.3
Firms
The economy features four types of …rms: (i) a continuum of …rms producing di¤erentiated
tradable intermediate goods; (ii) a continuum of monopolistically competitive exporting …rms
transforming domestic tradeable goods into exportable goods using a linear technology; (iii)
a continuum of monopolistically competitive importing …rms transforming foreign tradeable
goods into importable goods using a linear technology; (iv) a continuum of monopolistically
competitive …rms producing a …nal non-tradable good by combining domestically produced
intermediate goods with imported intermediate goods. In Appendix A we report the …rst-order
conditions characterizing the optimal solution to the typical …rm problem.
3.3.1
Intermediate-Good Firms
The intermediate goods sector is made by a continuum of monopolistically competitive producers
indexed by j 2 [0; 1]: The typical …rm j uses labor inputs and capital to produce intermediate
goods Yt (j) according to the following technology:
Yt (j) = At
where 0 <
h
L;
LCES;t (j)
N;
G
< 1,
OHtL
L+ N
L
NCES;t (j)
OHtN
N
1
uK
t Kt (j)
L
N
i1
G
KGt G ;
(24)
< 1; At denotes total factor productivity, LCES;t and NCES;t
denote CES aggregates of labor inputs hired as employees and as self-employed and atypical
workers. The …rst bundle represents a combination of skilled and unskilled labor inputs hired
in less competitive markets with more stable labor contracts, while the second bundle includes
labor inputs hired in the form of more ‡exible labor patterns. OHtL and OHtN stand for
overhead labor which captures the notion that a …rm must employ a minimum amount of labor
to produce any output (this includes tasks like management, supervision, breaks, meetings,
maintenance, time spent with government bureaucracy), while KGt is the stock of government
capital whose level depends on the public infrastructure investment decisions ItG and evolves
as KGt = (1
G )KGt 1
+ ItG ; with
G
being the depreciation rate. This productive role of
government capital in the spirit of Barro (1990), creates a potentially positive linkage between
13
government and output. Note that production exhibits decreasing returns to private inputs if
the (complementary) government capital inputs do not expand in a parallel manner.
The labor aggregates LCES;t and NCES;t are de…ned as follows:
1
L
LCES;t = syLL (efLL LYL;t )
1
NCES;t = syNNS (efNS N YS;t )
L 1
L
N 1
N
1
L
+ syLH (efLH LYH;t )
1
+ syNNA (efNA N YA;t )
where we have dropped index j to save on notation,
L;
N
L 1
L
N 1
N
L
L 1
;
N
N 1
(25)
;
(26)
> 1 measure the elasticity of
substitution between the categories of workers of each CES aggregate, the coe¢ cients efLL ;
efLH , efNS ; efNA measure e¢ ciency, the terms syLL , syLH ; syNS ; syNA represent the shares of
each category of workers in their respective aggregate and LYL;t , LYH;t , N YS;t ; N YA;t denote
the labor inputs. Labor inputs LYL;t , LYH;t , N YS;t ; are, in turn, CES bundles of di¤erentiated
labor inputs with elasticity of substitution equal to
LL ,
LH
and
NS ,
respectively, so that
at the optimum and after aggregation across the continuum of intermediated-good …rms j, the
demand schedule for each variety within each category will be as outlined in the previous section
on wage setting.
The production function (24) with (25) and (26) has a particular nesting structure which
deserves some more explanation. The idea here is to capture the fact that a production unit
needs to employ labor services both in stable and in more ‡exible patterns.12 As a matter of fact,
on the one hand, …rms need more stabilized workers (on whom they can always count) involved
in the core business activities and in those which are strictly functional to these activities
themselves, on the other, …rms externalize activities that do not involve core competencies,
relying on workers who supply their services as self-employed or atypical workers. Furthermore,
the possibility of having substitutability between self-employed and atypical is meant to capture
some particular features of the Italian labor markets. In the …rst place, atypical workers in Italy
are not necessarily low skilled and in most cases they have tertiary education.13 Secondly, as
already explained, the category of workers labeled as atypical, also includes a small fraction
of self-employed workers (the young), so to capture the phenomenon of the false independent
work. In addition, …rms tend to employ a core of permanent workers on whom an investment
in training is made to increase productivity and obtain better functional ‡exibility. Yet …rms
are also likely to employ a group of peripheral workers or rely on external services to be able to
better meet temporary changes in the economic conditions.
12
This nesting structure of the production function is then motivated by the need of modeling the duality
of the Italian labor market. However, we acknowledge that a functional form foreseeing a CES structure in
skilled labor inputs, self-employed workers and a sub-CES bundle in atypical and unskilled workers, may well
capture the imperfect substitutability between di¤erent labor inputs with more emphasis on skills and professional
aspects rather than on the characteristics of the ongoing contract. Other nesting hypotheses will be considered
in the future version of IGEM, since the quantitative e¤ects of policy interventions on hours worked and labor
remuneration of the single categories of workers can considerably change.
13
See ISFOL (2012). As an example, in 2010 about 30% of workers with tertiary education, since four years
from the …rst job, were still “temporary”.
14
Firms are assumed to pay social contributions at rates
W LH ,
f
W LL ;
f
NA
f
and
W NS ,
f
re-
spectively for skilled and unskilled employees, atypical workers and self-employed workers, and
may receive incentives in the form of subsidies for hiring workers with the (exception of selfemployed) at the di¤erentiated rates subLH ; subLL ; subNA : We also assume that a business tax
is in force which is based on the value added produced.14 The business tax rate is denoted by
Y;t :
The objective of each …rm j is to maximize the sum of expected discounted real pro…ts by
setting the optimal price Pt (j) and making choices about labor inputs and physical capital,
given the available technology (24), the demand schedule for variety j; Yt (j) =
Pt (j)
Pt
Y
Yt ,15
quadratic adjustment costs on price setting:
P (Pt (j))
with
p
> 0 and
P
=
1
P
2
P
1
P
t 1
Pt (j)
Pt 1 (j)
1
!2
Yt ;
(27)
2 [0; 1] denoting weight of past in‡ation in the indexation, and quadratic
adjustment costs on labor inputs changes:
LH (LYH (j)) =
LH
LL (LYL (j)) =
LL
NS (N YS (j)) =
NS
NA (N YA (j))
NA
where we assume that 0 <
NA
<
=
NS
2
2
2
2
<
2
LYH;t (j)
LYH;t 1 (j)
1
LYL;t (j)
LYL;t 1 (j)
1
N YS;t (j)
N YS;t 1 (j)
1
N YA;t (j)
N YA;t 1 (j)
1
LH
=
LL
Yt ;
(28)
Yt ;
(29)
2
2
Yt ;
(30)
Yt ;
(31)
2
in order to capture the higher costs
associated with changes in the labor inputs related to workers with stable contracts.
Optimal Price Setting The elasticity of substitution between products of di¤erentiated
intermediate goods,
Y;
determines the market power of each …rm. In steady state, the …rst
order condition for price setting reads as:
P =
1
1
Y
Y
Y
1
M CN ;
(32)
where M C N denotes the nominal marginal cost. The above result implies that in the steady
state the real marginal cost, M C = M C N =P; is equal to the inverse of the markup (measuring
14
This production tax is inteded to map the regional production tax (IRAP). The tax base is calculated from
the di¤erence between the value and costs of production excluding labor costs for permanet workers.
15
The intermediate good j is demanded by …nal good …rms to produce consumption and investment goods and
by exporters to produce tradable goods.
15
the degree of market power of intermediate-good producers) which, in turn, is decreasing in
the elasticity of substitution
1
Y
Y
(1
Y ):
Y
and increasing in the production tax rate
Y,
that is M C =
Clearly, in the absence of the business tax, the steady-state price markup will
only depend on the elasticity of substitution between intermediate goods.16 In this case, instead,
the price markup is shown to be increasing in the business tax rate. In this sense, market power
gives producers the possibility of shifting the burden of the business tax toward consumers. In
what follows we will show that this feature of the model is not innocuous for our results.
Under symmetry, the …rst-order condition to the
Capital and Labor Inputs Decisions
optimization problem with respect to physical capital inputs is given by:
(1
Y;t )
PtI K k
u r = (1
Pt t t
G ) (1
N ) M Ct
L
Yt
:
Kt
(33)
k
where uK
t is the capital utilization rate decided by households and rt is the rental cost.
Turning to the decisions on labor inputs, in steady state, the following …rst-order conditions
must hold for unskilled and skilled employees, atypical and self-employed workers:
W LL
1
P
=
L (1
W LH
P
=
L (1
subLL +
G) M C
1
W NA
1
P
=
N (1
G) M C
where I
Y
N
(1
G) M C
is an index variable. If I
Y
Y
(1
W LH
f
[I
Y
(1
Yt
OHtL
LCES;t
subNA +
W NA
f
Yt
W NS
f
Y
OH N
NCES
= 1 (I
Y
+ (1
1
L
Y;t )
Y)
1
N
(1
Y)
NCES
N YS
Y
)] =
1
L
(34)
1
sLLL efLL L ;
1
L
LCES;t
LYH
(1
I
+ (1
NCES
N YA
OH N
NCES
Y;t )
LCES
LYL
OH L
LCES
W NS
1+
P
=
[I
Y
subLH +
G ) M Ct
W LL
f
I
1
L
Y
)] =
sLH ef
L 1
L
LH
(35)
;
=
(36)
1
N
1
sNNS efNSN ;
=
(37)
1
N
1
N
1
sNNS efNSN ;
= 0), then the labor costs on permanent workers
16
Pro-competitive reforms in the production market are simulated by increasing the elasticity of substitution
between pairs of intermediate goods varieties Y :
16
can (cannot) be deduced from the tax base on business. Clearly, payroll taxes and subsidies
introduce a further wedge between the wage rate and the marginal revenue of labor inputs.
3.3.2
Exporting and Importing Firms
We assume the existence of a continuum of monopolistically competitive exporting …rms transforming domestic intermediate goods into exportable goods using a linear technology. This
implies that exporters are able to set the price for their product at a markup over their marginal cost. Furthermore, we assume that there are costs to adjusting prices:
PX (PX;t (j))
=
EXP
2
2
1
6
4
1
EXP
EXP
t 1
PX;t (j)
PX;t 1 (j)
32
7
15 EXPt ;
where PX;t (j) is the price set by the exporter in foreign currency for the good j,
1
EXP
EXP
t 1
(38)
EXP
> 0;
is a geometric average of past (gross) and long-run in‡ation prevail-
ing in the foreign market, where the weight of past in‡ation is determined by the indexation
parameter
EXP
2 [0; 1].
The typical exporting …rm will thus set the exporting price PX;t (j); so as to maximize the expected discounted value of future pro…ts, taking as given the adjustment cost (38), the exchange
rate St and the world demand for good j EXPt (j) =
PX;t (j)
PX;t
EXP
EXPt , where
EXP
> 1 is
the elasticity of substitution between tradeable goods, EXPt denotes the total demand of exporhR
i 1
1
1
EXP
tations and PX;t is the ideal export price index, given by PX;t = 0 PX;t (j)1 EXP dj
.
In steady state the markup charged by exporting …rms will be constant:
EXP
SPX =
1
EXP
P:
(39)
By analogy, the same logic applies to importers, which are domestic …rms setting prices in local
currency as a markup over the import price of intermediate goods produced abroad and facing
a demand IM Pt (j) =
PM;t (j)
PtM
IM P
IM Pt where
IM P
> 1 is the elasticity of substitution
between imported goods, IM Pt denotes the total demand of imported goods, PM;t (j) is the
price of the imported good expressed in domestic currency and PM;t is the ideal import price
hR
i 1
1
1
IM P
index, given by PM;t = 0 PM;t (j)1 IM P dj
. Since we assume an identical setup for
importing …rms, the quadratic cost function to adjusting prices is:
PM (PM;t (j))
where
IM P
> 0 and
IM P
=
IM P
2
"
1
IM P
1
IM P
t 1
PM;t (j)
PM;t 1 (j)
1
#2
IM Pt ;
(40)
2 [0; 1]. Notice that in steady state the optimal pricing condition
of the typical importing …rm is:
PM =
IM P
IM P 1
17
SP :
(41)
3.3.3
Final-Good Firms
In this new version of IGEM we assume that also …rms producing …nal non-tradable goods
operate in monopolistically competitive markets. Final goods can be used for private and public
consumption and for private and public investment. Final good producers are also subject to a
production tax at a rate
E:
This sector can be identi…ed with the retail sector.
The representative …rm producing the …nal non-tradable good Et (i) combines a bundle of
domestically produced intermediate goods YH;t (i) with a bundle of imported intermediate goods
IM Pt (i) according to a constant elasticity of substitution (CES) technology:
Et (i) = (1
where
IM P
IM P )
1
IM P
IM P 1
IM P
(YH;t (i))
+
1
IM P
IM P
IM P 1
IM P
(IM Pt (i))
IM P
IM P 1
;
(42)
is the elasticity of substitution between domestically produced goods and interna-
tionally produced goods,
IM P
represents the share of foreign intermediate goods used in the
production of the …nal goods and
Z
YH;t (i) =
1
YH;t (i; j)
Y
1
Y
dj
Y
1
Y
;
(43)
0
IM Pt (j) =
Z
1
IM Pt (i; j)
IM P 1
IM P
dj
IM P
IM P 1
;
(44)
0
where
Y,
IM P
> 1 denote the elasticities of substitution between the di¤erentiated intermedi-
ate goods produced at home and abroad. The typical …rm i faces a demand function for its own
E
PE;t (i)
PE;t
speci…c good of the type Et (i) =
Et ; where
E
> 1 is the elasticity of substitution
between di¤erentiated goods, PE;t (i) is the price of good i, PE;t denotes the aggregate price
index and Et is the aggregate demand for …nal goods.
At the optimum, after having imposed symmetry across …rms, as to simplify notation, we
have the demand of intermediate domestic and imported goods:
YH;t = (1
IM Pt =
IM P
M CE;t
1
E;t
IM P )
IM P
M CE;t
1
E;t
IM P
PM;t
Pt
Et ;
(45)
IM P
Et ;
(46)
where M CE;t denotes marginal cost.
We assume the existence of a quadratic cost function on price adjustment:
PE (PE;t (i))
where
E
> 0 and
E
=
E
2
"
1
E
t 1
1
E
PE;t (i)
PE;t 1 (i)
1
#2
Yt ;
(47)
2 [0; 1]. The typical …nal good-producing …rm will thus set the price
18
PE;t (i); so as to maximize the expected discounted value of future pro…ts, taking as given the
E
PE;t (i)
PE;t
adjustment cost (47) and the demand function Et (i) =
Et :
In steady state the optimal pricing condition of the typical …nal produced …rm is found to
be:
E
PE =
1
E
3.4
M CEN :
(48)
Fiscal and Monetary Authorities
The government purchases …nal goods for consumption CtG and investment ItG , makes transfers
to households T rt , gives subsidies to intermediate goods producers SU Bt , receives lump-sum
taxes T AXt and tax payments on labor income, consumption, capital and business, namely
LT AXt ; T V ATt ; KT AXt ; BT AXt ; and issues nominal bonds Bt .
The ‡ow budget constraint of the government in nominal terms is then:
Bt = Rt
+ PC;t CtG + PI;t ItG + Pt T rt +
1 Bt 1
Pt T AXt
(49)
Pt (LT AXt + T V ATt + KT AXt + IRAPt ) + Pt SU Bt ;
where
T AXt = sN R T AXtN R + (1
T rt =
sN R T rtN R
LL
t
LH
t
+sNS LNS W RNS
NS
t
+sNA LNA W RNA
NA
t
KT AXt =
Y;t
h
C
t
K
t
NS
f;t
rtK
Y
Y;t
K
sNS Lt;NS W RtNS + 1
Y;t
I
h
sLL Lt;LL W RtLL 1
+
+
+
sN R CtN R + (1
BT AXt =
1+
WLL
h;t
+
+sLH LLH W RLH
T V ATt =
L
subL
t +
(50)
sN R )T rtR ;
+ (1
LT AXt = sLL LLL W RLL
sN R )T AXtR
uK
t Kt
WLL
f;t
+
WLH
h;t
WNS
h;t
(51)
+
+
WNA
h;t
+
+
WLH
f;t
WNS
f;t
WNA
f;t
+
+
;
sN R )CtR ;
tcrkt
Y;t Yt +
A
subN
+
t
(53)
PI;t
It ;
Pt
N
WA
f;t
(54)
(55)
i
sNA Lt;NA W RtNA +
PI;t k k
u r Kt +
Pt t t
W LL
t
(52)
+ sLH Lt;LH W RtLH 1
H
subL
+
t
W LH
t
LH
NA
H
A
SU Bt = subtLL sLL LL W RLL + subL
+ subN
;
t sLH LH W R
t sNA NA W R
19
i
;
(56)
with W RLL = W LL =P; W RLH = W LH =P; W RNA = W NA =P and W RNS = W NS =P:
The lump-sum component of taxation is set endogenously according to the following “passive
rule" as meant by Leeper (1991):
Pt T AXt = Pt T AX + TB Bt
1
B + TD Dt + TY Pt (Yt
Yt
1) :
(57)
where TB ; TD and TY are policy parameters, T AX and B are the long-run level of lump-sump
taxation and of public debt, and Dt denotes the budget de…cit:
Dt = (Rt
1
1)Bt
Pt T AXt
1
+ PC;t CtG + PIG;t ItG + Pt T rt +
(58)
Pt (LT AXt + CV ATt + KT AXt + BT AXt ) + Pt SU Bt :
The monetary authority adopts a Taylor-type interest rate rule speci…ed as follows:
Rt
=
R
Rt 1
R
R
Yt
Yt 1
t
T
where R is the equilibrium nominal interest rate,
and
R;
;
Y, S
T
Y
St
St 1
S
1
R
(59)
is the monetary authority in‡ation target,
are policy parameters.
It should be noted that in order to isolate the e¤ects of the tax experiments and policy
reform scenarios, in what follows we switch o¤ any possible feedback channels coming from the
tax rule and the Taylor rule. For each scenario, in fact, we consider a deterministic simulation
of 1,000 quarters, where the …scal rule (57) and the Taylor rule (59) are neutralized for the …rst
400 quarters.
3.5
Aggregation and Foreign Asset Position
Since only Ricardian households hold …nancial assets, accumulate physical capital and own domestic …rms, equilibrium requires that the following conditions must be satis…ed: (1 sN R )BtR =
Bt , (1
R = B ; I = (1
sN R )BF;t
t
F;t
sN R )ItR ; (1
sN R )KtR = Kt ; (1
sN R )P ROtR = P ROt
while aggregate consumption is:
Ct = (1
sN R )CtR + sN R CtN R :
(60)
Equilibrium in the labor markets requires that the quantity of each category of labor employed in the intermediate good sector must be equal to the supply, hence:
LYL;t = sLL LL;t ;
(61)
LYH;t = sLH LH;t ;
(62)
N YS;t = sNS NS;t ;
(63)
N YA;t = sNA NA;t :
(64)
20
Aggregate capital accumulates as follows:
Kt+1 = It + (1
)Kt :
(65)
Since the …nal good can be used for private and public consumption and for private and public
investments, we have:
h
PC;t = PI;t = PE;t = (1
1
IM P )Pt
IM P
1
IM P PM;t
+
IM P
i
1
1
IM P
:
(66)
The economy’s net foreign asset position denominated in domestic currency evolves as:
St BF;t = Rt
where the risk premium
F
t
1
+
F
t 1
St BF;t
1
+ St PX;t EXPt
PM;t IM Pt ;
(67)
is assumed to be increasing in the aggregate level of foreign debt. As
in Schmitt-Grohé and Uribe (2003) we use the following functional form for the risk premium:
F
t
=
F
'F (eBRt
BRF
1); where 'F is a positive parameter, BRtF = St BF;t =Pt and BRF is
the steady state level of net foreign assets in real terms. Clearly, in the steady-state
F
t
= 0:
The resource constraint of the economy immediately follows:
Yt =
St PX;t
PM;t
PtC
Ct + CtG + It + ItG +
EXPt
IM Pt +
Pt
Pt
Pt
St PX;t
PM;t
PtC
+ P (Pt ) +
PM (PM;t ) +
PX (PX;t ) +
PE (PE;t )
Pt
Pt
Pt
+ LH (LYH ) + LL (LYL ) + NA (N YA ) + NS (N YS ) +
LH
W LH (Wt ) +
PI
+
+ t uK uK
t
Pt
+
LL
W LL (Wt )
PtI
R
I It :
Pt
+
NS
W NS (Wt )
+
(68)
NA
W NA (Wt )
The equilibrium equations of the model are reported in Appendix B.
4
Parametrization and Model Solution
In this section we summarize the parametrization of the model which is mainly based on calibration, with the exception of the main parameters governing the supply of labor inputs for which
we have used the estimates obtained with the microsimulation model EconLav. Speci…cally,
IGEM is calibrated on a quarterly basis in order to match steady-state ratios and some speci…c
features of the Italian economy over the period 2002-2008.
The parametrization is summarized in Tables 1a and 1b. We set the benchmark parameters
in line with the existing literature. The discount factor
is equal to 0:99, so to imply an annual
real interest rate of 4%. The rates of depreciation of private and public physical capital
K; G
are set to 0.025 (so to imply a 10% annual depreciation rate of capital). The capital share in the
intermediate goods production is equal to 0.3, hence 1
21
L
N
= 0:3, while the labor shares
are such that
L
=
N
= 0:35: In this version we have opted to not consider the contribution
of public capital on production and set
G
= 0: The CES parameters
L
and
N
are set at 1.4
according to Katz and Murphy (1992) estimates also used in QUEST III for Italy.
The elasticity of substitution between domestic goods in the intermediate sector,
Y;
is set
equal to 5 so to have a steady-state level of net markup equal to 25% which is consistent with
the value set in the Italian version of QUEST III with R&D (see D’Auria et al. 2009). The
elasticity of substitution in the …nal good sector,
E;
is set at 2.65 consistently with a Since in
IGEM tradeable goods are produced in the intermediate sector, we also set the elasticities of
substitution between imported and exported varieties,
IM P
and
EXP ;
at 5.
The contribution of imported intermediate goods to the …nal good production, summarized
by the parameter
IM P
is equal to 0.26, consistently with QUEST III, while the elasticity of
substitution between domestic and foreign intermediate varieties
IM P
is set at 1.1. The habit
persistence parameter of Ricardian households, hC R , is set to 0.7 as in QUEST III (see Ratto et
al. 2009), while that of non Ricardian households, hC N R , is set at 0.3. This di¤erent setting in
habit persistence between Ricardian and non Ricardian households re‡ects their relative ability
to change their consumption pro…le over time in response to shocks. The values we set for the
habit formation parameters are consistent with the estimates of Sommer (2007).
For simplicity, in this version, the steady-state in‡ation is set equal to zero,
assume full backward indexation of prices and wages,
P
=
W
= 1; and we
= 1:
Using the RCFL - ISTAT 2008 data, labor categories are de…ned as follows. Employees are
identi…ed with those workers with a stable labor contract and eligible of employment protection,
so belonging to the primary labor market. According to the available data, this category
amounts to 53% of the whole workforce. In turn, within this category the share of the employees
with tertiary education corresponds to the skilled workers and represents 11% of the workers
(i.e. sLH = 0:11), while the remaining share is identi…ed with the unskilled employees (i.e.
sLL = 0:42): According to the same data, the share of self-employed workers older than 35, is
21% and we set the model share sNS accordingly. As a matter of fact, we exclude from this
category of workers the young, since at early stages of their careers they tend to be precarious
and face the same di¢ culties of the workers with atypical contracts. Hence, the last category
of workers labeled as “atypical” includes young self-employed, apprentices, temporary workers
and other workers with atypical contracts characterized by weak security protection and low
…ring costs, so belonging to the secondary market. According to the data this residual fraction
of workers amounts to 26% (i.e. sNA = 0:26): In this version of the model we assume that non
Ricardian households supply only atypical labor (i.e.
LL
= 0), hence sNR = 0:26:It is worth
noting that
the employment composition among regular, temporary and self-employees as a percentage
of total employment in Italy has not changed over the last 13 years (see OECD 2016).
The tax system calibration points to heavy taxation on capital and labor income, where
di¤erent rates are considered for each labor category. The tax rate on consumption
to 0.17, while the tax rate on physical capital
K
22
C
is equal
is 0.33, consistently with the calibration used
in the Italian version of QUEST III (see D’Auria et al. 2009). For the tax rates on wage income
the calibration is based on the data taken from RFCL - ISTAT 2008. In particular, the average
tax rate on labor income paid by skilled employees
LL
is set at 0.24, for the self-employed
NS
LH
is equal to 0.27, that for the unskilled,
is 0.26 and for the atypical workers
NA
is 0.24.
The social contribution rates paid by …rms and workers are set, respectively, at 0.33 and 0.09
as legal rates of contribution. The tax rate in business,
Y;
is set at 0.04 to re‡ect the average
regional business tax that is levied on …rms’revenues. Turning to the parameters characterizing
the labor markets, according to the estimates based on EconLav microsimulation model, the
Frisch elasticity of labor supply for the employees is 0.30, while for the atypical component of the
labor force the Frisch elasticity is equal to 0.35. For the self-employed workers we set the Frisch
elasticity at 0.30, since we conjecture that the reactivity of their labor supply to changes in their
remuneration is closer to that experienced by workers with stable contracts. The elasticities of
substitution between di¤erent varieties of labor
LL ;
LH ;
NS
are all set at 2.65 in line with
the literature (see Forni et al. 2010), re‡ecting the limited competition protecting the insiders.
On the grounds that workers with stable contracts tend to be more prone to accumulate skills
and human capital than temporary workers, as emphasized by the empirical literature (see Boeri
and Garibaldi 2007 among others), the CES parameters measuring e¢ ciencies are calibrated to
capture this aspect. In particular, e¢ ciencies are set so as to generate a skill premium for skilled
workers (those with tertiary education only) of 50% with respect to the unskilled (consistently
with AMECO 2005 data on labor compensations). Also for self-employed we assume a 50%
higher remuneration than that granted to the atypical workers.
IGEM is implemented in a TROLL platform which uses a Newton-type algorithm to solve
non-linear deterministic models. The decision rules of the model are expressed in levels, because
we are often interested in simulating the long-run e¤ects of certain policy measures and see what
happens in a new steady state. Notably, in the context of forward-looking models analyzing
the e¤ects of a permanent shock involving a new steady state requires solving a two-point
boundary-problem, specifying the initial conditions for the predetermined variables as well as
the terminal conditions for the forward looking variables.17 While the determination of the
initial conditions is straightforward, since these are invariants to shocks, the determination of
the terminal conditions may be more di¢ cult especially in large models. The more rigorous
approach to solve this problem would make it necessary to derive the new steady state of
the model and use the theoretical equilibrium values as terminal conditions, however, in some
circumstances, this solution strategy can be taxing. Alternatively, one may opt to reformulate
the problem so that the terminal conditions are invariant to policy changes, as proposed by
Roeger and in’t Veld (1999). In this paper we have opted for the latter strategy.18
17
Deterministic simulations are generally carried out when studying the e¤ects of structural and/or …scal
reforms involving permanent changes in some structural parameters and/or tax rates. For several examples of
reform packages simulated adopting this solution method, see Roeger et al. (2008).
18
This is usually the preferred strategy when dealing with large scale models. See Roeger et al. (2008) and
(2009) for the QUEST III model.
23
5
Simulation Exercises
In this Section we undertake several simulation exercises with the aim of validating the model
and understanding its properties. In particular, we examine how some key macrovariables
respond to a range of policy interventions so as to simulate the implementation of structural
and tax reforms. It is worth stressing that we will not deal with speci…c reform provisions that
have been implemented or that Italian government is going to implement. In this respect, these
exercises are intended to be only illustrative of the model functioning. To the same extent,
the simulation hypotheses concerning the credibility, the timing, the speed and the size of the
shocks are entirely arbitrary. In addition, all agents have perfect foresight, therefore any possible
source of uncertainty about the underlying path of policy changes is ruled out by construction.
Our analysis considers four policy interventions: (i) 1% markup reduction in the …nal goods
sector; (ii) 1% markup reduction in the intermediate goods sector; (iii) a balanced budget tax
shift from the business to consumption (1% of output); (iv) a balanced budget shift from social
security contributions bearing on …rms to tax on consumption (1% of output).
As common practice in this kind of economic policy exercises, in order to consider the e¤ects
of the policy experiments in isolation, we switch o¤ any possible feedback channels coming from
the tax rule and the Taylor rule. For this reason, in each scenario, we consider a deterministic
simulation of 1,000 quarters, where the …scal rule and the interest rate rule are neutralized for
the …rst 400 quarters.19
5.1
Results
Tables 2-5 report the e¤ects of the policy interventions form the main macroeconomic variables.
In particular, all e¤ects are expressed in percentage deviations from the baseline, with the exception of the unemployment rates which, instead, are expressed in percentage point deviations
from their baseline level.
We …rst quantify the potential macroeconomic impact of pro-competitive provisions involving the …nal good market and the intermediate good market, in turn. This policy area includes
reform packages promoting market competition and favoring business and is mapped onto the
model through a reduction of the price markup. In this way we are going to diminish the rents
in favor of producers. In both simulations we only change the relevant markup, while all other
parameters remain at their baseline values. Table 2 shows the impact of a markup reduction
in the …nal good sector, which can be identi…ed with the retail sector. As expected the e¤ect
on output is positive already after one year, while the terms of trade worsens. Consumption
immediately increases, as a results of the major purchasing power of households. Labor of all
categories of workers increases thanks to the improved economic conditions.
19
It should be noted that in the context of deterministic simulations, policy rules can be safely neutralized
without a¤ecting the uniqueness and the stability properties of the rational expectations equilibrium. The
Blanchard-Khan conditions, in fact, relevant for real determinacy, are computed on the basis of the initial steady
state (i.e. the baseline) in which policy rules are operative and have the characteristics necessary to ensure
stability and uniqueness of the equilibrium.
24
Table 3 shows the e¤ects of a markup reduction of the same size now involving the intermediate good sector, which is identi…ed with the manufacturing sector. Clearly, a lower markup
implies an increase in output, consumption and investment. The unemployment rate decreases
for all the categories of workers as a result of the higher level of economic activity induced by
the lower level of ine¢ ciency. The higher capital stock increases the marginal product of labor,
yielding to a higher remuneration for all workers. The terms of trade deteriorates in response to
the reform. This e¤ect is simply the result of a decline in the export prices as a consequence of
higher competition in the domestic economy. The negative e¤ect on the terms of trade e¤ect, in
turn, mitigates the positive e¤ect on consumption and investment stemming from the reforms.
However, we notice that the overall impact is much larger in this second experiment. In the
…rst case, in fact, major competition in the …nal good sector implies that part of this expansion
is directed towards major imports.
Also, it is worth noticing that on impact labor and wages tend to increase for all the
components of the labor force while the unemployment rate leaps up for atypical workers and
consistently reduces for the others. This behaviour might be explained by the fact that in IGEM
atypical workers are the most volatile component of labor and they thus tend to rapidly adjust
their behaviour according to the policy reform implemented. In the case of price markup reforms
the ameliorating economic conditions will greatly push up the participation (willingness) of
atypical workers to the labour market and, as a consequence, the corresponding unemployment
rate (as de…ned in equation 23) will move up. In the long run, instead, the higher Frisch
elasticity set for atypical workers explains why labor tends to go higher than that for the other
workers. In the long run, however, the unemployment rate of all categories of workers decreases
thanks to the improved economic conditions.
We now consider two tax policy experiments. In particular we study the potential e¤ects of
two ex ante budget neutral tax shifts from business and labor to consumption.
Table 4 presents the case of a tax shift from business to consumption. Initially the e¤ects
are negative, since consumption declines as a result of the higher tax rate on consumption. The
contraction of demand and the stickiness of prices explains the slight drop of output during
the …rst year. After the second year, instead, the level of economic activity increases along
with consumption, investment, employment and real wages. Intuitively, shifting the burden of
taxation from business toward indirect taxes reduces distortions on output decisions. As we
have seen, in fact, the tax on business increases the markup charged by producers.
Table 5 shows a …scal experiment envisaging a shift from social security contributions to
consumption. This is a so-called …scal devaluation exercise. In particular, we cut the social
security contribution payroll taxes borne by employers and increase consumption taxes so as to
neutralize the budgetary e¤ects. By cutting the employer-portion of social security contributions
we are able to directly reduce labor cost, increasing labor demand and output. As expected,
we observe a positive e¤ect on investment, real wages and employment since thanks to the tax
25
shift unit labor costs are now lower. The short run negative e¤ects on aggregate consumption
is to be ascribed to the fact that, while consumption of Ricardian households increases because
of higher pro…ts, the higher consumption tax rate will hurt non-Ricardian households, who will
experience a drop in consumption because of their diminished net income. Put it di¤erently,
this tax policy involuntarily shifts the burden of taxation disproportionately to the side of nonRicardian households who, in general, are more vulnerable and exposed to economic changes
than Ricardian households. This redistributive e¤ect is particularly strong in the short run,
where adjustment costs prevent the immediate materialization of the positive e¤ects of the
tax reform. As in the previous case, the initial fall of consumption drives aggregate demand
downward and so output. At later stages, however, aggregate consumption increases, thanks to
the improved economic conditions and despite the worsening in the terms of trade due to the
real exchange rate depreciation.
6
Conclusion
This paper presents an extension of IGEM, the Italian General Equilibrium Model used as
simulation tool for economic policy analysis at the Department of the Italian Treasury. This
version of IGEM presents four speci…c key features: (i) imperfectly competitive …nal good sector;
(ii) involuntary unemployment; (iii) a business tax bearing on …rms; (iv) market frictions in the
labor market of atypical workers.
To illustrate the behavior of the model, we have undertaken four experiments with the aim
of illustrating the implications of these new features. In particular, we have shown the e¤ects
of di¤erent pro-competitive reform scenarios and of budget neutral tax shifts.
It should be emphasized that the analysis carried out in this paper basically concerns the
implications of unilateral reforms. Nonetheless, owing to the beggar-thy-neighbor nature of
such policies, it would be worthwhile conducting similar experiments in the context of a multicountry model, accounting for the possible spillover e¤ects across countries. A multi-country
framework will also allows to design more complex scenarios and to describe monetary policy
conduct and exchange rate behavior in a more realistic way. We leave this point for future
extensions.
Finally, a word of caution is needed since the quanti…cation of the economic impact of
economic reforms represents an extremely di¢ cult exercise. All results must be interpreted in
the light of the model used that, although built up with the purpose of assessing the e¤ects of
structural reforms, only provides a stylized representation of the economy under study.
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28
Appendix A
Solution to the Households’Problem
De…ning as
terms, and
R
t
t
the Lagrange multiplier associated to the budget constraint (9) expressed in real
to the capital accumulation equation (6), the …rst-order conditions for maximiza-
R , I R , K R and uK are given
tion of the lifetime utility function (3) with respect to CtR , BtR , BF;t
t
t
t+1
by:
1
CtR
R
t
= Et
Pt
St
R
t
Pt
qt
qt = E t
R
t+1
R
t
(1
where
t
= Pt =Pt
1,
I
t
I
t+1
t+1
= Et
1=
2
6
6
6
6
6
4
K K
t )rt
R
t+1
Pt+1
I
(1
C PC;t
t )
Pt
= (1 +
R
hC R C t 1
R
t+1
Pt+1
I
(A-3)
tcrtK ;
(A-4)
K
K )r K uK
t+1 t+1 t+1
uK
1
+
= PI;t =PI;t
1
+
K
uK
t+1
K
t K
and qt =
I
t
R
t
2
uK
2
Pt
PtI
uK
t
3
K uK
t+1 t+1 K
R
It+1
R
Kt+1
uK
2
1
uK
1
+
K) +
2
R
It+1
R
Kt+1
(A-2)
F
t )St+1 ;
+qt+1 (1
2
(A-1)
Rt ;
(Rt +
ItR
KtR
R
t ;
K
uK
t+1
1
1 = 0;
7
7
7
R
7+
It+1
R + 7
Kt+1
5
(A-5)
2
(A-6)
represents the shadow price of a unit of
investment good (i.e. the Tobin’s q).
The representative hand-to-mouth household chooses consumption so as to maximize (10)
given (11). We denote by
NR
t
the Lagrange multiplier of the budget constraint expressed in
real terms. The optimal condition with respect to C N R is given by:
1
CtN R
NR
hC N R C t 1
= (1 +
C PC;t
t )
Pt
NR
t ;
(A-7)
Wage Setting
The monopolistic professional order sets WtNS (hNS;t ) in order to maximize households’expected
utility (3), given the demand for its di¤erentiated labor services and subject to a convex adjustment costs function (12). At the optimum and imposing symmetry across di¤erentiated labor
29
services supplied as self-employed we have that the following condition must hold:
1+vNS
+
NS Ns;t
0 = ! NS
(
1)
NS
R
t
(A-8)
W NS
h;t
NS
t
1
WtNS
1
R
t W NS
1
W
WtNS1
W
t 1
+
t
1
W
WtNS
W
1
W
WtNS
1
!
NS
Wt+1
1
t
1
W
Yt +
WtNS1
W
t 1
NS
Wt+1
1
Et R
t+1 W NS
1
W NS
Ns;t t +
Pt
!
1
W
WtNS
Yt+1 :
In steady state, given symmetry, (A-8) boils down to (13).
For skilled labor services at the optimum the wage setting equation reads as
1+vLH
+
LH LH;t
0 = ! LH
(
1)
LH
R
t
(A-9)
1
W
W
t 1
+ Et
!
WtLH
1
R
t W LH
W LH
h;t
LH
t
1
t
W
LH
Wt+1
1
W
Pt
+
WtLH
WtLH
1
1
WtLH1
1
R
t+1 W LH
WtLH
W
1
WtLH1
W
t 1
1
!
LH
Wt+1
1
t
1
W
Yt +
W
WtLH
Yt+1 :
which in steady state gives (??).
The …rst-order condition for wage setting for unskilled labor services, after having imposed
symmetry is
0 = ! LL
(
LL
(1
1+vLL
+
LL LL;t
LL
t
1) 1
LL
)
R
t
(A-10)
+
W LL
h;t
LL N R
t
WtLL
Pt
+
WtLL
1
W LL
1
W
W
t 1
+
(1
LL
)
R
t+1
+
LL N R
t+1
WtLL1
1
W LL
t
W
1
W
!
LL
Wt+1
WtLL
WtLL
1
1
1
!t
1
W
W
1
WtLL1
LL
Wt+1
1
t
W
Yt +
1
W
WtLL
Yt+1 :
In steady state the above condition becomes (16).
The …rst-order condition for wage setting for the atypical workers, after having imposed
30
symmetry is
1+vNA
+
NA NA;t
0 = ! NA
(
NA
1)
NR
t
(A-11)
WtNA
1
NR
t
W NA
1
W
W
t 1
+
W NA
h;t
NA
t
1
WtNS1
1
W
t
W
WtNA
W
W
t 1
!
NA
Wt+1
1
R
Et N
t+1 W NA
W NA
NA;t t
Pt
!
1
1
1
1
W
t
Yt +
NA
Wt+1
1
1
WtNS
WtNS1
W
WtNS
Yt+1 :
In steady state the above condition becomes (22).
Solution to the Intermediate Good Producers Problem
Given technology, the adjustment costs on price setting (27) and on labor inputs (28)-(31) and
Y
Pt (j)
Pt
the demand schedule for its own variety j; Yt (j) =
Yt …rm j will make choices about
the price and labor inputs, so as to maximize the present discounted value of future pro…ts.
At the optimum and under symmetry we have the optimal pricing decision equation which
describes the time path of domestic in‡ation
[(1
Y;t ) (1
P
t
1
P
t:
Y)
+
P Et
t
P
t+1
1
Y ] Yt +
t
1
1
P
P
t 1
R
t+1
R
t
+ M Ct
!
1
P
!
P
(A-12)
Yt +
t 1
t
P
t+1
1
P
Yt+1 = 0;
and the demand for unskilled and skilled employees, atypical workers and labor services provided
by self-employed workers are:
WtLL
1
Pt
L (1
LL
LYL;t (j)
LYL;t 1 (j)
L
subL
t +
W LL
f;t
[I
Y
(1
Yt (j)
G ) M Ct (j)
LCES;t (j) OHtL
1 Yt
1
LYL;t
1 (j)
+
Y;t )
LCES;t (j)
LYL;t (j)
R
t+1
R LL
t
31
+ (1
I
1
L
LYL;t+1 (j)
LYL;t (j)
Y
)] =
1
L
sLL ef
(A-13)
L 1
L
LL
1 Yt+1
+
LYL;t+1 (j)
LYL;t (j)2
;
WtLH
Pt
LYH;t (j)
LYH;t 1 (j)
1 Yt
1
LYH;t
1 (j)
WtNA
1
Pt
N YA;t (j)
N YA;t 1 (j)
WtNS
1+
Pt
W NS
f;t
(1
Y
1 Yt
R
t+1
R LH
t
+
W NA
f;t
A
subN
+
t
(1
Y;t )
1
N YA;t
=
N
1 (j)
Y;t )
I
1
L
Y
(1
Y;t )
sLH ef
(A-14)
L 1
L
LH
1 Yt+1
+
LYH;t+1 (j)
LYH;t (j)2
=
1
N
NCES;t (j)
N YA;t (j)
;
(A-15)
1
1
N
sNNS efNSN +
N YA;t+1 (j)
N YA;t (j)
Yt (j)
G ) M Ct (j)
NCES;t (j) OHtN
(1
)] =
1
L
LYH;t+1 (j)
LYH;t (j)
R
t+1
R NA
t
+
+ (1
LCES;t (j)
LYH;t (j)
Yt (j)
G ) M Ct (j)
NCES;t (j) OHtN
N (1
NA
[I
Yt (j)
G ) M Ct (j)
LCES;t (j) OHtL
L (1
LH
W LH
f;t
H
subL
+
t
1
1 Yt+1
N YA;t+1 (j)
N YA;t (j)2
NCES;t (j)
N YS;t (j)
1
N
:
1
N
sNS ef
(A-16)
NS
N YS;t (j)
N YS;t 1 (j)
1 Yt
1
N YS;t
1 (j)
R
t+1
R NS
t
+
N YS;t+1 (j)
N YS;t (j)
1 Yt+1
N YS;t+1 (j)
N YS;t (j)2
:
In steady state the above conditions correspond to (32) and (34)-(37), respectively.
Exporting and Importing Firms
The typical exporting …rm will set the exporting price PX;t (j); so as to maximize the expected
discounted value of future pro…ts, taking as given the adjustment cost (38), the exchange rate
PX;t (j)
PX;t
St and the world demand for good j EXPt (j) =
EXP
EXPt . At the optimum and
imposing symmetry, the price of goods sold in the foreign market obeys to the following law of
motion:
(1
EXP
+
where
EXP
EXP;t
Et
2
6
4
R
t+1
R
t
EXP )
EXP;t
1
EXP
St PX;t
+
Pt
3
7
15
EXP
t 1
2
6
4
(
= PX;t =PX;t
t)
1:
EXP;t+1
1
EXP
EXP
EXP
EXPt +
(A-17)
EXP;t
EXP
3
7
15
1
EXP
EXPt +
t 1
(
t)
EXP;t+1
1
EXP
EXP
EXPt+1 = 0;
In steady state the above condition becomes (39).
The importing …rm will set its price in local currency as a markup over the import price of
32
N 1
N
NS
+
intermediate goods produced abroad given the demand IM Pt (j) =
PM;t (j)
PtM
IM P
IM Pt and
the adjustment cost function (40). At the optimum, we have:
(1
IM P )
IM P;t
1
IM P
IM P
t 1
+
where
IM P;t
IM P
Et
R
t+1
R
t
= PM;t =PM;t
PM;t St Pt
+
Pt
Pt
!
1:
IM P;t+1
1 IM P
t
IM P;t
1
1
IM P
!t
IM P
IM P
(A-18)
IM Pt +
1
IM P;t+1
1 IM P
1
IM P
IM Pt +
IM P
t
IM P
IM Pt+1 = 0;
In steady state the above condition simpli…es to (41).
Solution to the Final Good Producers Problem
The typical …nal good producer i will set the price PE;t (i); so as to maximize the expected
discounted value of future pro…ts, taking as given the adjustment cost (47), the price of inE
PE;t (i)
PE;t
termediate goods and the demand for good i; Et (i) =
Et . At the optimum and
imposing symmetry, the price of goods sold in the foreign market obeys to the following law of
motion:
(1
E
E)
PE;t
+
Pt
E
t
1
E
+
where
E;t
= PE;t =PE;t
E
1:
t
E
E
t+1
1
Et +
!
E
t
1
1 Yt
E
t 1
R
t+1
R
t
E M CE;t
!
E
1
E
t
t 1
E
t+1
1
E
(A-19)
E
E
+
Yt+1 = 0
In steady state the above condition becomes (48).
Appendix B
Eq.1: The Euler equation of the Ricardian households
R
t
= Et
Rt
R
t+1
t+1
Eq.2: The Lagrangian multiplier of the Ricardian households
R
t
=
Pt
PC;t (1 +
1
C)
t
33
CtR
hC R CtR 1
Eq.3: Consumption of the Non-Ricardian households
Pt
CtN R =
1+
C
t
1
PC;t
Pt
+
1+
C
t
Pt
1+
C
t
Pt
1+
C
t
NA
t
W NA
h;t
sNA
W RtNA NA;t
sN R
LL
t
W LL
h;t
IN R LL sLL
W RtLL LL;t +
sN R
W LL
W RtLL
1
PC;t
IN R LL sLL
sN R
PC;t
sN A
PC;t sN R
2
indexationW
t
W RtNA
W NA
2
indexationW
t
T AXtN R + T rtN R +
W RtNA1
1
t
W RtLL1
!2
t
1
!2
Yt +
Yt
Eq. 4: The Lagrangian multiplier of Non-Ricardian households
NR
t
=
Pt
PC;t (1 +
C)
t
1
CtN R
hC N R CtN R1
Eq. 5: Aggregate consumption
Ct = sN R CtN R + (1
sN R )CtR
Eq. 6: Wage equation of self-employed labor services
(
NS
R
t W NS
+
R
t+1 W NS
1)
R
t
1
NS
t
W NS
h;t
W RtNS
indexationW
t
W RtNS1
NS
W Rt+1
indexationW
t+1
W RtNS
1+vN
W RtNS NS;t = ! NS NS NS;t S +
!
W RtNS
1 Yt
t
t+
indexationW
W RtNS1
t
!
NS
W Rt+1
1
Y
t+1
t+1
indexationW
W RtNS
t+1
t+1
Eq.7: Wage equation of skilled employed workers
(
LH
R
t W LH
+
R
t+1 W LH
1)
R
t
1
LH
t
W LH
h;t
W RtLH
indexationW
t
W RtLH1
LH
W Rt+1
indexationW
t+1
W RtLH
1+vL
W RtLH LH;t = ! LH LH LH;t H +
!
W RtLH
1 Yt
t
t+
indexationW
W RtLH1
t
!
LH
W Rt+1
1
Y
t+1
t+1
indexationW
W RtLH
t+1
34
t+1
Eq. 8: Wage equation of unskilled employed workers
(
INR
1) (1
LL
LL
R
t
)
+ INR
W LL
LL N R
t
1
INR
LL
(1
W RtLL
+
W LL (1
LL
W Rt+1
W RtLL
indexationW
t+1
INR
R
t
)
LL
+ INR
!
1 Yt
t
W RtLL1 (hLL )
indexationW
t
W LL
h;t
LL
t
t+1
1+vLL
+
LL LL;t
LL N R
t
W RtLL
t
W RtLL1
indexationW
t
NR
) R
t+1 + I
!
1 Yt+1
W RtLL LL;t = ! LL
LL N R
t+1
LL
W Rt+1
t+1
W RtLL )
indexationW
t+1
Eq. 9: The supply of atypical labor services
+
NA
NR
t
1)
1
NA
t
1+vN
W NA
h;t
W RtNA NA;t = ! NA NA NA;t A +
!
NA
W
R
W RtNA
NR
t
1
Y
N
t
t
t+
t
W A
indexationW
indexationW
W RtNA1
W RtNA1
t
t
!
NA
NA
W Rt+1
W Rt+1
NR
1
Y
N
t+1
t+1
t+1 W A
indexationW
W RtNA
indexationW
W RtNA
t+1
t+1
(
t+1
Eq. 10: labor aggregate
LNt = sLL LL;t + sLH LH;t + sNS NS;t + sNA NA;t
Eq. 11: The tradeable goods production function
Yt = Xt
Eq. 12: Production function of the intermediate-goods producers
Xt = At
h
LCES;t
OHtL
L
NCES;t
OHtN
N
uK
t Kt
1
L
N
i1
Ix
G
Eq. 13: Employed labor CES aggregate
1
L
LCES;t = sxLL (efLL LXL;t )
L 1
L
1
L
+ sxLH (efLH LXH;t )
L 1
L
L
L 1
Eq. 14: Self-employed and atypical labor CES aggregate
1
N
NCES;t = sxNS (efNS N XS;t )
N 1
N
35
+ sx
1
N
NA
(efNA N XA;t )
N 1
N
N
N 1
KGt G
Eq. 15: Real wage index of employed workers
W RtL
2
=4
W RtLL (1
sxLL
+sxLH (1
subtLL
+
LH
subtLH + tW
f;t
LL
tW
f;t ) [I
) [I
Y
Y
(1
(1
Y;t )
+ (1
Y;t ) + (1
I
Y
)]
1
1
LH
Y )] W Rt
I
L
(efLL )
L
L
(efLH )
1
L
Eq. 16: Real wage index of self-employed and atypical workers
W RtN
8
<
W RtNS
WNS
f;t
sxNS
1+
(1
Y;t )
h
=
NA
NA
: +sx
A
1 subN
+ W
(1
NA W Rt
t
f;t
1
N
N
1
(efNS )
+
i1 N
(efNA ) N
Y;t )
1
Eq. 17: The demand of skilled employed labor
W RtLH 1
L (1
IX
H
subL
+
t
W LH
f;t
[I
Y
(1
Y;t )
1
L
LH
Xt
sx (efLH )
LCES;t OH L
LXH;t
1
1 Yt
LH
LXH;t 1
LXH;t
G ) M Ct
+
R
t+1
R LH
t
LXH;t+1
LXH;t
1 Yt+1
+ (1
L 1
L
I
Y
)] =
LCES;t
LXH;t
1
L
+
+
1
LXH;t+1
2
LXH;t
Eq. 18: The demand of unskilled employed labor
W RtLL 1
L (1
IX
L
subL
t +
W LL
f;t
[I
Y
(1
Y;t )
1
L
LL
Xt
sx (efLL )
LCES;t OH L
LXL;t
1
1 Yt
LL
LXL;t 1
LXL;t
G ) M Ct
+
R
t+1
R LL
T
LXL;t+1
LXL;t
36
1 Yt+1
+ (1
L 1
L
I
Y
)] =
LCES;t
LXL;t
+
1
LXL;t+1
2
LXL;t
1
L
+
91
=
;
1
N
1
31
5
1
L
Eq. 19: The demand of self-employed labor
W RtNS 1 +
N
(1
IX
WNS
f;t
(1
Y;t )
1
N
NS
Xt
sx (efNS )
NCES;t OH N
N XS;t
1
1 Yt
NS
N XS;t 1
N XS;t
G ) M Ct
+
R
t+1
R NS
T
N XS;t+1
N XS;t
1 Yt+1
=
NCES;t
N XS;t
N 1
N
1
N
+
+
1
N XS;t+1
2
N XS;t
Eq. 20:The demand of atypical labor
W RtNA 1
N (1
IX
G ) M Ct
subN
t +
R
t+1
R NA
T
(1
Y;t )
1
Xt
NCES;t OH
N XA;t
NA
N XA;t 1
+
W NA
f;t
sxNNA (efNA )
N
N XA;t+1
N XA;t
1 Yt
1
N XA;t
1 Yt+1
=
N 1
N
NCES;t
N XA;t
1
N
+
+
1
N XA;t+1
2
N XA;t
Eq. 21: Equilibrium in the labor market, unskilled employed workers
LXL;t = sLL LL;t
Eq. 22: Equilibrium in the labor market, skilled employed workers
LXH;t = sLH LH;t
Eq. 23: Equilibrium in the labor market, self-employed workers
N XS;t = sNS NS;t
Eq. 24: Equilibrium in the labor market, atypical workers
N XA;t = sNA NA;t
Eq. 25: Real wage
W Rt =
W RtNA N XA;t + W RtNS N XS;t + W RtLL LXL;t + W RtLH LXH;t
LNt
37
Eq. 26: Physical capital accumulation equation
Kt+1 = (1
K ) Kt
+ It
Eq. 27: The investment equation
qt
1=
It
Kt
I
tcrtK
K
Eq. 28: The Tobin’s q
Et
R
t+1
R
t
qt = Et
2
I
t+1
t+1
4
I
2
R
t+1
R
t
I
t+1
R
It+1
R
Kt+1
K
K
K
t+1 )rt+1 ut+1
(1
t+1
K
!2
+
R
It+1
R
Kt+1
I
K
K
t+1 ut+1 K
K
!
R
It+1
R
Kt+1
+ qt+1 (1
+
uK
1
K)
uK
t+1
Eq. 29: The demand of capital
(1
k K
Y;t ) rt ut
=
Pt
(1
PtI
IX
G ) (1
N ) M Ct
L
Xt
Kt
Eq. 30: The in‡ation equation
(1
Y;t ) (1
t
px
+
px Et
R
t+1
R
t
Y ) Yt +
t
1 Yt
+
indexationPt
!
indexationPt
t+1
indexationPt+1
+M Ct
Y Yt
38
1 Yt+1
=0
t+1
indexationPt+1
+
+
1 +
uK
2
2
uK
t+1
3
2
1 5
Eq. 31: Real pro…ts
[I
Y
W RtNS (1
(1
Y;t )
Y;t )
+ (1
1+
WNS
f;t
P ROt = (1
Y;t ) Yt +
2
L
W RtLL 1 subL
t +
4
I Y )]
H
+W RtLH 1 subL
+
t
W RtNA (1
N XS;t
PtI K K
r u Kt
Y;t )
Pt t t
(1
LH
2
NS
2
px
1
N XS;t
N XS;t 1
1
LL
Yt
NA
LXH;t
subN
t +
1
1
N XA;t
N XA;t 1
2
W LH
f;t
W NA
f;t
3
5+
N XA;t +
Yt +
2
LXL;t
LXL;t 1
2
LXL;t
2
indexationPt
Yt
2
1
t
2
2
LXH;t
LXH;t 1
Y;t )
W LL
f;t
Yt +
2
1
Yt
Eq. 32: Accumulation of public capital
KGt+1 = IGt + (1
KG ) KGt
Eq. 33: The ‡ow budget constraint of the government in real terms NEW
BRt =
Rt
1
BRt
t
T AXt
PtC
PI
Gt + t IGt + T rt +
Pt
Pt
(LT AXt + T V ATt + KT AXt + P ROT AXt + BT AXt ) +
1+
+SU Bt
Eq. 34: Transfers
T rt = sN R T rtN R + (1
sN R )T rtR
Eq. 35: Labor taxes
LT AXt = sLL LLL;t W RtLL
sLH LLH ;t W RtLH
sNS ;t LNS ;t W RtNS
sNA LNA;t W RtNA
39
LL
t
WLL
h;t
+
LH
t
NS
t
NA
t
+
+
+
+
WLL
f;t
+
WLH
h;t
+
WLH
f;t
+
WNs
h;t
+
WNS
f;t
+
WNA
h;t
+
WNA
f;t
Eq. 36: Consumption taxes
C PC;t
t
Pt
T V ATt =
sN R CtN R + (1
sN R )CtR
Eq. 37: Capital taxes net of tax credit
KT AXt =
PtI
Pt
K
t
rtK
K
uK
t Kt
tcrtK
PtI
It
Pt
Eq. 38: Fiscal rule
T AXt = T AX + TB BRt
+ TD DRt + TY Yt
1
Y
Eq. 39: Lump-sum taxes levied on Ricardian households
T AXtR = 1
R
sN
T AX T AXt
Eq. 40: Lump-sum taxes levied on Non-Ricardian households
R
T AXtN R = sN
T AX T AXt
Eq. 41: Real de…cit
Rt
DRt =
1
1
BRt
1
+
t
+T rt
PtC
PI
Gt + t IGt +
Pt
Pt
T AXt +
(LT AXt + CT AXt + KT AXt + P ROT AXt + BT AXt ) + SU Bt
Eq. 42: Business tax
BT AXt =
Y;t Yt
I
Y
Y;t
Y;t
Y;t
h
h
1+
NS
f;t
sNS Lt;NS W RtNS + 1
sLL Lt;LL W RtLL 1
L
subL
t +
PI;t k k
u r Kt
Pt t t
40
W LL
t
A
subN
+
t
N
WA
f;t
i
sNA Lt;NA W RtNA +
+ sLH Lt;LH W RtLH 1
H
subL
+
t
W LH
t
i
+
Eq. 43: Resource constraint of the economy
Yt =
St PX;t
PI
PtC
(Gt + Ct ) + t (It + IGt ) +
EXPt
Pt
Pt
Pt
2
I
It
px
t
I Pt
+
1
Y
+
t
P
2
2 Pt Kt
indexationt
+
2
+sLL
W LL
+sLH
W LH
sNS
+
W NS
W RtNS
2
W RtNA
W NA
2
P
indexationIM
t
uK
t
1 +
t
!2
!2
1
uK
2
2
uK
t
1
2
2
!2
Rt 1
R
r
EXP
2
PtC
2 Pt
St PX;t
Pt
E
Kt +
C
t
C
indexationEXP
t
!2
C
indexationPt
St
S
Eq. 45: Indexation - Prices
41
p
t 1
1
p
s
2
EXP
t
t
y
Et
Et 1
indexationPt =
Yt +
Yt
Eq. 44: Taylor rule
Rt
=
R
2
1
Yt
IM Pt +
1
N XA;t
N XA;t 1
NA
Yt +
Yt +
2
IM P
t
PM;t
Pt
uK
1
W RtNA1
indexationW
t
1
t
Yt +
2
1
Yt +
1
t
W RtLH1
W RtNS1
indexationW
t
2
2
LXH;t
LXH;t 1
LH
Kt +
K
1
t
W RtLL1
W RtLH
indexationW
t
IM P
2
indexationW
t
2
N XS;t
1
N XS;t 1
!2
NS
Yt +
2
2
PtI
Pt
1
W RtLL
2
+sNA
+
2
LXL;t
LXL;t 1
LL
PM;t
IM Pt
Pt
1
r
C
1
Yt
1
EXPt
Eq. 46: Indexation - Wages
indexationW
t =
W
1
W
t 1
Eq. 47: Welfare function of Ricardian Household
R
W elf areR
= log CtR
t
+
(1
hC R C t
1
+
sNS
! N (Ns;t )vNs +
sN R s
1
I N R LL )sLL
vL
! LL LL;tL +
1 sN R
sLH
! L (LH;t )vLH + Et W elf areR
t+1
sN R H
1
Eq. 48: Welfare function of Non-Ricardian Household
sL
sNA
vN
vL
NR
! NA NA;tA +I N R LL L ! LL LL;tL +
1 )+
sN R
sN R
R
W elf areN
= log(CtN R hC N R C t
t
R
Et W elf areN
t+1
Eq. 49: Total welfare
R
W elf aret = sN R W elf areN
+ (1
t
sN R )W elf areR
t
Eq. 50 Final good production function
Et = (1
IM P )
1
IM P
(YH;t )
IM P 1
IM P
+
IM P
1
IM P
(IM Pt )
IM P 1
IM P
Eq. 51: Imports demand
IM Pt =
IM P
M CE;t
1
E;t
IM P
PM;t
Pt
IM P
Et
Eq. 52: Domestic demand of internal production
YH;t = (1
IM P )
42
M CE;t
1
E;t
IM P
Et
IM P
IM P 1
Eq. 53: CPI in‡ation dynamics
PC;t
Et
Pt
pe
+
e
R
t+1
R
t
E
C
t
1 Yt
indexationpt
C
t+1
indexationpt+1
1
!
PC;t
Et +
Pt
C
t
indexationpt
c
t+1
indexationpt+1
Yt+1 +
Eq. 54: CPI
C
t
PC;t
PC;t 1
=
Eq. 55: Indexation
indexationPt
C
=
1
p
p
t 1
Eq. 56: Exports demand
EXPt =
PX;t
PC;t
EXP
!
EXP
W Dt
Eq. 57: Imported good price level
PM;t =
IM P
PM;t 1
t
Eq. 58: Domestic …nal good price level
Pt =
t Pt 1
Eq. 59: Foreign …nal good price level
Pt =
t Pt 1
Eq. 60: Foreign consumption price index
PC;t =
C
t
43
PC;t
1
+
E M CE;t Et
=0
Eq. 61: Exchange rate (non-linear UIP)
St
R
t
R Rt
t+1
= Et
+ rpbrft
St+1
t+1
Eq. 62: Trade balance as a share of GDP
PM;t
IM Pt =Yt
Pt
St PX;t
EXPt
Pt
T BYt =
Eq. 63: Terms of trade
T OTt =
St PX;t
PM;t
RER =
St PtC
PtC
Eq. 64: Real exchange rate
Eq. 65: Current account
CAt =
St PX;t
EXPt
Pt
Rt
PM;t
IM Pt +
Pt
1
1 + rpbrft
t
1
St
BRtF
St 1
Eq. 66: Foreign assets net position in real terms
BRtF =
Rt
1
+ rpbrft
t
1
St
BRtF
St 1
1
+
St PX;t
EXPt
Pt
F
BRF
Eq. 67: Risk premium
rpbrft =
'F (eBRt
Eq. 68: Investement goods price level
PI;t = PC;t
Eq. 69: Investement goods in‡ation
I
t
=
PI;t
PI;t 1
Eq. 70: Export price
PX;t =
EXP
PX;t 1
t
44
1)
PM;t
IM Pt
Pt
1
Eq. 71: Import price in‡ation
R
t
"
PM;t
IM P ) Pt IM Pt +
(1
+
IM P
IM P
t
IM P
t
1 IM Pt indexation
IM P + (1
t
!
P
indexationIM
t
R
t+1
IM P Et
IM P
t+1
1 IM Pt+1
P
indexationIM
t+1
IM P;t )
St Pt
Pt
IM P IM Pt
IM P
t+1
P
indexationIM
t+1
#
+
=0
Eq. 72: Export price in‡ation
R
t
"
(1
EXP
+ Et
St PX;t
Pt EXPt +
EXP
EXP
t
t
1 EXPt indexation
EXP + (1
! t
indexationEXP
t
R
t+1 EXP
EXP )
EXP
t+1
1 EXPt+1
indexationEXP
t+1
IM P;t ) EXP EXPt
EXP
t+1
indexationEXP
t+1
=0
Eq. 73: Import price indexation
P
indexationIM
=
t
IM P
t 1
1
IM P
IM P
Eq. 74: Export price indexation
indexationEXP
=
t
EXP
t 1
1
EXP
EXP
Eq. 75: Capital utilization
(1
K K
t )rt
+
K
t K
uK
1
uK
2
uK
t
1 =0
Eq. 76: Subsidies
LH
NA
H
SU Bt = subtLL sLL LL;t W RtLL + subL
+ subN
t sNA NA ;t W Rt
t sLH LH;t W Rt
Eq. 77: Tax on pro…ts
P ROT AXt =
45
P RO
P ROt
t
#
+
Eq. 78: Willingness to work - Self-employed
1
W NS
h;t
NS
t
W RtNS = ! Ns
vNs
s
Ns;t
R
t
Eq. 79: Unemployment - Self-employed
u
Ns;t
s
Ns;t
Ns;t
=
s
Ns;t
Eq. 80: Willingness to work - Skilled employees
1
WH
h;t
LH
t
W RtLH = ! LH
LsH ;t
vLH
R
t
Eq. 81: Unemployment - Skilled employees
LuH;t
=
LsH;t
LH;t
LsH;t
Eq. 82: Willingness to work NR- Unskilled employees
1
LL
t
WL
h;t
W RtLL = ! LL
(LsL (N R))vLL
NR
t
Eq. 83: Willingness to work R- Unskilled employees
1
LL
t
WL
h;t
W RtLL = ! LL
LsL;t (R)
vLL
R
t
Eq. 84: Willingness to work- Unskilled employees
LsL;t = I N R
LL
LsL;t (N R) + (1
INR
Eq. 85: Unemployment - Unskilled employees
LuL;t =
LsL;t
LL;t
LsL;t
46
LL
)LsL;t (R)
Eq. 86: Willingness to work - Atypical
1
W NA
NA
t
h;t
W RtNA = ! NA
s
NA;t
vNA
NR
t
Eq. 87: Unemployment - Atypical
u
NA;t
=
s
NA;t
NA;t
s
NA;t
Eq. 88: Unemployment
U N EM Pt =
s +s
s
sLL LsL;t + sLH LsH;t + sNA NA;t
NS NS;t
(sLL LL;t + sLH LH;t + sNA NA;t + sNS NS;t )
s +s
s
sLL LsL;t + sLH LsH;t + sNA NA;t
NS NS;t
Eq. 89: Domestic absorption
Pt YH;t = Pt Yt
47
St PX;t EXPt
Table1a: Parametrization
Parameter
K
Description
Value
Discount factor
0.99
Depreciation rate of K
0.025
KG
G
Depreciation rate of
0.025
L
Production function parameter, LL and LH workers
0.35
N
Production function parameter, NS and NA workers
0.35
G
Production function parameter, public capital
0
IM P
Share of foreign goods in total consumption
0.26
EXP
Share of foreign goods in total consumption for the rest of the world
0.26
hC R
Habit parameter, Ricardian households
0.7
hC N R
Habit parameter, non-Ricardian households
0.3
E
Elasticity of substitution between …nal goods
2.65
Y
Elasticity of substitution between domestic intermediate goods
5
EXP
Elasticity of substitution between exported intermediate goods
5
IM P
Elasticity of substitution between imported intermediate goods
5
IM P
Elasticity of substitution between domestic and foreign intermediate varieties
1.1
P
Price backward indexation
1
W
Wage backward indexation
1
Steady-state in‡ation
1
48
Table 1b: Parametrization
Parameter
Description
Value
sLH
Share of skilled employees
0.11
sNS
Share of self-employed
0.21
sNA
Share of atypical workers
0.26
sNR
Share of non Ricardian households
0.26
L
Elasticity of substitution, skilled and unskilled employees
1.4
N
Elasticity of substitution, atypical and self-employed workers
1.4
LH
Elasticity of substitution, skilled employees
2.65
LL
Elasticity of substitution, unskilled employees
2.65
Ns
Elasticity of substitution, self-employed workers
2.65
vLH
Preference parameter, skilled employees
8.01
vLL
Preference parameter, unskilled employees
8.36
vNA
Preference parameter, atypical workers
12.76
vNs
Preference parameter, self-employed workers
8.00
C
Tax rate of consumption
0.17
K
Tax rate on physical capital
0.33
Y
Tax rate on business
0.04
LL
Average tax rate on unskilled employees
0.24
Social contributions on unskilled employees
0.09
Contributions levied on …rms, unskilled employees
0.33
Average tax rate on skilled employees
0.27
Social contributions on skilled employees
0.09
Contributions levied on …rms, skilled employees
0.33
Average tax rate on self-employed
0.26
Social contributions on self-employed
0.09
Contributions levied on …rms, self-employed
0.00
Average tax rate on atypical workers
0.24
Social contributions on atypical workers
0.09
Contributions levied on …rms, atypical workers
0.27
W LL
h
W LL
f
LH
W LH
h
W LH
f
NS
WNs
h
WNs
f
NA
WNA
h
WNA
f
49
Table 2: Macroeconomic Impact of 1% Markup Reduction in the Final Good Sector
Years
Output
Consumption
Investment
Labor
Labor - unskilled workers
Labor - skilled workers
Labor - self-employed workers
Labor - atypical workers
Real wages - total
Real wages - unskilled workers
Real wages - skilled workers
Real wages - self-employed workers
Real wages - atypical workers
Unemployment rate - total
Unemployment rate - unskilled workers
Unemployment rate - skilled workers
Unemployment rate - self-employed workers
Unemployment rate - atypical workers
Terms of trade
1
0.03
0.67
0.09
0.01
0.01
0.01
0.01
0.01
0.27
0.27
0.27
0.27
0.27
-0.66
-0.74
-0.74
-0.73
0.11
-0.14
2
0.11
1.46
0.41
0.03
0.04
0.03
0.03
0.03
-0.04
-0.04
-0.04
-0.03
-0.04
-1.03
-1.12
-1.11
-1.11
-0.06
-0.17
50
3
0.13
1.54
0.31
0.05
0.06
0.04
0.05
0.05
0.00
0.00
0.00
0.01
-0.01
-0.91
-0.99
-0.98
-0.98
-0.05
-0.04
4
0.15
1.55
0.34
0.07
0.08
0.06
0.06
0.07
0.03
0.02
0.02
0.04
0.01
-0.92
-1.01
-0.99
-0.99
-0.06
-0.07
5
0.17
1.58
0.36
0.09
0.10
0.07
0.08
0.08
0.02
0.02
0.02
0.04
0.01
-0.95
-1.04
-1.02
-1.01
-0.08
-0.10
10
0.25
1.64
0.46
0.16
0.18
0.13
0.12
0.16
0.04
0.03
0.04
0.08
0.01
-1.05
-1.15
-1.12
-1.09
-0.15
-0.20
20
0.35
1.74
0.63
0.23
0.26
0.21
0.15
0.29
0.07
0.06
0.08
0.14
0.01
-1.16
-1.28
-1.24
-1.16
-0.27
-0.31
Table 3: Macroeconomic Impact of 1% Markup Reduction in the Intermediate Good Sector
Years
Output
Consumption
Investment
Labor
Labor - unskilled workers
Labor - skilled workers
Labor - self-employed workers
Labor - atypical workers
Real wages - total
Real wages - unskilled workers
Real wages - skilled workers
Real wages - self-employed workers
Real wages - atypical workers
Unemployment rate - total
Unemployment rate - unskilled workers
Unemployment rate - skilled workers
Unemployment rate - self-employed workers
Unemployment rate - atypical workers
Terms of trade
1
0.18
0.40
-0.12
0.15
0.17
0.12
0.17
0.11
0.43
0.42
0.42
0.43
0.42
-0.68
-0.77
-0.74
-0.76
0.17
0.19
2
0.45
1.17
0.29
0.39
0.45
0.30
0.42
0.29
0.07
0.05
0.06
0.07
0.04
-1.44
-1.57
-1.50
-1.54
-0.26
-0.04
51
3
0.63
1.39
0.28
0.61
0.69
0.47
0.64
0.46
0.09
0.07
0.07
0.10
0.05
-1.61
-1.75
-1.65
-1.70
-0.41
-0.14
4
0.81
1.53
0.36
0.81
0.91
0.64
0.84
0.62
0.12
0.09
0.10
0.14
0.07
-1.85
-2.01
-1.89
-1.94
-0.56
-0.37
5
0.96
1.67
0.45
0.99
1.11
0.79
1.01
0.77
0.12
0.09
0.11
0.16
0.07
-2.10
-2.27
-2.13
-2.18
-0.71
-0.57
10
1.58
2.24
0.84
1.68
1.87
1.45
1.62
1.43
0.16
0.12
0.16
0.27
0.08
-3.05
-3.29
-3.08
-3.07
-1.36
-1.32
20
2.27
2.98
1.50
2.40
2.62
2.24
2.11
2.32
0.25
0.21
0.28
0.51
0.10
-4.12
-4.45
-4.22
-3.97
-2.22
-2.07
Table 4: Macroeconomic Impact of a Tax Shift from the Business to Consumption - 1% of
Output
Years
Output
Consumption
Investment
Labor
Labor - unskilled workers
Labor - skilled workers
Labor - self-employed workers
Labor - atypical workers
Real wages - total
Real wages - unskilled workers
Real wages - skilled workers
Real wages - self-employed workers
Real wages - atypical workers
Unemployment rate - total
Unemployment rate - unskilled workers
Unemployment rate - skilled workers
Unemployment rate - self-employed workers
Unemployment rate - atypical workers
Terms of trade
1
-0.06
-0.55
-0.70
0.07
0.13
0.08
0.00
0.02
0.89
0.91
0.91
0.91
0.90
-1.29
-1.53
-1.51
-1.48
0.84
0.10
2
0.16
0.45
0.11
0.21
0.35
0.22
0.05
0.06
-0.04
0.00
0.01
0.02
-0.01
-2.72
-3.03
-2.97
-2.89
-0.07
-0.23
52
3
0.23
0.60
-0.06
0.33
0.54
0.35
0.09
0.11
-0.05
0.01
0.02
0.04
-0.01
-2.64
-2.97
-2.89
-2.76
-0.10
-0.05
4
0.30
0.63
-0.03
0.43
0.70
0.46
0.12
0.15
-0.01
0.06
0.08
0.11
0.04
-2.73
-3.09
-2.98
-2.82
-0.12
-0.16
5
0.38
0.70
0.02
0.52
0.83
0.56
0.16
0.20
-0.03
0.06
0.07
0.11
0.03
-2.86
-3.24
-3.12
-2.91
-0.17
-0.26
10
0.63
0.93
0.18
0.85
1.28
0.96
0.29
0.40
-0.03
0.09
0.12
0.20
0.02
-3.24
-3.70
-3.54
-3.19
-0.38
-0.57
20
0.84
1.15
0.43
1.08
1.57
1.31
0.34
0.69
0.03
0.16
0.22
0.38
0.03
-3.52
-4.03
-3.87
-3.33
-0.66
-0.80
Table 5: Macroeconomic Impact of a Fiscal Devaluation - 1% of Output
Years
Output
Consumption
Investment
Labor
Labor - unskilled workers
Labor - skilled workers
Labor - self-employed workers
Labor - atypical workers
Real wages - total
Real wages - unskilled workers
Real wages - skilled workers
Real wages - self-employed workers
Real wages - atypical workers
Unemployment rate - total
Unemployment rate - unskilled workers
Unemployment rate - skilled workers
Unemployment rate - self-employed workers
Unemployment rate - atypical workers
Terms of trade
1
-0.04
-0.44
-0.84
0.13
0.19
0.12
0.01
0.14
0.99
1.02
1.03
1.03
1.02
-1.48
-1.73
-1.71
-1.66
0.79
0.16
2
0.26
0.78
0.07
0.35
0.49
0.31
0.07
0.38
-0.06
0.02
0.02
0.04
0.01
-3.14
-3.47
-3.40
-3.28
-0.37
-0.23
53
3
0.38
1.00
-0.10
0.54
0.75
0.49
0.13
0.59
-0.08
0.03
0.04
0.07
0.01
-3.12
-3.47
-3.35
-3.18
-0.57
-0.08
4
0.50
1.08
-0.05
0.72
0.98
0.66
0.19
0.80
-0.05
0.09
0.10
0.14
0.07
-3.29
-3.66
-3.51
-3.28
-0.74
-0.25
5
0.62
1.20
0.02
0.88
1.18
0.81
0.24
0.99
-0.08
0.09
0.10
0.15
0.06
-3.50
-3.89
-3.72
-3.44
-0.93
-0.40
10
1.05
1.62
0.26
1.46
1.86
1.41
0.46
1.76
-0.12
0.13
0.17
0.27
0.07
-4.20
-4.66
-4.44
-3.95
-1.70
-0.93
20
1.49
2.09
0.67
1.97
2.39
2.01
0.60
2.67
-0.07
0.22
0.31
0.51
0.10
-4.86
-5.36
-5.13
-4.35
-2.58
-1.39
Ministry of Economy and Finance
Department of the Treasury
Directorate I: Economic and Financial Analysis
Address:
Via XX Settembre, 97
00187 - Rome
Websites:
www.mef.gov.it
www.dt.mef.gov.it/it/
e-mail:
[email protected]
Telephone:
+39 06 47614202
+39 06 47614197
Fax:
+39 06 47821886