MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
Spatial General Equilibrium Model with Discrete Choice of
Differentiated Products for the assessment of International
Trade. An application to the EuromidBridge project
Alexandrina Ioana Scorbureanu
ATINER Conference, Greece
Friday, 22 March 2008
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
ROADMAP
1
MOTIVATION
2
THE MODEL
3
DEMAND SIDE
4
SUPPLY SIDE
5
TRADE AND GOVERNMENT
6
EQUILIBRIUM CONDITIONS AND RESULTS
7
CONCLUSIONS
8
AKNOWLEDGEMENTS
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
MOTIVATION
I
Assessment of trade flows and trade policy across different locations or
countries, by making use of the EXACT AGGREGATION
I
EMPLOYMENT and CONSUMPTION behavior across regions
I
Compare EFFICIENCY between TRANSPORTS and MANUFACTURING
industries across regions
I
Transportation POLICY assessment across regions (environmental taxes,
congestion, etc.)
I
Assess PURCHASING POWER across regions
I
Evaluation of TRADE across regions: case EUROMIDBRIDGE
Mediterranean infrastructures project
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
GENERIC SET-UP
By DIFFERENCE with respect to the current literature:
I
Discrete choice decisions in the consumer’s behavior among goods
produced in different locations - exact aggregation;
I
Cost of transport among the regions;
I
Transport supply and demand.
GENERIC SET-UP:
I
Exogenous labor supply
I
Transport cost applies only to inter-regional (freight) trade flows Intra-regional trade has zero-transport cost
I
No intermediary consumption of commodities
I
No re-sales of imported goods
I
Competitive industries
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
A GEOGRAPHICAL REPRESENTATION
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
CONSUMER BEHAVIOR
The consumer computes a two-level choice before deciding his consumption
bundle:
I
A second level choice over varieties in each industry (e.g. for clothing:
made in Italy, made in France, made in USA, etc.)
I
A first-level choice over different industries (e.g. food, clothing,
apparel,etc.)
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
UTILITY FUNCTION AND PROBABILITY OF CHOICE.
THE DEMAND SYSTEM
Following McFadden(1981), we choose a particular form for the H-Generalized
Extreme Value function (applied to the nested logit choice system) and derive
probabilities of choice from linearly additive random utility functions.
I
I
Individuals have random utility functions over varieties (each variety r 0 is
chosen with a probability Probr 0 ); the utility functions depend positively
on variety’s intrinsic characteristics (quality) and negatively on the
variety’s market price;
The choice of variety r 0 over other varieties of goods is given by the
probability that this particular variety to be chosen among the sum of all
alternatives available on the market
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
UTILITY, CHOICE AND AGGREGATED DEMAND
I
I
I
I
Utility from choosing industry j 0 is then aggregated at the level of an
industry: consistent with the log-sum of expected utilities given by each
variety that form the analised industry
Aggregate conditional demand at variety level (lr 0 j individuals) is given by
the conditional probability associated to the variety choice multiplied by
the elasticity of the variety’s demand
Aggregate demand at industry level (Nrj 0 individuals) is easily obtained by
replacing the variety aggregate demand formula into the industrial
aggregation
Aggregate demand in a country (or region) is furthermore obtained by
summing up over industries the corresponding demand functions
aggregated at the local (regional) industry level
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
SUPPLIERS: PRODUCTION
I
The PRODUCTION firms - a representative CES technology for each
industry j
I
The resulting factor demands and price at factory gate:
h
i
P α−t α/ω σ
Kj∗dem = Yr∗0 j r 0 r 0 wK j
;
h
i
Pr 0 r 0 (1−α)−t(j)(1−α)/ω σ
∗dem
∗
Lr 0 j = Yr 0
;
wL
h ρ
ρ i1/ρ
Zr∗dem
= ω1j α Kj∗dem + (1 − α) L∗dem
;
0j
0
rj
1−ρ ρ−1
ρ−1 tj
∗
∗dem
∗dem
Pr 0 r 0 j = wK + wL + ω Yr 0 j
α Kj
+ (1 − α) Lr 0 j
(1)
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
SUPPLIERS: TRANSPORT FIRMS
I
The representative TRANSPORT firm - a CES technology
I
The resulting factor demands obtained from the firm’s total cost
minimization program are, at the optimum level:
h
i
αt (tj −ψe ) σt
Kr∗tdem
= Zrsup
0
0
h wK
i
sup (1−αt )(tj −ψe ) σt
L∗tdem
=
Z
0
0
r
r
wL
tj =
ψe
σt −1
(2)
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
TRADE COSTS AND THE GOVERNMENT
I
TRADE prices across regions follow an iceberg-typology:
Pr 0 rj = 1 + τr 0 rj · Pr 0 r 0 j .
where
1. τr 0 rj = tj Dr 0 r
2. Prr 0 j = pr 0
i 1
h
1−η
3. Pr 0 = pj 0 = ∑r 0 βr 0 j 0 Pr1−η
0 rj 0
I
In a simplified version, revenues from the exogenous environmental tax
applied to transports are used to pay labor - the only production factor
used by the Government
I
The LABOR DEMAND on behalf of the government is therefore derived:
wK (1−αt ) αt tdem
= w1L ψe
Lr 0 ;
LGdem
r0
wL αt
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
EQUILIBRIUM CONDITIONS (1)
I
Labor and capital market equilibriums for region r 0
I
Goods and transport markets equilibriums across regions must clear
I
The ratio between QUANTITY DEMAND of the same variety r 0 across
two different consumer regions r , r 00 at variety level is:
1
Xrr 0 j
lrr 0 j
Dr 00 r 0 +σt −1 ν
· EXP
X 00 0 = l 00 0 · D 0 ψe +σt −1
r r j
r r j
rr
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
EQUILIBRIUM CONDITIONS (2)
Moreover...
I
The VALUE of aggregated variety demand ratio between two regions:
Prr 0 j Xrr 0 j
Pr 00 r 0 j Xr 00 r 0 j
I
=
lrr 0 j
lr 00 r 0 j
1
·
( σψt −1
+Drr 0 )(Dr 00 r 0 +σt −1) ν
e
1
( σψt −1
+Dr 00 r 0 )(Drr 0 ψe +σt −1) ν
e
· EXP
The ratio of total LABOR EMPLOYMENT in production/ transport
activities IN A REGION r 0 is:
h
iσ
σ
h
iσ
wL t α−1
∑j Ldem
wL
r0j
J Y 0 tj −Pr 0 ωj
=
sup
∑
r
j
Tdem
σ
ωj
Z [(α −1)(ψ −t )] t j=1
L
r0
r0
t
e
j
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
CONCLUSIONS: Analytical results (1)
Our model provides the following analytical results:
1. ratio between value of consumption in any couple of regions is directly
correlated to the distance among regions, consumers preferences and
technologies used in manufacturing and transports industries;
2. ratio of transport price for a good across regions is determined by the ratio
of weighted averaged technology levels, where weights are determined
according to taste parameters and geographical location of firms
3. relative aggregated consumption of a country for a good increases with its
population level and decreases with its distance to the region in which the
good is produced;
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
CONCLUSIONS: Analytical results (2)
Some other additional analytical results are:
1. the ratio between the number of employees in transportation vs.production
increases as the distance (the transportation cost) across regions gets
higher (and countries get dispersed, for instance countries separated by the
Mediterranean Sea) or as the labor share in transportation increases, other
things being constant;
2. a region is more likely to export goods,if factor prices are high and it is
likely to export less, if distance between regions is high (transport cost is
higher)
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
FURTHER DEVELOPMENTS
I
Estimation method using Middle Asian data, in order to provide an
empirical support to the model
I
Calibration and numerical results from a pre-simulation: 2-reg X 8-industry
X 2-variety model
I
Introduction of the Intermediary consumption (in the firms’ production
function)
I
Considering region-specific transport technologies
I
Endogenous labor supply and the introduction of income effects through
the elastic demand of varieties
I
Consider different transport alternatives (sea, train, road, etc.)
MOTIVATION
THE MODEL
DEMAND SIDE
SUPPLY SIDE
TRADE AND GOVERNMENT
EQUILIBRIUM CONDITIONS AND RESULTS
CONCLUSIONS
AKNOWLEDGEMENTS
Aknowledgements1
EUROMIDBRIDGE is a transport corridor that provides direct links to Middle
Asia through existing infrastructures.Its gravitational center is at Verona
Freight Village (IT); it is linked with North European and Italian ports. It
continues through the Mediterranean Sea and enters Israel through Haifa port.
It continues in West Bank with Jenin industrial area and passes through
Jordan. A proposal has been made to assess new trade patterns among the
triangular-economy Israel-Palestine-Jordan under EUROMIDBRIDGE Project
scheme for 2007, that aims to evaluate actual trade potential in this area, in
order to compare actual situation with an transport investments scenario. This
paper is a part of the preliminary analysis.
1
Contact: Michela Sironi, [email protected], Director of EUROMIDBRIDGE Project;
Federico Perali, [email protected], Director of Research, Department of Economic Sciences,
University of Verona