Spatial General Equilibrium Model with Discrete Choice of - - PowerPoint PPT Presentation

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

◮ Assessment of trade flows and trade policy across different locations or

countries, by making use of the EXACT AGGREGATION

◮ EMPLOYMENT and CONSUMPTION behavior across regions ◮ Compare EFFICIENCY between TRANSPORTS and MANUFACTURING

industries across regions

◮ Transportation POLICY assessment across regions (environmental taxes,

congestion, etc.)

◮ Assess PURCHASING POWER across regions ◮ 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:

◮ Discrete choice decisions in the consumer’s behavior among goods

produced in different locations - exact aggregation;

◮ Cost of transport among the regions; ◮ Transport supply and demand.

GENERIC SET-UP:

◮ Exogenous labor supply ◮ Transport cost applies only to inter-regional (freight) trade flows -

Intra-regional trade has zero-transport cost

◮ No intermediary consumption of commodities ◮ No re-sales of imported goods ◮ 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:

◮ A second level choice over varieties in each industry (e.g. for clothing:

made in Italy, made in France, made in USA, etc.)

◮ 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.

◮ Individuals have random utility functions over varieties (each variety r′ is

chosen with a probability Probr ′); the utility functions depend positively

• n variety’s intrinsic characteristics (quality) and negatively on the

variety’s market price;

◮ The choice of variety r′ 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

◮ Utility from choosing industry j′ 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 ′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′ 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

◮ The PRODUCTION firms - a representative CES technology for each

industry j

◮ The resulting factor demands and price at factory gate:

K ∗dem

j

= Y ∗

r ′j

Pr′r′α−tjα/ω

wK

σ ; L∗dem

r ′j

= Y ∗

r ′

Pr′r′(1−α)−t(j)(1−α)/ω

wL

σ ; Z ∗dem

r ′j

=

1 ωj

• α
• K ∗dem

j

ρ +(1−α)

• L∗dem

r ′j

ρ1/ρ ; Pr ′r ′j = wK +wL + tj

ω

• Y ∗

r ′j

1−ρ α

• K ∗dem

j

ρ−1 +(1−α)

• L∗dem

r ′j

ρ−1 (1)

MOTIVATION THE MODEL DEMAND SIDE SUPPLY SIDE TRADE AND GOVERNMENT EQUILIBRIUM CONDITIONS AND RESULTS CONCLUSIONS AKNOWLEDGEMENTS

SUPPLIERS: TRANSPORT FIRMS

◮ The representative TRANSPORT firm - a CES technology ◮ The resulting factor demands obtained from the firm’s total cost

minimization program are, at the optimum level: K ∗tdem

r ′

= Z sup

r ′

αt(tj−ψe)

wK

σt L∗tdem

r ′

= Z sup

r ′

(1−αt)(tj−ψe)

wL

σt 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

◮ TRADE prices across regions follow an iceberg-typology:

Pr ′rj =

• 1+τr ′rj
• ·Pr ′r ′j.

where

• 1. τr′rj = tjDr′r
• 2. Prr′j = pr′
• 3. Pr′ = pj′ =
• ∑r′ βr′j′P1−η

r′rj′

• 1

1−η

◮ 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

◮ The LABOR DEMAND on behalf of the government is therefore derived:

LGdem

r ′

= 1

wL ψe

wK (1−αt)

wLαt

αt Ltdem

r ′

;

MOTIVATION THE MODEL DEMAND SIDE SUPPLY SIDE TRADE AND GOVERNMENT EQUILIBRIUM CONDITIONS AND RESULTS CONCLUSIONS AKNOWLEDGEMENTS

EQUILIBRIUM CONDITIONS (1)

◮ Labor and capital market equilibriums for region r′ ◮ Goods and transport markets equilibriums across regions must clear ◮ The ratio between QUANTITY DEMAND of the same variety r′ across

two different consumer regions r,r′′ at variety level is:

Xrr′j Xr′′r′j = lrr′j lr′′r′j ·

Dr′′r′+σt−1

Drr′ψe+σt−1

1

ν ·EXP

MOTIVATION THE MODEL DEMAND SIDE SUPPLY SIDE TRADE AND GOVERNMENT EQUILIBRIUM CONDITIONS AND RESULTS CONCLUSIONS AKNOWLEDGEMENTS

EQUILIBRIUM CONDITIONS (2)

Moreover...

◮ The VALUE of aggregated variety demand ratio between two regions:

Prr′jXrr′j Pr′′r′jXr′′r′j = lrr′j lr′′r′j · ( σt −1

ψe +Drr′)(Dr′′r′+σt−1) 1 ν

( σt −1

ψe +Dr′′r′)(Drr′ψe+σt−1) 1 ν ·EXP

◮ The ratio of total LABOR EMPLOYMENT in production/ transport

activities IN A REGION r′ is:

∑j Ldem

r′j

LTdem

r′

=

w σt

L

• α−1

wL

σ Z sup

r′ [(αt−1)(ψe−tj)]σt ∑J

j=1 Yr ′j

tj−Pr′ωj

ωj

σ

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
• f 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

◮ Estimation method using Middle Asian data, in order to provide an

empirical support to the model

◮ Calibration and numerical results from a pre-simulation: 2-reg X 8-industry

X 2-variety model

◮ Introduction of the Intermediary consumption (in the firms’ production

function)

◮ Considering region-specific transport technologies ◮ Endogenous labor supply and the introduction of income effects through

the elastic demand of varieties

◮ 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

• rder to compare actual situation with an transport investments scenario. This

paper is a part of the preliminary analysis.

1Contact: Michela Sironi, michela.sironi@univr.it, Director of EUROMIDBRIDGE Project;

Federico Perali, federico.perali@univr.it, Director of Research, Department of Economic Sciences, University of Verona