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 MOTIVATION 1 THE MODEL 2 DEMAND SIDE 3 SUPPLY SIDE 4 TRADE AND GOVERNMENT 5 EQUILIBRIUM CONDITIONS AND RESULTS 6 CONCLUSIONS 7 AKNOWLEDGEMENTS 8
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 Prob r ′ ); the utility functions depend positively on 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 ( l r ′ 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: � P r ′ r ′ α − t j α / ω � σ K ∗ dem = Y ∗ ; j r ′ j w K � P r ′ r ′ (1 − α ) − t ( j )(1 − α ) / ω � σ L ∗ dem = Y ∗ ; r ′ j r ′ w L � ρ � ρ � 1 / ρ � � � 1 Z ∗ dem K ∗ dem L ∗ dem = +(1 − α ) ; α r ′ j ω j j r ′ j � 1 − ρ � � ρ − 1 � ρ − 1 � w K + w L + t j � � � K ∗ dem L ∗ dem P r ′ r ′ j = Y ∗ α +(1 − α ) ω r ′ j j r ′ j (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: � α t ( t j − ψ e ) � σ t Z sup K ∗ tdem = r ′ r ′ w K � (1 − α t )( t j − ψ e ) � σ t Z sup (2) L ∗ tdem = r ′ r ′ w L ψ e t j = σ t − 1
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: � � P r ′ rj = 1+ τ r ′ rj · P r ′ r ′ j . where 1. τ r ′ rj = t j D r ′ r 2. P rr ′ j = p r ′ 1 � � ∑ r ′ β r ′ j ′ P 1 − η 1 − η 3. P r ′ = p j ′ = r ′ rj ′ ◮ 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: � w K (1 − α t ) � α t L tdem L Gdem = 1 w L ψ e ; r ′ w L α t 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: � D r ′′ r ′ + σ t − 1 � 1 X r ′′ r ′ j = l rr ′ j X rr ′ j ν · EXP l r ′′ r ′ j · D rr ′ ψ e + σ t − 1
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: 1 ( σ t − 1 ψ e + D rr ′ )( D r ′′ r ′ + σ t − 1) P r ′′ r ′ j X r ′′ r ′ j = l rr ′ j P rr ′ j X rr ′ j ν ν · EXP l r ′′ r ′ j · 1 ( σ t − 1 ψ e + D r ′′ r ′ )( D rr ′ ψ e + σ t − 1) ◮ The ratio of total LABOR EMPLOYMENT in production/ transport activities IN A REGION r ′ is: � σ � w σ t � t j − P r ′ ω j α − 1 ∑ j L dem � σ r ′ [( α t − 1)( ψ e − t j )] σ t ∑ J L wL r ′ j = j =1 Y r ′ j Z sup L Tdem ω j r ′
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)
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