GRAVITY WITH GRAVITAS: The Gravity Model

The empirical literature cited above pays no more than lip service to theoretical justification. We show in this section how taking the theory seriously provides a different model to estimate with a much more useful interpretation.
Anderson [1979] presented a theoretical foundation for the gravity model based on constant elasticity of substitution (CES) preferences and goods that are differentiated by region of origin. Subsequent extensions (Bergstrand [1989,1990], Dear-dorff [1998]) have preserved the CES preference structure and added monopolistic competition or a Hecksher-Ohlin structure to explain specialization. A contribution of this paper is our manipulation of the CES expenditure system to derive an operational gravity model with an elegantly simple form. On this basis we derive a decomposition of trade resistance into three intuitive components: (i) the bilateral trade barrier between region i and region j, (ii) i’s resistance to trade with all regions, and (iii) j’s resistance to trade with all regions.
The first building block of the gravity model is that all goods are differentiated by place of origin. Following Deardorff [1998], we assume that each region is specialized in the production of only one good. The supply of each good is fixed.
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The second building block is identical, homothetic preferences, appro imated by a CES utility function. If c*j is consumption by region j consumers of goods from region i, consumers in region j maximize
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subject to the budget constraint
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Here j is the elasticity of substitution between all goods, q* is a positive distribution parameter, + is the nominal income of region j residents, and p*j is the price of region i goods for region j consumers. Prices differ between locations due to trade costs that are not directly observable, and the main objective of the empirical work is to identify these costs. Let p* denote the exporter’s supply price, net of trade costs, and let t*j be the trade cost factor between i and j. Then p*j = p*t*j.