Gravity Redux: Estimation of gravity-equation coefficients, elasticities of substitution, and general equilibrium comparative statics under asymmetric bilateral trade costs

A large class of models with CES utility and iceberg trade costs are now known to generate isomorphic “gravity equations.” Economic interpretations of these gravity equations vary in terms of two basic elements: the exporter's “mass” variable and the elasticity of trade with respect to true ad valorem “trade costs.” In this paper, we offer three potential contributions. First, we formulate and estimate a structural gravity equation based on the standard Krugman model of monopolistic competition and increasing returns. In the context of this model, a key parameter, the elasticity of substitution in consumption (σ), can be estimated precisely – even without observable true ad valorem trade-cost measures – using exporter's population and observable variables that influence trade costs. Second, in the empirical context of the well-known McCallum Canadian–U.S. “border puzzle,” our approach – allowing estimation of σ – yields considerably different general equilibrium comparative static trade-flow and economic welfare effects than those in an Armington endowment economy and assumed values of σ. Moreover, our predicted trade flows and GDPs are highly correlated with their respective observed values in the case of bilaterally symmetric or asymmetric Canadian–U.S. border effects. Third, a Monte Carlo analysis confirms unbiased and precise estimates of all coefficients, the elasticity of substitution, and comparative statics using our approach.