## Structural Estimation of a Gravity Model of Trade with the Constant-Difference-of-Elasticities Preferences

This paper presents a general equilibrium gravity model of trade based on the preferences of the constant difference of elasticities of substitution. Hanoch (1975) illustrates its advantages in terms of parsimony and flexibility. It is the first parsimonious non-homothetic model introduced into the gravity model that both separates substitution effects from income effects and has non-constancy substitution elasticities. These features of the demand model—together with the structural estimation procedure devised in this paper—allow nesting several prominent theoretical motivations (e.g., the standard and non-homothetic CES models) for the gravity model, and exploring the merits of this more general model. They also allow identifying the elasticity of trade costs with respect to distance and asymmetric border coefficients from the elasticity of trade flows with respect to trade costs, that are not easily identified in most previous studies.

## Implicit Utility and the Canonical Gravity Model (work in progress)

(with Russell H. Hillberry)

The primary advantage of structural approaches to estimating the gravity model of trade is that they allow a transparent mapping of regression coefficients to structural parameters. Unfortunately, existing approaches are unable to separately identify trade costs and trade responses without using additional data. We demonstrate that theoretical structure is alone sufficient for identifying the constant elasticity of substitution parameter separately from trade costs. We adopt an implicitly indirect representation of utility and use a mathematical program with equilibrium constraints to structurally estimate the model. We apply the estimator to the canonical example of interregional trade in the U.S. and Canada. Our estimated substitution elasticity is 4.012 and the implied tariff-equivalent border cost is 49.1%.

## Estimation of an Implicit, Indirect Demand System (work in progress)

(with Paul V. Preckel)

Preference structures in applied general equilibrium models are often limited to constant-elasticity-of-substitution or CES forms due to the desire for global regularity. Hanoch [Hanoch, 1975. Production and Demand Models with Direct or Indirect Implicit Additivity. Econometrica, Vol. 43, No.3] uses implicit, additive relationships--a generalization of the CES--to obtain more flexible demand relationships (e.g., separation of substitution effects from income effects beyond the non-homotheticity and non-constancy substitution elasticities). However, the estimation of these models as demand systems has proven to be difficult and most published work in this area has focused on approaches that involve approximations. Here we use the Global Trade Analysis Project (GTAP) and the World Bank (International Comparison Program) databases to estimate an implicitly indirect demand relationship, the constant difference of elasticity or CDE, directly in a maximum likelihood framework. In doing this, we argue that its global regularity conditions stated in Hanoch (1975) have been slightly overstated, and that correcting these conditions facilitates estimation. We introduce a normalization scheme that is beneficial for the scaling of the parameter values and which appears to have little impact on the

*economic performance*of the estimated system.