## "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. This paper develops a new method of computing counterfactual equilibrium which works best for large and complex general equilibrium models, and particularly those models that use implicit demand models.

## "Estimation of an Implicit Additive Indirect Demand System" (Working Paper) (Slides)

(with Paul V. Preckel)

Preference structures in applied general equilibrium models are often limited to constant-elasticity-of-substitution (CES) forms due to the desire for global regularity. Hanoch (1975) uses indirect, implicit additive relationships—a generalization of the CES--to obtain more flexible demand relationships that are globally regular. These preference relationships unlink substitution effects from income effects in ways that go beyond relaxation of homotheticity, and are more flexible than their direct dual. However, the estimation of these models as demand systems has proven to be challenging, and most published work in this area has focused on estimation approaches that involve approximations or that cannot fully identify parameter values in the preference relationships. Our approach is direct, it avoids approximations, and it appears that parameters are identified. We demonstrate the estimation using the readily accessible Global Trade Analysis Project (GTAP) and the World Bank (International Comparison Program) databases, estimating the constant difference of elasticity or CDE directly in a maximum likelihood framework. In doing this, we show that the global regularity conditions stated in Hanoch (1975) can be slightly relaxed, and that the relaxed parametric conditions facilitate 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.## "Implicit Utility and the Canonical Gravity Model" (Working Paper) (Slides)

(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 structural estimation methods are unable to separately identify trade costs and the trade elasticity without incorporating external data. We demonstrate that theoretical structure is alone sufficient for identifying all of the structural parameters of the canonical constant elasticity of substitution (CES) gravity model. We accomplish this by adopting an implicitly indirect representation of utility and estimating structurally using a mathematical program with equilibrium constraints. Our estimate of the elasticity of substitution is much smaller than in much of the rest of the literature, an outcome that we attribute to Pigou’s Law, which ties income and substitution elasticities together in demand systems that assume additive preferences. This restriction is undesirable in demand systems, generally, and is a critical weakness for the canonical gravity model, a model that is commonly used to interpret the geographic trade pattern and to infer the welfare gains from trade.