Estimation of an Implicit Additive Indirect Demand System

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.