A Model with Pairwise Differing Elasticities of Substitution

Abstract

After the theoretical chapters on the use of elasticities of substitution and on maximum likelihood estimation of nonlinear models with linear constraints on the functional form, the following chapters will be devoted to specification, estimation and testing around actual estimation-consistent import allocation models. We already argued in Chapter 2 that the widespread CES import allocation model could need improvement because it contained only one single relative price effect for all bilateral import demand equations. In terms of elasticities of substitution (ES), the ES are all equal and constant in this model. At the same time it was brought forward, however, that such an alternative model would only be feasible if it could be estimated with approximately the same ease as the CES model, and if it could be applied to a relatively large linkage model, i.e. a model with a large number of trade partners. Concerning estimation of the CES model, we saw that the method which was the least arbitrary in a number of respects would be the method of maximum likelihood. It would therefore not be an objection if our alternative model would have to be estimated by this method as well. Because we are dealing with estimation-consistent import allocation models which should satisfy linear constraints on the functional form, the theory developed in the previous chapter therefore is of direct use for the maximum likelihood estimation of these models.