Flexible Consumer Demand Functions and Linear Estimation: Reply

Abstract

We are grateful to Wohlgenant for pointing out that the approximation of utility by real income requires that the underlying (flexible) utility function be homothetic. Indeed Diewert's proof of correspondence between utility changes and real income changes (as measured by superlative index numbers) relies on homotheticity. We thus concur with Wohlgenant that the three functional forms proposed by us are best regarded as statistical demand functions integrable into an arbitrary neoclassical utility function only at some base point. However, it is not clear that this is the reason for implausible expenditure elasticities obtained in the TL model as we move from sample means. This functional form (and the other two used in the study) provide a flexible approximation to some true consumption-expenditure relationship. It is unlikely to give reasonable estimates of elasticities at expenditure levels which are less than half the mean or nearly twice as high. What is interesting is that elasticities for all the food grains decline as expenditure levels rise.