Demand Systems with Unit Values: A Comparsion of Two Specifications

The availability of quantity information along with expenditure information in some household surveys allows the estimation of price reactions on the basis of unit values. We compare two specifications that have been proposed in this context by Deaton (1990) and Crawford et al. (1997) in order to take account of quality effects reflected in the unit values. Using simulated data for a two-good model, and keeping Marshallian elasticities fixed, we compare true and pseudo-true quantity and quality elasticities. Expenditure elasticities are close, but we find large differences in price elasticities and even sign reversals. This suggests that, while convenient in the situation where prices are not observable, these specifications lack flexibility.