Semiparametric indirect utility and consumer demand

A semiparametric model of consumer demand is considered. In the model, the indirect utility function is specified as a partially linear, where utility is nonparametric in expenditure and parametric (with fixedor varying-coefficients) in prices. Because the starting point is a model of indirect utility, rationality restrictions like homogeneity and Slutsky symmetry are easily imposed. The resulting model for expenditure shares (as functions of expenditures and prices) is locally given by a fraction whose numerator is partially linear, but whose denominator is nonconstant and given by the derivative of the numerator. The basic insight is that given a local polynomial model for the numerator, the denominator is given by a lower-order local polynomial. The model can thus be estimated using modified versions of local polynomial modeling techniques. For inference, a new asymmetric version of the wild bootstrap is introduced. Monte Carlo evidence that the proposed techniques work is provided as well as an implementation of the model on Canadian consumer expenditure and price micro-data.