Linear and Quadratic Spline Models for Consumer Demand Functions

Abstract

This paper combines flexible functional form techniques, which provide local approximations to indirect preferenc es with respect to prices and incomes, with spline techniques that provide global approximations with respect to real income. The main technical problem is that real income or utility is an unobserved variable. Starting with the normalized quadratic expenditure functio n, linear and quadratic spline models are introduced theoretically and are empirically estimated using Japanese consumer data for four goods fo r the years 1970-87. The semi-nonparametric literature initiated by A. R. Gallant is reviewed and a limited semi-nonparametric property is claimed to hold for the spline models presented in the paper.