Specification of household engel curves by nonparametric regression

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Abstract
This paper demonstrates the usefulness of nonparametric regression analysis for functional specfication of houshold Engel curves. After a brief review in section 2 of the literature on demand functions and equivalence scales and the functional specifications used, we first discuss in section 3 the issues of using income versus total expenditure, the origin and nature of the error terms in the light of utility theroy, and the interpretation of empirical demand functions. we shall reach the unorthodox view that household demand functions should be interpreted as conditional expectations relative to prices, household composition and either income or the conditional expectation of total expenditure (rather that total expenditure itself), where the latter conditional expectation is taken relative to income, prices and household composition. these two forms appear to be equivalent. this result also solves the simultaneity problem: the error variance matrix is no longer singular. Moreover, the errors are in general heteroskedastic. In section 4 we discuss the model and the data, and in section 5 we review the nonparametric kernal regression approach. In section 6 we derive the functional form of our household engel curves from nonparametric regression results, using the 1980 budget survey for the netherlands, in order to avoid model misspecification. thus the modl is derived directly from the data, without restricting its functional form. the nonparametric regression results are then translated to suitable parametric functional specifications, i.e., we choose parametric functional forms in accordance with the nanparametric regression results. these parametric specification are estimated by least squares, and various parameter restrictions are tested in order to simplify the models. this yields very simple final specifications of the household engel curves involved, namely linear functions of income and the number of children in two age groups.

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