Nonparametric Estimation of Additive Models with Homogeneous Components

Abstract

The importance of homogeneity as a restriction on functional forms has been well recognized in economic theory. Imposing additive separability is also popular since many economics models become easier to interpret and estimate when the explanatory variables are additively separable. In this paper we combine the two restrictions and propose a two step nonparametric procedure for estimating additive models whose unknown component functions may be homogeneous of known degree. In the first step we obtain preliminary estimates of the components by imposing homogeneity on local linear fits. In the second step these pilot estimates are marginally integrated to produce estimators of the additive components which possess optimal rates of convergence. We derive the asyptotic theory of these two step estimators and illustrate their use on data colllected from livestock farms in Wisconsin.