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 asymptotic theory of these two-step estimators and illustrate their use on data collected from livestock farms in Wisconsin.
We thank Stefan Sperlich for providing us with the cleaned up data for the application in section 4, and Xenia Matschke for some useful comments. The authors also acknoweledge support by the Deutsche Forschungsgemeinschaft via SFB 373 at Humboldt University, Berlin.
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Härdle, W., Kim, W., Tripathi, G. (2001). Nonparametric Estimation of Additive Models with Homogeneous Components. In: Debreu, G., Neuefeind, W., Trockel, W. (eds) Economics Essays. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04623-4_11
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DOI: https://doi.org/10.1007/978-3-662-04623-4_11
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