Estimation of Derivatives for Additive Separable Models

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Abstract
Additive regression models have a long history in nonparametric regression. It is well known that these models can be estimated at the one dimensional rate. Until recently, however, these models have been estimated by a backfitting procedure. Although the procedure converges quickly, its iterative nature makes analyzing its statistical properties difficult. Recently, an integration approach has been studied that allows for the derivation of a closed form for the estimator. Although they seem to be competing procedures for the same problem, their interpretation is in fact different. For none of them the quite important question in economics of derivative estimation has been investigated so far. This paper extends the approach of marginal integration to the simultaneous estimation of both the function and its derivatives by combining the integration procedure with a local polynomial approach. Thus, we additionally get a design adaptive estimator. Finally the merits of this procedure with respect to the estimation of a production function subject to separability conditions are discussed. The procedure is applied to livestock production data from Wisconsin, showing performance and handling of these methods in practice. We demonstrate e.g., that there is some evidence of increasing returns to scale for larger farms.This work was first revised in 1995. The research was supported by the Deutsche Forschungsgemeinschaft, SFB 373. The first author, E.Severance-Lossing died in 1996; the mentioned address refers to the second author.