Estimation of derivates for additive separable models

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. Furthermore it is unclear how to estimate derivatives with this approach since it does not give a closed form for the estimator. Recently, an integration approach has been studied that allows for the derivation of a closed form for the estimator. This paper extends this approach to the simultaneous estimation of both the function and its derivatives by combining the integration procedure with a local polynomial approach. 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. It is shown that there is some evidence of increasing return to scale for larger farms.