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Estimation of derivates for additive separable models

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  • Severance-Lossin, E.
  • Sperlich, Stefan

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. 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.

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  • Severance-Lossin, E. & Sperlich, Stefan, 1997. "Estimation of derivates for additive separable models," SFB 373 Discussion Papers 1997,30, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199730
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    1. Härdle, Wolfgang & Linton, O., 1995. "Nonparametric Regression," SFB 373 Discussion Papers 1995,29, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    8. Härdle, Wolfgang & Tsybakov, A. B., 1994. "Additive Nonparametric Regression on Principal Components," SFB 373 Discussion Papers 1994,39, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    2. Stefan Profit & Stefan Sperlich, 2004. "Non-uniformity of job-matching in a transition economy - A nonparametric analysis for the Czech Republic," Applied Economics, Taylor & Francis Journals, vol. 36(7), pages 695-714.

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