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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.

Suggested Citation

  • 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. Paul Driscoll & Jeff Alwang & Anya McGuirk, 1992. "Testing Hypotheses of Functional Structure: Some Rules for Determining Flexibility of Restricted Production Models," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 74(1), pages 100-108.
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    6. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
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    1. 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.
    2. Lijian Yang & Wolfgang Hardle & Jens Nielsen, 1999. "Nonparametric Autoregression with Multiplicative Volatility and Additive mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 579-604, September.

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