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Estimation of Derivatives for Additive Separable Models

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  • Severance-Lossin, E.
  • Sperlich, S.
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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Suggested Citation

  • Severance-Lossin, E. & Sperlich, S., 1995. "Estimation of Derivatives for Additive Separable Models," SFB 373 Discussion Papers 1995,60, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199560
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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.
    2. 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.
    3. Paul J. Driscoll & Richard Boisvert, 1991. "Dual Second- and Third-Order Translog Models of Production," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 73(4), pages 1146-1160.
    4. Hardle, W. & Marron, J., 1989. "Bootstrap Simultaneous Error Bars For Nonparametric Regression," LIDAM Discussion Papers CORE 1989023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. Blackorby, Charles & Primont, Daniel & Russell, R. Robert, 1977. "On testing separability restrictions with flexible functional forms," Journal of Econometrics, Elsevier, vol. 5(2), pages 195-209, March.
    7. Guilkey, David K & Lovell, C A Knox & Sickles, Robin C, 1983. "A Comparison of the Performance of Three Flexible Functional Forms," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 591-616, October.
    8. 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.
    9. 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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