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Nonparametric stochastic frontier estimation via profile

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  • Carlos Martins-Filho

    (Department of Economics, University of Colorado)

  • Feng Yao

    (Department of Economics, West Virginia University)

Abstract

We consider the estimation of a nonparametric stochastic frontier model with composite error density which is known up to a finite parameter vector. Our primary interest is on the estimation of the parameter vector, as it provides the basis for estimation of firm specific (in)efficiency. Our frontier model is similar to that of Fan et al. (1996), but here we extend their work in that: a) we establish the asymptotic properties of their estimation procedure, and b) propose and establish the asymptotic properties of an alternative estimator based on the maximization of a conditional profile likelihood function. The estimator proposed in Fan et al. (1996) is asymptotically normally distributed but has bias which does not vanish as the sample size n??. In contrast, our proposed estimator is asymptotically normally distributed and correctly centered at the true value of the parameter vector. In addition, our estimator is shown to be efficient in a broad class of semiparametric estimators. Our estimation procedure provides a fast converging alternative to the recently proposed estimator in Kumbhakar et al. (2007). A Monte Carlo study is performed to shed light on the finite sample properties of these competing estimators.

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Bibliographic Info

Paper provided by Department of Economics, West Virginia University in its series Working Papers with number 10-09.

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Length: 49 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:wvu:wpaper:10-09

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Keywords: stochastic frontier models; nonparametric frontiers; profile likelihood estimation.;

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References

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  1. Kumbhakar, Subal C. & Park, Byeong U. & Simar, Leopold & Tsionas, Efthymios G., 2007. "Nonparametric stochastic frontiers: A local maximum likelihood approach," Journal of Econometrics, Elsevier, Elsevier, vol. 137(1), pages 1-27, March.
  2. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 21(02), pages 358-389, April.
  3. Clifford Lam & Jianqing Fan, 2008. "Profile-kernel likelihood inference with diverging number of parameters," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 31548, London School of Economics and Political Science, LSE Library.
  4. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, Elsevier, vol. 46(1-2), pages 141-163.
  5. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, Elsevier, vol. 6(1), pages 21-37, July.
  6. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, Elsevier, vol. 106(1), pages 1-25, January.
  7. Carlos Martins-Filho & Feng Yao, 2010. "A note on some properties of a skew-normal density," Working Papers 10-10, Department of Economics, West Virginia University.
  8. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-44, June.
  9. Carlos Martins-Filho & Feng Yao, 2006. "A Note on the Use of V and U Statistics in Nonparametric Models of Regression," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 58(2), pages 389-406, June.
  10. Martins-Filho, Carlos & Yao, Feng, 2007. "Nonparametric frontier estimation via local linear regression," Journal of Econometrics, Elsevier, Elsevier, vol. 141(1), pages 283-319, November.
  11. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, Elsevier, vol. 19(2-3), pages 233-238, August.
  12. Fan, Yanqin & Li, Qi & Weersink, Alfons, 1996. "Semiparametric Estimation of Stochastic Production Frontier Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(4), pages 460-68, October.
  13. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 84(4), pages 655-76, August.
  14. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, Elsevier, vol. 140(2), pages 375-400, October.
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Cited by:
  1. Carlos Martins-Filho & Feng Yao, 2010. "A note on some properties of a skew-normal density," Working Papers 10-10, Department of Economics, West Virginia University.

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