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Nonparametric stochastic frontiers: a local maximum likelihood approach. (English) Zbl 1360.62131
Summary: This paper proposes a new approach to handle nonparametric stochastic frontier (SF) models. It is based on local maximum likelihood techniques. The model is presented as encompassing some anchorage parametric model in a nonparametric way. First, we derive asymptotic properties of the estimator for the general case (local linear approximations). Then the results are tailored to a SF model where the convoluted error term (efficiency plus noise) is the sum of a half normal and a normal random variable. The parametric anchorage model is a linear production function with a homoscedastic error term. The local approximation is linear for both the production function and the parameters of the error terms. The performance of our estimator is then established in finite samples using simulated data sets as well as with a cross-sectional data on US commercial banks. The methods appear to be robust, numerically stable and particularly useful for investigating a production process and the derived efficiency scores.

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62P20 Applications of statistics to economics
Full Text: DOI
[1] Aigner, D.J.; Lovell, C.A.K.; Schmidt, P., Formulation and estimation of stochastic frontier production function models, Journal of econometrics, 6, 21-37, (1977) · Zbl 0366.90026
[2] Aragon, Y., Daouia, A., Thomas-Agnan, C., 2002. Nonparametric frontier estimation: a conditional quantile-based approach. Discussion paper, GREMAQ et LSP, Université de Toulouse \(\langle\)http://www.univ-tlse1.fr/GREMAQ/Statistique/adt1202.pdf⟩. · Zbl 1062.62252
[3] Cazals, C.; Florens, J.P.; Simar, L., Nonparametric frontier estimation: a robust approach, Journal of econometrics, 106, 1-25, (2002) · Zbl 1051.62116
[4] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the inefficiency of decision making units, European journal of operational research, 2, 429-444, (1978) · Zbl 0416.90080
[5] Daouia, A., Simar, L., 2004. Nonparametric efficiency analysis: a multivariate conditional quantile approach. Journal of Econometrics, forthcoming. · Zbl 1247.91133
[6] Deprins, D.; Simar, L.; Tulkens, H., Measuring labor inefficiency in post offices, (), 243-267
[7] Fan, J.; Gijbels, I., Local polynomial modelling and its applications, (1996), Chapman & Hall London · Zbl 0873.62037
[8] Fan, J.; Heckman, N.E.; Wand, M.P., Local polynomial kernel regression for generalized linear models and quasi-likelihood functions, Journal of the American statistical association, 90, 141-150, (1995) · Zbl 0818.62036
[9] Fan, Y.; Li, Q.; Weersink, A., Semiparametric estimation of stochastic production frontier models, Journal of business and economic statistics, 14, 460-468, (1996)
[10] Farrell, M.J., The measurement of productive efficiency, Journal of the royal statistical society, A120, 253-281, (1957)
[11] Gozalo, P.; Linton, O., Local nonlinear least squares: using parametric information in nonparametric regression, Journal of econometrics, 99, 63-106, (2000) · Zbl 0999.62031
[12] Hall, P.; Simar, L., Estimating a changepoint, boundary or frontier in the presence of observation error, Journal of the American statistical association, 97, 523-534, (2002) · Zbl 1073.62521
[13] Jondrow, J.; Lovell, C.A.K.; Materov, I.S.; Schmidt, P., On the estimation of technical inefficiency in stochastic frontier production models, Journal of econometrics, 19, 233-238, (1982)
[14] Kumbhakar, S.C.; Lovell, C.A.K., Stochastic frontier analysis, (2000), Cambridge University Press New York · Zbl 0968.62080
[15] Kumbhakar, S.C., Tsionas, E.G., 2002. Nonparametric stochastic frontier models. Manuscript presented at the NAPWII, June 2002, Schenectady, New York.
[16] Kumbhakar, S.C.; Tsionas, E.G., The joint measurement of technical and allocative inefficiencies: an application of Bayesian inference in nonlinear random-effects models, Journal of the American statistical association, 100, 736-747, (2005) · Zbl 1117.62374
[17] Meeusen, W.; van den Broeck, J., Efficiency estimation from cobb – douglas production function with composed error, International economic review, 8, 435-444, (1977) · Zbl 0366.90025
[18] Park, B.U.; Simar, L., Efficient semiparametric estimation in a stochastic frontier model, Journal of the American statistical association, 89, 929-936, (1994) · Zbl 0804.62100
[19] Park, B.U.; Sickles, R.C.; Simar, L., Stochastic panel frontiers: a semiparametric approach, Journal of econometrics, 84, 273-301, (1998) · Zbl 1008.62718
[20] Park, B.U.; Sickles, R.C.; Simar, L., Semiparametric efficient estimation of AR(1) panel data models, Journal of econometrics, 117, 279-309, (2003) · Zbl 1138.62346
[21] Park, B.U., Sickles, R.C., Simar, L., 2006. Semiparametric efficient estimation in dynamic panel data models. Discussion 0315, Institut de Statistique, UCL, Belgium \(\langle\)http://www.stat.ucl.ac.be⟩; Journal of Econometrics, to be published.
[22] Simar, L.; Wilson, P.W., Statistical inference in nonparametric frontier models: the state of the art, Journal of productivity analysis, 13, 49-78, (2000)
[23] Tibshirani, R.; Hastie, T.J., Local likelihood estimation, Journal of the American statistical association, 82, 559-567, (1987) · Zbl 0626.62041
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