Document Type: Research Paper


1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran. Iran


In this paper we develop an approach that synthesizes the best features of the two main methods in the estimation of production efficiency. Speci cally, our approach first allows for statistical noise, similar to Stochastic frontier analysis, and second, it allows modeling multiple-inputs-multiple-outputs technologies without imposing parametric assumptions on production relationship, similar to what is done in non-parametric methods. The methodology is based on the theory of local maximum likelihood estimation and extends recent works of Kumbhakar et al. We will use local-spherical coordinate system to transform multi-input multi-output data to more exible system which we can use in our approach.We also illustrate the performance of our approach with simulated example.

[1] Aigner DJ., Lovell CAK., Schmidt P., 1997. Formulation and estimation of stochastic frontier models. Journal of Econometrics 6, 21-37.
[2] Atkinson SE., Primont D., 2002. Stochastic estimation of rm technology, and productivity growth using shadow cost and distance function. Journal of Econometrics 108, 203-225.
[3] Cazals C., Florens JP., Simar L., 2002. Nonparametric frontier estimation: a Robust approach. Journal of Econometrics 106, 1-25.
[4] Charnes A., Cooper WW., Rhodes E., 1978. Measuring the ineciency of decision making units. European Journal of Operational Research 2, 429-444.
[5] Chambers, R.G., Y.H. Chung, Fare R., 1998. Proft, Directional Distance Functions and Nerlovian Efficiency. Journal of Optimization Theory and Applications 98, 351{364.
[6] Daouia A, Simar L., 2007. Nonparametric efficiency analysis: a multivariate conditional quantile approach. Journal of Econometrics 140, 375-400.
[7] Daraio C, Simar L., 2007. Advanced Robust and nonparametric methods in efficiency analysis: methodology and applications. Springer, New York.
[8] Daraio C, Simar L., Wilson PW., 2013. Measuring Firm Performance using Nonparametric Quantile-type Distances. TSE Working Papers 13-412, Toulouse School of Economics (TSE).
[9] Debreu G., 1951. The coecient of resource utilization. Econometrica 19, 273-292
[10] Deprins D, Simar L, Tulkens H., 1984. Measuring labor inefficiency in post offices. In: Marchand M, Pestieau P, Tulkens H (eds) The performance of public enterprises: concepts and measurements.Amsterdam. North-Holland, pp 243-267.
[11] Fan J., Gijbels I., 1996. Local polynomial modelling and itsapplications. Chapman and Hall, London.
[12] Farrell MJ., 1957. The measurement of productive eciency. Journal of the Royal Statistical Society 120, 253-281.
[13] Fare, R., Grosskopf, S. and Lovell C.A.K., 1985. The Measurement of E ciency of Production. Boston, Kluwer-Nijho Publishing.
[14] Fare, R., and Grosskopf S., 2000. Theory and application of dierectional distance functions. Journal of Productivity Analysis 13, 93-103.
[15] Greene WH., 1990. A gamma-distributed stochastic frontier model. Journal of Econometrics 46, 141-163.
[16] Gstach D., 1998. Another approach to data envelopment analysis in noisy environments: DEA +. Journal of Productivity Analysis 9, 161-176.
[17] Hall P., Simar L., 2002. Estimating a changepoint, boundary or frontier in the presence of observation error. Journal of the American Statistical Association 97, 523-534.
[18] Jondrow J., Lovell CAK., Materov IS., Schmidt P., 1982. On the estimation of technical inefficiency in stochastic frontier production models. Journal of Econometrics 19, 233-238.
[19] Kneip A., Park BU., Simar L., 1998. A note on the convergence of nonparametric DEA estimators for production efficiency scores. Econometric theory 14, 783-793.
[20] Kneip A., Simar L., 1996. A general framework for frontier estimation with panel data. Journal of Productivity Analysis 7, 187-212
[21] Kneip A., Simar L., Wilson PW., 2008. Asymptotics and consistent bootstraps for DEA estimators in nonparametric frontier models. Econometric Theory 24, 1663-1697
[22] Kumbhakar SC., Park BU., Simar L., Tsionas EG., 2007. Nonparametric stochastic frontiers: a local likelihood approach. Journal of Econometrics 137, 1-27.
[23] Land KC., Lovell CAK., Thore S., 1993. Chance-constrained data envelopment analysis. Managerial and Decision Economics 14, 541-554.
[24] Lovell, K.C.A., Pastor J., 1995. Units invariant and translation invariant DEA models. Operations Research Letters 18, 147{151.
[25] Meeusen W., van den Broek J., 1977. Eciency estimation from Cobb-Douglas production function with composed error. International economic review 8, 435-444.
[26] Olesen OB., Petersen NC., 1995. Chance-constrained eciency evaluation. Management Science 41, 442-457.
[27] Park B., Simar L., Weiner Ch., 2000. The FDH estimator for productivity eciency scores: asymptotic
properties. Econometric Theory 16, 855-877.

[28] Park B., Simar L., Zelenyuk V. 2008. Local likelihood estimation of truncated regression and its partial
derivatives: theory and application. Journal of Econometrics 146, 185-198.
[29] Simar L., 2007. How to improve the performances of DEA/FDH estimators in the presence of noise. Journal
of Productivity Analysis 28, 183-201.
[30] Simar L., Vanhems A., Wilson PW. 2012. Statistical inference for DEA estimators of directional distances. European Journal of Operational Research 230, 853-864.
[31] Simar L., Wilson PW., 2008. Statistical inference in nonparametric frontier models: recent developments and
perspectives. In: Fried H, Lovell CAK, Schmidt S (eds) The measurement of productive efficiency, 2nd edn. Oxford University Press, Oxford.
[32] Simar L., Wilson PW., 2010. Inference from cross-sectional, stochastic frontier models. Econometric Reviews 29, 62-98.
[33] Stevenson RE., 1980. Likelihood functions for generalized stochastic frontier estimation. Journal of Econometrics 13, 57-66.
[34] Shephard, R.W., 1970. Theory of Cost and Production Function. Princeton University Press, Princeton, New-Jersey.