Abstract
We study the construction of confidence intervals for efficiency levels of individual firms in stochastic frontier models with panel data. The focus is on bootstrapping and related methods. We start with a survey of various versions of the bootstrap. We also propose a simple parametric alternative in which one acts as if the␣identity of the best firm is known. Monte Carlo simulations indicate that the parametric method works better than the␣percentile bootstrap, but not as well as bootstrap methods that make bias corrections. All of these methods are valid␣only for large time-series sample size (T), and correspondingly none of the methods yields very accurate confidence intervals except when T is large enough that the identity of the best firm is clear. We also present empirical results for two well-known data sets.
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References
Battese GE, Coelli TJ (1988) Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data. J Econom 38:387–399
Coelli TJ (1995) Estimators and hypothesis tests for a stochastic frontier function: a Monte Carlo analysis. J Prod Anal 6:247–268
Cornwell C, Schmidt P, Sickles RC (1990) Production frontiers with cross-sectional and time-series variation in efficiency levels. J Econom 46:185–200
Davison AC, Hinkley DV (1997) Bootstrap methods and their applications. Cambridge University Press, Cambridge
Efron B (1982) The Jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics, Philadelphia
Efron B (1985) Bootstrap confidence intervals for a class of parametric problems. Biometrika 72:45–58
Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall, New York
Erwidodo (1990) Panel data analysis on farm-level efficiency, input demand and output supply of rice farming in West Java, Indonesia. PhD dissertation, Department of Agricultural Economics, Michigan State University
Hall P, Härdle W, Simar L (1993) On the inconsistency of bootstrap distribution estimators. Comput Stat Data Anal 16:11–18
Hall P, Härdle W, Simar L (1995) Iterated bootstrap with applications to frontier models. J Prod Anal 6:63–76
Horrace WC, Schmidt P (1996) Confidence statements for efficiency estimates from stochastic frontier models. J Prod Anal 7:257–282
Horrace WC, Schmidt P (2000) Multiple comparisons with the best with economic applications. J Appl Econom 15:1–26
Kim Y (1999) A study in estimation and inference on firm efficiency. PhD dissertation, Department of Economics, Michigan State University
Kim Y, Schmidt P (1999) Marginal comparisons with the best and the efficiency measurement problem. Unpublished Manuscript, Department of Economics, Michigan State University
Koop G, Osiewalski J, Steel MF (1997) Bayesian efficiency analysis through individual effects: hospital cost frontiers. J Econom 76:77–106
Kumbhakar SC (1996) Estimation of cost efficiency with heteroscedasticity: an application to electric utilities. J R Stat Soc D Stat 45:319–335
Lee YH (1991) Panel data models with multiplicative individual and time effects: application to compensation and frontier production functions. PhD dissertation, Department of Economics, Michigan State University
Lee YH, Schmidt P (1993) A production frontier model with flexible temporal variation in technical efficiency. In: Fried HO, Lovell CAK, Schmidt SS (eds) The measurement of productive efficiency. Oxford University Press, New York
Olson JA, Schmidt P, Waldman D (1980) A Monte Carlo study of estimators of stochastic frontier models. J Econom 13:67–82
Osiewalski J, Steel M (1998) Numerical tools for the Bayesian analysis of stochastic frontier models. J Prod Anal 10:103–117
Park BU, Simar L (1994) Efficient semiparametric estimation in a stochastic frontier model. J Am Stat Assoc 89:929–936
Pitt MM, Lee LF (1981) The measurement and sources of technical inefficiency in the Indonesian weaving industry. J Dev Econ 9:43–64
Schmidt P, Sickles RC (1984) Production frontiers and panel data. J Bus Econ Stat 2:367–374
Simar L (1992) Estimating efficiencies from frontier models with panel data: a comparison of parametric, non-parametric and semi-parametric methods with bootstrapping. J Prod Anal 3:171–203
Simar L, Wilson P (1998) Sensitivity of efficiency scores: how to bootstrap in nonparametric frontier models. Manage Sci 44:49–61
Simar L, Wilson P (2000) A general methodology for bootstrapping in nonparametric frontier models. J Appl Stat 27:779–802
Acknowledgments
Peter Schmidt gratefully acknowledges support under a Marie Curie Transfer of Knowledge Fellowship of the European Community’s Sixth Framework Program at the University of Crete during Fall 2006 under contract MTKD-CT-014288.
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Kim, M., Kim, Y. & Schmidt, P. On the accuracy of bootstrap confidence intervals for efficiency levels in stochastic frontier models with panel data. J Prod Anal 28, 165–181 (2007). https://doi.org/10.1007/s11123-007-0058-2
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DOI: https://doi.org/10.1007/s11123-007-0058-2