Simar, Leopold and Zelenyuk, Valentin (2004): On testing equality of distributions of technical efficiency scores. Published in: Econometric Reviews , Vol. 25, No. 4 (December 2006): pp. 497522.

PDF
MPRA_paper_28003.pdf Download (212kB)  Preview 
Abstract
The challenge of the econometric problem in production efficiency analysis is that the very efficiency scores to be analyzed are unobserved. Recently, statistical properties have been discovered for a class of estimators popular in the literature, known as data envelopment analysis (DEA) approach. This opens a wide range of possibilities for a wellgrounded statistical inference about the true efficiency scores from their DEAestimates. In this paper we investigate possibility of using existing tests for equality of two distributions for such a context. Considering statistical complications pertinent to our context, we consider several approaches to adapt the Li (1996) test to the context and explore their performance in terms of the size and the power of the test in various Monte Carlo experiments. One of these approaches showed good performance both in the size and in the power, thus encouraging for its wide use in empirical studies.
Item Type:  MPRA Paper 

Original Title:  On testing equality of distributions of technical efficiency scores 
Language:  English 
Keywords:  Kernel Density Estimation and Tests, Bootstrap, DEA 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C24  Truncated and Censored Models ; Switching Regression Models ; Threshold Regression Models C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General D  Microeconomics > D2  Production and Organizations > D24  Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity 
Item ID:  28003 
Depositing User:  Valentin Zelenyuk 
Date Deposited:  11. Jan 2011 21:05 
Last Modified:  31. Dec 2015 01:12 
References:  Anderson, N., Hall, P., Titterington, D. M. (1994). Two sample test statistics for measuring discrepancies between two multivariate probability density functions using kernelbased density estimates. Journal of Multivariate Analysis 50:41–54. Debreu, G. (1951). The coefficient of resource utilization. Econometrica 19:273–292. Fan, Y., Ullah, A. (1999). On goodnessoffit tests for weakly dependent processes using kernel method. Journal of Nonparametric Statistics 11(1–3):337–60. Färe, R., Grosskopf, S. (1996). Intertemporal Production Frontiers: With Dynamic DEA. Boston: Kluwer Academic. Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society, Series A, General, 120, part 3:253–281. Gijbels, I., Mammen, E., Park, B. U., Simar, L. (1999). On estimation of monotone and concave frontier functions. Journal of the American Statistical Association 94:220–228. Hall, P. (1984). Central limit theorem for integrated square error of multivariate nonparametric density estimators. Annals of Statistics 14:1–16. Henderson, D. J., Russell, R. R. (2005). Human capital and convergence: a productionfrontier approach. International Economic Review 46:1167–1205. Henderson, D., Zelenyuk, V. (2004). Testing for catchingup: statistical analysis of DEA efficiency estimates. Discussion Paper #0431 of Institute of Statistics, University Catholique de Louvain, Belgium. Kneip, A., Park, B., Simar, L. (1998). A note on the convergence of nonparametric DEA estimators for production efficiency scores. Econometric Theory 14:783–793. Kneip, A., Simar, L., Wilson, P. (2003). Asymptotics for DEA estimators in nonparametric frontier models. Discussion Paper #0317, Institut de Statistique, Université Catholique de Louvain, Belgium. Korostelev, A., Simar, L., Tsybakov, A. B. (1995). On estimation of monotone and convex boundaries. Publ. Statist. Univ. Paris XXXIX 1:3–18. Kumar, S., Russell, R. R. (2002). Technological change, technological catchup, and capital deepening: relative contributions to growth and convergence. American Economic Review 92/3:527–548. Li, Q. (1996). Nonparametric testing of closeness between two unknown distribution functions. Econometric Reviews 15:261–274. Li, Q. (1999). Nonparametric testing the similarity of two unknown density functions: local power and bootstrap analysis. Nonparametric Statistics 11:189–213. Leibenstein, H. (1966). Allocative efficiency vs. ’Xefficiency. American Economic Review 56:392–415. Leibenstein, H., Maital, S. (1992). Empirical estimation and partitioning of Xinefficiency: a dataenvelopment approach. American Economic Review 82:428–433. Mammen, E. (1992). When Does Bootstrap Work? Asymptotic Results and Simulations. New York: Springer. Russell, R. R. (1990). Continuity of measures of technical efficiency. Journal of Economic Theory 51:255–267. Schuster, E. (1985). Incorporating support constraints into nonparametric estimators of densities. Communications in Statistics, Theory and Methods 14:1123–1136. Shephard, R. (1970). Theory of Cost and Production Functions. Princeton: Princeton University Press. Sheather, S., Jones, M. (1991). A reliable databased bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B 53:683–690. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman and Hall. Simar, L., Wilson, P. (1998). Sensitivity of efficiency scores: how to bootstrap in nonparametric frontier models. Management Science 44(1):49–61. Simar, L., Wilson, P. (2000a). A general methodology for bootstrapping in nonparametric frontier models. Journal of Applied Statistics 27:779–802. Simar, L., Wilson, P. (2000b). Statistical inference in nonparametric frontier models: the state of the art. Journal of Productivity Analysis 13:49–78. Simar, L., Wilson, P. (2006). Estimation and inference in twostage, semiparametric models of production processes. Journal of Econometrics, forthcoming. Simar, L., Zelenyuk, V. (2003). Statistical inference for aggregates of Farrelltype efficiencies. Discussion Paper #0324, Institut de Statistique, Université Catholique de Louvain, Belgium (Journal of Applied Econometrics, forthcoming). Zelenyuk, V., Zheka, V. (2006). Corporate governance and firm’s efficiency: the case of a transitional country, Ukraine. Journal of Productivity Analysis 25:143–168. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/28003 