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Statistical inference and nonparametric efficiency: A selective survey

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Abstract

The purpose of this paper is to provide a brief and selective survey of statistical inference in nonparametric, deterministic, linear programming-based frontier models. The survey starts with nonparametric regularity tests, sensitivity analysis, two-stage analysis with regression, and nonparametric statistical tests. It then turns to the more recent literature which shows that DEA-type estimators are maximum likelihood, and, more importantly the results concerning the asymptotic properties of these estimators. Also included is a discussion of recent attempts to employ resampling methods to derive empirical distributions for hypothesis testing.

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References

  • Afriat, S. (1972). “Efficiency Estimation of Production Functions.” International Economic Review 13:3, Oct, 568–598.

    Google Scholar 

  • Aigner, D.J. and S.F. Chu. (1968). “On Estimating the Industry Production Function.” American Economic Review 58, 226–239.

    Google Scholar 

  • Atkinson, S. and P. Wilson. (1995). “Comparing Mean Efficiency and Productivity Scores from Small Samples: A Bootstrap Methodology.” Journal of Productivity Analysis.

  • Banker, R.D. (1993). “Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foun- dation.” Management Science 39:10, 1265–1273.

    Google Scholar 

  • Banker, R.D. (1995). “Hypothesis Testing Using Data Envelopment Analysis.” Journal of Productivity Analysis, this volume.

  • Banker, R.D. and H. Chang. (1993). “Tests of Returns to Scale for Monotone Concave Production Functions.” Working paper.

  • Banker, R.D. and H. Chang. (1995). “A Simulation Study of Hypothesis Tests for Differences in Efficiencies.” International Journal of Production Economics..

  • Banker, R.D. and H. Chang. (1995). “A Simulation Study of Efficiency Differences for Multiple Outputs with Measurement Error.” Working paper.

  • Banker, R.D., H. Chang, and K.K. Sinha. (1994). “Tests to Evaluate the Separability or Substitutability of Inputs to a Production System.” Working paper.

  • Banker, R.D and A. Maindiratta. (1988). “Nonparametric Analysis of Technical and Allocative Efficiencies in Production.” Econometrica 56:6, 1315–1332.

    Google Scholar 

  • Banker, R.D. and A. Maindiratta. (1992). “Maximum Likelihood Estimation of Monotone and Concave Produc- tion Functions.” Journal of Productivity Analysis 3:4, 401–415.

    Google Scholar 

  • Charnes, A. and W.W. Cooper. (1963). “Deterministic Equivalence for Optimizing and Satisficing under Chance Constraints.” Operations Research 11:1, 18–39.

    Google Scholar 

  • Davison, A.C., D.V. Hinkley, and E. Schechtman. (1986). “Efficient Bootstrap Simulation.” Biometrika 73, 555–566.

    Google Scholar 

  • Deprins, D. and L. Simar. (1989a). “Estimation de Frontière Dèterministes avec Facteurs Exogéne d'Inefficacité”. Annales d'Economie et de Statistique 14, 117–150.

    Google Scholar 

  • Deprins, D. and L. Simar. (1989b). “Estimating Technical Inefficiencies with Corrections for Environmental Conditions with an Application to Railway Companies.” Annals of Public and Cooperative Economics 60:1, Jan–Mar, 81–102.

    Google Scholar 

  • Desai, Anad, Samuel J. Ratick, and Arie Schinnar. (1994). “DEA with Stochastic Variations in Data.” Working Paper Series 94-51, November, Max M. Fisher College of Business, The Ohio State University.

  • Diewert, W.E. and C. Parkan. (1983). “Linear Programming Tests of Regularity Conditions for Production Frontiers.” In W. Eichhorn, et al. (eds.), Quantitative Studies of Production and Prices, Würzburg and Vienna: Physica-Verlag.

    Google Scholar 

  • Efron, B.(1979). “Bootstrapping Methods: Another Look at the Jackknife.” Annals of Statistics 7, 1–26.

    Google Scholar 

  • Efron, B. and R.J. Tibshirani. (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.

    Google Scholar 

  • Färe, R. (1988). Fundamentals of Production Theory. Berlin: Springer-Verlag.

    Google Scholar 

  • Färe, R. and S. Grosskopf. “Nonparametric Tests of Regularity, Farrell Efficiency and Goodness-of-Fit.” Journal of Econometrics (forthcoming).

  • Färe, R., S. Grosskopf, and C.A.K. Lovell. (1985). The Measurement of Efficiency of Production. Boston: Kluwer-Nijhoff.

    Google Scholar 

  • Färe, R., S. Grosskopf, and C.A.K. Lovell. (1994). Production Frontiers. Cambridge, U.K.: Cambridge Univer- sity Press.

    Google Scholar 

  • Färe, R., S. Grosskopf, and W. Weber. (1989). “Measuring School District Performance.” Public Finance Quar- terly 17:4, 409–429.

    Google Scholar 

  • Färe, R. and G. Whittaker. (1995). “An Intermediate Input Model of Dairy Production Using Complex Survey Data.” Journal of Agricultural Economics 46:2, 201–213.

    Google Scholar 

  • Farrell, M.J.(1957). “The Measurement of Productive Efficiency.” Journal of the Royal Statistical Society, Series A, General, 125:2, 252–267.

    Google Scholar 

  • Ferner, G., S. Grosskopf, K. Hayes, and S. Yaisawarng. (1993). “Economies of Diversification in the Banking Industry: A Frontier Approach.” Journal of Monetary Economics 31, 229–249.

    Google Scholar 

  • Ferrier, G.D. and J.G. Hirschberg, (forthcoming). “Bootstrapping DEA Efficiency Scores: With an Application to Italian Banks.” Journal of Productivity Analysis.

  • Ferrier, G.D. and J.G. Hirschberg. (1995). “A Form of Stochastic Data Envelopment Analysis: Applying the Bootstrap to DEA.” Mimeo.

  • Grosskopf, S. and K. Hayes. (1993). “Local Public Sector Bureaucrats and Their Input Choices.” Journal of Urban Economics 33, 151–166.

    Google Scholar 

  • Grosskopf, S., K. Hayes, and J. Hirschberg. (1995). “Fiscal Stress and the Production of Public Safety: A Distance Function Approach.” Journal of Public Econimics 57, 277–296.

    Google Scholar 

  • Grosskopf, S. and S. Yaisawarng. (1990). “Economices of Scope in the Provision of Local Public Services.” National Tax Journal 43, 61–74.

    Google Scholar 

  • Gstach, Dieter. (1994). “The Right Answers from the Wrong Model?” Mimeo, Vienna University for Economics and Business Administration.

  • Hall, Peter, Wolfgang Härdle, and Leopold Simar. (1995). “Iterated Bootstrap with Applications to Frontier Models.” Journal of Productivity Analysis 6:1, 63–76.

    Google Scholar 

  • Hanoch, G. and M. Rothschild. (1972). “Testing the Assumptions of Production Theory: A Nonparametric Approach.” Journal of Political Economy 89:4, 878–892.

    Google Scholar 

  • Kittelsen, Sverre. (1995). “Monte Carlo Simulations of DEA Efficiency Measures and Hypothesis Tests.” In Using Data Envelopment Analysis to Measure Production Efficiency in the Public Sector. Thesis for the degree of Dr. Polit, at the Department of Economics, University of Oslo, also presented at the Georgia Productivity Workshop, October 1994.

  • Korostelev, A.P., L. Simar, and A.B. Tsybakov. (1992). “Efficient Estimation of Monotone Boundaries.” Discussion paper 9209, Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, to appear in Annals of Statistics.

  • Korostelev, A.P., L. Simar, and A.B. Tsybakov. (1995). “On Estimation of Monotone and Convex Boundaries.” Publications de l'Institut de Statistique de l'Université de Paris 39:1, 3–18.

    Google Scholar 

  • Land, K.C., C.A.K. Lovell, and S. Thore. (1988). “Chance-Constrained Efficiency Analysis.” Working paper, Department of Economics, University of North Carolina, Chapel Hill, NC.

    Google Scholar 

  • Land, K.C., C.A.K. Lovell, and S. Thore. (1993). “Chance-Constrained Data Envelopment Analysis.” Managerial and Decision Economics 14:6, 541–554.

    Google Scholar 

  • Lovell, C.A.K., L.C. Walters, and L.L. Wood. (1995). “Stratified Models of Education Production using Modified DEA and Regression Analysis.” In A. Charnes, W.W. Cooper, A.Y. Lewin, and L.M. Seiford, (eds). Data Envelopment Analysis: Theory, Methodology and Applications, Boston, Kluwer, 329–352.

    Google Scholar 

  • Olesen, O.B. and N.C. Petersen. (1995). “Chance Constrained Efficiency Evaluation.” Management Science 41:3, 442–457.

    Google Scholar 

  • Reifschneider, D. and R. Stevenson. (1991). “Systematic Departures from the Frontier: A Framework for the Analysis of Firm Inefficiency.” International Economic Review 32:3, 715–724.

    Google Scholar 

  • Schmidt, P. (1976). “On the Statistical Estimation of Parametric Frontier Production Functions.” Review of Economics and Statistics May, 238–239.

  • Seaver, B.L. and K.P. Triantis. (1989). “The Implications of Using Messy Data to Estimate Production-Frontier-Based Technical Efficiency Measures.” The Journal of Business and Economic Statistics 7, 49–59.

    Google Scholar 

  • Seaver, B.L. and K. P. Triantis. (1992). “A Fuzzy Clustering Approach Used in Evaluating Technical Efficiency Measures in Manufacturing.” Journal of Productivity Analysis 3:4, 337–363.

    Google Scholar 

  • Sengupta, J. (1987). “Data Envelopment Analysis for Efficiency Measurement in the Stochastic Case.” Computers and Operations Research 14:2, 117–129.

    Google Scholar 

  • Shephard, R.W. (1970). Theory of Cost and Production Functions. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Silverman, B.W.(1986). Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.

    Google Scholar 

  • Simar, L. (1992). “Estimating Efficiencies from Frontier Models with Panel Data: A Comparison of Parametric, Non-Parametric and Semi-Parametric Methods with Bootstrapping.” Journal of Productivity Analysis 3:1/2, 171–191.

    Google Scholar 

  • Simar, L., C.A.K. Lovell, and P. Vanden Eeckaut. (1994). “Stochastic Frontiers Incorporating Exogenous Influ- ences on Efficiency.” Discussion Paper 9403, Institut de Statistique, Université Catholique de Louvain, Belgium.

    Google Scholar 

  • Simar, L. and P.W. Wilson. (1995). “Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models.” Mimeo.

  • Sitter, R.R.(1992). “A Resampling Procedure for Complex Survey Data.” Journal of the American Statistical Association 87, 755–765.

    Google Scholar 

  • Thiry, B. and H. Tulkens. (1989). “Productivity, Efficiency and Technical Progress: Concepts and Measurement.” Annales de L'Economie Publique Sociale et Coopérative 60:1, 9–42.

    Google Scholar 

  • Thiry, B. and H. Tulkens. (1992). “Allowing for Technical Inefficiency in Parametric Estimates of Production Functions.” Journal of Productivity Analysis 3:1/2, 45–66.

    Google Scholar 

  • Thrall, R.M.(1988). “Classification Transitions Under Expansion of Inputs and Outputs in Data Envelopment Analysis.” Managerial and Decision Economics 10, 159–162.

    Google Scholar 

  • Timmer, C.P.(1971). “Using a Probabilistic Frontier Production Function to Measure Technical Efficiency.” Journal of Political Economy 79, 776–794.

    Google Scholar 

  • Valdmanis, V. (1992). “Sensitivity Analysis for DEA Models: An Empirical Example Using Public vs. NFP Hospitals.” Journal of Public Economics 48, 185–205.

    Google Scholar 

  • Varian, H.(1984). “The Nonparametric Approach to Production Analysis.” Econometrica 52:3, May, 579–597.

    Google Scholar 

  • Varian H.(1985). “Nonparametric Analysis of Optimizing Behavior with Measurement Error.” Journal of Econo-Metrics 30:1/2, 445–458.

    Google Scholar 

  • Varian, H. (1990). “Goodness-of-Fit in Demand Analysis.” Journal of Econometrics 46, 125–140.

    Google Scholar 

  • Wilson, Paul W. (1993). “Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Out- puts.” Journal of Business & Economic Statistics, 11:3, 319–323.

    Google Scholar 

  • Wilson, Paul W. (1995). “Detecting Influential Observations in Data Envelopment Analysis.” Journal of Productivity Analysis 6:1, 27–46.

    Google Scholar 

  • Wilson, Paul W. and Leopold Simar. (1995). “Bootstrap Estimation for Nonparametric Efficiency Estimates.” Mimeo.

  • Yaisawarng, S. (1989). “Recovering Short-Run Price Efficiency: Theory and Application.” Ph.D. dissertation, Southern Illinois University, Carbondale, IL.

    Google Scholar 

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Grosskopf, S. Statistical inference and nonparametric efficiency: A selective survey. J Prod Anal 7, 161–176 (1996). https://doi.org/10.1007/BF00157039

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