Measuring Firm Performance using Nonparametric Quantile-type Distances
When faced with multiple inputs X ∈ Rp + and outputs Y ∈ Rq +, traditional quantile regression of Y conditional on X = x for measuring economic efficiency in the output (input) direction is thwarted by the absence of a natural ordering of Euclidean space for dimensions q (p) greater than one. Daouia and Simar (2007) used nonstandard conditional quantiles to address this problem, conditioning on Y ≥ y (X ≤ x) in the output (input) orientation, but the resulting quantiles depend on the a priori chosen direction. This paper uses a dimensionless transformation of the (p + q)-dimensional production process to develop an alternative formulation of distance from a realization of (X, Y ) to the efficient support boundary, motivating a new, unconditional quantile frontier lying inside the joint support of (X, Y ), but near the full, efficient frontier. The interpretation is analogous to univariate quantiles and corrects some of the dis- appointing properties of the conditional quantile-based approach. By contrast with the latter, our approach determines a unique partial-quantile frontier independent of the chosen orientation (input, output, hyperbolic or directional distance). We prove that both the resulting efficiency score and its estimator share desirable monotonic- ity properties. Simple arguments from extreme-value theory are used to derive the asymptotic distributional properties of the corresponding empirical efficiency scores (both full and partial). The usefulness of the quantile-type estimator is shown from an infinitesimal and global robustness theory viewpoints via a comparison with the previous conditional quantile-based approach. A diagnostic tool is developed to find the appropriate quantile-order; in the literature to date, this trimming order has been fixed a priori. The methodology is used to analyze the performance of U.S. credit unions, where outliers are likely to affect traditional approaches.
|Date of creation:||Mar 2013|
|Date of revision:||Nov 2013|
|Publication status:||Published in Econometric Reviews, vol. 36, n°1-3, 2017, p. 156-181.|
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- Simar, Léopold & Vanhems, Anne, 2012.
"Probabilistic characterization of directional distances and their robust versions,"
Journal of Econometrics,
Elsevier, vol. 166(2), pages 342-354.
- Simar, Léopold & Vanhems, Anne, 2010. "Probabilistic Characterization of Directional Distances and their Robust Versions," TSE Working Papers 10-195, Toulouse School of Economics (TSE).
- Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
- W. Frame & Tim Coelli, 2001. "U.S. Financial Services Consolidation: The Case of Corporate Credit Unions," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 18(2), pages 229-241, March.
- Daouia, Abdelaati & Simar, Léopold, 2005. "Robust nonparametric estimators of monotone boundaries," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 311-331, October.
- Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(02), pages 358-389, April.
- Wilson, Paul W, 1993. "Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Outputs," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 319-323, July.
- A. Charnes & W. W. Cooper & E. Rhodes, 1981. "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through," Management Science, INFORMS, vol. 27(6), pages 668-697, June.
- Fried, Harold O. & Lovell, C. A. Knox & Yaisawarng, Suthathip, 1999. "The impact of mergers on credit union service provision," Journal of Banking & Finance, Elsevier, vol. 23(2-4), pages 367-386, February.
- Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2009. "Frontier Estimation and Extreme Values Theory," TSE Working Papers 10-165, Toulouse School of Economics (TSE).
- Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2009. "Frontier Estimation and Extreme Values Theory," IDEI Working Papers 611, Institut d'Économie Industrielle (IDEI), Toulouse.
- Smith, Donald J, 1984. " A Theoretic Framework for the Analysis of Credit Union Decision Making," Journal of Finance, American Finance Association, vol. 39(4), pages 1155-1168, September.
- George E. Battese & Greg S. Corra, 1977. "Estimation Of A Production Frontier Model: With Application To The Pastoral Zone Of Eastern Australia," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 21(3), pages 169-179, December.
- Scott Frame, W. & Karels, Gordon V. & McClatchey, Christine A., 2003. "Do credit unions use their tax advantage to benefit members? Evidence from a cost function," Review of Financial Economics, Elsevier, vol. 12(1), pages 35-47.
- Kenneth Spong, 2000. "Banking regulation : its purposes, implementation, and effects," Monograph, Federal Reserve Bank of Kansas City, number 2000bria.
- Kenneth Spong, 1994. "Banking regulation : its purpose, implementation, and effects," Monograph, Federal Reserve Bank of Kansas City, number 1994bria.
- Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1663-1697, December.
- Alois Kneip & Léopold Simar & Paul W. Wilson, 2006. "Asymptotics and Consistent Bootstraps for DEA Estimators in Non-parametric Frontier Models," Bonn Econ Discussion Papers bgse12_2006, University of Bonn, Germany.
- Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, vol. 24(1), pages 93-121, 09.
- Cinzia Daraio & Leopold Simar, 2003. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," LEM Papers Series 2003/17, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
- Léopold Simar, 2003. "Detecting Outliers in Frontier Models: A Simple Approach," Journal of Productivity Analysis, Springer, vol. 20(3), pages 391-424, November.
- Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
- Fried, Harold O. & Knox Lovell, C. A. & Eeckaut, Philippe Vanden, 1993. "Evaluating the performance of US credit unions," Journal of Banking & Finance, Elsevier, vol. 17(2-3), pages 251-265, April.
- Manuel Landajo & Javier de Andrés & Pedro Lorca, 2008. "Measuring firm performance by using linear and non-parametric quantile regressions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(2), pages 227-250.
- Goddard, John A. & McKillop, Donal G. & Wilson, John O. S., 2002. "The growth of US credit unions," Journal of Banking & Finance, Elsevier, vol. 26(12), pages 2327-2356.
- Battese, George E. & Corra, Greg S., 1977. "Estimation Of A Production Frontier Model: With Application To The Pastoral Zone Of Eastern Australia," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 21(03), December.
- Berger, Allen N, 2003. " The Economic Effects of Technological Progress: Evidence from the Banking Industry," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(2), pages 141-176, April.
- Allen N. Berger, 2002. "The economic effects of technological progress: evidence from the banking industry," Finance and Economics Discussion Series 2002-50, Board of Governors of the Federal Reserve System (U.S.).
- Wheelock, David C. & Wilson, Paul W., 2008. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 209-225, July.
- David C. Wheelock & Paul W. Wilson, 2007. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Working Papers 2005-027, Federal Reserve Bank of St. Louis.
- Hall, Peter & Nussbaum, Michael & Stern, Steven E., 1997. "On the Estimation of a Support Curve of Indeterminate Sharpness," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 204-232, August.
- Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
- Michael Falk, 1989. "A note on uniform asymptotic normality of intermediate order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(1), pages 19-29, March.
- Hwang, J. H. & Park, B. U. & Ryu, W., 2002. "Limit theorems for boundary function estimators," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 353-360, October.
- Bauer, Keldon, 2008. "Detecting abnormal credit union performance," Journal of Banking & Finance, Elsevier, vol. 32(4), pages 573-586, April.
- Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
- Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
- Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June. Full references (including those not matched with items on IDEAS)