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Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations

  • David C. Wheelock
  • Paul Wilson

This paper examines the technical efficiency of U.S. Federal Reserve check processing offices over 1980–2003. We extend results from Park et al. (2000) and Daouia and Simar (2007) to develop an unconditional, hyperbolic, a-quantile estimator of efficiency. Our new estimator is fully non-parametric and robust with respect to outliers; when used to estimate distance to quantiles lying close to the full frontier, it is strongly consistent and converges at rate root-n, thus avoiding the curse of dimensionality that plagues data envelopment analysis (DEA) estimators. Our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices.

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Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 2005-027.

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Date of creation: 2007
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Handle: RePEc:fip:fedlwp:2005-027
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  1. David C. Wheelock & Paul W. Wilson, 1997. "New evidence on returns to scale and product mix among U.S. commercial banks," Working Papers 1997-003, Federal Reserve Bank of St. Louis.
  2. R. Alton Gilbert & David C. Wheelock & Paul W. Wilson, 2002. "New evidence on the Fed's productivity in providing payments services," Working Papers 2002-020, Federal Reserve Bank of St. Louis.
  3. David C. Wheelock & Paul Wilson, 2003. "Robust nonparametric estimation of efficiency and technical change in U.S. commercial banking," Working Papers 2003-037, Federal Reserve Bank of St. Louis.
  4. 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.
  5. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
  6. Simar, L. & Wilson, P.W., . "Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models," CORE Discussion Papers RP 1304, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Paul W. Bauer & Gary D. Ferrier, 1996. "Scale economies, cost efficiencies, and technological change in Federal Reserve payments processing," Proceedings, Board of Governors of the Federal Reserve System (U.S.), pages 1004-1044.
  8. Léopold Simar & Paul Wilson, 2000. "Statistical Inference in Nonparametric Frontier Models: The State of the Art," Journal of Productivity Analysis, Springer, vol. 13(1), pages 49-78, January.
  9. David C. Wheelock & Paul W. Wilson, 1995. "Why do banks disappear? The determinants of U.S. bank failures and acquisitions," Working Papers 1995-013, Federal Reserve Bank of St. Louis.
  10. Kneip, A & Park, B-U & Simar, L, 1996. "A Note on the Convergence of Nonparametric DEA Efficiency Measures," Papers 9603, Catholique de Louvain - Institut de statistique.
  11. 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.
  12. Ludwig Kuntz & Stefan Scholtes, 2000. "Measuring the Robustness of Empirical Efficiency Valuations," Management Science, INFORMS, vol. 46(6), pages 807-823, June.
  13. Bauer, Paul W. & Hancock, Diana, 1993. "The efficiency of the Federal Reserve in providing check processing services," Journal of Banking & Finance, Elsevier, vol. 17(2-3), pages 287-311, April.
  14. David C. Wheelock & Paul Wilson, 2004. "Trends in the efficiency of Federal Reserve check processing operations," Review, Federal Reserve Bank of St. Louis, issue Sep, pages 7-20.
  15. Allen N. Berger & David B. Humphrey, 1997. "Efficiency of financial institutions: international survey and directions for future research," Finance and Economics Discussion Series 1997-11, Board of Governors of the Federal Reserve System (U.S.).
  16. Geoffrey R. Gerdes & Jack K . Walton II, 2002. "The use of checks and other noncash payment instruments in the United States," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Aug, pages 360-374.
  17. Léopold Simar, 2003. "Detecting Outliers in Frontier Models: A Simple Approach," Journal of Productivity Analysis, Springer, vol. 20(3), pages 391-424, November.
  18. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
  19. Gallant, A. Ronald, 1982. "Unbiased determination of production technologies," Journal of Econometrics, Elsevier, vol. 20(2), pages 285-323, November.
  20. Barnett, William A. & Geweke, John & Wolfe, Michael, 1991. "Seminonparametric Bayesian estimation of the asymptotically ideal production model," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 5-50.
  21. Chalfant, James A. & Gallant, A. Ronald, 1985. "Estimating substitution elasticities with the Fourier cost function : Some Monte Carlo results," Journal of Econometrics, Elsevier, vol. 28(2), pages 205-222, May.
  22. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
  23. Gilbert, R. Alton & Wilson, Paul W., 1998. "Effects of Deregulation on the Productivity of Korean Banks," Journal of Economics and Business, Elsevier, vol. 50(2), pages 133-155, March.
  24. 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.
  25. Leopold Simar & Paul Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 779-802.
  26. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
  27. Cooper, Russel J & McLaren, Keith R, 1996. "A System of Demand Equations Satisfying Effectively Global Regularity Conditions," The Review of Economics and Statistics, MIT Press, vol. 78(2), pages 359-64, May.
  28. 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 319-23, July.
  29. 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.
  30. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(06), pages 855-877, December.
  31. 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.
  32. Wheelock, David C & Wilson, Paul W, 1995. "Explaining Bank Failures: Deposit Insurance, Regulation, and Efficiency," The Review of Economics and Statistics, MIT Press, vol. 77(4), pages 689-700, November.
  33. Guilkey, David K & Lovell, C A Knox & Sickles, Robin C, 1983. "A Comparison of the Performance of Three Flexible Functional Forms," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 591-616, October.
  34. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
  35. 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.
  36. Marcus Porembski & Kristina Breitenstein & Paul Alpar, 2005. "Visualizing Efficiency and Reference Relations in Data Envelopment Analysis with an Application to the Branches of a German Bank," Journal of Productivity Analysis, Springer, vol. 23(2), pages 203-221, 05.
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