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Robust, dynamic nonparametric benchmarking: the evolution of cost-productivity and efficiency among U.S. credit unions

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David C. Wheelock
Paul Wilson

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Abstract

This paper develops a new methodology for estimating cost-productivity and efficiency change that benchmarks the performance of individual firms against an estimated a-quantile. We adapt the estimators of Daouia and Simar (2007) and Wheelock and Wilson (2008a) to the estimation of cost efficiency where input prices and some outputs are fixed. Theoretical results demonstrate that our new estimator retains the root-n convergence, asymptotic normality, and other desirable properties of the original estimators. We show how the estimator can be used to construct a cost analog of the widely-used Malmquist productivity index. In addition, we propose a new decomposition of the Malmquist index to reveal the sources of changes in scale efficiency that affect changes in cost-productivity. We examine changes in the efficiency and productivity of U.S. credit unions between 1989 and 2006. We find that productivity increased among the largest 20-percent of credit unions, as well as for credit unions that grew substantially in size during 1989-2006.

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Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 2009-008.

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Date of creation: 2009
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Handle: RePEc:fip:fedlwp:2009-008

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Keywords: Credit unions;

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  1. 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 1155-68, September. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Bauer, Keldon, 2008. "Detecting abnormal credit union performance," Journal of Banking & Finance, Elsevier, vol. 32(4), pages 573-586, April. [Downloadable!] (restricted)
  5. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Leggett, Keith J. & Strand, Robert W., 2002. "Membership growth, multiple membership groups and agency control at credit unions," Review of Financial Economics, Elsevier, vol. 11(1), pages 37-46. [Downloadable!] (restricted)
  9. 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 141-76, April.
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  10. 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. [Downloadable!] (restricted)
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  11. 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. [Downloadable!] (restricted)
  12. Wheelock, David C. & Wilson, Paul W., 2001. "New evidence on returns to scale and product mix among U.S. commercial banks," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 653-674, June. [Downloadable!] (restricted)
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  13. W. Frame & Tim Coelli, 2001. "U.S. Financial Services Consolidation: The Case of Corporate Credit Unions," Review of Industrial Organization, Springer, vol. 18(2), pages 229-241, March. [Downloadable!] (restricted)
  14. 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. [Downloadable!]
  15. 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.
  16. 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. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
  18. 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. [Downloadable!] (restricted)
  19. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October. [Downloadable!] (restricted)
  20. 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. [Downloadable!] (restricted)
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