Empirical Economics

, Volume 49, Issue 1, pp 185–211 | Cite as

Estimation of banking technology under credit uncertainty

  • Emir MalikovEmail author
  • Diego Restrepo-Tobón
  • Subal C. Kumbhakar


Credit risk is crucial to understanding banks’ production technology and should be explicitly accounted for when modeling the latter. The banking literature has largely accounted for risk using ex-post realizations of banks’ uncertain outputs and the variables intended to capture risk. This is equivalent to estimating an ex-post realization of bank’s production technology which, however, may not reflect optimality conditions that banks seek to satisfy under uncertainty. The ex-post estimates of technology are likely to be biased and inconsistent, and one thus may call into question the reliability of the results regarding banks’ technological characteristics broadly reported in the literature. However, the extent to which these concerns are relevant for policy analysis is an empirical question. In this paper, we offer an alternative methodology to estimate banks’ production technology based on the ex-ante cost function. We model credit uncertainty explicitly by recognizing that bank managers minimize costs subject to given expected outputs and credit risk. We estimate unobservable expected outputs and associated credit risk levels from banks’ supply functions via nonparametric kernel methods. We apply this framework to estimate production technology of U.S. commercial banks during the period from 2001 to 2010 and contrast the new estimates with those based on the ex-post models widely employed in the literature.


Ex-ante cost function Production uncertainty Productivity Returns to scale Risk 

JEL Classification

C10 D81 G21 



Restrepo acknowledges financial support from the Colombian Fulbright Commission, the Colombian Administrative Department of Science, Technology and Innovation (Colciencias) and EAFIT University.


  1. Antle JM (1983) Testing the stochastic structure of production: a flexible moment-based approach. J Bus Econ Stat 1(3):192–201Google Scholar
  2. Berger AN, Humphrey DB (1997) Efficiency of financial institutions: international survey and directions for future research. Eur J Oper Res 98(2):175–212CrossRefGoogle Scholar
  3. Berger AN, Mester LJ (1997) Inside the black box: what explains differences in the efficiencies of financial institutions? J Bank Finance 21(7):895–947CrossRefGoogle Scholar
  4. Berger AN, Mester LJ (2003) Explaining the dramatic changes in performance of US banks: technological change, deregulation, and dynamic changes in competition. J Financial Intermed 12(1):57–95CrossRefGoogle Scholar
  5. Berger AN, Hanweck GA, Humphrey DB (1987) Competitive viability in banking: scale, scope, and product mix economies. J Monet Econ 20(3):501–520CrossRefGoogle Scholar
  6. Chavas JP (2004) Risk analysis in theory and practice. Elsevier, San DiegoGoogle Scholar
  7. Clark JA (1996) Economic cost, scale efficiency, and competitive viability in banking. J Money Credit Bank 28(3):342–364CrossRefGoogle Scholar
  8. Deaton A, Muellbauer J (1980) An almost ideal demand system. Am Econ Rev 70:312–326Google Scholar
  9. Denny M, Fussy M, Waverman L (1981) The measurement and interpretation of total factor productivity in regulated industries, with an application to Canadian Telecommunications. In: Cowing TG, Stevenson RE (eds) Productivity measurement in regulated industries, chap 8. Academic Press, New YorkGoogle Scholar
  10. Feldstein MS (1971) Production with uncertain technology: some economic and econometric implications. Int Econ Rev 12:27–38CrossRefGoogle Scholar
  11. Feng G, Serletis A (2009) Efficiency and productivity of the US banking industry, 1998–2005: evidence from the Fourier cost function satisfying global regularity conditions. J Appl Econom 24(1):105–138CrossRefGoogle Scholar
  12. Feng G, Serletis A (2010) Efficiency, technical change, and returns to scale in large US banks: panel data evidence from an output distance function satisfying theoretical regularity. J Bank Finance 34(1):127–138CrossRefGoogle Scholar
  13. Feng G, Zhang X (2012) Productivity and efficiency at large and community banks in the US: a Bayesian true random effects stochastic distance frontier analysis. J Bank Finance 36(7):1883–1895CrossRefGoogle Scholar
  14. Freixas X, Rochet J (2008) Microeconomics of Banking. MIT Press, CambridgeGoogle Scholar
  15. Hughes JP, Mester LJ (1993) A quality and risk-adjusted cost function for banks: evidence on the “too-big-to-fail doctrine. J Prod Anal 4(3):293–315CrossRefGoogle Scholar
  16. Hughes JP, Mester LJ (1998) Bank capitalization and cost: evidence of scale economies in risk management and signaling. Rev Econ Stat 80(2):314–325CrossRefGoogle Scholar
  17. Hughes JP, Mester LJ (2013) Who said large banks don’t experience scale economies? Evidence from a risk-return-driven cost function. J Financial Intermed 22(4):559–585CrossRefGoogle Scholar
  18. Hughes JP, Lang W, Mester LJ, Moon CG (1996) Efficient banking under interstate branching. J Money Credit Bank 28(4):1045–1071CrossRefGoogle Scholar
  19. Hughes JP, Lang W, Mester LJ, Moon CG (2000) Recovering risky technologies using the almost ideal demand system: an application to US banking. J Financial Serv Res 18(1):5–27CrossRefGoogle Scholar
  20. Hughes JP, Mester LJ, Moon CG (2001) Are scale economies in banking elusive or illusive?: Evidence obtained by incorporating capital structure and risk-taking into models of bank production. J Bank Finance 25(12):2169–2208CrossRefGoogle Scholar
  21. Just RE, Pope RD (1978) Stochastic specification of production functions and econometric implications. J Econom 7:67–86CrossRefGoogle Scholar
  22. Just RE, Pope RD (eds) (2002) A comprehensive assessment of the role of risk in US agriculture. Kluwer, NorwellGoogle Scholar
  23. Kumbhakar SC, Lovell CAK (2000) Stochastic frontier analysis. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  24. Kumbhakar SC, Lozano-Vivas A (2005) Deregulation and productivity: the case of Spanish banks. J Regul Econ 27:331–351CrossRefGoogle Scholar
  25. Li Q, Racine J (2004) Cross-validated local linear nonparametric regression. Statistica Sinica 14(2):485–512Google Scholar
  26. McAllister PH, McManus D (1993) Resolving the scale efficiency puzzle in banking. J Bank Finance 17(2):389–405CrossRefGoogle Scholar
  27. Moschini G (2001) Production risk and the estimation of ex-ante cost functions. J Econom 100(2):357–380CrossRefGoogle Scholar
  28. Pope RD, Chavas JP (1994) Cost functions under production uncertainty. Am J Agric Econ 76(2):196–204CrossRefGoogle Scholar
  29. Pope RD, Just RE (1996) Empirical implementation of ex ante cost functions. J Econom 72(1):231–249CrossRefGoogle Scholar
  30. Pope RD, Just RE (1998) Cost function estimation under risk aversion. Am J Agric Econ 80(2):296–302CrossRefGoogle Scholar
  31. Racine J, Li Q (2004) Nonparametric estimation of regression functions with both categorical and continuous data. J Econom 119(1):99–130CrossRefGoogle Scholar
  32. Restrepo-Tobón DA, Kumbhakar SC, Sun K (2013) Are US commercial banks too big? Working Paper, Binghamton UniversityGoogle Scholar
  33. Sealey CW, Lindley JT (1977) Inputs, outputs, and a theory of production and cost at depository financial institutions. J Finance 32(4):1251–1266CrossRefGoogle Scholar
  34. Shen CH, Chen YK, Kao LF, Yeh CY (2009) Bank liquidity risk and performance. Working PaperGoogle Scholar
  35. Solow RM (1957) Technical change and the aggregate production function. Rev Econ Stat 39(3):312–320CrossRefGoogle Scholar
  36. Wheelock DC, Wilson PW (2001) New evidence on returns to scale and product mix among US commercial banks. J Monet Econ 47(3):653–674CrossRefGoogle Scholar
  37. Wheelock DC, Wilson PW (2012) Do large banks have lower costs? New estimates of returns to scale for US banks. J Money Credit Bank 44(1):171–199CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Emir Malikov
    • 1
    • 2
    Email author
  • Diego Restrepo-Tobón
    • 3
  • Subal C. Kumbhakar
    • 4
  1. 1.Department of EconomicsState University of New York at BinghamtonBinghamtonUSA
  2. 2.Department of EconomicsSt. Lawrence UniversityCantonUSA
  3. 3.Department of FinanceEAFIT UniversityMedellínColombia
  4. 4.Department of EconomicsState University of New York at BinghamtonBinghamtonUSA

Personalised recommendations