IDEAS home Printed from
   My bibliography  Save this article

Productivity and efficiency at large and community banks in the US: A Bayesian true random effects stochastic distance frontier analysis


  • Feng, Guohua
  • Zhang, Xiaohui


This paper compares the productivity and efficiency of large banks and community banks in the United States over the period 1997–2006. This comparison is performed by estimating a true random effects stochastic distance frontier model—a model that is capable of disentangling unobserved heterogeneity from inefficiency—within a Bayesian framework. We find that failure to consider unobserved heterogeneity results in a misleading ranking of banks and mismeasured technical efficiency, productivity growth, and returns to scale. Our results show that, compared with community banks, large banks have experienced much higher productivity growth and higher levels of returns to scale. Our estimates of total factor productivity growth show a clear downward trend for both large and community banks, and our decomposition of the output-distance-function-based Divisia productivity index indicates that technical change is the driving force behind this trend.

Suggested Citation

  • Feng, Guohua & Zhang, Xiaohui, 2012. "Productivity and efficiency at large and community banks in the US: A Bayesian true random effects stochastic distance frontier analysis," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1883-1895.
  • Handle: RePEc:eee:jbfina:v:36:y:2012:i:7:p:1883-1895 DOI: 10.1016/j.jbankfin.2012.02.008

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. van den Broeck, Julien & Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1994. "Stochastic frontier models : A Bayesian perspective," Journal of Econometrics, Elsevier, pages 273-303.
    2. Feng, Guohua & Serletis, Apostolos, 2010. "A primal Divisia technical change index based on the output distance function," Journal of Econometrics, Elsevier, pages 320-330.
    3. Berger, Allen N. & Mester, Loretta J., 2003. "Explaining the dramatic changes in performance of US banks: technological change, deregulation, and dynamic changes in competition," Journal of Financial Intermediation, Elsevier, vol. 12(1), pages 57-95, January.
    4. Cole, Rebel A. & Goldberg, Lawrence G. & White, Lawrence J., 2004. "Cookie Cutter vs. Character: The Micro Structure of Small Business Lending by Large and Small Banks," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(02), pages 227-251, June.
    5. O'Donnell, Christopher J. & Coelli, Timothy J., 2005. "A Bayesian approach to imposing curvature on distance functions," Journal of Econometrics, Elsevier, pages 493-523.
    6. Diewert, W. Erwin & Fox, Kevin J., 2008. "On the estimation of returns to scale, technical progress and monopolistic markups," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 174-193, July.
    7. D. W. Jorgenson & Z. Griliches, 1967. "The Explanation of Productivity Change," Review of Economic Studies, Oxford University Press, vol. 34(3), pages 249-283.
    8. Feng, Guohua & Serletis, Apostolos, 2010. "Efficiency, technical change, and returns to scale in large US banks: Panel data evidence from an output distance function satisfying theoretical regularity," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 127-138, January.
    9. Fernandez, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 1997. "On the use of panel data in stochastic frontier models with improper priors," Journal of Econometrics, Elsevier, vol. 79(1), pages 169-193, July.
    10. Stiroh, Kevin J., 2000. "How did bank holding companies prosper in the 1990s?," Journal of Banking & Finance, Elsevier, vol. 24(11), pages 1703-1745, November.
    11. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    12. Berger, Allen N. & Miller, Nathan H. & Petersen, Mitchell A. & Rajan, Raghuram G. & Stein, Jeremy C., 2005. "Does function follow organizational form? Evidence from the lending practices of large and small banks," Journal of Financial Economics, Elsevier, vol. 76(2), pages 237-269, May.
    13. Guohua Feng & Apostolos Serletis, 2009. "Efficiency and productivity of the US banking industry, 1998-2005: evidence from the Fourier cost function satisfying global regularity conditions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 105-138.
    14. Rosen, Richard J, 2003. " Is Three a Crowd? Competition among Regulators in Banking," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(6), pages 967-998, December.
    15. Mitchell A. Petersen & Raghuram G. Rajan, 2002. "Does Distance Still Matter? The Information Revolution in Small Business Lending," Journal of Finance, American Finance Association, vol. 57(6), pages 2533-2570, December.
    16. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    17. Luis Orea, 2002. "Parametric Decomposition of a Generalized Malmquist Productivity Index," Journal of Productivity Analysis, Springer, vol. 18(1), pages 5-22, July.
    18. Sealey, Calvin W, Jr & Lindley, James T, 1977. "Inputs, Outputs, and a Theory of Production and Cost at Depository Financial Institutions," Journal of Finance, American Finance Association, vol. 32(4), pages 1251-1266, September.
    19. Fare, Rolf & Shawna Grosskopf & Mary Norris & Zhongyang Zhang, 1994. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries," American Economic Review, American Economic Association, vol. 84(1), pages 66-83, March.
    20. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Diego Restrepo-Tobón & Subal Kumbhakar & Kai Sun, 2015. "Obelix vs. Asterix: Size of US commercial banks and its regulatory challenge," Journal of Regulatory Economics, Springer, vol. 48(2), pages 125-168, October.
    2. Kao, Chiang & Liu, Shiang-Tai, 2014. "Measuring performance improvement of Taiwanese commercial banks under uncertainty," European Journal of Operational Research, Elsevier, vol. 235(3), pages 755-764.
    3. Feng, Guohua & Gao, Jiti & Peng, Bin & Zhang, Xiaohui, 2017. "A varying-coefficient panel data model with fixed effects: Theory and an application to US commercial banks," Journal of Econometrics, Elsevier, vol. 196(1), pages 68-82.
    4. Chaohua Dong & Jiti Gao & Bin Peng, 2016. "Another Look at Single-Index Models Based on Series Estimation," Monash Econometrics and Business Statistics Working Papers 19/16, Monash University, Department of Econometrics and Business Statistics.
    5. Robert McKeown, 2017. "Where are the economies of scale in Canadian banking?," Working Papers 1380, Queen's University, Department of Economics.
    6. Emir Malikov & Subal C. Kumbhakar & Mike G. Tsionas, 2016. "A Cost System Approach to the Stochastic Directional Technology Distance Function with Undesirable Outputs: The Case of us Banks in 2001–2010," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1407-1429, November.
    7. Sarmiento Paipilla, N.M. & Galán, Jorge E., 2015. "The Influence of Risk-taking on Bank Efficiency : Evidence from Colombia," Discussion Paper 2015-036, Tilburg University, Center for Economic Research.
    8. repec:kap:jproda:v:48:y:2017:i:2:d:10.1007_s11123-017-0515-5 is not listed on IDEAS
    9. Emir Malikov & Diego Restrepo-Tobón & Subal Kumbhakar, 2015. "Estimation of banking technology under credit uncertainty," Empirical Economics, Springer, vol. 49(1), pages 185-211, August.
    10. Sarmiento, Miguel & Galán, Jorge E., 2014. "Heterogeneous effects of risk-taking on bank efficiency : a stochastic frontier model with random coefficients," DES - Working Papers. Statistics and Econometrics. WS ws142013, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Eskelinen, Juha & Kuosmanen, Timo, 2013. "Intertemporal efficiency analysis of sales teams of a bank: Stochastic semi-nonparametric approach," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5163-5175.
    12. Robert McKeown, 2017. "Costs, size and returns to scale among Canadian and U.S. commercial banks," Working Papers 1382, Queen's University, Department of Economics.
    13. Diego A. Restrepo-Tobón & Subal C. Kumbhakar & Kai Sun, 2013. "Are U.S. Commercial Banks Too Big?," DOCUMENTOS DE TRABAJO CIEF 010943, UNIVERSIDAD EAFIT.
    14. Diego Restrepo-Tobón & Subal Kumbhakar, 2015. "Nonparametric estimation of returns to scale using input distance functions: an application to large U.S. banks," Empirical Economics, Springer, vol. 48(1), pages 143-168, February.
    15. Galán, Jorge & Ramos, Sofía B. & Veiga, Helena, 2015. "An analysis of the dynamics of efficiency of mutual funds," DES - Working Papers. Statistics and Econometrics. WS ws1517, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. repec:eee:ememar:v:32:y:2017:i:c:p:52-73 is not listed on IDEAS
    17. Feng, Guohua & Zhang, Xiaohui, 2014. "Returns to scale at large banks in the US: A random coefficient stochastic frontier approach," Journal of Banking & Finance, Elsevier, vol. 39(C), pages 135-145.
    18. Cristina Bernini & Paola Brighi, 2012. "Modeling the effects of Geographical Expansion Strategies on the Italian Minor Banks' Efficiency," Working Paper series 72_12, Rimini Centre for Economic Analysis.

    More about this item


    Productivity; True random effects stochastic distance frontier; Bayesian estimation;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jbfina:v:36:y:2012:i:7:p:1883-1895. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.