IDEAS home Printed from
   My bibliography  Save this article

Spatial scale and product mix economies in U.S. banking with simultaneous spillover regimes


  • Glass, Anthony J.
  • Kenjegaliev, Amangeldi
  • Kenjegalieva, Karligash


The literature on bank scale economies focuses on the familiar type of returns to scale that are internal to the firm. Using a spatial approach, we analyze returns to scale for banks that are made up of external (i.e., spillover) economies. We extend ray-scale economies (RSE), expansion-path scale economies (EPSE) and expansion-path subadditivity (EPSU) to the spatial case. This involves introducing direct and composite and decomposed indirect RSE, EPSE and EPSU. These direct and indirect measures relate to the cost implications for a firm from a change in: (i) the firm’s output levels that are, as is standard, under its control; and (ii) the composite/decomposed spillover effect on the firm’s output levels, which is primarily, but not entirely, outside its control. We include an application to U.S. banks (1998–2015) that allows a bank to simultaneously belong to a number of spatial networks, which is typically what we observe for firms. For large banks we find constant direct RSE and EPSE, and zero composite indirect RSE and constant composite indirect EPSE. These composite indirect results do not counteract any policy suggestions from the direct RSE and EPSE concerning the debate on whether there should be size caps on very large U.S. banks. The direct RSE and EPSE for large banks suggest that these banks use society’s resources efficiently to provide their services. Size caps on very large banks would place downward pressure on these direct RSE and EPSE results, which could lead to large banks using society’s resources inefficiently.

Suggested Citation

  • Glass, Anthony J. & Kenjegaliev, Amangeldi & Kenjegalieva, Karligash, 2020. "Spatial scale and product mix economies in U.S. banking with simultaneous spillover regimes," European Journal of Operational Research, Elsevier, vol. 284(2), pages 693-711.
  • Handle: RePEc:eee:ejores:v:284:y:2020:i:2:p:693-711
    DOI: 10.1016/j.ejor.2019.12.036

    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. Vivas, Ana Lozano, 1997. "Profit efficiency for Spanish savings banks," European Journal of Operational Research, Elsevier, vol. 98(2), pages 381-394, April.
    2. Hirtle, Beverly, 2007. "The impact of network size on bank branch performance," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3782-3805, December.
    3. J. Paul Elhorst & Sandy Fréret, 2009. "Evidence Of Political Yardstick Competition In France Using A Two‐Regime Spatial Durbin Model With Fixed Effects," Journal of Regional Science, Wiley Blackwell, vol. 49(5), pages 931-951, December.
    4. Hughes, Joseph P. & Mester, Loretta J., 2013. "Who said large banks don’t experience scale economies? Evidence from a risk-return-driven cost function," Journal of Financial Intermediation, Elsevier, vol. 22(4), pages 559-585.
    5. Berger, Allen N. & Rosen, Richard J. & Udell, Gregory F., 2007. "Does market size structure affect competition? The case of small business lending," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 11-33, January.
    6. Baumol, William J, 1982. "Contestable Markets: An Uprising in the Theory of Industry Structure," American Economic Review, American Economic Association, vol. 72(1), pages 1-15, March.
    7. Kovner, Anna & Vickery, James & Zhou, Lily, 2015. "Do big banks have lower operating costs?," Journal of Financial Perspectives, EY Global FS Institute, vol. 3(1), pages 157-196.
    8. Berger, Allen N. & Roman, Raluca A., 2017. "Did Saving Wall Street Really Save Main Street? The Real Effects of TARP on Local Economic Conditions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(5), pages 1827-1867, October.
    9. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1973. "Transcendental Logarithmic Production Frontiers," The Review of Economics and Statistics, MIT Press, vol. 55(1), pages 28-45, February.
    10. Allen N. Berger & Asli Demirgüč-Kunt & Joseph G. Haubrich & Ross Levine, 2004. "Introduction: Bank concentration and competition: an evolution in the making," Proceedings, Federal Reserve Bank of Cleveland, pages 433-451.
    11. Bolt, Wilko & Humphrey, David, 2015. "Assessing bank competition for consumer loans," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 127-141.
    12. Pesaran M.H. & Schuermann T. & Weiner S.M., 2004. "Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 129-162, April.
    13. Qu, Xi & Lee, Lung-fei, 2015. "Estimating a spatial autoregressive model with an endogenous spatial weight matrix," Journal of Econometrics, Elsevier, vol. 184(2), pages 209-232.
    14. Berger, Allen N. & Hanweck, Gerald A. & Humphrey, David B., 1987. "Competitive viability in banking : Scale, scope, and product mix economies," Journal of Monetary Economics, Elsevier, vol. 20(3), pages 501-520, December.
    15. Berger, Allen N, et al, 2004. "Bank Concentration and Competition: An Evolution in the Making," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(3), pages 433-451, June.
    16. Anthony J. Glass & Karligash Kenjegalieva & Robin C. Sickles, 2016. "Returns to scale and curvature in the presence of spillovers: evidence from European countries," Oxford Economic Papers, Oxford University Press, vol. 68(1), pages 40-63.
    17. Wheelock, David C. & Wilson, Paul W., 2009. "Robust Nonparametric Quantile Estimation of Efficiency and Productivity Change in U.S. Commercial Banking, 1985–2004," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 354-368.
    18. Garrett, Thomas A. & Marsh, Thomas L., 2002. "The revenue impacts of cross-border lottery shopping in the presence of spatial autocorrelation," Regional Science and Urban Economics, Elsevier, vol. 32(4), pages 501-519, July.
    19. 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.
    20. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    21. Richard W. Fisher & Harvey Rosenblum, 2012. "Vanquishing too big to fail," Annual Report, Federal Reserve Bank of Dallas, pages 1-5.
    22. Ana Lozano-Vivas & Fotios Pasiouras, 2014. "Bank Productivity Change and Off-Balance-Sheet Activities Across Different Levels of Economic Development," Journal of Financial Services Research, Springer;Western Finance Association, vol. 46(3), pages 271-294, December.
    23. Elhorst, J. Paul & Lacombe, Donald J. & Piras, Gianfranco, 2012. "On model specification and parameter space definitions in higher order spatial econometric models," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 211-220.
    24. Bibi, Uzma & Balli, Hatice Ozer & Matthews, Claire D. & Tripe, David W.L., 2018. "Impact of gender and governance on microfinance efficiency," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 53(C), pages 307-319.
    25. Sam Langfield & Marco Pagano, 2016. "Bank bias in Europe: effects on systemic risk and growth," Economic Policy, CEPR;CES;MSH, vol. 31(85), pages 51-106.
    26. Bera, Anil K. & Doğan, Osman & Taşpınar, Süleyman, 2018. "Simple tests for endogeneity of spatial weights matrices," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 130-142.
    27. David C. Wheelock & Paul W. Wilson, 2018. "The evolution of scale economies in US banking," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 16-28, January.
    28. Asmild, Mette & Matthews, Kent, 2012. "Multi-directional efficiency analysis of efficiency patterns in Chinese banks 1997–2008," European Journal of Operational Research, Elsevier, vol. 219(2), pages 434-441.
    29. Glass, Anthony & Kenjegalieva, Karligash & Paez-Farrell, Juan, 2013. "Productivity growth decomposition using a spatial autoregressive frontier model," Economics Letters, Elsevier, vol. 119(3), pages 291-295.
    30. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
    31. Zhiguo He & In Gu Khang & Arvind Krishnamurthy, 2010. "Balance Sheet Adjustments during the 2008 Crisis," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 58(1), pages 118-156, August.
    32. Boarnet, Marlon G. & Glazer, Amihai, 2002. "Federal grants and yardstick competition," Journal of Urban Economics, Elsevier, vol. 52(1), pages 53-64, July.
    33. David C. Wheelock & Paul W. Wilson, 2012. "Do Large Banks Have Lower Costs? New Estimates of Returns to Scale for U.S. Banks," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(1), pages 171-199, February.
    34. Asmild, Mette & Zhu, Minyan, 2016. "Controlling for the use of extreme weights in bank efficiency assessments during the financial crisis," European Journal of Operational Research, Elsevier, vol. 251(3), pages 999-1015.
    35. 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.
    36. Glass, Anthony J. & Kenjegalieva, Karligash, 2019. "A spatial productivity index in the presence of efficiency spillovers: Evidence for U.S. banks, 1992–2015," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1165-1179.
    37. Clark, Jeffrey A & Siems, Thomas F, 2002. "X-Efficiency in Banking: Looking beyond the Balance Sheet," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(4), pages 987-1013, November.
    Full references (including those not matched with items on IDEAS)


    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:ejores:v:284:y:2020:i:2:p:693-711. 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: (Haili He). 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.