Journal of Regulatory Economics

, Volume 48, Issue 2, pp 125–168 | Cite as

Obelix vs. Asterix: Size of US commercial banks and its regulatory challenge

  • Diego Restrepo-Tobón
  • Subal C. Kumbhakar
  • Kai Sun
Original Article


Big banks pose substantial costs to society in the form of increased systemic risk and government bailouts during crises. So the question is: Should regulators limit the size of banks? To answer this question, regulators need to assess the potential costs of such regulations. If big banks enjoy substantial scale economies (i.e., average costs get lower as bank size increases), limiting the size of banks through regulations may be inefficient and likely to reduce social welfare. However, the literature offers conflicting results regarding the existence of economies of scale for the biggest US banks. We contribute to this literature using a novel approach to estimating nonparametric measures of scale economies and total factor productivity (TFP) growth. For US commercial banks, we find that around 73 % of the top one hundred banks, 98 % of medium and small banks, and seven of the top ten biggest banks by asset size exhibit substantial economies of scale. Likewise, we find that scale economies contribute positively and significantly to their TFP growth. The existence of substantial scale economies raises an important challenge for regulators to pursue size limit regulations.


Bank regulation Economies of scale Returns to scale Nonparametric methods 

JEL Classification

L51 G21 G28 D24 L25 C14 



We would like to thank the Editor and two anonymous referees for their helpful and insightful comments. However, the authors are solely responsible for the views expressed in this article. Restrepo-Tobón acknowledges financial support from the Colombian Fulbright Commission; the Colombian Administrative Department of Science, Technology and Innovation (Colciencias); and EAFIT University.

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Allen, J., & Liu, Y. (2007). Efficiency and economies of scale of large Canadian banks. Canadian Journal of Economics, 40(1), 225–244.CrossRefGoogle Scholar
  2. Amel, D., Barnes, C., Panetta, F., & Salleo, C. (2004). Consolidation and efficiency in the financial sector: A review of the international evidence. Journal of Banking & Finance, 28(10), 2493–2519.CrossRefGoogle Scholar
  3. Arellano, M., & Honore, B. (2001). Panel data models: Some recent developments. In J. J. Heckman & E. Leamer (Eds.), Handbook of Econometrics (chap. 53) (Vol. 5, pp. 3229–3290). Amsterdam: Elsevier.Google Scholar
  4. Bai, J. (2009). Panel data models with interactive fixed effects. Econometrica, 77(4), 1229–1279.CrossRefGoogle Scholar
  5. Bauer, P., Berger, A., & Humphrey, D. (1993). Efficiency and productivity growth in US banking. In H. Fried & C. Lovell (Eds.), The measurement of productive efficiency: Techniques and applications (pp. 386–413). New York: Oxford University Press. S S.Google Scholar
  6. Berger, A. N., & Humphrey, D. (1994). Bank scale economies, mergers, concentration, and efficiency: The US experience. Center for Financial Institutions Working Papers.Google Scholar
  7. Berger, A. N., & Humphrey, D. B. (1992). Megamergers in banking and the use of cost efficiency as an antitrust defense. Antitrust Bulletin, 37, 541.Google Scholar
  8. Berger, A. N., & Mester, L. J. (1997). Inside the black box: What explains differences in the efficiencies of financial institutions? Journal of Banking & Finance, 21(7), 895–947.CrossRefGoogle Scholar
  9. Berger, A. N., & Mester, L. J. (2003). Explaining the dramatic changes in performance of US banks: Technological change, deregulation, and dynamic changes in competition. Journal of Financial Intermediation, 12(1), 57–95.CrossRefGoogle Scholar
  10. Berger, A. N., Hanweck, G. A., & Humphrey, D. B. (1987). Competitive viability in banking: Scale, scope, and product mix economies. Journal of Monetary Economics, 20(3), 501–520.CrossRefGoogle Scholar
  11. Berger, A. N., Demsetz, R. S., & Strahan, P. E. (1999). The consolidation of the financial services industry: Causes, consequences, and implications for the future. Journal of Banking & Finance, 23(2–4), 135–194.CrossRefGoogle Scholar
  12. Borts, G. H. (1954). Increasing returns in the railway industry. The Journal of Political Economy, 62(3), 316–333.Google Scholar
  13. Boyd, J., & Heitz, A. (2012). The social costs and benefits of too-big-to-fail banks: A “bounding” exercise. Technical report, University of Minnesota.Google Scholar
  14. Camacho, F. T., & Menezes, F. M. (2009). Access pricing and investment: A real options approach. Journal of Regulatory Economics, 36(2), 107–126.CrossRefGoogle Scholar
  15. Chamberlain, G. (1984). Panel data. In Z. Griliches & M. Intriligator (Eds.), Handbook of econometrics (Vol. 2, pp. 1248–1318). Amsterdam: Elsevier. chap 22.Google Scholar
  16. Clark, J. A. (1988). Economies of scale and scope at depository financial institutions: A review of the literature. Economic Review, 73(8), 17–33.Google Scholar
  17. Clark, J. A. (1996). Economic cost, scale efficiency, and competitive viability in banking. Journal of Money, Credit and Banking, 28(3), 342–364.CrossRefGoogle Scholar
  18. Daniels, K. N., & Tirtiroglu, D. (1998). Total factor productivity growth in US commercial banking for 1935–1991: A latent variable approach using the kalman filter. Journal of Financial Services Research, 13, 119–135. doi: 10.1023/A:1007922103037.CrossRefGoogle Scholar
  19. Das, A., & Kumbhakar, S. (2012). Productivity and efficiency dynamics in Indian banking: An input distance function approach incorporating quality of inputs and outputs. Journal of Applied Econometrics, 27(2), 205–234.CrossRefGoogle Scholar
  20. Davies, R., & Tracey, B. (2014). Too big to be efficient? The impact of implicit subsidies on estimates of scale economies for banks. Journal of Money, Credit and Banking, 46(s1), 219–253.CrossRefGoogle Scholar
  21. Denny, M., Fuss, M., & Waverman, L. (1979). Productivity measurement in regulated industries, Academic Press, chap The measurement and interpretation of total factor productivity in regulated industries, with an application to Canadian telecommunications (pp. 179–212).Google Scholar
  22. DeYoung, R. (1991). The efficiencies defense and commercial bank merger regulation. Review of Industrial Organization, 6(3), 269–282.CrossRefGoogle Scholar
  23. DeYoung, R. (2010). Scale economies are a distraction. The Region, 10(3), 7.Google Scholar
  24. Diewert, W. E., & Fox, K. J. (2008). On the estimation of returns to scale, technical progress and monopolistic markups. Journal of Econometrics, 145(1–2), 174–193.CrossRefGoogle Scholar
  25. Ellig, J., & Giberson, M. (1993). Scale, scope, and regulation in the Texas gas transmission industry. Journal of Regulatory Economics, 5(1), 79–90.CrossRefGoogle Scholar
  26. Evanoff, D. D., Israilevich, P. R., & Merris, R. C. (1990). Relative price efficiency, technical change, and scale economies for large commercial banks. Journal of Regulatory Economics, 2(3), 281–298.CrossRefGoogle Scholar
  27. Evans, L., & Guthrie, G. (2006). Incentive regulation of prices when costs are sunk. Journal of Regulatory Economics, 29(3), 239–264.CrossRefGoogle Scholar
  28. Farrell, J., & Shapiro, C. (2001). Scale economies and synergies in horizontal merger analysis. Antitrust Law Journal, 68(3), 685–710.Google Scholar
  29. Feldman, R. (2010). Size and regulatory reform in finance: Important but difficult questions. The Region, Federal Reserve Bank of Minneapolis, 10, 7.Google Scholar
  30. 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. Journal of Applied Econometrics, 24(1), 105–138.CrossRefGoogle Scholar
  31. 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. Journal of Banking & Finance, 34(1), 127–138.CrossRefGoogle Scholar
  32. 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. Journal of Banking & Finance, 36(6), 1883–1895.CrossRefGoogle Scholar
  33. Foreman, R. D., & Beauvais, E. (1999). Scale economies in cellular telephony: Size matters. Journal of Regulatory Economics, 16(3), 297–306.CrossRefGoogle Scholar
  34. Fraquelli, G., Piacenza, M., & Vannoni, D. (2005). Cost savings from generation and distribution with an application to Italian electric utilities. Journal of Regulatory Economics, 28(3), 289–308.CrossRefGoogle Scholar
  35. Gandhi, P., & Lustig, H. (In press). Size anomalies in US bank stock returns. Journal of Finance, pp. 1–39.Google Scholar
  36. Glass, V., & Stefanova, S. K. (2012). Economies of scale for broadband in rural United States. Journal of Regulatory Economics, 41(1), 100–119.CrossRefGoogle Scholar
  37. Greene, W. (2005a). Fixed and random effects in stochastic frontier models. Journal of Productivity Analysis, 23, 7–32. doi: 10.1007/s11123-004-8545-1.CrossRefGoogle Scholar
  38. Greene, W. (2005b). Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. Journal of Econometrics, 126(2), 269–303.CrossRefGoogle Scholar
  39. Hardle, W., & Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. The Annals of Statistics, 21(4), 1926–1947.CrossRefGoogle Scholar
  40. Hayfield, T., & Racine, J. S. (2008). Nonparametric econometrics: The np package. Journal of Statistical Software, 27(5), 1–32.Google Scholar
  41. Hughes, J. P., & Mester, L. J. (1998). Bank capitalization and cost: Evidence of scale economies in risk management and signaling. Review of Economics and Statistics, 80(2), 314–325.CrossRefGoogle Scholar
  42. Hughes, J. P., & Mester, L. J. (2010). Efficiency in banking: Theory, practice, and evidence. In A. Berger, P. Molyneux, & J. Wilson (Eds.), The oxford handbook of banking (chap. 19) (pp. 336–357). New York: Oxford University Press.Google Scholar
  43. Hughes, J. P., & Mester, L. J. (2013). Who said large banks don’t experience scale economies? Evidence from a risk-return-driven cost function. Journal of Financial Intermediation, 22(4), 559–585.CrossRefGoogle Scholar
  44. Hughes, J. P., Lang, W., Mester, L. J., & Moon, C. G. (1996). Efficient banking under interstate branching. Journal of Money, Credit and Banking, 28(4), 1045–1071.CrossRefGoogle Scholar
  45. Hughes, J. P., Lang, W., Mester, L. J., & Moon, C. G. (2000). Recovering risky technologies using the almost Ideal demand system: An application to US banking. Journal of Financial Services Research, 18, 5–27.CrossRefGoogle Scholar
  46. Hughes, J. P., Mester, L. J., & Moon, C. G. (2001). Are scale economies in banking elusive or illusive?: Evidence obtained by incorporating capital structure and risk-taking into models of bank production. Journal of Banking & Finance, 25(12), 2169–2208.CrossRefGoogle Scholar
  47. Humphrey, D. (1992). Flow versus stock indicators of banking output: Effects on productivity and scale economy measurement. Journal of Financial Services Research, 6(2), 115–135.CrossRefGoogle Scholar
  48. Humphrey, D. B. (1991). Productivity in banking and effects from deregulation. Economic Review, 1(Mar), 16–28.Google Scholar
  49. Humphrey, D. B. (1993). Cost and technical change: Effects from bank deregulation. Journal of Productivity Analysis, 4(1/2), 9–34.CrossRefGoogle Scholar
  50. Hunter, W. C., & Timme, S. G. (1986). Technical change, organizational form, and the structure of bank production. Journal of Money, Credit and Banking, 18(2), 152–166.CrossRefGoogle Scholar
  51. Hunter, W. C., & Timme, S. G. (1991). Technological change in large US commercial banks. The Journal of Business, 64(3), 339–362.CrossRefGoogle Scholar
  52. Johnson, S. (2012). Tarullo telegraphs Fed’s plans to cap bank size. Bloomberg News’ Column.
  53. Kinne, K. (1998). The “efficiency defense” in the US American merger policy. Technical report, HWWA Discussion Paper.Google Scholar
  54. Kolasky, W. J., & Dick, A. R. (2003). The merger guidelines and the integration of efficiencies into antitrust review of horizontal mergers. Antitrust Law Journal, 71, 207–251.Google Scholar
  55. Kumbhakar, S., & Lozano-Vivas, A. (2005). Deregulation and productivity: The case of Spanish banks. Journal of Regulatory Economics, 27(3), 331–351.CrossRefGoogle Scholar
  56. Kumbhakar, S., & Sun, K. (2012). Estimation of TFP growth: A semiparametric smooth coefficient approach. Empirical Economics, 43(1), 1–24.CrossRefGoogle Scholar
  57. Kumbhakar, S., Lien, G., Flaten, O., & Tveters, R. (2008). Impacts of Norwegian milk quotas on output growth: A modified distance function approach. Journal of Agricultural Economics, 59(2), 350–369.CrossRefGoogle Scholar
  58. Kumbhakar, S. C., & Wang, D. (2007). Economic reforms, efficiency and productivity in Chinese banking. Journal of Regulatory Economics, 32(2), 105–129.CrossRefGoogle Scholar
  59. Lagerlof, J. N., & Heidhues, P. (2005). On the desirability of an efficiency defense in merger control. International Journal of Industrial Organization, 23(9–10), 803–827.CrossRefGoogle Scholar
  60. Laudati, L. L. (1981). Note: Economies of scale: Weighing operating efficiency when enforcing antitrust law. Fordham Law Review, 49, 771–801.Google Scholar
  61. Li, Q., & Racine, J. (2007). Nonparametric econometrics: Theory and practice. Princeton: Princeton University Press.Google Scholar
  62. Li, Q., & Racine, J. S. (2010). Smooth varying-coefficient estimation and inference for qualitative and quantitative data. Econometric Theory, 26(06), 1607–1637.CrossRefGoogle Scholar
  63. Li, Q., Huang, C. J., Li, D., & Fu, T. T. (2002). Semiparametric smooth coefficient models. Journal of Business & Economic Statistics, 20(3), 412–422.CrossRefGoogle Scholar
  64. Malikov, E., Restrepo-Tobón, D., Kumbhakar, S.C. (2014). Estimation of banking technology under credit uncertainty. Empirical Economics Forthcoming, 1–27.Google Scholar
  65. McAfee, R. P., Mialon, H. M., & Williams, M. A. (2004). What is a barrier to entry? American Economic Review, 94(2), 461–465.CrossRefGoogle Scholar
  66. Mester, L. J. (1994). How efficient are third district banks? Business Review, 1–3.Google Scholar
  67. Mester, L. J. (1996). A study of bank efficiency taking into account risk-preferences. Journal of Banking & Finance, 20(6), 1025–1045.CrossRefGoogle Scholar
  68. Mester, L. J. (1997). Measuring efficiency at US banks: Accounting for heterogeneity is important. European Journal of Operational Research, 98(2), 230–242.CrossRefGoogle Scholar
  69. Mukherjee, K., Ray, S. C., & Miller, S. M. (2001). Productivity growth in large US commercial banks: The initial post-deregulation experience. Journal of Banking & Finance, 25(5), 913–939.CrossRefGoogle Scholar
  70. Nauges, C., & Van Den Berg, C. (2008). Economies of density, scale and scope in the water supply and sewerage sector: A study of four developing and transition economies. Journal of Regulatory Economics, 34(2), 144–163.CrossRefGoogle Scholar
  71. Restrepo-Tobón, D., Kumbhakar, S. (2013). Profit efficiency of US commercial banks: A decomposition. Technical report 13–18, EAFIT University, Binghamton University.Google Scholar
  72. Restrepo-Tobón, D., & Kumbhakar, S. (2014). Nonparametric estimation of returns to scale using input distance functions: An application to large US banks. Empirical Economics, 48(1), 143–168.CrossRefGoogle Scholar
  73. Robinson, P. (1988). Root-n-consistent semiparametric regression. Econometrica: Journal of the Econometric Society, 56(4), 931–954.CrossRefGoogle Scholar
  74. Rogers, K. (1998). Nontraditional activities and the efficiency of US commercial banks. Journal of Banking & Finance, 22(4), 467–482.CrossRefGoogle Scholar
  75. Schmalensee, R. (2004). Sunk costs and antitrust barriers to entry. American Economic Review, 94(2), 471–475.CrossRefGoogle Scholar
  76. Sealey, C., & Lindley, J. (1977). Inputs, outputs, and a theory of production and cost at depository financial institutions. Journal of Finance, 32(4), 1251–1266.CrossRefGoogle Scholar
  77. Semenick Alam, I. M. (2001). A nonparametric approach for assessing productivity dynamics of large US banks. Journal of Money, Credit and Banking, 33(1), 121–139.CrossRefGoogle Scholar
  78. Shaffer, S. (1994). A revenue-restricted cost study of 100 large banks. Applied Financial Economics, 4(3), 193–205.CrossRefGoogle Scholar
  79. Stern, G., & Feldman, R. (2009 June). Addressing TBTF by shrinking financial institutions: An initial assessment. Federal Reserve Bank of Minneapolis: The Region (pp. 8–13).Google Scholar
  80. Stiroh, K. J. (2000). How did bank holding companies prosper in the 1990s? Journal of Banking & Finance, 24(11), 1703–1745.CrossRefGoogle Scholar
  81. Tirtiroglu, D., Daniels, K. N., & Tirtirogu, E. (2005). Deregulation, intensity of competition, industry evolution, and the productivity growth of US commercial banks. Journal of Money, Credit and Banking, 37(2), 339–360.CrossRefGoogle Scholar
  82. Wang, H. J., & Ho, C. W. (2010). Estimating fixed-effect panel stochastic frontier models by model transformation. Journal of Econometrics, 157(2), 286–296.CrossRefGoogle Scholar
  83. Wheelock, D. C., & Wilson, P. W. (1999). Technical progress, inefficiency, and productivity change in US banking, 1984–1993. Journal of Money, Credit and Banking, 31(2), 212–234.CrossRefGoogle Scholar
  84. Wheelock, D. C., & Wilson, P. W. (2001). New evidence on returns to scale and product mix among US commercial banks. Journal of Monetary Economics, 47(3), 653–674.CrossRefGoogle Scholar
  85. Wheelock, D. C., & Wilson, P. W. (2011). Are credit unions too small? Review of Economics and Statistics, 93(4), 1343–1359.CrossRefGoogle Scholar
  86. Wheelock, D. C., & Wilson, P. W. (2012). Do large banks have lower costs? New estimates of returns to scale for US banks. Journal of Money, Credit and Banking, 44(1), 171–199.CrossRefGoogle Scholar
  87. Williamson, O. E. (1968). Economies as an antitrust defense: The welfare tradeoffs. American Economic Review, 58(1), 18–36.Google Scholar
  88. Williamson, O. E. (1977). Welfare aspects of industrial markets (pp. 237–271) (Economies as an antitrust defense revisited). Leiden: Springer.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Diego Restrepo-Tobón
    • 1
  • Subal C. Kumbhakar
    • 2
    • 3
  • Kai Sun
    • 4
  1. 1.EAFIT UniversityMedellínColombia
  2. 2.Binghamton UniversityBinghamtonUS
  3. 3.University of Stavanger Business SchoolStavangerNorway
  4. 4.University of SalfordSalfordUK

Personalised recommendations