A dynamic stochastic frontier model with threshold effects: U.S. bank size and efficiency

Abstract

Common/Single frontier methodologies that are used to analyze bank efficiency and performance can be misleading because of the homogeneous technology assumption. Using the U.S. banking data over 1984-2010, our dynamic methodology identifies a few data-driven thresholds and distinct size groups. Under common frontier assumption, the largest banks appear to be 22% less efficient on average than how they are in our model. Also, in the common frontier model, smaller banks seem to be relatively more efficient compared to their larger counterparts. Hence, common policies or regulations may not be well-balanced about controlling the banks of different sizes on the spectrum.

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Notes

  1. 1.

    Throughout this paper, whenever we refer to “technology”, we mean the production possibilities frontier (or simply the frontier) corresponding to that particular technology. Hence, at a given time period, if two groups of banks have different frontiers, we say that these groups of banks have different production technologies. See Färe and Primont (1990) for relevant discussions.

  2. 2.

    For other banking studies that examine efficiencies include Berger and Humphrey (1997), Vivas (1997), Muñiz (2002), Brissimis et al. (2010), Paradi et al. (2012), Galán et al. (2015), Dong et al. (2016), Tsionas (2017), and Delis et al. (2017).

  3. 3.

    See Tsionas (2002), El‐Gamal and Inanoglu (2005), Greene (2005), and Almanidis (2013) for a few examples.

  4. 4.

    This means that the econometric issue in estimating the best-practice technologies may not necessarily be solved by simply increasing the flexibility of the functional forms or using non-parametric methods that ignore state dependence.

  5. 5.

    Alternative approaches for dealing with heterogeneous technologies in the stochastic frontier models were considered by Tsionas (2002), Huang (2004), and Greene (2005) in a random parameters model framework, as well as the latent class model employed by Orea and Kumbhakar (2004), El‐Gamal and Inanoglu (2005), and Greene (2005). These methodologies require the parameters to be re-estimated with new information and this update may become computationally expensive, especially when the sample size is relatively large. In contrast, the threshold effect model’s parsimonious setup would allow the individual units to switch groups, as a result of change in certain characteristics such as size, without requiring a re-estimation of the parameters.

  6. 6.

    There are many different size groups defined and used by banking researchers and authorities. The cutoff points in almost all cases are arbitrarily selected.

  7. 7.

    In this paper, whenever we refer to a bank as “small” or “large”, this reference would be vaguely saying that the bank belongs to one of the bank groups in our sample that has relatively smaller or larger asset sizes compared to the other groups in our sample. Hence, in this context, even though a bank that has $1 billion asset size may be considered as large compared to smaller community banks in the sector, we consider this bank as a relatively small bank compared to the other banks in our sample with much larger asset sizes.

  8. 8.

    Durbin and Koopman (2012) provide details on the Kalman filter estimation techniques.

  9. 9.

    Other examples to the models where the one-sided error term is dynamic include Hultberg et al. (2004) and Ahn and Sickles (2000).

  10. 10.

    The Call Reports contain detailed data on a bank’s on-balance and off-balance sheet assets and liabilities, capital structure, income from earning assets, expenses, and other bank-specific structural and geographical characteristics.

  11. 11.

    www.chicagofed.org

  12. 12.

    It is worth mentioning that, the number of unique community banks over the sample period exceeds 11,000 and their total number of observations is more than 750,000.

  13. 13.

    See DeYoung (2013) for more discussion.

  14. 14.

    See Kaparakis et al. (1994), Wheelock and Wilson (1995, 2001), Sickles (2005), Greene (2005), Kutlu (2012), and Almanidis (2013) among others.

  15. 15.

    See Baltensperger (1980) and Berger and Humphrey (1992) for the production and value-added approaches discussions.

  16. 16.

    Note that, although the total assets variable is a commonly employed threshold variable in the banking literature and in practice to assign banks in group sizes, there are other variables/factors that can also be employed separately or in combination to segment the banking industry. Such variables/factors may include a strategy mix, marketing, risk-taking, etc. A proper quantification of these factors in a multi-threshold model framework would potentially complete another piece of the banking technology/strategy puzzle.

  17. 17.

    In our view, these output and input variables cover the majority of outputs and inputs produced by an average bank operating in the U.S. commercial banking industry.

  18. 18.

    A translog function provides the second-order Taylor series approximation to any arbitrary function at a single point. In addition, the translog output distance function does not restrict the returns to scale measures and factor demand elasticities to be constant, as is required in the Cobb-Douglas output distance function case.

  19. 19.

    See Färe and Primont (2012) for more discussion on the scale elasticity measures for distance functions.

  20. 20.

    Appendix A explains the CSSW and LCSS models in detail.

  21. 21.

    For example, the fixed effects estimator of Schmidt and Sickles (1984), CSS estimators, and the Kalman filter estimator of DKS.

  22. 22.

    See Berger (1993), Berger and Hannan (1998), and Kutlu (2012) for more details.

  23. 23.

    To preserve the space, we do not report the estimates of the CSSW model, which are qualitatively similar to the estimates obtained under the LCSS model. The CSSW model estimates for the six groups and the single group are available upon request.

  24. 24.

    The details are provided in the website of the bank at www.westamerica.com

  25. 25.

    This is based on the empirical distribution of the returns to scale values around their median values.

  26. 26.

    See for example McAllister and McManus (1993) and Wheelock and Wilson (2001).

References

  1. Adams RM, Berger AN, Sickles RC (1999) Semiparametric approaches to stochastic panel frontiers with applications in the banking industry. J Bus Economic Stat 17:349–358

    Google Scholar 

  2. Ahn SC, Sickles RC (2000) Estimation of long-run inefficiency levels: a dynamic frontier approach. Econom Rev 19:461–492

    Google Scholar 

  3. Aigner DJ, Lovell CAK, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. J Econ 6:21–37

    Google Scholar 

  4. Alam IMS (2001) A nonparametric approach for assessing productivity dynamics of large US banks. J Money Credit Bank 33:121–139

    Google Scholar 

  5. Almanidis P (2013) Accounting for heterogeneous technologies in the banking industry: a time-varying stochastic frontier model with threshold effects. J Product Anal 39:191–205

    Google Scholar 

  6. Baltensperger E (1980) Alternative approaches to the theory of the banking firm. J Monetary Econ 6:1–37

    Google Scholar 

  7. Battese EG, Heshmati A, Hjalmarsson L (2000) Efficiency of labour use in the swedish banking industry: A stochastic frontier approach. Empir Econ 25:623–640

    Google Scholar 

  8. Battese GE, Corra GS (1977) Estimation of a production frontier model: With application to the pastoral zone of eastern australia. Aust J Agric Econ 21:169–179

    Google Scholar 

  9. Berger AN (1993) “Distribution-free” estimates of efficiency in the US banking industry and tests of the standard distributional assumptions. J Product Anal 4:261–292

    Google Scholar 

  10. Berger AN, Hannan TH (1998) The efficiency cost of market power in the banking industry: a test of the “quiet life” and related hypotheses. Rev Econ Stat 80:454–465

    Google Scholar 

  11. Berger AN, Hasan I, Zhou M (2009) Bank ownership and efficiency in china: What will happen in the world’s largest nation? J Bank Financ 33:113–130

    Google Scholar 

  12. Berger AN, Hasan I, Zhou M (2010) The effects of focus versus diversification on bank performance: Evidence from chinese banks. J Bank Financ 34:1417–1435

    Google Scholar 

  13. Berger AN, Humphrey DB (1992) Measurement and efficiency issues in commercial banking, Output measurement in the service sectors. University of Chicago Press, Chicago, IL, USA, pp. 245–300

  14. Berger AN, Humphrey DB (1997) Efficiency of financial institutions: International survey and directions for future research. Eur J Operational Res 98:175–212

    Google Scholar 

  15. Berger AN, Mester LJ (2003) Explaining the dramatic changes in performance of US banks: technological change, deregulation, and dynamic changes in competition. J Financial Intermediation 12:57–95

    Google Scholar 

  16. Brewer E, Jagtiani J (2013) How much did banks pay to become too-big-to-fail and to become systemically important? J Financial Serv Res 43:1–35

    Google Scholar 

  17. Brissimis SN, Delis MD, Tsionas EG (2010) Technical and allocative efficiency in European banking. Eur J Operational Res 204:153–163

    Google Scholar 

  18. Chang T-P, Hu J-L, Chou RY, Sun L (2012) The sources of bank productivity growth in china during 2002–2009: a disaggregation view. J Bank Financ 36:1997–2006

    Google Scholar 

  19. Christopoulos DK, Tsionas EG (2001) Banking economic efficiency in the deregulation period: results from heteroscedastic stochastic frontier models. Manch Sch 69:656–676

    Google Scholar 

  20. Coelli TJ, Perelman S (1999) A comparison of parametric and non-parametric distance functions: with application to European railways. Eur J operational Res 117:326–339

    Google Scholar 

  21. Coelli TJ, Perelman S (2000) Technical efficiency of European railways: A distance function approach. Appl Econ 32:1967–1976

    Google Scholar 

  22. Cornwell C, Schmidt P, Sickles RC (1990) Production frontiers with cross-sectional and time-series variation in efficiency levels. J Econ 46:185–200

    Google Scholar 

  23. Davies RB (1987) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74:33–43

    Google Scholar 

  24. Delis M, Iosifidi M, Tsionas MG (2017) Endogenous bank risk and efficiency. Eur J Operational Res 260:376–387

    Google Scholar 

  25. Demirgüç-Kunt A, Huizinga H (2013) Are banks too big to fail or too big to save? International evidence from equity prices and cds spreads. J Bank Financ 37:875–894

    Google Scholar 

  26. DeYoung R (2013) Modeling economies of scale in banking. Efficiency and Productivity Growth: Modelling in the Financial Services Industry. John Wiley & Sons, Ltd, West Sussex, UK, pp. 49–75

  27. Dong Y, Firth M, Hou W, Yang W (2016) Evaluating the performance of chinese commercial banks: a comparative analysis of different types of banks. Eur J Operational Res 252:280–295

    Google Scholar 

  28. Durbin J, Koopman SJ (2012) Time series analysis by state space methods. Oxford University Press, Oxford, UK

  29. Duygun M, Kutlu L, Sickles RC (2016) Measuring productivity and efficiency: a Kalman filter approach. J Product Anal 46:155–167

    Google Scholar 

  30. El‐Gamal MA, Inanoglu H (2005) Inefficiency and heterogeneity in Turkish banking: 1990–2000. J Appl Econ 20:641–664

    Google Scholar 

  31. Färe R, Primont D (1990) A distance function approach to multioutput technologies. South Econ J 56:879–891

    Google Scholar 

  32. Färe R, Primont D (2012) Multi-output production and duality: Theory and applications. Springer Science & Business Media, New York, NY, USA

  33. Frank B (2015) Getting Frank on Dodd-Frank. Third Way. http://www.thirdway.org/transcript/getting-frank-on-dodd-frank

  34. Galán JE, Veiga H, Wiper MP (2015) Dynamic effects in inefficiency: evidence from the colombian banking sector. Eur J Operational Res 240:562–571

    Google Scholar 

  35. Greene W (2005) Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. J Econ 126:269–303

    Google Scholar 

  36. Hansen BE (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64:413–430

    Google Scholar 

  37. Hansen BE (1999) Threshold effects in non-dynamic panels: estimation, testing, and inference. J Econ 93:345–368

    Google Scholar 

  38. Hansen BE (2000) Sample splitting and threshold estimation. Econometrica 68:575–603

    Google Scholar 

  39. Huang Y (2004) Appendix b: a guide to state operating aid programs for elementary and secondary education, In: Yinger J (ed) Helping children left behind: state aid and the pursuit of educational equity. MIT Press, Cambridge, MA

  40. Hultberg PT, Nadiri MI, Sickles RC (2004) Cross-country catch-up in the manufacturing sector: Impacts of heterogeneity on convergence and technology adoption. Empir Econ 29:753–768

    Google Scholar 

  41. Isik I (2007) Bank ownership and productivity developments: evidence from turkey. Stud Econ Financ 24:115–139

    Google Scholar 

  42. Kalman RE (1960) A new approach to linear filtering and prediction problems. J Fluids Eng 82:35–45

    Google Scholar 

  43. Kaparakis EI, Miller SM, Noulas AG (1994) Short-run cost inefficiency of commercial banks: a flexible stochastic frontier approach. J Money Credit Bank 26:875–893

    Google Scholar 

  44. Kraft E, Tırtıroğlu D (1998) Bank efficiency in croatia: a stochastic-frontier analysis. J Comp Econ 26:282–300

    Google Scholar 

  45. Kumbhakar SC, Wang D (2007) Economic reforms, efficiency and productivity in chinese banking. J Regulatory Econ 32:105–129

    Google Scholar 

  46. Kutlu L (2012) US banking efficiency, 1984–1995. Econ Lett 117:53–56

    Google Scholar 

  47. Lang G, Welzel P (1999) Mergers among german cooperative banks: a panel-based stochastic frontier analysis. Small Bus Econ 13:273–286

    Google Scholar 

  48. Lin X, Zhang Y (2009) Bank ownership reform and bank performance in china. J Bank Financ 33:20–29

    Google Scholar 

  49. McAllister PH, McManus D (1993) Resolving the scale efficiency puzzle in banking. J Bank Financ 17:389–405

    Google Scholar 

  50. Meeusen W, van den Broeck J (1977) Efficiency estimation from Cobb-Douglas production function with composed errors. Int Economic Rev 18:435–444

    Google Scholar 

  51. Mehdian S, Perry M, Rezvanian R (2007) The effect of globalization on efficiency change, technological progress and the productivity growth of U.S. small and large banks. N Am J Finance Bank Res 1:1–21

    Google Scholar 

  52. Mukherjee K, Ray SC, Miller SM (2001) Productivity growth in large US commercial banks: the initial post-deregulation experience. J Bank Financ 25:913–939

    Google Scholar 

  53. Muñiz M (2002) Separating managerial inefficiency and external conditions in data envelopment analysis. Eur J Operational Res 143:625–643

    Google Scholar 

  54. O’Donnell CJ, Coelli TJ (2005) A bayesian approach to imposing curvature on distance functions. J Econ 126:493–523

    Google Scholar 

  55. Oliveira RdF, Schiozer RF, Barros LAdC (2015) Depositors’ perception of “too-big-to-fail”. Rev Financ 19:191–227

    Google Scholar 

  56. Orea L, Kumbhakar SC (2004) Efficiency measurement using a latent class stochastic frontier model. Empir Econ 29:169–183

    Google Scholar 

  57. Paradi JC, Zhu H, Edelstein B (2012) Identifying managerial groups in a large canadian bank branch network with a dea approach. Eur J Operational Res 219:178–187

    Google Scholar 

  58. Schmidt P, Sickles RC (1984) Production frontiers and panel data. J Bus Economic Stat 2:367–374

    Google Scholar 

  59. Sealey CW, Lindley JT (1977) Inputs, outputs, and a theory of production and cost at depository financial institutions. J Financ 32:1251–1266

    Google Scholar 

  60. Sickles RC (2005) Panel estimators and the identification of firm-specific efficiency levels in parametric, semiparametric and nonparametric settings. J Econ 126:305–334

    Google Scholar 

  61. Slovik P (2012) Systemically Important Banks and Capital Regulation Challenges. Working Paper No 916. OECD Economics Department

  62. Tsionas EG (2002) Stochastic frontier models with random coefficients. J Appl Econ 17:127–147

    Google Scholar 

  63. Tsionas MG (2017) Microfoundations for stochastic frontiers. Eur J Operational Res 258:1165–1170

    Google Scholar 

  64. Vivas AL (1997) Profit efficiency for Spanish savings banks. Eur J Operational Res 98:381–394

    Google Scholar 

  65. Wheelock DC, Wilson PW (1995) Explaining bank failures: deposit insurance, regulation, and efficiency. Rev Econ Stat 77:689–700

    Google Scholar 

  66. Wheelock DC, Wilson PW (1999) Technical progress, inefficiency, and productivity change in US banking, 1984–1993. J Money Credit Bank 31:212–234

    Google Scholar 

  67. Wheelock DC, Wilson PW (2001) New evidence on returns to scale and product mix among US commercial banks. J Monetary Econ 47:653–674

    Google Scholar 

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Correspondence to Levent Kutlu.

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Almanidis, P., Karakaplan, M.U. & Kutlu, L. A dynamic stochastic frontier model with threshold effects: U.S. bank size and efficiency. J Prod Anal 52, 69–84 (2019). https://doi.org/10.1007/s11123-019-00565-6

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Keywords

  • Dynamic Stochastic Frontier
  • Bank Efficiency
  • Bank Heterogeneity

JEL classification

  • C13
  • C23
  • D24
  • G21
  • G28