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Scale and efficiency measurement using a semiparametric stochastic frontier model: evidence from the U.S. commercial banks

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Abstract

In this paper, we use the local maximum likelihood (LML) method proposed by Kumbhakar et al. (J Econom, 2007) to estimate stochastic cost frontier models for a sample of 3,691 U.S. commercial banks. This method relaxes several deficiencies in the econometric estimation of frontier functions. In particular, we relax the assumption that all banks share the same production technology and provide bank-specific measures of returns to scale and cost inefficiency. The LML method is applied to estimate the cost frontiers in which a truncated normal distribution is used to model technical inefficiency. This formulation allows the cost frontier, inefficiency effects and heteroskedasticity in both noise and inefficiency components to be quite flexible.

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References

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

    Article  Google Scholar 

  • Battese GE, Coelli TJ (1995) A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empir Econ 20:325–332

    Article  Google Scholar 

  • Berger A, Humphrey D (1991) The dominance of inefficiencies over scale and product mix economies in banking. J Monetary Econ 28:117–148

    Article  Google Scholar 

  • Berger AN, Mester LJ (1997) Inside the black box: what explain differences in the efficiency of financial institutions? J Bank Financ 21:895–947

    Article  Google Scholar 

  • Boyd JH, Graham SL (1991) Investigating the banking consolidation trend. Q Rev Federal Bank Minneap 3–15

  • Broeck van den J, Koop G, Osiewalski J, Steel MFJ (1994) Stochastic frontier models: a Bayesian perspective. J Econom 61:273–303

    Article  Google Scholar 

  • Caudill SB, Ford JM, Gropper DM (1995) Frontier estimation and firm-specific inefficiency measures in the presence of heteroskedasticity. J Bus Econ Stat 13:105–111

    Article  Google Scholar 

  • Cazals C, Florens J-P, Simar L (2002) Nonparametric frontier estimation: a robust approach. J Econom 106:1–25

    Article  Google Scholar 

  • Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision-making units. Eur J Oper Res 2:429–444

    Article  Google Scholar 

  • Hadri K (1999) Estimation of a doubly heteroscedastic stochastic frontier cost function. J Bus Econ Stat 17:359–363

    Article  Google Scholar 

  • Jondrow J, Lovell CAK, Materov IS, Schmidt P (1982) On the estimation of technical inefficiency in the stochastic frontier production function model. J Econom 19:233–238

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kumbhakar SC, Ghosh S, McGuckin T (1991) A generalized production frontier approach for estimating determinants of inefficiency in U.S. dairy farms. J Bus Econ Stat 9:279–286

    Article  Google Scholar 

  • Kumbhakar SC, Lovell CAK (2000) Stochastic frontier analysis. Cambridge University Press, New York

    Google Scholar 

  • Kumbhakar SC, Park BU, Simar L, Tsionas EG (2007) Nonparametric stochastic frontiers: a local maximum likelihood approach. J Econ 137: 1–27

    Google Scholar 

  • McManus DA (1994a) Making the Cobb–Douglas functional form an efficient nonparametric estimator through localization. Manuscript, Board of Governors of the Federal Reserve Bank

  • McManus DA (1994b) The nonparametric translog with application to banking scale and scope economies. In: Proceedings of the Business and Economic Statistics Section, Am Stat Assoc

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

    Article  Google Scholar 

  • Meeusen W, van den Broeck J (1977) Efficiency estimation from Cobb–Douglas production functions with composed error. Int Econ Rev 8:435–444

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Pagan A, Ullah A (1999) Nonparametric econometrics. Cambridge University Press, Cambridge

    Google Scholar 

  • Park BU, Sickles RC, Simar L (1998) Stochastic panel frontiers: a semiparametric approach. J Econom 84:273–301

    Article  Google Scholar 

  • Simar L, Wilson PW (2000) Statistical inference in nonparametric frontier models: the state of the art. J Product Anal 13:49–78

    Article  Google Scholar 

  • Stevenson RE (1980) Likelihood functions for generalized stochastic frontier estimation. J Econom 13:57–66

    Article  Google Scholar 

  • Tibshirani R (1984) Local likelihood estimation. Ph.D. thesis, Stanford University

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

    Article  Google Scholar 

  • Wang H-J (2002) Heteroskedasticity and non-monotonic efficiency effects of a stochastic frontier model. J Product Anal 18:241–253

    Article  Google Scholar 

  • Wang D, Kumbhakar SC (2006) Strategic groups and heterogeneous technologies: An application to the US banking industry. Manuscript SUNY Binghamton, New York

    Google Scholar 

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

    Article  Google Scholar 

  • Yatchew A (1998) Nonparametric regression techniques in economics. J Econ Lit 36:669–721

    Google Scholar 

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Correspondence to Subal C. Kumbhakar.

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Kumbhakar, S.C., Tsionas, E.G. Scale and efficiency measurement using a semiparametric stochastic frontier model: evidence from the U.S. commercial banks. Empirical Economics 34, 585–602 (2008). https://doi.org/10.1007/s00181-007-0137-2

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  • DOI: https://doi.org/10.1007/s00181-007-0137-2

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