Abstract
This paper investigates the productivity and efficiency of large bank holding companies (BHCs) in the United States over the period 2004–2013, by estimating a translog stochastic distance frontier (SDF) model with time-varying heterogeneity. The main feature of this model is that a multi-factor structure is used to disentangle time-varying unobserved heterogeneity from inefficiency. Our empirical results strongly suggest that unobserved heterogeneity is not only present in the U.S. banking industry, but also varies over time. Our results from the translog SDF model with time-varying heterogeneity show that the majority of large BHCs in the U.S. exhibit increasing returns to scale, a small percentage exhibit constant returns to scale, and an even smaller percentage exhibit decreasing returns to scale. Our results also show that on average the BHCs have experienced small positive or even negative technical change and productivity growth.
Similar content being viewed by others
Notes
There are two reasons why our analysis focuses on BHCs rather than individual commercial banks. First, total assets controlled by BHCs accounts for 99% of the industry assets in 2012 (Federal Reserve Board Annual Report 2012). Second, important business decisions are typically made at bank holding company level (Stiroh 2000).
If (14) represents a panel data model with common factors where some factors are observable, (14) can be written as
$$\begin{array}{*{20}{l}} {q_{it}} \hfill & \hskip-8pt = \hfill &\hskip-7pt {{\boldsymbol{z \prime}\!}_{it} {\boldsymbol{\beta }} + {\boldsymbol{f \prime}\!\!}_{1,t} \gamma _{1,i} + {\boldsymbol{f \prime }\!\!}_{2,t} {\mathrm{\gamma }\!}_{2,i} + u_{it} + v_{it}} \hfill \\ {} \hfill & \hskip-8pt = \hfill &\hskip-7pt {\widetilde {\boldsymbol{z \prime }\!}_{it} \widetilde {\boldsymbol{\beta }}_i + {\boldsymbol{f \prime }\!\!}_{2,t} {\mathrm{\gamma }}_{2,i} + u_{it} + v_{it}{\mathrm{,}}} \hfill \end{array}$$(15)where f 1,t is a h 1 × 1 vector of unobservables; f 2,t is a h 2 × 1 vector of unobservables; \(\widetilde {\boldsymbol{z}}_{it} = ({\boldsymbol{z}}_{it},{\boldsymbol{f \prime }\!\!}_{1,t})\); and \(\widetilde \beta _i = (\beta {\prime},\gamma\prime_{\!\!1,i} ){\prime}\). (15) is a random coefficient model with a new factor structure, represented by \({\boldsymbol{f \prime }\!\!}_{2,t} \gamma _{2,i}\). The identification restriction thus becomes \(h_2 \le (T - 1)/2\). Accordingly, the prior and posterior distribution for \(\widetilde {\boldsymbol{\beta }}_i\) needs to be changed. But, our specifications and discussions regarding the new factor structure remain the same. Further, if f 1,t is a constant scalar (say f 1), the above model reduces to
\(q_{it} = {\boldsymbol{z \prime }\!}_{it} \beta + w_i + {\boldsymbol{f \prime }\!\!}_{2,t} \gamma _{2,i} + u_{it} + v_{it},\)
where w i = f 1 γ 1,i . The identification restriction is still h 2 ≤ (T − 1)/2.
$1 billion is widely accepted as a cutoff for separating large and small BHCs/banks (see, for example, Cole et al. 2004).
The use of a balanced panel might result in survivorship bias. However, we also note that the use of an unbalanced panel may potentially distort inter-temporal comparisons of banking sector efficiency.
References
Ahn SC, Lee YH, Schmidt P (2007) Stochastic frontier models with multiple time-varying individual effects. J Prod Anal 27:1–12
Ahn SC, Lee YH, Schmidt P (2013) Panel data models with multiple time-varying individual effects. J Econ 174(1):1–14
Berger AN, Mester LJ (2003) Explaining the dramatic changes in the performance of U.S. banks: technological change, deregulation, and dynamic changes in competition. J Financial Intermed 12:57–95
Berger AN, Miller NH, Petersen MA, Rajan RG, Stein JC (2005) Does function follow organizational form? Evidence from the lending practices of large and small banks. J Financial Econ 76:237–269
Caves DW, Christensen LR, Diewert WE (1982) The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica 50:1393–1414
Cole RA, Goldberg LG, White LJ (2004) Cookie cutter vs. character: the micro structure of small business lending by large and small banks. J Financial Quant Anal 39:227–251
Daniel DL, Longbrake WA, Murphy NB (1973) The effect of technology on bank economies of scale for demand deposits. J Finance 28, 31–146
Demsetz RS, Strahan PE (1997) Diversification, size, and risk at bank holding companies. J Money, Credit Bank 29(3):300–313
Dick AA (2006) Nationwide branching and its impact on market structure, quality, and bank performance. J Bus 79(2):567–592
Davies R, Tracey B (2014) Too big to be efficient? The impact of implicit subsidies on estimates of scale economies for banks. J Money, Credit Bank 46(1):219–253
El-Gamal MA, Inanoglu H (2005) Inefficiency and heterogeneity in Turkish banking: 1990–2000. J Appl Econ 5:641–664
Färe R, Grosskopf S (1994) Cost and revenue constrained production. Springer-Verlag New York, Inc., New York
Färe R, Primont D (1995) Multi-output production and duality: theory and applications. Kluwer Academic, Netherlands
Färe R, Grosskopf S, Lovell CAK (1993) Derivation of shadow prices for undesirable outputs: a distance function approach. Rev Econ Stat 75(2):374–380
Federal Reserve Board Annual Report (2012). http://www.federalreserve.gov/publications/annual-report/2012-contents.htm
Federal Reserve Board (2013). A User’s Guide for the Bank Holding Company Performance Report, http://www.federalreserve.gov/boarddocs/supmanual/bhcpr/UsersGuide13/default.htm
Feng G, Serletis A (2010) A primal Divisia technical change index based on the output distance function. J Econ 159:320–330
Feng G, Zhang X (2012) Productivity and efficiency at large and community banks in the U.S.: a Bayesian true random effects stochastic distance frontier analysis. J Bank Finance 36(7):1883–1895
Feng G, Zhang X (2014) Returns to scale at large banks in the US: a random coefficient stochastic frontier approach. J Bank Finance 39:135–145
Fernandez C, Osiewalski J, Steel MFJ (1997) On the use of panel data in stochastic frontier models with improper priors. J Econ 79:169–193
Fuss M (1994) Productivity growth in Canadian telecommunications. Canadian J Econom 27(2):371–392
Geweke J, Zhou G (1996) Measuring the pricing error of the arbitrage pricing theory. Rev Financial Stud 9(2):557–587
Geweke J, Durham G, Xu H (2015) Bayesian inference for logistic regression models using sequential posterior simulation. In: SK Upadhyay, U Singh, DK Dey and A Loganathan (eds) Current Trends in Bayesian Methodology with Applications, Chapter 14, Chapman and Hall, Florida, p 289–312
Hannan TH, Hanweck GA (1998) Bank insolvency risk and the market for large certificates of deposit. J Money Credit Bank 20(2):203–211
Hirtle B (2007) The impact of network size on bank branch performance. J Bank Finance 31:3782–3805
Hughes JP, Mester LJ (1993) A quality and risk-adjusted cost function for banks: evidence on the “too-big-to-fail” doctrine. J Prod Anal 4:293–315
Hughes JP, Mester LJ (1998) Bank capitalization and cost: evidence of scale economies in risk management and signaling. Rev Econ Stat 80(2):314–325
Hughes JP, Mester LJ (2013) Who said large banks don’t experience scale economies? Evidence from a risk-return driven cost function. J Financial Intermed 22:559–585
Hulten CR (1992) Growth accounting when technical change is embodied in capital. Am Econ Rev 82(4):964–980
Kass R, Raftery A (1995) Bayes factors and model uncertainty. J Am Stat Assoc 90:773–795
Kim S, Shephard N, Chib S (1998) Stochastic volatility: likelihood inference and comparison with ARCH models. Rev Econ Stud 65:361–393
Koop G, Steel M (2003) Bayesian analysis of stochastic frontier models. Baltagi B (ed) A Companion to Theoretical Econometrics. Blackwell, MA
Lovell CAK (2003) The decomposition of malmquist productivity indexes. J Prod Anal 20(3):437–458
Lovell CAK, Richardson S, Travers P, Wood LL (1994) Resources and functionings: a new view of inequality in Australia. In: Eichhorn W (eds) Models and Measurement of Welfare and Inequality. Springer-Verlag Press, Berlin, p 787–807
Mester LJ (1997) Measuring efficiency at US banks: accounting for heterogeneity is important. Eur J Oper Res 98:230–242
Murray JD, White RW (1983) Economies of scale and economies of scope in multiproduct financial institutions: a study of British Columbia credit unions. J Finance 38:887–902
O’Donnell CJ, Coelli TJ (2005) A Bayesian approach to imposing curvature on distance functions. J Econ 126:493–523
Orea L (2002) Parametric decomposition of a generalized malmquist productivity index. J Prod Anal 18:5–22
Reiss PC, Wolak FA (2007) Structural econometric modeling: Rationales and examples from industrial organization. In: Handbook of Econometrics, Heckman JJ, Leamer EE (eds) North-Holland, The Netherlands, p 4277–4412
Rosen RJ (2003) Is three a crowd? Competition among regulators in banking. J Money, Credit Bank 35:967–998
Rossi CV (1998) Mortgage banking cost structure: resolving an enigma. J Econ Bus 50:219–234
Sealey C, Lindley J (1977) Inputs, outputs, and a theory of production and cost at depository financial institutions. J Finance 32:1251–1266
Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002) Bayesian measures of model complexity and fit. J Royal Stat Soc, Series B 64:583–640
Stiroh KJ (2000) How did bank holding companies prosper in the 1990s? J Bank Finance 24:1703–1745
Tierney L (1994) Markov chains for exploring posterior distributions (with discussion). Annals Stat 22:1701–1762
Wheelock DC, Wilson PW (2012) Do large banks have lower costs? New estimates of returns to scale for U.S. banks. J Money, Credit Bank 44(1):171–199
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Rights and permissions
About this article
Cite this article
Feng, G., Peng, B. & Zhang, X. Productivity and efficiency at bank holding companies in the U.S.: a time-varying heterogeneity approach. J Prod Anal 48, 179–192 (2017). https://doi.org/10.1007/s11123-017-0515-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11123-017-0515-5
Keywords
- Productivity and efficiency
- Bank holding companies
- Translog stochastic distance frontier model with time-varying heterogeneity
- Bayesian estimation