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The B.E. Journal of Economic Analysis & Policy

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Volume 13, Issue 2 (Sep 2013)


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Solving the Endogeneity Problem in Empirical Cost Functions: An Application to US Banks

Mark G. Lijesen
  • Corresponding author
  • VU University, Amsterdam, Netherlands
  • Email:
Published Online: 2013-09-07 | DOI: https://doi.org/10.1515/bejeap-2012-0070


Empirical cost functions tend to ignore that firm differences in output levels depend on differences in cost levels and hence suffer from an endogeneity problem. We argue that traditional solutions for the endogeneity problem are insufficient for solving the problem and propose a structural approach to solve the problem. We apply both the traditional and the alternative models to panel data on large banks and found that a hybrid version yields results that are fully compatible with economic theory, whereas the traditional model provides theoretically incorrect in-sample predictions of scale elasticities.

Keywords: costs; firm size; translog; economies of scale; endogeneity


  • Altunbaș, Y., E. P. M. Gardener, P. Molyneux, and B. Moore. 2001. “Efficiency in European Banking.” European Economic Review 45:1931–55. [Crossref]

  • Altunbaș, Y., P. Molyneux, and J. Thornton. 1997. “Big-Bank Mergers in Europe: An Analysis of the Cost Implications.” Economica 64:317–29. [Crossref]

  • Berger, A. N., J. H. Leusner, and J. J. Mingo. 1997. “The Efficiency of Bank Branches.” Journal of Monetary Economics 40:141–62. [Web of Science] [Crossref]

  • Brander, J. A., and A. Zhang. 1990. “Market Conduct in the Airline Industry: An Empirical Investigation.” RAND Journal of Economics 21(4):567–83. [Crossref]

  • Bresnahan, T. F. 1981. “Duopoly Models with Consistent Conjectures.” American Economic Review 71:934–45.

  • Chua, C. L., H. Kew, and J. Yong. 2005. “Airline Code-Share Alliances and Costs: Imposing Concavity on Translog Cost Function Estimation.” Review of Industrial Organization 26:461–87. [Crossref]

  • Diewert, W. E., and T. J. Wales. 1987. “Flexible Functional Forms and Global Curvature Conditions.” Econometrica 55(1):43–68. [Crossref]

  • Farrell, J., and C. Shapiro. 2000. “Scale Economies and Synergies in Horizontal Merger Analysis.” Antitrust Law Journal 68:685–710.

  • Feng, G., and A. Serletis. 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 and Finance 34(1):127–38. [Crossref] [Web of Science]

  • Fries, S., and A. Taci. 2005. “Cost Efficiency of Banks in Transition: Evidence from 289 Banks in 15 Post-Communist Countries.” Journal of Banking and Finance 29:55–81. [Crossref]

  • Goh, M., and J. Yong. 2006. “Impacts of Code-Share Alliances on Airline Cost Structure: A Truncated Third-Order Translog Estimation.” International Journal of Industrial Organization 24:835–66. [Crossref]

  • Hughes, J. P., and L. J. Mester. 1998. “Bank Capitalization and Cost: Evidence of Scale Economies in Risk Management and Signalling.” The Review of Economics and Statistics 80(2):314–25. [Crossref]

  • Humphrey, D. B. 1993. “Costs and Technical Change: Effects from Bank Deregulation.” The Journal of Productivity Analysis 4:9–34. [Crossref]

  • Levinsohn, J., and A. Petrin. 2003. “Estimating Production Functions Using Inputs to Control for Unobservables.” Review of Economic Studies 70(2):317–42. [Crossref]

  • Mountain, D. C., and H. Thomas. 1999. “Factor Price Misspecification in Bank Cost Function Estimation.” Journal of International Financial Markets, Institutions & Money 9:163–82. [Crossref]

  • Olley, G. S., and A. Pakes. 1996. “The Dynamics of Productivity in the Telecommunications Equipment Industry.” Econometrica 64(6):1263–97. [Crossref]

  • Perry, M. K. 1982. “Oligopoly and Consistent Conjectural Variations.” Bell Journal of Economics 14:301–14.

  • Ryan, D. L., and T. J. Wales. 2000. “Imposing Local Concavity in the Translog and Generalized Leontief Cost Functions.” Economics Letters 67:253–60. [Crossref]

  • Torres, M., and C. J. Morrison Paul. 2006. “Driving Forces for Consolidation or Fragmentation of the US Water Utility Industry: A Cost Function Approach with Endogenous Output.” Journal of Urban Economics 59:104–20. [Crossref]

About the article

Received: 2012-12-10

Accepted: 2013-08-19

Published Online: 2013-09-07

The endogeneity problem discussed here also arises when estimating production functions. Olley and Pakes (1996) and Levinsohn and Petrin (2003) introduce methods to account for serially correlated unobserved shocks to the production technology. Note that the scope of this article is wider though.

It can be checked that the entire line of reason holds for oligopoly markets. The assumption of P = MC does not drive the result and is merely used here for clarity.

The question whether fixed effects estimation provides a sufficient solution for the endogeneity problem is an empirical one and will be assessed in Section 4.

The alternative assumption, allowing θ to be firm- and time-specific, is discussed in Appendix B.

Estimating eq. [3] implies that market price P can be viewed as a parameter. This requires that the product under scrutiny is sufficiently homogeneous (so that the law of one price holds) and that variations in price over time are limited within the period of analysis.

Note that the expression on the right-hand side of eq. [4] boils down to marginal costs divided by average costs, which equals the scale elasticity (see Goh and Yong, 2006).

The derivation of the multi-product case can be found in Appendix A.

Again, see Appendix A for the derivation of this function.

We performed the same analysis using the five-product specification adopted by Hughes and Mester (1998), which yielded similar results.

A version of the model with dummy variables for all quarters included provided similar results.

Both other conditions, and do hold for both specifications.

The study by Feng and Serletis (2010) is very similar, as it uses the same product definition and geographical scope, and their time period lies within that of our study. They estimate a translog production function and find increasing returns to scale, which is similar to finding economies of scale in a cost function.

Note that we have no test statistic for the significance of scale economies in the adjusted version, but the scatter plot in Figure 2 clearly suggests a significant difference from unity at the mean.

Citation Information: The B.E. Journal of Economic Analysis & Policy, ISSN (Online) 1935-1682, ISSN (Print) 2194-6108, DOI: https://doi.org/10.1515/bejeap-2012-0070. Export Citation

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