Abstract
This article develops a new method of estimating inefficiencies in joint production and shows that unlike the approaches utilized in the previous studies of inefficiency, this method maintains a consistent relationship between the error term of a profit function and the error terms of its price derivatives. A useful by-product of the method is a proof of a Hotelling-like lemma that relates stochastic input demand and output supply functions to stochastic profit functions. While the previous studies fit a single frontier to data on all firms, this paper estimates a frontier unique to every observed firm to allow each one to have a different potential of achieving maximal levels of profit. The new method is applied in the analysis of annual data, 1984–1989, for U.S. commercial banks. Both the analytical and numerical results of the paper show that the residual that the previous studies attribute to inefficiency includes the effects of excluded variables and of inaccuracies in the specified functional forms. Once accurate estimates of these effects are subtracted from the residual, the distortions in the measured inefficiencies should be considerably reduced. Consequently, this article considers how such estimates might be obtained.
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Akhavein, Jalal D., Allen N. Berger, and David B. Humphrey. (1995). “The Effects of Bank Mega-Mergers on Efficiency and Prices: Evidence from the Profit Function.” Working Paper, Federal Reserve Board, Washington, DC.
Basmann, Robert L. (1988). “Causality Tests and Observationally Equivalent Representations of Econometric Models.” Journal of Econometrics, Annals 39, 69-104.
Berger, Allen N., Diana Hancock, and David B. Humphrey. (1993). “Bank Efficiency Derived from the Profit Function.” Journal of Banking and Finance 17, 317-347.
Berger, Allen N., William C. Hunter, and Stephen G. Timme. (1993). “The Efficiency of Financial Institutions: A Review and Preview of Research Past, Present, and Future.” Journal of Banking and Finance 17, 221-249.
Diewert, W. Erwin, and Lawrence Ostensoe. (1988). “Flexible Functional Forms for Profit Functions and Global Curvature Conditions.” In W. A. Barnett, E. R. Berndt, and H. White (eds.), Dynamic Econometric Modeling. Cambridge, England: Cambridge University Press.
Gallant, A. Ronald. (1981). “On the Bias in Flexible Functional Forms and an Essentially Unbiased Form: The Fourier Flexible Form.” Journal of Econometrics 15, 211-245.
Judge, George G., William E. Griffiths, R. Carter Hill, Helmut Lütkepohl, and Tsoung-Chao Lee. (1985). The Theory and Practice of Econometrics (2nd ed.). New York: John Wiley & Sons.
Lehmann, Erich L. (1983). Theory of Point Estimation. New York: John Wiley & Sons.
Lovell, C. A. Knox, and Robin C. Sickles. (1983). “Testing Efficiency Hypothesis in Joint Production: A Parametric Approach.” The Review of Economics and Statistics LXV, 51-58.
Pratt, John W., and Robert Schlaifer. (1984). “On the Nature and Discovery of Structure.” Journal of the American Statistical Association 79, 9-21, 29–33.
Pratt, John W., and Robert Schlaifer. (1988). “On the Interpretation and Observation of Laws.” Journal of Econometrics 38, 23-52.
Rao, C. R. (1973). Linear Statistical Inference and its Applications (2nd ed.). New York: John Wiley & Sons.
Sickles, Robin C., David Good, and Richard L. Johnson. (1986). “Allocative Disortions and the Regulatory Transition of the U.S. Airline Industry.” Journal of Econometrics 33, 143-163.
Swamy, P. A. V. B., Roger K. Conway, and Peter von zur Muehlen. (1985). “The Foundations of Econometrics—Are There Any?” Econometric Reviews 4, 1-61, 101–119.
Swamy, P. A. V. B., and Jatinder S. Mehta. (1975). “Bayesian and Non-Bayesian Analysis of Switching Regressions and of Random Coefficient Regression Models.” Journal of the American Statistical Association 70, 593-602.
Swamy, P. A. V. B., Jatinder S. Mehta, and Rao N. Singamsetti. (1995). “Circumstances in Which Different Criteria of Estimation Can Be Applied to Estimate Policy Effects.” Journal of Statistical Planning and Inference, forthcoming.
Swamy, P. A. V. B., Jatinder S. Mehta, Peter von zur Muehlen, and George S. Tavlas. (1991). “Some Problems with Identification in Parametric Models and their Solutions.” Greek Economic Review 13, 287-312.
Swamy, P. A. V. B., and Peter von zur Muehlen. (1988). “Further Thoughts on Testing for Causality with Econometric Models.” Journal of Econometrics, Annals 39, 105-147.
Swamy, P. A. V. B., and George S. Tavlas. (1992). “Is It Possible to Find an Econometric Law That Works Well in Explanation and Prediction?” Journal of Forecasting 11, 17-33.
Swamy, P. A. V. B., and George S. Tavlas. (1995). “Random Coefficient Models: Theory and Applications.” Journal of Economic Surveys 9, 165-196.
Varian, Hal R. (1984). Microeconomic Analysis (2nd ed.). New York: W.W. Norton & Company.
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Akhavein, J.D., Swamy, P.A.V.B., Taubman, S.B. et al. A General Method of Deriving the Inefficiencies of Banks from a Profit Function. Journal of Productivity Analysis 8, 71–93 (1997). https://doi.org/10.1023/A:1007776431663
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DOI: https://doi.org/10.1023/A:1007776431663