The Informativeness of Stochastic Frontier and Programming Frontier Efficiency Scores: Cost Efficiency and Other Measures of Bank Holding Company Performance

Robert A. Eisenbeis, Gary D. Ferrier, and Simon H. Kwan
Federal Reserve Bank of Atlanta
Working Paper 99-23
December 1999

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This paper examines the properties of the X-inefficiencies in U.S. bank holding companies derived from both stochastic and linear programming frontiers. This examination allows the robustness of results across methods to be compared. While we find that calculated programming inefficiency scores are two to three times larger than those estimated using a stochastic frontier, the patterns of the scores across banks and time are similar, and there is a relatively high correlation of the rankings of banks' efficiencies under the two methods. However, when we examine the "informativeness" of the efficiency measured by the two different techniques, we find some large differences. We find evidence that the stochastic frontier scores are more closely related to risk-taking behavior, managerial competence, and bank stock returns. Based on these findings, we conclude that while both methods produce informative efficiency scores, for this data set decision makers should put more weight on the stochastic frontier efficiency estimates.

JEL classification: C13, C14, C21, D21, G21

Key words: stochastic frontier, data envelope analysis, X-inefficiencies, banks and bank holding companies, informativeness principle

The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Robert A. Eisenbeis, Research Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, NW, Atlanta, Georgia 30303-2713, 404/498-8851, 404/498-8956 (fax),; Gary D. Ferrier, Department of Economics, College of Business Administration, University of Arkansas, Fayetteville, Arkansas 72701, 501/575-3266, 501/575-7687 (fax); or Simon H. Kwan, Senior Economist, Economic Research Department, Federal Reserve Bank of San Francisco, 101 Market Street, Mail Stop 1130, San Francisco, California 94105, 415/974-3190, 415/974-2168,