Annex 1. An Illustration of Data Envelopment Analysis
The following chart illustrates the concept of technical and allocative efficiency used in Data Envelopment Analysis. A fully-efficient bank that uses two inputs (x1, x2) to produce one output (y) has a certain production possibility frontier denoted by the unit isoquant I. A bank that produces at point a, which is inferior to the optimal production, has a technical inefficiency that is measured by the distance ab or in relative terms, the ratio ab/ao which gives the percentage by which both inputs would have to be reduced by the bank to attain full technical efficiency. Conversely, the technical efficiency score is denoted by TE = 1- ab/ao = bo/ao. Therefore, the efficiency scores are normalized to between 0 and 1, expressing in percentage terms the degree of efficiency with respect to the leading bank(s) or “best practices.”
Allocative efficiency (AE) is depicted by the distance between a point on the isoquant and the isocost line Wwhose slope is the ratio of the input prices, -w1/w2. The additional distance bc represents the reduction in production costs that would be obtained by changing the input mix in favor of using more of the relatively inexpensive factor x2 and, thus, moving along the isoquant to attain the allocatively (and technically) efficient point d.
Adler, G., M. Mansilla and T. Wezel, 2009, “Modernizing Bank Regulation in Support of Financial Deepening: The Case of Uruguay,” IMF Working Paper No. 09/199 (Washington: International Monetary Fund).
Battese, G.E. and T. Coelli, 1988, “Prediction of Firm-Level Technical Efficiencies With a Generalised Frontier Production Function and Panel Data,” Journal of Econometrics (38), pp. 387–399.
Coelli, T., 1996, “A Guide to FRONTIER Version 4.1: A Computer Program for Stochastic Frontier Production and Cost Function Estimation,” CEPA Working Paper, University of New England, Armidale (Australia).
Coelli, T., D.S.P. Rao and G.E. Battese, 1998, “An Introduction to Efficiency and Productivity Analysis” (London: Kluwer Academic Publishers).
Wezel, T., 2010a, “Bank Efficiency Amid Foreign Entry: Evidence from the Central American Region,” IMF Working Paper No. 10/95 (Washington: International Monetary Fund).
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Prepared by Torsten Wezel (MCM). I thank the very useful comments received from the staff of the Banco Central del Uruguay.
All calculations exclude the restructured public mortgage bank Banco Hipotecario del Uruguay.
Includes cash, deposits at the Central Bank (including required reserves), and deposits in other banks.
The interest rate margin represents a weighted average of peso and dollar rates on loans and on deposits.
Gross earnings (“resultado bruto”) are defined as net revenue from financial intermediation (i.e. interest and non-interest revenue less respective expenses from lending and provision of services) less loan loss provisioning and exchange rate-induced changes in the valuation of assets and liabilities.
For a more detailed explanation of DEA see Coelli, Rao and Battese (1998). As a non-parametric approach DEA does not correct for measurement errors and other white noise.
With 2006 as base year, the drop in productivity (median) is derived as follows: 100*0.825*1.265*0.896=93.5.
While SFA accounts for measurement errors, it requires assumptions about the production function and is subject to issues of econometric misspecifications.
While vi picks up the impact of measurement errors and other noise factors on output values, yi, and is therefore iid