A Thick Frontier Analysis for 1996

V. A Thick Frontier Analysis for 1996

The preceding analysis implicitly assumed that all thrifts in each year operated on the same cost frontier with the same underlying efficiency. Several authors, e.g., Bauer et al. 1993, Berger and Humphrey 1992, 1991 and Berger and Mester 1997a, 1997b, however, have questioned this assumption and used a thick cost frontier to address the issue of varying efficiency levels between groups of financial institutions. By recognizing that there are observed cost differences inefficiency which do not reflect random error, the thick frontier methodology reduces distributional assumptions on the error term in cost function regressions and provides more precise empirical measures. 12 A more general cost function regression decomposes the stochastic error into two parts as: lnC 5 C~ p,q 1 p; 13 lnC 5 C~ p,q 1 m 1 n, where C p,q is a general cost function as above; p is the composite error term; m represents firm-specific inefficiencies both allocative and technical which raise costs above best practice, and n is a true random error which represents measurement error or luck. The thick cost frontier approach decomposes the composite error and isolates the inefficiency component, m, by comparing the average efficiency of large subsamples of the available data. The complete sample is divided into quartiles based on average costs and it is then assumed that variation from expected values within each quartile represents random error, n, while variation between quartiles represents more fundamental ineffi- ciencies or exogenous differences, m. By estimating a separate regression for each quartile, therefore, the error terms are more likely to meet the statistical assumptions, e.g., n is mean zero and finite variance. 13 Following Berger and Mester 1997b, the 1,202 thrifts in 1996 were divided into four quartiles based on the residual that was obtained from the cost function estimation described in Section IV. 14 Thrifts with the smallest residuals were assumed to be cost efficient low m, while large residuals were indicative of cost inefficiency large m. Table 4 shows descriptive statistics for the thrifts in each quartile and the total of 1,202 thrifts in 1996. The lowest cost quartile shows the smallest average cost residual by definition, and there is a steady increase in average costs total cost divided by total assets across the four quartiles. The lowest cost quartile also shows the highest return on average assets ROA, return on average equity ROE, and Tier 1 Risk-Based Capital Ratio. These 300 thrifts appear to be the most cost efficient and the most successful, as one would expect. There is not, however, any definite trend in average size across the quartiles. 15 The system for the SUR analysis, equations 7 to 9, was then reestimated separately for each quartile in 1996. To compare behavioral differences across thrifts with varying 12 See Berger and Humphrey 1992, especially page 257, for a discussion of the econometric advantages. 13 The data envelopment analysis DEA approach is another alternative, which assumes that the random error component is zero, so that all unexplained variation represents inefficiency. 14 As an alternative, Bauer et al. 1993 created quartiles based on total costs per dollar of total assets. 15 To conserve space, the thick frontier analysis is reported only for 1996. The results for 1991 are similar and are available upon request. 154 K. J. Stiroh levels of efficiency, both the AES and the MES for the lowest cost quartile and the highest cost quartile were calculated using the estimated parameters not shown and mean values from each quartile, respectively. This approach compares behavioral differences between the two quartiles that reflect both technology as determined by the estimated parameters and behavioral variation as determined by the mean values. Table 5 reports the results. The estimated substitution patterns show some similarity between the two groups—all own-price AES were negative as expected, substitution was most responsive to a change Table 4. 1996 Summary Statistics by Efficiency Quartile Variables Cost Quartiles Total Lowest Second Third Highest Total assets 576,379.9 451,667.5 523,137.9 611,622.6 540,746.4 2,198,571.3 1,658,846.8 2,629,598.0 1,833,243.8 2,111,602.8 ROA 0.669 0.467 0.434 0.266 0.459 0.593 0.466 0.573 1.644 0.959 ROE 5.793 4.814 4.697 3.686 4.747 6.394 5.677 7.342 9.827 7.506 Tier 1 ratio 24.878 19.403 18.881 19.799 20.738 14.167 9.096 10.496 15.868 12.915 Average cost 0.056 0.059 0.061 0.065 0.060 0.007 0.007 0.008 0.021 0.013 Cost residual 20.268 20.066 0.052 0.285 0.001 0.144 0.038 0.037 0.177 0.232 No. obs. 300 300 301 301 1202 Standard deviations are in parentheses. Quartiles are based on a residual from equation 7, estimated for 1,202 thrifts in 1996. Table 5. Elasticities of Substitution by Cost Quartile in 1996 Allen Elasticities of Substitution AES - s jk Lowest Cost Highest Cost Capital Labor IBL Capital Labor IBL Capital 212.289 Capital 27.384 30.344 27.431 Labor 0.728 22.957 Labor 1.839 21.452 2.838 12.824 9.159 8.251 IBL 0.880 0.699 20.257 IBL 0.393 0.340 20.214 10.402 9.974 10.974 3.633 3.673 3.963 Morishima Elasticities of Substitution MES - M jk Lowest Cost Highest Cost Capital Labor IBL Capital Labor IBL Capital 0.841 0.851 Capital 0.938 0.791 32.475 28.269 31.477 22.472 Labor 0.707 0.701 Labor 0.905 0.493 23.401 12.257 27.485 6.763 IBL 0.845 0.711 IBL 0.379 0.346 10.894 10.273 3.902 3.805 t statistics are in parentheses. Elasticities are defined in equations 10–12. Measuring Input Substitution in Thrifts 155 in the price of capital, and the MES appeared asymmetric— but there were also several interesting differences between the two quartiles. The MES asymmetry appeared larger for the highest cost thrifts, which is consistent with their relatively high cost structure. If these thrifts cannot respond as quickly or easily to a change in a particular price, one would expect them to be less efficient and incur higher costs. Second, the own-price AES were generally larger for the lowest cost quartile. Third, the AES overstated the elasticity of substitution between capital and labor for the entire industry, but not for the lowest cost quartile separately. Both of these results imply more flexible substitution patterns for the lowest cost thrifts. Finally, the lowest cost quartile shows larger MES in terms of capitalIBL and laborIBL, but smaller MES in terms of capitallabor substitution. This suggests that the highest cost thrifts are the most restricted with regard to interest-bearing liabilities.

VI. Conclusions