The stability of bank efficiency rankings when risk preferences and objectives are different

Abstract

We analyze the stability of efficiency rankings of German universal banks between 1993 and 2004. First, we estimate traditional efficiency scores with stochastic cost and alternative profit frontier analysis. Then, we explicitly allow for different risk preferences and measure efficiency with a structural model based on utility maximization. Using the almost ideal demand system, we estimate input- and profit-demand functions to obtain proxies for expected return and risk. Efficiency is then measured in this risk-return space. Mean risk-return efficiency is somewhat higher than cost and considerably higher than profit efficiency (PE). More importantly, rank–order correlation between these measures are low or even negative. This suggests that best-practice institutes should not be identified on the basis of traditional efficiency measures alone. Apparently, low cost and/or PE may merely result from alternative yet efficiently chosen risk-return trade-offs.

Keywords:

• risk
• efficiency
• banks
• Germany

Acknowledgements

Substantial parts of this paper result from research conducted at the Utrecht School of Economics. I thank participants of the 2nd Deloitte conference on risk management in Antwerp and the Bundesbank seminar series for helpful comments. I am furthermore indebted to Jaap Bos, Jim Kolari, Clemens Kool, Christoph Memmel, Daniel Porath and two anonymous referees for most valuable input. I thank the Deutsche Bundesbank for providing me with the data. The opinions expressed here, however, are personal and do not necessarily reflect those of the Deutsche Bundesbank. All remaining errors are, of course, my own.

Notes

1. Review studies are, for example, Berger and Humphrey (1997) and Amel et al. (2004).

2. Most studies follow an early suggestion by Hughes and Mester (1993) and account for risk by specifying an additional netput in the production constraint of banks, namely equity capital.

3. Specification choices of parametric methods, such as SFA, are discussed in Kumbhakar and Lovell (2000). Non-parametric methods, such as Data Envelopment Analysis, avoid any distributional assumptions (Coelli et al. 2005), but are more sensitive to measurement error. Because the latter is a well-known problem in banking data we opt here for SFA (Mountain and Thomas 1999).

4. Due to well-known problems to measure output prices in banking, most PE studies are in fact so-called alternative PE analyses. Humphrey and Pulley (1997) suggest to allow banks some output market power. Thus, banks choose prices subject to an additional pricing opportunity constraint.

5. A number of European cross-country studies also include German banks, for example, Maudos et al. (2002) or Cavallo and Rossi (2001). By and large, reported CE is around 20% in the early 1990s. But most studies cover only a very small fraction of German banking. For example, Cavallo and Rossi (2001) sample 442 banks from six countries, while already in Germany alone around 3500 banks were in operation at the time under investigation.

6. Some studies use efficiency to determine bank mergers and failures (Koetter et al. 2007) or to analyze the effects of German bank consolidation (Lang and Welzel 1999). Since efficiency measurement itself is of subordinated interest there, we do not review these studies here.

7. Out of 3907 that operating between 1993 and 2004, only 4.7% were stock incorporated banks. Out of these 187 banks even fewer were also listed and traded on stock exchanges.

8. For example, Porath (2006) estimates probabilities of cooperative and savings bank default in this way and specifies proxies for solvency, market, and credit risk.

9. Evidence on market power among German banks is provided by Hempell (2004).

10. That is to say, , where superscripts indicate utility maximization, profit maximization and cost minimization, respectively.

11. We use for both the cost and alternative profit frontier the translog functional form and a fixed effect panel estimator described below. For details regarding CE and PE estimation with German bank data see Koetter (2006).

12. According to Deaton and Muehlbauer (1980) the parameters on the consumed goods’ prices are defined as and

13. For example Diamond and Rajan (2000) discuss the endogeneity of equity capital.

14. In fact, we also estimated the system pooled over all years and with alternative estimation techniques such as three-stage least squares with virtually no changes in terms of economic implications for RRE and the relation to CE and PE reported below.

15. Results for CE and PE reported below also include this control vector h for heterogeneity in the deterministic kernel of the respective frontiers.

16. Altunbas et al. (2001) also report differing standard CE and PE measures across groups.

17. Alternatively, one may argue to estimate separate frontiers for these banking groups. However, Coelli et al. (2005) point out that efficiency scores are relative measures. Therefore, a comparison of efficiency scores derived from different benchmarks is not possible. Since we focus here on (rank) stability across CE, PE and RRE for Germany's banking system as a whole, we directly account for systematic differences in the specification of the cost, profit and risk-return frontiers, respectively.

18. More specifically, in each year we create quartiles. Respective mean total assets in millions of € for size classes I through IV are 5500, 339, 131 and 46, respectively.

19. We avoid to assume a priori any (linear) development of an individual bank's RRE but rather allow it to develop unrestrictedly over time.

20. Koetter et al. (2006) report an interbank loan share of total assets for large banks of one-third in 2003. Smaller banks also expanded this share on average by 7.4% each year since 2002.

21. Including latent liabilities from discounted commercial paper (‘Wechsel’), guarantees, collateral for third party debt, irrevocable credit commitments and other OBS.

22. As pointed out by a referee, the common approach in the literature to use imputed input prices can be problematic since prices should be strictly exogenous. Mountain and Thomas (1999) suggest therefore to drop input prices entirely from estimation. Instead, Koetter (2006) calculates a bank's input prices as the average of all other banks operating in it's regional market. He reports that only CE levels are around five percentage points lower but that rankings are fairly stable. Since we are here especially interested in the latter and to ease comparability with other studies, we therefore follow here the standard approach followed in the majority of efficiency analyses.

23. Parameter estimates of cost and alternative profit frontier estimates are available upon request. To control for fixed time effects all reported results are estimated with yearly indicator variables.

24. In addition, we conducted for all specifications log-likelihood ratio tests if OLS is preferable compared with SFA and reject these hypotheses, too (Kumbhakar and Lovell 2000).

25. Reported CE and PE estimates result accordingly from cost and profit frontiers, where h is specified in the deterministic kernel, too.

26. Since efficiency measures are not normally distributed we do not use t-tests.

27. We applied a selection procedure along the lines of Hosmer and Lemshow (2000). Out of an initial total of around 150 candidate covariates for banks’ risk profiles, we select the reported vector on the basis of stepwise regression. More details on choosing a financial profile to predict the risk of bank default can be found in the aforementioned studies.