Threshold effects of financial status on the cost frontiers of financial institutions in nondynamic panels

Abstract

This article applies Hansen's (1999, 2000) threshold regression model to estimate translog cost frontiers in the hope of shedding light on the banking industry's production processes and the extent of its Technical Efficiency (TE). The threshold technique allows for the existence of multiple technologies of production, distinguished by an exogenous threshold variable. Strong evidence of multiple technologies is found in the industry irrespective of which financial indicator, as constructed by factor analysis, defines the threshold variable. Cost savings and scale economies among the various underlying technologies are compared herein. We also highlight the differences between the threshold results and the conventional cost frontier.

Acknowledgements

The authors thank the editors and the anonymous referees for helpful suggestions. Partial financial support from the National Science Council (NSC 93-2416-H-032-012), Executive Yuan, Taiwan, The Republic of China, are gratefully acknowledged.

Notes

¹ The factor analysis procedure will be applied to financial ratios relevant to commercial banks in order to extract objective traits and characteristics of the performance measurement.

² Many studies have employed the Fourier flexible form to estimate technical efficiencies, e.g. Mitchell and Onvural (1996) and Berger and DeYoung (1997). However, Berger and Mester (1997, pp. 923–924) found that both the translog and the Fourier form yield a small difference on average efficiency scores and little difference in efficiency dispersion or rank. The same results are also found by Vennet (2002). Nevertheless, Beccalli (2004) and An et al. (2007) adopted the translog function to gauge efficiency measures, because of the availability of a small sample. We therefore choose to utilize the translog specification in this article.

³Hansen (1999) showed that the asymptotic distribution of the likelihood ratio test statistic is nonstandard yet free of nuisance parameters.

⁴ The estimation and test procedures using GAUSS programming software are available from Professor B. Hansen's homepage at http://www.ssc.wisc.edu/~bhansen

⁵ Admittedly, it is a potential difficulty that is yet to be solved regarding which explanatory variables alter between regimes.

⁶ There are two equivalent ways of imposing the homogeneity restriction in input prices. First, one can normalize the cost function by w ₁–say, such that a cost function can be reformulated as C/w ₁ = C(w ₂/w ₁,w ₃/w ₁,y ₁,y ₂). In doing so, the first input is viewed as the numeraire. Second, instead of normalizing price variables, the constraint is directly imposed on the coefficients of input prices. The first alternative is chosen by this article due to its simplicity.

⁷ It is, however, significant at the 10% level for factor 1. Given the medium size of 312 sample observations, we choose not to consider this possibility.

⁸ To verify whether the difference between these mean TE scores, obtained by the three models, reaches statistical significance, we use the nonparametric Kruskal–Wallis test and the standard test of the equality of two means pair by pair. Both tests reject the null of equalling mean TE scores for these pairs of mean TE scores at the 5% level.