Efficiency in banking: a meta-regression analysis

Abstract

One learns two main lessons from studying the great quantity of banking efficiency literature. These lessons regard the heterogeneity in results and the absence of a comprehensive review aimed at understanding the reasons for this variability. Surprisingly, although this issue is well-known, it has not been systematically analyzed before. In order to fill this gap, we perform a Meta-Regression-Analysis (MRA) by examining 1661 efficiency scores retrieved from 120 papers published over the period 2000–2014. The meta-regression is estimated by using the Random Effects Multilevel Model (REML) because it controls for within- and between-study heterogeneity. The analysis yields four main results. First, parametric methods yield lower levels of banking efficiency than nonparametric studies. This holds true even after controlling for the approach used in selecting the inputs and outputs of the frontier. Secondly, we show that banking efficiency is highest when using the value-added approach, followed by estimates from studies based on the intermediation method, whereas those based on the hybrid approach are the lowest. Thirdly, efficiency scores are also determined by the quality of studies and the number of observations and variables used in the primary papers. As far as the effects of sample size, dimension and quality of papers are concerned, there are significant differences in sign and magnitude between parametric and nonparametric studies. Finally, cost efficiency is found to be higher than profit efficiency. Interestingly, MRA results are robust to the potential outliers in efficiency and sample size distributions.

Keywords:

• banking industry
• frontier models
• efficiency
• meta-analysis
• study design

JEL Classifications:

• C13
• C14
• C80
• D24
• G21
• L25

Acknowledgements

The authors would like to thank Sergio Destefanis, Kristiaan Kerstens, Damiano Silipo, the participants of the EWEPA 2013 Conference held in Helsinki and three anonymous referees for very useful comments and suggestions on earlier versions of this paper. Editorial assistance by Martin Brimble and John Richard Broughton is also acknowledged. The usual disclaimer applies. At the time of writing this paper Graziella Bonanno was a post-doc visiting student at the Royal Docks Business School, University of East London, Docklands Campus, London, UK. She received a Research Fellowship from the Regione Calabria and EU Commission. The views and opinions expressed in this article are those of the authors and do not necessarily reflect the official policy or position of the EU Commission and the Regione Calabria.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Poot (2012) counts 626 papers that applied MRA to economics between 1980 and 2010, with an exponential growth in the 2000s. About three quarters of these MRA applications were published in field-specific journals, several appeared in ‘top’ journals (American Economic Review, Journal of Banking & Finance, Journal of Political Economy, Review of Economics and Statistics and Economic Journal), whilst the remainder are working-papers or book-chapters.

2. The wide spectrum of recent MRA applications in economics includes the tax impact on corporate debt financing (Feld, Heckemeyer, and Overesch 2013), the financial liberalization-growth nexus (Bumann, Hemres, and Lensink 2013), misalignments in real exchange rates (Ègert and Halpern 2006), the demand for gasoline (Havranek et al. 2012), labor supply elasticities (Chetty et al. 2011), the relationship between FDI and taxation (Feld and Heckemeyer 2011), the effect of active labor market policies (Card, Kluve, and Weber 2010), aid effectiveness (Doucouliagos and Paldam 2009), the role of distance in bilateral trade (Disdier and Head 2008), the 2% β-Convergence (Abreu, de Groot, and Florax 2005) and a variety of other environmental and transport issues (summarized in van den Bergh and Button 1997).

3. The choice of 2000 as a starting year of the analysis is due to the following reasons. Without any limitation, the time to create the metadata set would explode as the literature is massive. In this regard it is also important to say that the pre-2000 studies have been reviewed in several qualitative surveys (above all, see, Berger and Humphrey 1997; Coelli and Perelman 1999; Fethi and Pasourias 2010). Finally, the literature on banking efficiency significantly multiplied and diversified after 2000, which makes it a useful starting date.

4. We implement a test of differences in means for each sub-group. We always reject the null hypotheses of equality in means, except for two cases, which regard (1) the panel data versus cross-section data (p-value is equal to 0.1726) and (2) the intermediation approach versus the added-value approach (p-value is equal to 0.2072).

5. In panel c of Figure 6, the density referring to Cobb-Douglas is apart from translog and Fourier because the scale of frequencies is very different.

6. Technically, REML first estimates the between-study variance, τ², and then estimates the coefficients, β, with the weighted least squares procedure and using as weights 1/(σ_i² + τ²), where σ_i² is the standard error of the estimated effect in study i. The word ‘multilevel’ refers to the structure of the metadata set, which combines observations at the single estimates level and observations at the study level (Harbord and Higgins 2008; Thompson and Sharp 1999).

7. In selecting the explanatory variables of our meta-regressions, we bear in mind that the focus is to verify whether the methodology choices followed in primary works matter in determining the average level of banking efficiency. See Appendix B for the description of each variable.

8. Splitting the sample should allow better evaluation of the role of specific methodological choices. For instance, this is the case of the dummy Cobb-Douglas: in Model 4 the ‘zeros’ only refer to functional forms other than Cobb-Douglas and not to point-observations from nonparametric studies, as in Model 3. The same applies for the dummy VRS. Even though assumptions on return to scale are possible whatever the method, many parametric studies do not report which returns to scale they use and there is no way to understand the assumption. While the procedure followed in Models 4 and 5 is more appropriate compared with Model 3, it is interesting to point out that the results do not change when moving from Model 3 to Model 4 or to Model 5 (see Table 3).

9. In performing a sensitivity analysis, we restrict the sample to 1–99%, 5–95% and 10–90% intervals of the distribution of efficiency scores (Models 1, 2 and 3 of Table 4) and sample size (Models 4, 5 and 6 of Table 4).

10. When considering Model 1, both value-added and intermediation approaches over-perform compared with the hybrid approach and share the same effect (). In moving to Model 2, we find that, on average, the value-added approach yields the highest level of efficiency, followed by the intermediation and the hybrid approaches (and ).