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1. Introduction
The financial services industries in Western European countries have become highly integrated ever since the completion of the Single Market for Financial Services in 1993. Banking industries there have experienced a wide range of fundamental changes in their regulatory and competitive environments, including the reduction or elimination of trade and entry barriers to those markets in the European Union (EU). Banks are soon facing an increasingly competitive atmosphere not only from domestic markets, but also from abroad. Bank managers must adopt the best technologies to efficiently produce an array of financial products in order to gain excess profit and to be viable. In this wave of international economic integration, the cost efficiency of EU banks is a core issue worth to be deeply investigated.
Banks tend to take up more risk as the global economy becomes increasingly integrated and liberalized. As noted by González (2005) and Fiordelisi et al. (2011), the growing competition reduces the market power of banks thereby reducing their charter value. Chortareas et al. (2013) point out that excessive financial liberalization might provide an incentive for financial institutions to take greater risks, which might incur recent subprime crisis and European crises. In addition, banks in such an integrated and interconnected market as the EU are more likely to be exposed to global shocks (Camilla et al., 2013). How to successfully weather the financial crisis, particularly in the future, appears to be an important topic, and this is intimately associated with banks’ efficiency, since a cost efficient bank is able to offer various financial services to its customers in a lower cost and earn higher profits. This prompts the initial motivation for this study, aiming at investigating the efficiency of Western European banking industries.
Many previous studies that carry out international comparisons among banks of different nations estimate either a common frontier for those banks by pooling all
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observations together, or a group (country) specific frontier for each nation. The former approach implicitly assumes that banks from different countries have access to the same technology, which appears to be impractical, since each country has its own cultural traditions, resource endowments, and political and legal systems. These characteristics affect the behavior and willingness of banks to undertake new innovations. Different regulatory environments, for example, lead to either universal banking countries, such as Germany and Switzerland, or separated banking countries such as Belgium and the US (Allen and Rai, 1996). Universal banking countries permit commercial banks to engage in nontraditional activities such as investment, trading, real estate, and insurance, while separated banking countries do not. Barth et al. (2004) and Chortareas et al. (2012) describe some of the background information on regulatory and supervisory differences.
The latter approach attempts to obtain individual production frontiers for each country, which allows for measuring the country-specific efficiency scores for each sample bank. This method avoids making the strong assumption that all banks of different countries under consideration share the same technology. However, the so-derived efficiency scores are not comparable due to the fact that they are evaluated against different frontiers that represent dissimilar standard. The foregoing dilemma motivates Battese et al. (2004) and O’Donnell et al. (2008) to propose a mixed two-step approach to find the metafrontier production function that facilitates efficiency comparisons of different groups.
Their two-step procedure combines the conventional stochastic frontier approach (SFA) in the first step to estimate the group-specific frontiers with the mathematical programing technique in the second step to estimate the mefafrontier production function. Clearly, these two steps involve the use of distinct approaches, i.e., the econometric and non-parametric approaches. The former requires specifying a
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specific functional form with statistical noise, while the latter is function-free and unable to immune from random shocks. One potential limitation on the programming technique is that the parameter estimates are lack of statistical properties due to the linear (or quadratic) programming is deterministic in essence and its estimates are inclined to be confounded with shocks. Although Battese et al. (2004) suggest using simulation and bootstrapping methods to derive standard errors of the coefficient estimates, no statistical properties of the coefficient estimates and their standard errors have been inferred. Furthermore, to adjust for the effects of environments on the efficiency of a bank, the programming technique has to rely on, e.g., the two-stage method or three-stage methods (Fried et al. 2002).1 Conversely, the SFA of Battese and Coelli (1995) enables ones to examine the determinants of the efficiency scores in a single step.2
The current paper employs the newly developed model by Huang et al. (2012) to estimate and compare the cost efficiencies of banks in Western European countries.
The major difference between the new approach and the mixed approach of Battese et al. (2004) and O’Donnell et al. (2008) lies in the second step relating to the estimation of the metafrontier. Specifically, the metafrontier in the second step of the new model is still estimated by the SFA, rather than the linear or quadratic programming (QP). In this manner, the parameter estimates and their standard errors have known statistical properties. In addition, the technology gap ratio can be specified as a set of environmental variables, characterizing the exogenous differences faced by groups or countries. We can also refer the new metafrontier as the stochastic metafrontier (SMF), as opposed to the deterministic metafrontier derived by the mixed approach.
1 The method involves solving a linear programming problem to obtain some efficiency measures in a first-stage analysis. In the second stage, one regresses the measures from the first stage upon the environmental variables.
2 Wang and Schmidt (2002) find evidence supporting one-step models whenever one is interested in the effects of exogenous variables on efficiency levels, in which their analysis is based on the “scaling property”.
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In summary, the present study attempts to extend the deterministic metafrontier translog (TL) cost function to the more general SMF Fourier flexible (FF) cost function that has several advantages. First, since the technology parameters of the SMF are estimated by the maximum likelihood (ML), the conventional statistical inferences for parameter estimates can be directly drawn without relying on simulations or bootstrapping techniques. Second, the technology gaps can be treated as a one-sided error term, which, together with the statistical noise, constitutes the composed error. Finally, macroeconomic environmental conditions can be modeled as the determinants of the technology gaps, like the one proposed by Battese and Coelli (1995). The variance of the one-sided error term is heteroscedastic, as pointed out by Kumbhakar and Lovell (2003), which may be preferable and consistent with reality.
Although the translog cost function has been widely used by numerous practitioners to characterize the production technology of banking sectors, it is criticized as being merely able to locally approximate a true but unknown cost function, forcing large and small banks to lie on a symmetric U-shaped ray average cost curve, and producing biased measures of scale economies for bans of various sizes. See, for example, McAllister and McManus (1993), Wheelock and Wilson (2001), and Huang and Wang (2004). In contrast, the FF functional form of Gallant (1982) is the global approximation to the underlying cost function as closely as desired in Sobolev norm. Many empirical studies confirm that the FF function provides a better fit for financial institution data than the translog specification, e.g., McAllister and McManus (1993), Mitchell and Onvural (1996), Berger and Mester (1997), and Berger et al. (1997). The FF has now received more emphasis in the recent efficiency literature, e.g., Altunbaş et al. (2000, 2001a, b), Williams and Gardener (2003), Kraft et al. (2006), Das and Das (2007), Beccalli and Frantz (2009), Feng and Serletis (2009), Huang et al. (2011a, b), to mention a few. Therefore, the FF
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cost function should be a preferable choice to the standard translog form and can better describe the underlying technology adopted by banking sectors.
On the basis of the above framework, this paper is capable of assessing and comparing the efficiency scores among the banking industries of EU members under the uniform benchmark, i.e., the estimated metafrontier FF cost function. More specific, the bank-specific environmental variables are taken into account in the first step when the individual country-specific FF cost frontiers are estimated for each country. Next, the macroeconomic environmental variables are considered in the second step when the metafrontier FF cost function is estimated. These efforts intend to further shed light on banks’ performance in Western European countries during the transition period of financial reform, market integration, and financial crisis.
The rest of the paper is organized as follows. Section 2 briefly reviews the literature on metafrontier model and empirical studies specifically about banks’
efficiency in Western European countries. Section 3 formulates the metafrontier FF cost function and depict the estimation procedure. Section 4 introduces the data and variable definitions. Section 5 conducts the empirical study, while the last section concludes the paper.
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