2. An Overview of Recent Literature
2.2 Western European Banking Performance
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the case of multiple outputs and inputs, making it particularly suitable for characterizing multi-output firms such as financial institutions and insurance companies.
Although the metafrontier approach allows researchers to correctly perform efficiency comparison among different groups and has drawn much attention to academic researchers, e.g., Bos and Schmiedel (2007), Chen and Song (2008), Moreira and Bravo-Ureta (2010), Mariano et al. (2011), and Lu and Chen (2012), it suffers from some potential methodological limitations as mentioned in the previous section. A more recent study by Huang et al. (2012) elaborate the metafrontier production function and propose a new two-step approach to construct the SMF. This novel approach first estimates technical efficiency with respect to group-specific frontiers, followed by measuring the technology gap ratio with respect to the metafrontier under the framework of the SFA, instead of using mathematical programming techniques. It can be shown that the model of Battese et al. (2004) and O’Donnell et al. (2008) is a special case of the new two-step approach.
2.2 Western European Banking Performance
Recently, the efficiency measurement of banking industries is of great concern because of the prevalence of deregulation, globalization, and financial innovation in the industry, as well as the intensified competition that raises operation and global risks. In the ongoing integration of European financial markets, the structure of banking industries has experienced rapid changes. Whether the efficiency scores of European banks tends to be equalized is an interesting issue and worth thoroughly investigated. Different frontier approaches based on either parametric or nonparametric techniques have been carried out in order to evaluate and compare banks’ efficiencies in Western Europe and other areas. Berger and Humphrey (1997),
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Goddard et al. (2001), Berger (2007), Fethi and Pasiouras (2010), and Hughes and Mester (2012) offer excellent reviews on this matter. Table 1 summarizes the relevant literature with a particular focus on international comparison of banking efficiencies in Western European countries.
Many earlier works have already performed cross-country comparisons by estimating a global cost frontier for the commercial banks in European countries.
Allen and Rai (1996) adopt both SFA and DFA (distribution-free approach) to compare cost efficiency (CE) measures across 15 developed countries (including 11 Western European countries) for the period 1988-1992. They divide those sample countries into universal banking and separated banking countries, corresponding to different regulatory environments. Using a translog specification, evidence is found that universal banks are more efficient than those of non-universal banks, and financial institutions in France, Italy, United Kingdom, and United State are the most inefficient. Altunbaş et al. (2001a) extends the translog cost frontier to the FF cost frontier and analyze banking efficiency of 15 European countries during the period 1989-1997. Their empirical results suggest that banks can save total costs by reducing managerial and other inefficiencies. The X-inefficiency of EU banks reveals a gradually decreasing secular trend over the sample period.
The above studies attempt to construct a common frontier for all banks from different countries, implicitly assuming that banks from various countries undertake a common production technology. Even though this setting allows for a direct comparison of efficiency levels, it fails to account for potential technology heterogeneity among sample countries, leading to misspecification. Meanwhile, the roles played by environmental variables on the determination of a bank’s cost efficiency have drawn much attention to empirical researchers. See, for example, Dietsch and Lozano-Vivas (2000), Cavallo and Roosi (2002), Lozano-Vivas et al.
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Table 1 Listing of selected studies of West European banking Efficiency by distinct frontier techniques
Authors Countries Period Methods / Specifications Measures
Part A. Common frontier
Allen and Rai (1996) Austria, Belgium, Denmark, Finland, France, Germany, Italy, Spain, Sweden, Switzerland, UK
1988-1992 SFA, DFA / TL CE
Altunbaş et al. (2001a) Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden, UK
1989-1997 SFA / FF CE
Vennet (2002) Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, UK
1995-1996 SFA / TL, FF CE, PE
Casu and Girardone (2004)
France, Germany, Italy, Spain, UK 1993-1997 SFA, DEA / FF, TL CE, PE
Part B. Common frontier with environmental variables Dietsch and
Lozano-Vivas (2000)
France, Spain 1988-1992 DFA / TL CE
Lozano-Vivas et al.
(2001)
Belgium, Denmark, France, Germany, Italy, Luxembourg, Netherlands, Portugal, Spain, UK
1993 DEA, B&M (1996) TE
Lozano-Vivas et al.
(2002)
Belgium, Denmark, France, Germany, Italy, Luxembourg, Netherlands, Portugal, Spain, UK
1993 DEA, B&M (1996) TE
Cavallo and Roosi (2002)
France, Germany, Italy, Netherlands, Spain, UK 1992-1997 SFA, B&C (1995) / TL CE
Casu and Molyneux France, Germany, Italy, Spain, UK 1993-1997 DEA, Tobit / n.a. TE
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Denmark, France, Germany, Italy, Spain, UK 1990-1998 SFA, B&C (1995) / FF CE
Beccalli (2004) Italy, UK 1995-1998 SFA, B&C (1995) / TL CE Beccalli and Frantz
(2009)
Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, UK
1991-2005 SFA, B&C (1995) / FF CE, PE
Chortareas (2013) Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden, Switzerland, UK
2001-2009 DEA, truncated regression / n.a.
TE
Part C. National frontier
Berger et al. (2000) France, Germany, Italy, UK, US 1992-1997 SFA / FF CE, PE Weill (2004) France, Germany, Italy, Spain, Switzerland 1992-1998 SFA, DEF, DEA / FF CE Part D. Metafrontier
Bos and Schmiedel (2007)
Austria, Belgium, Denmark, France, Germany, Greece, Italy, Luxembourg, Netherlands, Norway Portugal, Spain, Sweden, Switzerland, UK
1993-2004 SFA, quadratic programming
TL CE, PE
Kontolaimou and Tsekouras (2010)
Austria, Belgium, France, Germany, Italy, Spain, 1997-2004 DEA n.a. TE
Huang et al. (2011a) Austria, Belgium, Denmark, France, Germany, Italy, Portugal, Spain, Switzerland
1994-2003 SFA, quadratic programming
FF CE
Notes: B&M (1996) denotes Banker and Morey (1996); B&C (1995) denotes Battese and Coelli (1995).
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(2001,2002), Beccalli (2004), Beccalli and Frantz (2009), Battaglia et al. (2010), who carry out international comparisons among countries using common frontiers that take environmental conditions into account. Cavallo and Roosi (2002) employ the model of Battese and Coelli (1995) and define a bank’s size, bank organization types, and bank balance indicators as the environmental variables. Their results suggest that banks in Germany are more efficient than others.
Differing from the conventional use of a common frontier, the metafrontier function proposed by Battese et al. (2004) is so constructed as to envelope the group-specific frontiers of a set of countries. Under this framework, Bos and Schmiedel (2007) use the translog cost function to estimate comparable efficiency measures for 15 Western European commercial banks during the period 1993-2004.
They intend to address the question that whether a single European banking market shares a common benchmark frontier. The results support the existence of a single European banking market and the average efficiency measures obtained by the pooled (common) frontier tend to underestimate in comparison with those obtained by the metafrontiers. Huang et al. (2011a) extend the metafrontier production function to the metafrontier FF cost function with time-varying technical inefficiency. They conclude that the mean TGRs are generally increasing over time and that European banks are inclined to adopt more advanced technology during the sample period.
Another strand of contemporary literature compares the efficiency of banks across European nations by estimating individual national frontiers. Berger et al.
(2000) claim that estimating individual frontiers avoids the comparison problem arising from the environmental differences across nations. They employ the SFA to estimate the cross-border banking efficiency and compare foreign-owned with domestic-owned banks in France, Germany, Spain, the United Kingdom, and the United States, covering 1992-1997. The outcomes show that domestic banks in these
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countries outperform foreign banks in terms of cost efficiency, supporting the home field advantage hypothesis. Weill (2004) estimates the cost efficiency of banks in 5 European countries, i.e., France, Germany, Italy, Spain, and Switzerland, using various methods of the SFA, DFA, and DEA for the period 1992-1998. It is crucial to note that the efficiency scores obtained by the foregoing two papers are in fact not directly comparable, because these measures are gauged against different group frontiers, rather than a common frontier or metafrontier.
To sum up, all of the aforementioned works that involve cross-country comparisons of efficiency count on either estimating a common frontier or group specific production frontiers, but not both. The common frontier approach requires the imposition of homogeneous technology adopted by all banks of different countries, which is inconsistent with the reality and hence results in biased parameter estimates and efficiency measures. Moreover, the individual frontiers approach suffers from the problem of incomparability arising from heterogeneous benchmarks for banks from different countries. The current paper attempts to solve those difficulties under the framework of the new metafrontier FF cost function that seems to be advantageous over the mixed approach.
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3.1 The Fourier Flexible Cost Function
The FF function is a semi-parametric approach that expands the standard translog functional form by adding a set of trigonometric Fourier series. See, for example, Altunbaş et al. (2001), Huang and Wang (2003, 2004), and Huang et al.
(2011a, b). These additional terms consist of various sine and cosine functions that are mutually orthogonal. Gallant (1982) shows that the FF function is capable of approximating the true (but unknown) function as closely as desired in Sobolev norm.
Let
W
=( W
1, ,…W ′
N)
be an N-vector of input prices andY
=( Y
1, ,…Y
M)
′ be anM-vector of output quantities. The FF cost frontier (
lnf X
t( )
it ) of bank i at time t , for a given country (group) j, is formulated as:( )
0( ) ( )
1mth (log)output quantities and the nth (log)input prices, respectively, T represents
the time trend. Since the trigonometric function of sine and cosine are defined over 0