The purpose of this survey is to supply a methodological analysis for the joint appraisal of efficiency and market power of single Bankss. The proposed method utilizes the separate deductions of the new empirical industrial organisation and the stochastic frontier literatures and suggests designation utilizing the local upper limit likeliness ( LML ) technique. Through LML, appraisal of market power of single Bankss becomes executable, while a figure of restrictive theoretical and empirical premises are relaxed. The empirical analysis is carried out on the footing of EMU bank informations. Market power estimations indicate reasonably competitory behavior in general ; nevertheless, heterogeneousness in market power estimations is significant across Bankss. The latter consequence suggests that the pattern of some Bankss perverts from the mean reasonably competitory behaviour, a determination that has of import policy deductions. Finally, efficiency and market power present a negative relationship, which is in line with the alleged “ quiet life hypothesis ” .

JEL categorization: L11 ; C14 ; G21

Keywords: Efficiency ; Market power ; Local maximum likeliness

## 1. Introduction

The empirical mold of bank efficiency and market power day of the months back at least to the 1980s, yet it remains an attractive research country from both a micro and a macroeconomic point of view. Several surveies have estimated bank efficiency utilizing production, cost or net income frontiers. Their analysis is based on the appealing construct that runing efficiency may be estimated as an linear constituent of the stochastic mistake term.[ 1 ]Many other surveies used the deductions of the new empirical industrial organisation ( NEIO ) literature ( see Bresnahan, 1989 ) to measure the competitory conditions predominating at the banking-industry degree. The focal point of the NEIO literature has been the coincident appraisal of a supply relation and a demand map so as to place the so called “ divinatory fluctuation snap ” or “ behavior parametric quantity ” , which serves as a step of market power. Both these subdivisions of empirical mold experienced a lively development, yet this did non forestall them from staying reasonably separate.[ 2 ]At first sight this seems uneven as it is now by and large acknowledged that market power surveies that ignore inefficiency obtain indexs of market power that are potentially badly colored ( see e.g. Berg and Kim, 1998 ) . However, besides the implied misspecification, there has non been peculiar attempt to correlate bank-level steps of market power with efficiency estimations, likely owing to the systematic trouble in mensurating market power exercised by single Bankss.

The fresh characteristic of the present paper is that it provides a model for the joint appraisal of efficiency and market power at the single bank-level. Obtaining bank-level estimations of operating efficiency utilizing stochastic or additive scheduling frontiers is a comparatively easy undertaking. Similarly, utilizing the deductions of the NEIO literature, the competitory conditions in banking markets can be estimated at the industry degree on the footing of supply and demand maps. By uniting these two strands of literature, bank-level estimations of operating efficiency and industry-level estimations of competitory behavior can be obtained at the same time, as in the fresh recent survey of Maudos and de Guevara ( 2007 ) .[ 3 ]Phrased otherwise, one may gauge a system comprising of a cost map ( that is needed to obtain estimations of the fringy cost ) and the usual supply relation and demand map of NEIO literature, and obtain an estimation for the behavior parametric quantity ( at the industry degree ) and bank-level estimations of efficiency.

Trouble arises, nevertheless, in the appraisal of bank-level behavior parametric quantities ( firm-specific indexs of market power ) and, to this intent, bing literature proposes appraisal of Lerner indices or computation of the Tobin ‘s Q. Yet, usage of the former step encompasses the instead restrictive premise of a changeless marginal cost for the industry or for categories of Bankss within the industry, which is so used to cipher firm-specific price-cost borders. In bend, appraisal of the fringy cost requires farther premises sing the functional signifier of the implicit in production relationship. Furthermore, it has been shown late that parametric stochastic frontier efficiency estimations may be debatable if the specified functional signifier is non a good contemplation of the informations ( Kumbhakar et al. , 2007 ) . This consequence of course extends to estimations of the Lerner index, as their derivation requires premises related to the form of the production relationship, and therefore similar defects apply.[ 4 ]Tobin ‘s Q in bend, even though rather utile as a placeholder for market power, requires information on the market value of assets that may non be by and large available ( particularly for non-listed companies ) , while it does non arise from standard industrial organisation theory.

In an attempt to do advancement on the consistent appraisal of bank-level market power, utilizing widely available beginnings of bank informations, this paper proposes appraisal of the cost-supply-demand system utilizing the rule of local upper limit likeliness ( LML ) . LML, introduced by Tibshirani and Hastie ( 1987 ) , has been late employed to gauge stochastic frontiers by Kumbhakar et Al. ( 2007 ) and Kumbhakar and Tsionas ( 2007 ) . Since LML allows for observation-specific coefficients through localisation, the behavior parametric quantity is besides made firm-specific and serves as an index of market power possessed by single Bankss. In add-on, usage of the LML rule nowadayss at least two other advantages. First, the restrictive premise of a planetary parametric functional signifier ( such as the Cobb-Douglas, translog or Fourier ) that is needed to gauge fringy cost is avoided and, therefore, the theoretical account is robust to such possible misspecification. Note that in this manner the fringy cost is besides made firm-specific and the debatable characteristic of a changeless marginal cost across Bankss or categories of Bankss in the appraisal of the Lerner index is accounted for. Second, since the parametric quantities are localized at each observation, flexibleness is non an issue and the usage of a general additive signifier for both the supply relation and the demand map gives a clear economic significance to each and every coefficient that is made firm-specific through localisation. This besides implies that LML allows for full control of the unobservable heterogeneousness in bank behaviour, without utilizing parametric premises on fixed or random effects. Naturally, the above generalisations ease concerns raised in the industrial organisation literature by Corts ( 1999 ) and Genesove and Mullin ( 1998 ) as respects the reading of the behavior parametric quantity and, hence, they may be rather of import in pulling robust decisions about the efficiency and market power degrees or their possible relationship.

The empirical model is constructed in footings of an bing simple theoretical theoretical account of the banking industry[ 5 ]and is applied to a panel of EMU Bankss. The chief grounds behind this pick is that ( I ) there exists a ample and comprehensive literature on the measuring of efficiency and market power of Bankss in this part, ( two ) we have good priors sing the construction of the specific banking systems and ( three ) sufficient information is by and large available. The findings indicate that the empirical model provides rather sensible estimations for both efficiency and market power. The EMU banking system is characterized by reasonably competitory patterns ; nevertheless, what could non be uncovered in old surveies is that the distribution of market power of Bankss has a significant discrepancy ( i.e. important differences in market power are observed between Bankss ) . Finally, the bank-level estimations of market power are adversely related with the efficiency tonss, a determination that conforms to the of import deductions of the “ quite life hypothesis ” as formed by Hicks and tested by Berger and Hannan ( 1998 ) on the banking industry.[ 6 ]

Besides supplying consistent estimations of efficiency and market power, we view the proposed technique as a valuable tool in researching theoretical relationships in banking that require informations on the market power of single establishments. For illustration, surveies researching the relationship between market power and ( I ) denationalizations, ( two ) brotherhood dickering power, ( three ) fiscal liberalisation, ( four ) efficiency effects of amalgamations and ( V ) regulative restructuring and efficiency may profit from the suggested attack. As discussed above, this is chiefly because the figure of observations will be well increased as market power estimations are made bank-specific through localisation.

The remainder of this paper is structured along the undermentioned lines. Section 2 provides an overview of the theoretical background and presents the empirical theoretical account. Section 3 carries out the empirical analysis in footings of the EMU banking sector and discusses the consequences. Finally, Section 4 summarizes the chief decisions.

## 2. Theoretical background and econometric theoretical account

2.1. Theory and designation

In this subdivision we provide a method for the joint appraisal of market power in end products and runing efficiency, both at the firm-level. We model the representative bank, but a similar analysis may be carried out for any other industry. Several surveies have individually assessed the efficiency and competitory conditions of the banking industry, and this experience provides utile feedback for the present analysis.[ 7 ]However, the present survey perverts from old literature in two ways. First, we opt for the coincident appraisal of market power and efficiency and back the market power estimations are made firm-specific. We base our attack on the Cournot-type theoretical model of Uchida and Tsutsui ( 2005 ) , which has besides been employed by Brissimis et Al. ( 2008 ) . In peculiar, see a set of one Bankss, confronting at clip T industry demand for loans Lt, and seek to maximise the undermentioned net income map:

` ( 1 )

where I are the net incomes of bank I at clip T, rl bases for the loaning rate, cubic decimeter is the value of loans made by single Bankss, rubidium is the involvement rate on bonds Bs, rd is the sedimentation rate, vitamin D is the value of sedimentations and C is the operating cost map. The representative bank ‘s job is to and the first order conditions for this job are

and ( 2 )

where is the market demand snap for loans and represents the well-known divinatory fluctuation snap of the new industrial organisation ( NEIO ) literature. In theory, the scope of possible values for I? is given by ( 0,1 ) . In the particular instance of Cournot behaviour, i.e. , I? is merely the end product portion of the ith bank. In the instance of perfect competition, I?=0 ; under pure monopoly, I?=1 ; and, eventually, I? & lt ; 0 would connote pricing below fringy cost and could ensue, for illustration, from a non-optimizing behaviour of Bankss in their loaning policy.

The first equation of System ( 2 ) may be estimated if one has proper informations on the output of authorities bonds. However, such information is by and large unavailable and, hence, we omit the bond rate from the estimated equation by uniting the two equilibrium conditions of System ( 2 ) . The resulting equation is:

( 3 )

Following Uchida and Tsutsui ( 2005 ) , we further simplify our estimated equation by rearranging Eq. ( 3 ) and specifying as the gross of bank I generated by loans. This transmutation yields the undermentioned look:

( 4 )

Note that unlike old surveies, the firm-level nature of the divinatory snap parametric quantity I? is reserved, which is in fact closer to the theoretical priors of the NEIO literature ( see Bresnahan, 1989 ) .

In most of the empirical applications of this type the fringy cost is non available, but has to be estimated on the footing of a cost map. Appraisal of a cost map is normally carried out at the same time with a supply relation similar to Eq. ( 4 ) and an appropriate demand map that helps placing I? from I· . Following this paradigm, we specify a translog cost map of the undermentioned signifier:

( 5 )

where tungsten is the monetary value of inputs and bars over the variables represent divergences from their agencies. This focus of the variables is an easy manner to cut down multicollinearity, which is a ill-famed job of the translog functional signifier ( for a similar execution of the translog, see Brissimis et al. , 2008 and Uchida and Tsutsui, 2005 ) . Substituting the variables and parametric quantities of Eq. ( 5 ) into the several derived functions of Eq. ( 4 ) , we obtain the following estimable supply relation:

( 6 )

Finally, in order to place I? from I· , we specify the undermentioned opposite loan demand map:

( 7 )

where, gross domestic product is existent GDP in changeless monetary values, macgdp is the capitalisation of the stock market over GDP, Ir is the annual bond rate and Ta is entire assets ( placeholder for bank size ) . The variables gross domestic products and macgdp are exogenic variables that affect demand and Ir is a sensible placeholder for the monetary value of a demand replacement for loans ( for a thorough treatment on the variables included in the demand equation, see Shaffer, 1999 ) .

At this point, note that this optimisation model implicitly assumes that each bank is runing on its cost map. Yet, there exists an extended literature on bank-level efficiency proposing that establishments operate at inefficient degrees, which in many instances are rather important ( for reappraisals, see Hughes and Mester, 2008 ; Berger and Humphrey, 1997 ) . However, if inefficiency is non taken into history the optimisation theoretical account may go irrelevant and the corresponding prejudice may be rather terrible as the degree of inefficiency additions. This of import issue has been foremost noted by Berg and Kim ( 1998 ) and it has besides been acknowledged by Koetter and Poghosyan ( 2009 ) . Most of the old literature on competition merely disregards this job and merely few surveies resort to the inclusion of lone efficient houses into the theoretical account of competition ( e.g. Berg and Kim, 1998 ) . In this paper, we allow for inefficiency in the cost map by break uping the error term in Eq. ( 5 ) to a constituent u related to bank efficiency and the staying perturbation v. In other words, Eq. ( 5 ) is treated as in the standard stochastic frontier analysis ( see Coelli et al. , 2005 ) , and hence by gauging at the same time Eqs. ( 5 ) , ( 6 ) and ( 7 ) one can obtain estimations of both firm-level efficiency and industry-level competition.

2.2. Econometric process

What remains as a challenge is the designation of the divinatory fluctuations snap I? at the bank-level. This is accomplished by pulling on a non-parametric appraisal technique, in peculiar the local upper limit likeliness ( LML ) technique, to gauge the system specified supra. To present some notation, see a system of equations, dwelling of a vector of dependent variables y, a vector of independent variables x and a vector of unknown parametric quantities I?i?ZI? . In vector notation this system can be written as, i=1, aˆ¦ , n, i?¦ is a vector map and. The usual parametric upper limit likeliness ( ML ) calculator is

( 8 )

where, n is the figure of observations, m is the dimensionality of I? , I© denotes the criterion normal cumulative distribution map. The ML calculator of maximizes the concentrated log-likelihood map

( 9 )

where. Its covariance matrix can be computed as, whereand is the K x m gradient of the complete system with regard to the parametric quantities evaluated by the ML calculator.

LML appraisal of the corresponding non-parametric theoretical account involves a figure of stairss. First, we specify a meat map of the signifier, zi?ZRd, where vitamin D is the dimensionality of xi, H=h*S, H & gt ; 0 is the bandwidth and S is the sample covariance matrix of xi. Then, by taking a peculiar point xi?ZX, we may work out the undermentioned job:

where, , following the standardization. A solution to this job provides parametric quantity estimations.[ 8 ]Besides notice that the weights W do non affect unknown parametric quantities ( if h is fixed ) .

We proceed by concentrating the log-likelihood map above with regard to I© to obtain the undermentioned local calculator

( 11 )

and replacing in Eq. ( 8 ) we obtain

( 12 )

Eq. ( 10 ) can be maximized numerically with regard to I? to obtain. Notice that the local calculator is merely the covariance matrix of leaden remainders, so in fact LML appraisal of the type proposed here can be described as an iterated SUR calculator in a decently weighted theoretical account ( the weights are computed in progress ) .

It is possibly of import to analyse what the methodological analysis described above achieves. First, as the chief part of the paper implies, we provide a methodological analysis for the joint appraisal of market power and efficiency, both at the single house degree. Note, that in making so, we implicitly suggest a new method to obtain an index of market power for the single houses in the sample. This is accomplished because estimations of market power ( and of all coefficients ) are made bank-specific through localisation. However, besides note that ( unlike old surveies in the NEIO literature ) this process allows for the derivation of bank-level fringy costs in the appraisal of the cost map. Given the important concerns of the industrial organisation and banking literatures sing the infliction of a changeless marginal cost across Bankss when gauging the Lerner index, we view this as a important methodological promotion. Second, we provide parameter estimatesthat depend on ten, and hence the job of functional signifier specification in cost theoretical accounts is solved. Third, the covariance matrix I© is made map of x, so efficaciously we allow for heteroskedasticity of unspecified, non-parametric signifier in all mistake footings of the system. Fourth, exactly because we are able to do all parametric quantities firm-specific, we efficaciously take the premise of normalcy from the mistake footings. Last, but non least, the fact that LML ( and in fact any other local method ) allows for observation-specific parametric quantity estimations suggests a plausible method to place parametric quantity heterogeneousness, which may be of great importance in bespeaking single bank schemes. Given all of the above, we feel that this is an highly general theoretical account that solves many of the jobs associated with the appraisal of NEIO cost-demand-supply systems. Similar statements have been made by Kumbhakar et Al. ( 2007 ) and Kumbhakar and Tsionas ( 2007 ) for the non-parametric appraisal of stochastic frontier theoretical accounts.

At this phase, nevertheless, we besides need to do a figure of critical comments refering the proposed methodological analysis. First, the theoretical model assumes the being of market power merely in the end product side. In other words, the possible presence of monopsony power in bank sedimentations is non accounted for. Within a really similar theoretical model, Shaffer ( 1999 ) showed that in the presence of monopsony power, the grade of monopoly power would be overstated by the estimations, but the overall being and magnitude of competitory conditions would be accurately reflected. Therefore, even though our specification has the consequence of misattributing market power on the input side to that of the end product side, no information of policy significance is lost. Second, statistical trials for monopoly or competitory equilibrium ( i.e. trials of I?=1 or I?=0, severally ) are non easy to execute if one does non build assurance intervals. In general, assurance intervals have to be calculated from abrasion, a process that may be computationally intensive. In the empirical application below we construct assurance intervals for I? to exemplify the part within which a bank is considered to act competitively or monopolistically. Note, nevertheless, that the behavior parametric quantity I? provides a uninterrupted index of competition ( with higher values reflecting more market power and frailty versa ) . Therefore, if this index is to be used in a subsequent phase of analysis ( e.g. to gauge the relationship between M & A ; As and market power as in Konings et al. , 2005 ) , gauging the degree of market power is sufficient. Finally, note that as with every non-parametric technique, LML has to be applied to big datasets to avoid the alleged “ expletive of dimensionality ” . Fortunately, this is non an issue for micro-level surveies such as ours, where big datasets are comparatively easy to happen. In contrast, this may be a existent obstruction for empirical economic experts that face little samples.

## 3. Empirical application

3.1. Dataset

The present survey uses an imbalanced dataset of EMU[ 9 ]commercial Bankss crossing the period 1999-2006 ( drumhead statistics of the variables used are presented in Table 1 ) . This period covers the flood tide of a comparatively stable and to the full liberalized fiscal environment in the EMU. Banks are still comparatively of import fiscal mediators in the EMU. It is noticeable that with respect to the comparative size of traditional bank intermediation, as measured by the ratio of retentions of bank-related assets to other intermediated assets, the euro country lies about 1.5 times higher than the US.[ 10 ]Note that we decide to curtail the analysis to the EMU states and non the whole of the EU because major differences are present in the banking systems of the Central and Eastern European states. Obviously, comparing the recent survey of Koutsomanoli-Filippaki et Al. ( 2009 ) that focuses on some of the new EU states with surveies of the EMU states ( see e.g. Maudos and De Guevara, 2007 ; Carbo-Valverde et al. , 2007 ) we note considerable differences in the findings. It is besides interesting to observe that the Carbo-Valverde et Al. ( 2007 ) survey signifies the first grounds that cross-country differences in the efficiency degrees of EMU states are non considerable, therefore heightening our belief that the sample used is suited for the purposes of our paper.

Following standard pattern in banking industry surveies ( see e.g. Brissimis et al. , 2008 ) , we define the monetary value of inputs ( tungsten ) as the ratio of capital and forces disbursals to entire assets and the sedimentation rate ( rd ) as the ratio of involvement disbursals to entire sedimentations. To be consistent with our theoretical underpinnings ( retrieve that this is a Cournot-type theoretical account ) , we assume that the loaning rate ( rl ) is equal between Bankss ( see e.g. Shaffer 1999 ) and we obtain its value from the International Financial Statistics.[ 11 ]Note that this figure is different between EMU states, a fact that may be the beginning of heterogeneousness. To account for this and other possible heterogeneousness in the macroeconomic and/or institutional environment of the states considered we include state dummy variables in the inefficiency term of the cost map as discussed below. In add-on, in one of the hardiness cheques to be discussed in the empirical consequences subdivision that follows, we besides include capitalisation ( measured by the ratio of equity to assets ) and recognition hazard ( measured by the ratio of non-performing loans to entire loans ) in the cost equation.

Theoretical priors suggest that coefficients on end products and inputs in the cost map should bear a positive mark. The same is expected for the coefficient on gross domestic product ( g1 ) in the demand equation. If Ir is interpreted as the monetary value of a replacement for bank loans, so its coefficient should besides be positive. Furthermore, extra stock market capitalisation may diminish loan demand and, hence, macgdp is expected to bear a negative mark. Finally, larger Bankss are more easy accessible and better recognized by clients, connoting that the relationship between the logarithm of Ta ( placeholder for bank size ) and the loaning rate should be – in general – positive.[ 12 ]All bank-level informations were obtained from BankScope. The macroeconomic informations were obtained from the World Bank ‘s World Development Indicators and informations for macgdp from the Beck et Al. ( 2000 ) database, as updated in 2007. After using some choice standards to the original dataset,[ 13 ]we end up with a panel of 560 EMU commercial Bankss, matching to 2023 observations. For a formal definition of the variables and some descriptive statistics, see Table 1.

3.2. Basic empirical consequences

As discussed above, Eqs. ( 5 ) , ( 6 ) and ( 7 ) are at the same time estimated with LML to bring forth estimations for both efficiency and competition on an observation-specific footing. Execution of the LML method described above entails an appropriate pick about the bandwidth parametric quantity H.[ 14 ]We choose h utilizing the method of cross-validation. Specifically, we solve the LML job for all informations points but for observation J, and define for some,

( 13 )

for all j=1,2, aˆ¦ , n. The pointis chosen to be the median of the dataset. Then, we pick the H that minimizes, where denotes the fitted value of based on h. Cross proof can be implemented based on appraisal of the full system by e.g. SUR. In making this, we end up with a bandwidth parametric quantity equal to 0.707.[ 15 ]

Another practical issue in the appraisal process concerns the possible heterogeneousness in the environmental conditions faced by European Bankss, which may straight act upon the mistake constituent U associated with cost efficiency in Eq. ( 5 ) .[ 16 ]A popular method used to account for this unfavorable judgment is that of Battese and Coelli ( 1995 ) , who assume that a figure of exogenic variables may straight act upon steadfast efficiency. Under this attack, the inefficiency term U of the mistake constituent in Eq. ( 5 ) is made a map of exogenic country-specific determiners of inefficiency. In the context of the present analysis, we use a clip tendency ( T ) to account for possible tendencies in efficiency, existent GDP per capita ( gdpcap ) to account for inter-country differences in income, the one-year rising prices rate ( inf ) as a placeholder for monetary value stableness and an index that accounts for inter-country differences in capital demands ( caprq ) .[ 17 ]Detailed informations beginnings for these variables ( obtained from the Barth et al. , 2001 database ) and descriptive statistics are given in Table 1.

Finally, we construct bootstrap assurance intervals for the chief variable of involvement I? . Our analysis used nonparametric bootstrap percentile assurance intervals to deduce the hypotheses I?=0 ( matching to a absolutely competitory behaviour ) and I?=1 ( matching to a monopolistic behaviour ) . Since we are interested in those values of I? that attack 0 and 1,[ 18 ]we merely want a value for the “ upper edge of competitory behaviour ” ( above 0 ) and a “ lower edge of monopolistic behaviour ” ( below 1 ) . Therefore, if the estimated coefficients on market power autumn within the “ 0-upper ” and “ lower-1 ” bounds, so the corresponding Bankss are identified with competitory and monopolistic behaviour, severally. The LML arrested development was performed with 1000 bootstrap reproductions, by repairing the design matrix and resampling from the possible responses conditional on each intervention combination. The bootstrap distribution of each arrested development coefficient was compiled, and the 5th and 95th percentiles of the empirical distribution formed the bounds for the 95 % bootstrap percentile intervals.

Appraisal consequences are reported in Table 2 and in Figure 1. In peculiar, the first column of Table 2 ( baseline specification ) reports mean values of the estimated coefficients, the findings being really near to outlooks sing the mark and magnitude. For illustration, both inputs and end products have a positive impact on costs, while the consequence of all of the variables in the demand locus meets the outlooks specified in the old subdivision. In add-on, the degree of these coefficients is really near to that identified in old surveies of bank efficiency that employ either parametric ( see e.g. Lensink et al. , 2008 ) or non-parametric ( Kumbhakar et al. , 2007 ) frontiers. Even though we can non do any remarks sing the significance of the determiners of efficiency if we do non build assurance intervals, we note that gdpcap is negatively related with inefficiency ( which is intuitive since in more comfortable states Bankss have better entree to new engineerings ) , inf is negatively related ( besides intuitive as increased costs associated with higher rising prices of course make operative inefficiencies ) and caprq has a negative but really little coefficient. All in all, the above consequences heighten our belief about the cogency and hardiness of the attack followed.

Table 2 besides studies norm values for market power ( I? ) and efficiency ( eff ) estimates. For the market power estimates we besides report the intervals for the hypotheses of competitory and monopolistic behaviour. In the baseline specification ( column I ) average market power stands at 0.297, denoting reasonably competitory pattern in general but non absolutely competitory ( since the value is comparatively low but non within the 0-0.107 edge ) . Overall, these findings reflect similar consequences with some of the old literature ( see e.g. Bikker and Haaf, 2002, Maudos and de Guevara, 2007 ) .[ 19 ]Furthermore, the mean efficiency degree stands at about 0.88. Average efficiency has been by and large increasing over the 2000-2007 period, making a high ( 0.92 ) in 2006. It is interesting that there is a autumn in 2007, which may reflect the beginning of the fiscal crisis.[ 20 ]

Note that a cardinal virtue of the appraisal method is that it to the full explains the unobservable heterogeneousness across Bankss by leting for bank-level estimated coefficients. A clear image sing the degree and extend of heterogeneousness of the bank-specific coefficients is obtained by the diagrammatic representation of the bank-level estimations ( the estimations of the baseline equation are used ) . Figure 1 nowadayss distributions of the estimated coefficients for the chief variables of our analysis ( we do non describe the coefficients on the multiplicative and the mistake footings in Eqs. 5 and 6 but these are available upon petition ) .[ 21 ]Interestingly, the distributions of the coefficients of some parametric quantities are rather broad, which implies that there are of import differences in bank behaviour. This is likely declarative of the still existing broad differences between the 12 EMU banking systems examined. For illustration, in some states ( e.g. Greece ) earlier findings suggest that the market is dominated by some large Bankss with considerable grade of market power ( see Delis et al. , 2008 ) . We expect these differences to decrease merely if European fiscal integrating further develops ; nevertheless, the recent fiscal convulsion may change in many respects the national banking behavior.

Similar decisions are drawn by looking at the distribution of efficiency estimations, as most Bankss are between 0.7 and 0.96 per cent efficient. As respects I? , note that most Bankss obtain values between 0 and 0.6. All in all, the considerable discrepancy of the coefficients indicates significant heterogeneousness in the market power of Bankss and bring outing this type of parametric quantity heterogeneousness is one of the attractive characteristics of LML.

3.3. Sensitivity analysis

We inquire into the hardiness of these baseline consequences in a figure of extra ways.[ 22 ]First, we experimented with a bank-level loaning rate ( proxied by the ratio of involvement income to entire loans ) as in Uchida and Tsutsui ( 2005 ) . The mean appraisal consequences ( mean coefficients ) presented in the 2nd column of Table 2 remained practically unchanged ; nevertheless there exist some outliers, giving a comparatively big discrepancy for the estimated coefficients and the mistake footings. Therefore, and combined with the blemished theoretical reading of our theoretical account when we include a bank-level rate, we conclude that preciseness of the estimations in this instance is inferior. Second, alternatively of utilizing a translog specification for the cost equation, we employ a simple Cobb-Douglas cost map and we manipulate the gross equation consequently. Give the fact that LML should non be sensitive to the specified functional signifier, we do non anticipate important alterations in the consequences, which is so the instance ( see 3rd column in Table 2 ) .

Another indispensable concern might be that these consequences are someway an artefact of how the frontier theoretical accounts were implemented in footings of the variables used to determine the frontier. To turn to this issue we re-estimated the theoretical account by accounting for capitalisation ( measured by the ratio of equity capital to entire assets ) , for recognition hazard ( measured by the ratio of non-performing loans to entire loans ) and for bank specialisation ( measured by the ratio of entire loans to entire assets ) . Specifically, we used these variables ( I ) as bank inputs in the cost map, ( two ) as determiners of inefficiency and ( three ) both as inputs and as determiners of inefficiency. Even though alterations of efficiency and market power estimations were non above the 5 % threshold, we feel that equity, risk-taking and specialisation are better viewed as elements of bank decision-making and therefore are more suitably considered as inputs. The consequences obtained from this specification are reported in the 4th column of Table 2 and demo no important alteration in the mean coefficients. Efficiency degrees are a small spot lower on norm, which could be attributed to the addition in the figure of inputs. The undistinguished consequence of La may uncover that bank specialisation is likely better modeled as a determiner of market power, non an input of production ( see interesting parts of Carbo et al. , 2009 ; Maudos and de Guevara, 2007 ) .[ 23 ]

It is likely of import to observe that besides the endogeneity of the loaning rate ( which is accounted for by the system appraisal ) , the input monetary values may besides be endogenous variables. We examine this by augmenting our analysis based on the simple LML process described above with local generalized method of minutes ( LGMM ) arrested developments. LGMM, foremost proposed by Lewbel ( 2007 ) , was implemented in a dynamic panel informations context by Tran and Tsionas ( 2008 ) . It can be considered as an extension to the instrumental variables parametric theoretical account because it allows the arrested development coefficients of the parametric portion to change harmonizing to the smooth coefficient theoretical account.[ 24 ]As instruments we use the meats of first two slowdowns of the monetary value of inputs ( for more on these issues, see Tran and Tsionas, 2008 ) . The consequences, reported in column V of Table 2, suggest that the estimations on I? are non driven by the usage of the LGMM method. Therefore, we feel confident that appraisal on the footing of the LML process is robust to such possible endogeneity.

As a concluding exercising, we consider a theoretical account of market power that does non include an inefficiency term in the cost map. The consequences are reported in the last column of Table 2 and, in line with outlooks, describe a important downward prejudice for I? , since puting all Bankss on the efficient frontier lowers the degree of market power unnaturally. Hence, we may hold to be disbelieving sing industry-specific estimations of market power obtained from empirical surveies that do non include an inefficiency term. Given the above, we use the baseline consequences in the remainder of our treatment.

3.4. The relationship between efficiency and market power estimations

Naturally, an interesting inquiry that follows the analysis above is what the relationship between efficiency and market power estimations looks like. Figure 2 illustrates this relationship once more utilizing the efficiency and market power estimations obtained from the baseline equation. The relationship identified is clearly negative with a incline equal to -0.19 ( the correlativity coefficient is important at the 1 per cent degree ) . Therefore, we find important grounds for the so called “ quiet life hypothesis ” , a determination really similar to that of Berger and Hannan ( 1998 ) .[ 25 ]More specifically, Berger and Hannan provide at least four interconnected grounds about why market power ( in footings of industry concentration in their survey ) and runing efficiency are negatively correlated, while they suggest that associated public assistance losingss are well higher than the losingss originating from traditional industrial organisation theory on monopoly power. Yet, in malice of the negative relationship between operating efficiency and market power for the mean bank, Figure 2 shows that the most efficient Bankss of the sample possess comparatively high market power. This is likely a notable comment, which may propose some grade of contrary causality in the relationship between market power and efficiency. Phrased otherwise, Bankss with more efficient direction or production engineerings have lower costs and therefore higher net incomes, which allows them to derive big markets portions and market power. Notably, this mechanism lies at the bosom of the “ efficient construction hypothesis ” ( see Demsetz, 1973 ) and may be present extra explanatory enterprise for the comparatively high I? observed for the most efficient Bankss.

## 4. Reasoning comments

This survey provided an empirical model for the joint appraisal of efficiency and market power of single Bankss. The theoretical account is applied to the EMU and US banking industries and the findings suggest that most Bankss are characterized by reasonably competitory behaviour. In add-on, a clear negative relationship is identified between the degree of market power and efficiency of single Bankss, a consequence in line with the theory underlying the quite life hypothesis of Hicks. It is deserving observing, nevertheless, that the most efficient Bankss possess market power higher than norm, a finding consistent with the efficient construction hypothesis. Finally, an interesting consequence from a policy position is that big intra-industry differences are observed in the market power possessed by Bankss. This surely calls for different stance of regulative policies towards Bankss with different degree of market power.

The numerical illustrations suggest that the methodological analysis provides clear economic deductions that are in line with theoretical and empirical priors and utile in at east two waies. First, the degree of market power of single houses is quantified and 2nd bank-level grounds is presented for widely debated issues of banking theory. True, it is rather ill-defined whether one can pull general deductions on the efficiency-competition link from the findings on developed banking systems. Naturally, more research is needed that will integrate the experience in emerging or passage economic systems. Furthermore, we feel that other policy-related inquiries on the relationship between bank-level efficiency or – more significantly – market power and a figure of economic- or policy-oriented components like ordinance and risk-taking may be addressed on the footing of the proposed methodological analysis. Since we hope that this survey provides a utile tool, this is a desideratum for future research.

## Recognitions

The writers would wish to thank an anon. referee, Saul Lach, Ike Mathur ( editor ) , Nikos Vettas and seminar participants in Athens University of Economics and Business for really helpful remarks.