Bank efficiency and risk in European banking

Transcription

1 Bank efficiency and risk in European banking Anastasia Koutsomanoli-Filippaki a and Emmanuel Mamatzakis b February 009 Abstract An open debate in the literature relates to the relationship between bank efficiency and risk. This paper provides empirical evidence that sheds new light into the dynamic interactions between risk and efficiency, using a large panel data set that includes 5 listed banks operating in the enlarged European Union (EU) over the period 998 to 006. As a measure of bank risk we opt for a Merton type distance to default, while inefficiency is derived using a stochastic frontier approach for both a cost and a profit function. We also estimate productive inefficiency using a directional technology distance function framework. Then, we employ a Panel-VAR model to derive orthogonalised impulse response functions, which show responses of the main variables, risk and inefficiency, to orthogonal shocks. Most evidence shows that the effect of a one standard deviation shock of the distance to default on inefficiency is negative and large in magnitude, especially in the case of productive inefficiency, further insinuating that the distance to default causes inefficiency. There is some limited evidence of a reverse causation, but the impact of a shock in bank inefficiency on risk is small and lasts for a very short period of time. As part of a sensitivity study, we perform a similar analysis for high-financial developed vs. low-financial developed countries, as well as for banks with different structure of ownership. JEL classification: G; G8; D. Key words: bank inefficiency, default risk, panel VAR, causality. a Council of Economic Advisors, Ministry of Economy and Finance, Greece. b Department of Economics, University of Macedonia, Greece. tzakis@uom.gr Preliminary version, please do not quote without permission.

2 . Introduction A major challenge that financial institutions in general and banks in particular face is the impact of risk on their operations. This has become crucial in the context of the current financial turmoil which has highlighted a miss-assessment of risk on behalf of both banks and investors with overwhelming implications for financial stability. The importance of risk is certainly not limited to the banking sector, yet it bears greater weight for this sector, given the hefty financial and economic repercussions of a bank failure. These consequences are not limited to financial losses for the stakeholders i.e. shareholders, clients, and deposit guarantee schemes as well as to loss of competition, but can also potentially cause destabilization of the financial system through contagion mechanisms, leading to a banking crisis. Bank failures further disrupt the flow of credit to local communities, reduce money supply and have lingering effects on the real economy. The new financial environment that evolved over the last five to ten years, which is characterized by enhanced financial liberalization and integration, rapid development of new financial products and technologies, as well as consolidation in the banking industry and increasing competition, poses additional pressure on banks with regards to effectively manage their risk, while ensuring a high level of efficiency in their operations (Moshirian, 008). At the same time, supervisors and regulators have the dual task of both safeguarding financial stability and promoting financial efficiency. The importance of efficiency measures as instruments for the analysis of bank performance is unequivocal, as documented by its long tradition in the literature (see Berger and Humphrey 997 for a review) and has attracted the attention of both researchers and policy makers. Efficiency scoring provides an accurate evaluation of the performance of individual banks, but also of the industry as a whole, while it entails information regarding the overall stability of financial markets. In a similar vein, the importance of risk in the banking industry has been widely recognised, especially as a crucial determinant of financial stability. Despite the importance of identifying the interaction between risk and efficiency, providing empirical evidence remains a challenge. Goodhart et al. (004) argue that financial stability and its main underlying determinant, risk, are endogenously determined together with economic efficiency within a general equilibrium model, whilst they point to the existence of a trade-off between them. This could indicate a possible negative relationship between efficiency and risk. However, other studies, (see Allen and Gale, 004 and Boyd and De Nicolo, 005) argue that such a trade-off may not exist, leading to inconclusive results regarding the interaction between risk and efficiency. Empirical evidence is, thus, warranted so as to examine this relationship. Nevertheless, if, on one hand, it has been a high task in theory to model the interaction between risk and efficiency, it is equally challenging to provide empirical evidence. The aim of this paper is to fill this gap in the literature and to provide for the first time a comprehensive assessment of the interaction between bank efficiency and bank risk in the EU banking industry. The estimation of this relationship is challenging for several reasons, but mainly due to measurement issues. Among the plethora of risk measures proposed in the literature, our choice of the distance to default is justified on

3 the grounds that it is an all-encompassing measure of default risk for banks (Gropp et al., 004). Specifically, it combines information about stock returns with leverage and volatility information, thus capturing the most important determinants of default risk. Another challenge is choosing an appropriate efficiency measure. Given that there is no consensus in the literature regarding the measurement of efficiency, we opt for a variety of efficiency measures to ensure that our estimations are not sensitive to measurement related issues. In particular, we employ the Stochastic Frontier Approach and estimate the so-called traditional inefficiency scores derived from a cost and a profit function, while we also employ as an alternative approach the directional technology distance function developed in 990s (Chambers et al., 996) to estimate productive inefficiency. Having measured bank risk and inefficiency, we should opt for an appropriate econometric methodology to study the interaction among them. As the theory has not offered any silver bullets regarding what causal relationships one should expect to observe, we select a novel econometric approach that permits all variables in the model to enter as endogenous without applying a-priori restrictions. Specifically, we apply a panel Vector Autoregression (VAR) analysis to estimate the underlying dynamic relationships between inefficiency and risk and thus isolate the impulse responses to shocks in the variables of our model. By using VAR on panel data we are able to disentangle the complex underlying relationship between inefficiency and risk, while permitting for bank specific unobserved heterogeneity. In particular, we focus on two main questions. First, how do the VAR s endogenous variables, inefficiency and risk, respond dynamically to their own and other variables shocks? Second, which shocks are the primary causes of variability in the inefficiency and risk variables? The panel VAR gives answers as it is a reduced form system of equations that is free of imposing strong a-priori assumptions concerning the endogeneity of variables, while it allows estimation of orthogonalised Impulse-Response Functions (IRFs). These impulse-response functions describe the response of one variable to the orthogonal innovations in another variable in the system, while holding all other shocks equal to zero. Also, within the Panel-VAR we estimate variance decompositions that separate the response of the variance of variables to shocks. As part of a sensitivity analysis, we extend our study to investigate the relationship between efficiency and default risk across banks with different types of ownership and across financial systems with different levels of financial development. Several studies have found that foreign banks perform more poorly on average than private domestic institutions in developed nations (e.g., DeYoung and Nolle 996, Berger et al., 000), though results seem to be reversed in the case of developing countries (i.e., Bonin et al., 005; Claessens et al., 00; Fries and Taci, 005). Foreign ownership is also found to be associated with more competitive national banking systems (e.g., Claessens and Laeven 004, Martinez Peria and Mody 004); and more business credit availability (e.g., Berger et al., 004) in developing countries. Thus, we examine the interaction between efficiency and risk for banks with different types of ownership by dividing our sample into two mutually exclusive groups of credit institutions, that is, foreign and domestic banks. Likewise, given the heterogeneity observed across European financial systems, especially between old and new EU member states, we seek to explore whether the level of financial development affects results. Despite the increasing degree of 3

4 financial integration achieved over the last couple of years, European financial systems vary widely with respect to many dimensions such as size, depth, efficiency, competition. Demirguc-Kunt and Huizinga (000) argue that the level of financial development has a significant impact on bank performance. To this end, we construct an index of financial development proposed by Demirguc-Kunt and Levine (996) and we examine the interaction between efficiency and risk across high and low financial development countries. This paper contributes to the literature in several ways: first, to our knowledge, this is the first study to examine the underlying dynamic relationship between bank efficiency and risk within a Panel VAR context for EU banks, which allows us to infer empirical evidence on a highly debated issue in finance theory. Secondly, we employ a Merton type market-based measure of risk, which is the distance to default, considered to be a more comprehensive measure of risk than the commonly used index-number proxies based on accounting data. Thirdly, we estimate three alternative efficiency measures, as a way to strengthen the validity of our results. Fourth, we use a large and up-to-date dataset that covers the vast majority of listed banks in the enlarged EU, and that was compiled by combining three different databases. Fifth, we perform a sensitivity analysis and examine whether the relationship between risk and efficiency is influenced by bank ownership type and by the level of financial development. A first glimpse at the results shows that the higher the distance to default the lower the inefficiency scores. The reverse causal relationship can not be excluded for all cases studied, but the empirical evidence is much weaker. Moreover, the sensitivity analysis confirms the initial findings for the importance of bank risk to inefficiency, whereas some variability is also observed. The rest of the paper is structured as follows: Section presents a brief review of the literature and analyses the main hypotheses we test in our study. The empirical specification of the models employed is provided in Section 3, while Section 4 deals with data issues and describes the variables used in our analysis. Section 5 provides the empirical estimations and discusses our main results. Finally, section 6 offers some concluding remarks and possible policy implications.. Literature review and hypotheses. Efficiency literature As a result of rapid changes in the structure of the financial services industry and advances in financial and non-financial technologies, a proliferation of studies on bank efficiency has emerged, focusing mainly on the US banking industry (e.g., Mester, 996; Berger and Mester, 997). Although European research on efficiency has not matched the volume of US studies, this has begun to change in recent years (see for example, Allen and Rai, 996; Altunbas et al., 00; Lozano-Vivas et al., 00, 00; Maudos et al., 00; Casu and Molyneux, 003), while a more recent strand of the literature has focused on transition economies, where particular attention has been given to the relationship between ownership and performance in light also of the increasing presence of foreign investors in these financial systems (see, for example, Grigorian and Manole, 00; Green et al., 004; Bonin et al., 005; Fries 4

5 and Taci, 005; Rossi et al., 005; Yildirim and Philippatos, 007). Nevertheless, a detailed review of the literature on banking efficiency is beyond the scope of this paper (for excellent reviews see Berger and Humphrey, 997 and Berger et al., 000). Instead, in light of this study, our interest lies in the relationship between efficiency and risk, which, despite its importance, has hardly been studied in the literature. Most researchers have focused on the relationship between efficiency and credit risk, usually proxied by bad loans, problem loans or loan loss provisions. Berger and DeYoung (997) provide an excellent analysis on the possible relationship between credit risk, efficiency and bank capital, offering four alternative hypotheses, i.e. the bad management, the bad luck, the skimping and the moral hazard hypotheses (Berger and DeYoung, 997). They employ Granger-causality techniques to test these four hypotheses and conclude that cost efficiency may be an important indicator of future problem loans and problem banks in the US. Williams (004) undertakes a similar analysis for the European banking industry and finds that the bad management hypothesis prevails for European banks. Recently, Podpiera and Weill (008) address the question of the causality between non-performing loans and cost efficiency in a transition country (Czech Republic) so as to examine whether either of these factors is a major determinant of bank failures and find evidence in support of the bad management hypothesis, according to which deteriorations in cost efficiency precede increases in non-performing loans. A related strand of the literature has examined the relationship between risk and efficiency by incorporating in the efficient frontier various aspects of risk. For instance, Mester (996), and Hughes et al. (000) among others, point out that failure to adequately account for risk can have a significant impact on relative efficiency scores. Berg et al. (99) made the original observation and included nonperforming loans in a nonparametric study of bank production, whereas the concept to parametric estimations is applied in Hughes and Mester (993). Some other studies use equity capital as a control for risk (e.g. Altunbas et al., 00; Maudos et al., 00), while others incorporate loan loss provisions in their efficiency estimation (e.g. Altunbas et al., 000; Pastor and Serrano, 005). Finally, a third strand of the literature applies a two-stage approach to examine the link between efficiency and risk, where inefficiency is regressed on a set of variables capturing risk. This type of analysis does not provide evidence of causality between the two concepts, but rather examines whether certain risk characteristics are more prevalent among inefficient banks. Among the studies that have incorporated credit risk in their analysis we can mention Carvallo and Kasman (005), and Yildirim and Philippatos (007). On the other hand, Maudos et al. (00) and Hauner (004) employed the standard deviation of ROA to measure risk. Both studies found that banks that are bad at managing their risks are also bad at managing their costs while Maudos et al. (00) also found a positive correlation between profit efficiency and risk. Pastor and Serrano (005) find that adjustments for risk are important in the case of profit efficiency but not in the case of cost efficiency for a sample of European banks, while they also distinguish between exogenous and endogenous credit risk. 5

6 . Default risk literature The measurement of bank default risk has attracted significant attention in the literature as a result of the detrimental effects of a potential bank failure that can jeopardise the stability of the entire financial system. Among the quantitative tools used for assessing financial stability, the use of market-based risk measures has gained momentum over the last years. These measures aim at supplementing more traditional analyses based on financial and income account statements with the added advantage of using the forward-looking information incorporated into security prices, which, contrary to balance-sheet data, are available at a high frequency and even on a real-time basis. One particular market-based measure, the distance-to-default measure, first introduced commercially by Moody s KMV in 990, has become a widely used indicator of default risk. Empirical studies have mainly examined the ability of bank default probabilities to predict bank failures. For example, Gropp et al. (004) analysed the ability of the distance-to-default and bond spreads to signal bank fragility and found leading properties for both indicators, with the distance-to-default exhibiting lead times of 6 to 8 months. Studies focusing on default probability of individual banks in transition countries are rare with some exceptions. Chan-Lau et al. (004) measured bank vulnerability in emerging markets using the distance-to-default for 38 banks in 4 emerging market countries and showed that it can predict a bank's credit deterioration up to nine months in advance. Moreover, Godelewski (004) calculated default probabilities for a sample of emerging banking markets including some transition economies so as to investigate the coherence between bank ratings and default probabilities. Liu et al. (004) propose an extension of the Merton s type distance to default by incorporating stochastic interest rates, which they empirically apply to a sample of Canadian banks. Moreover, Chan-Lau and Sy (007) introduce the concept of distance-to-capital, which is an extension of distance-to-default that accounts for pre-default regulatory actions such as those prescribed in a prompt-corrective-actions framework. They show that both risk measures can be analysed using the same theoretical framework but differ depending on the level of capital adequacy thresholds and asset volatility. In a more recent study Lepetit et al. (008) investigate the relationship between bank risk and product diversification in the European banking industry. Among other risk measures they also employ bank distance-to-default and argue that there exist links between bank income structure and risk. In particular, they show that banks expanding into non-interest income activities present higher risk and higher insolvency risk than banks which mainly supply loans, while a higher share of trading activities is never associated with higher risk and for small banks it implies, in some cases, lower asset and default risks. In this section, we briefly review some of the studies that have examined banks default risk within various contexts, although one should bear in mind that a thorough review of the relative literature is beyond the scope of this paper. 6

7 .3 Hypotheses to be tested The aim of this paper is to combine the above two different strands of the literature and to examine the causal relationship between default risk and bank efficiency, within a panel VAR context. The empirical analysis that follows is designed to examine the possible underlying short run interactions among risk and inefficiency. The following hypotheses would be tested: Hypothesis : An increase in bank default risk causes an increase in bank inefficiency. This hypothesis, which closely relates to the bad luck hypothesis of Berger and DeYoung (997), states that an increase in bank risk, which is translated into an increase in bank s probability of default, will cause managers to operate less efficiently. This is because bank managers that face soaring risk will have to take additional precautions and to incur additional risk-monitoring costs so as to preserve the quality of bank portfolio. In other words, bank managers will divert their attention away from solving day-to-day operational problems and from pursuing efficiency improving strategies to preventing a further deterioration of their financial position. In the extreme case that a bank is in a perilous financial situation, close to or bellow the threshold of default, it will face dear costs in order to defend its safety and soundness record to supervisors and market participants. In both cases, one would expect that higher costs, caused by an increase in bank default risk, would trigger an increase in bank inefficiency. Thus, under this hypothesis, we expect higher bank default risk to reduce efficiency. Another possible explanation for the positive relationship from risk to inefficiency is the efficient market hypothesis (Fama, 965). Since our measure of risk is primarily influenced by developments in the stock exchange, and in particular securities prices that incorporate forward-looking information, events such as the recent credit and liquidity crises, should find their way on bank stock prices that, in turn, would feed into a higher probability of default. Lowering the distance to default then would affect inefficiency measures, which are derived from balance-sheet data that reflect developments with a quarter or even an annual lag. Thus, in the context of an efficient stock market the causality would run from risk to inefficiency. Hypothesis : An increase in bank inefficiency causes an increase in bank default risk. An extension of the bad management hypothesis (Berger and DeYoung, 997) could provide a possible explanation for the positive, but reverse, causal relationship running from inefficiency to risk. In this case, low scores of inefficiency could be seen as signals of poor senior management practices, which apply not only in day-today operations but also to risk monitoring and management. Poor managers that do not sufficiently monitor their operating expenses, nor do they effectively increase their profitability, as reflected in low measured cost and profit efficiency, could also practice inadequate risk management techniques. For instance, 'bad' managers may take on negative net present value projects, or invest in lower quality loans. Thus, the reduction in measured efficiency, caused by bad management, may lead to poor risk management practices and unavoidably to mounting risks. As risks pick up, 7

8 unexpected losses start to materialise, while soaring delinquencies further deteriorate a bank s financial position. Thus, under this hypothesis, low efficiency would cause higher default risk. Hypothesis 3: A reduction in bank inefficiency causes an increase in bank default risk. According to this hypothesis, the relationship between risk and inefficiency could be negative. Under the moral hazard hypothesis (see Gorton and Rosen, 995), entrenched managers of an efficient bank may have the incentive and a larger degree of manoeuvre from stakeholders to follow an expansionary strategy, which ex-post could be shown to be excessively risky. This could also be related to the skimping hypothesis developed by Berger and DeYoung (997). Under this hypothesis banks seem more efficient because they may opt to cut operating costs at the expense of facing higher risk in the future. Similarly, other things being equal, under this hypothesis an increase in bank inefficiency in the short run could cause a reduction in risk taking activities that eventually may result to a reduction in bank default risk with a lag. 3. Empirical Methodology: Efficiency and Risk measurement This paper seeks to measure three dimensions of bank performance: productive, cost, and profit efficiency. The first concept corresponds to what we call technical efficiency and is a purely physical notion, which is defined in terms of distance to a production frontier without recourse to price information. On the other hand, the concepts of cost and profit efficiency are based on the assumption that financial firms pursue some economic behavioural goal, such as cost minimization or profit maximization and, accordingly, are defined in terms of distance to an economic (cost or profit) frontier. As a measure of risk, we follow the methodology based on the seminal works on option pricing of Black and Scholes (973) and the market value of risky debt of Merton (974). Essentially the problem is set around the notion of estimating the default probability of a certain bank and the underlying distance to default. 3. Directional technology distance function: productive efficiency To model the production function and measure productive efficiency, we depart from the traditional Shephard distance functions and use the directional technology distance function proposed by Chambers et al. (996). Directional distance functions are extremely useful tools not only because they are natural performance measures (see Färe et al., 007) but also because they entail an extremely flexible description of technology without restricting banks to optimize in a single direction (i.e., input or output). We assume that technology (T) for each bank is defined as the set of all feasible inputoutput vectors: 3 3 It is assumed that the technology satisfies the axioms listed in Färe and Primont (003). 8

9 T k = {( x k, y k ): x N R +, y M R +, x can produce y}. () where k is the number of banks and x k R N + are inputs used to produce y k R M + outputs. The directional technology distance function completely characterizes technology and allows firms to optimize by seeking simultaneously the maximum expansion of outputs (y) and contraction of inputs (x) that is technologically feasible. Given a directional vector, denoted by g = (g x, g y ), g x R N + and g y R M +, that determines the direction in which technical efficiency is assessed, the directional distance function can be defined as: 4 r D ( x, y; g, g ) = sup β ) T x y { β : ( x βg, y + g T} x y. () We choose to set g = (g x, g y ) = (, ) which implies that the amount by which a bank r could increase outputs and decrease inputs will be D T ( x, y;, ) units of x and y. 5 For a bank that is technically efficient, the value of the directional distance function would be zero, while values of D r ( x, y, g, g ) > 0 indicate inefficient production. T x y To empirically implement the measurement of efficiency and productivity, we opt for a parametric stochastic frontier approach. We parameterize the directional distance function via a flexible quadratic functional form which permits the imposition of the translation property. Technical progress is captured by a trend variable. The directional distance function is thus parameterized as: r N M N N DT ( x, y; g x, g y, t, θ ) = α 0 + α n xn + β m ym + α n' n xn xn n= m= n= n' = M M N M + β mm ym ym + γ mn ym xn m= m = n= m= N M + δ t + δ t + ψ ntxn + μmtym + ε (3) n= m= where θ = (α,β,γ,δ,μ,ψ) is a vector of parameters to be estimated and ε is a random error assumed to be independently and identically distributed with mean zero and r variance σ ε. Subtracting DT ( x, y; g x, g y, t, θ ) = u from both sides of (3) yields a functional form with a composite error term ε -u. The one-sided error term u represents bank-specific inefficiency and is assumed to be generated by truncation (at zero) of a normal distribution with mean μ and varianceσ. u 4 The properties of the directional distance function are described in Chambers et al. (998) and Färe and Grosskopf (004). Among other things, the translation property says that if we translate the inputoutput vector (x,y) into, then the value of the distance function is reduced by ( x λ g x, y + λ g y ) the scalar. The translation property is the additive analogue of the homogeneity property in the case of the translog function. 5 In the multiple output case the sum of individual bank efficiencies will be equal to the industry efficiency level if a common directional vector is used or if each bank is allocatively efficient (see Färe and Primont, 003; Färe and Grosskopf, 004). 9

10 The parameters of the quadratic function must satisfy a set of restrictions, including the usual restrictions for symmetry ( a nn = an n, β n n = β n n ) and the following restrictions that impose the translation property: N α g + M n n n= m= M mm g y = m m= β g m m N =, α nn g x = 0, n =,,N, n n= N β 0, m =,..., M, ψ n = 0 and μ m = 0 (4) n= The theoretical restrictions given in (4) are used to form a model that is suitable for estimation (see Färe et al., 005). In particular, we use the translation property (see footnote 5) to obtain a specification of the parameterized quadratic function given by Equation (3), in which one of the inputs, labour, is selected as the dependent variable. We estimate the stochastic frontier model in (3) via a maximum likelihood procedure parameterized in terms of the variance parameters σ = σ + σ and γ = σ / σ. M m= s u ε u s 3. Stochastic cost and profit frontier To estimate cost and alternative profit inefficiency, we employ the stochastic frontier approach (SFA), as developed by Aigner et al. (977) and Meeusen and Van den Broeck (977). This approach incorporates both noise and inefficiency into the model specification in a composite error term and imposes distributional and independence assumptions to disentangle the two error components. In particular, in the case of the cost frontier, we assume the following specification: TC it = f (P it, Y it, N it, Z it ) + v it + u it (5) where TC it denotes observed total cost for bank i at year t, P is a vector of input prices Y is a vector of outputs of the firm, N is a vector of fixed netputs and Z is a vector of control variables. The error term is disentangled in two components: the first one, v i, corresponds to the random fluctuations and is assumed to follow a symmetric normal distribution around the frontier, while the second one, u i, accounts for the firm s inefficiency that may raise costs above the best-practice level and is assumed to follow a half-normal distribution. To empirically implement the cost frontier, we opt for the following translog specification: 6 lntc i = α 0 + i ai ln P i + i + δ ij ln Pi ln Υj + i j β i ln Y i + ½ a i φ lnν i i i j ij ln Pi ln Pj +½ β ij ln Υ ln Υ i j i j +½ φ ij ln N i ln N j i j + i j ξ ij ln Pi ln N j 6 For simplification, we omit the subscripts for time ( t ). 0

11 + i j + kd i + ζ ij lnyi ln N j + θ t + ½ t i Z i i θ μ it ln Pi + κ it lny i + + i i i ν it ln N i ξ + u i + v i (6) Standard linear homogeneity and symmetry restrictions in all quadratic terms are imposed in accordance with economic theory, while we also include both country and time effects. The stochastic frontier model (6) is estimated via a maximum likelihood procedure parameterized in terms of the variance parameters σ / σ. u ε σ = σ + σ and γ = For the profit efficiency analysis, we formulate the profit function in a similar way. Following the justification of Berger and Mester (997), we prefer the alternative profit function instead of the standard profit function. 7 The alternative profit function uses the same variables as the cost function, which implies that output prices are free to vary and affect profits. The dependent variable now becomes ln(π+θ+), where θ indicates the absolute value of the minimum value of profits (π) over all banks in the sample. This transformation allows us to take the natural log of profits, given that profits can also take negative values. Also in the case of the profit function, the composite error term becomes ε i = v i u i where u i is assumed to follow an exponential distribution The distance to default Although at an initial stage of our study, we also used other measures of risks, our choice of the distance to default is warranted. The main determinants of the distance to default are: the market value of the bank assets, which provides information of its prospects, the asset risks, measuring the uncertainty or risk, and lastly the leverage, which provides insights over the bank s contractual liabilities. To briefly state a standard methodology, based on the Black and Scholes (973) option pricing theory, Merton (974) showed that the market value of the bank s assets follows a stochastic process that is a geometric Brownian motion with a drift: dmv B = μmv B dt+σ B MV B dz (7) where MV B and dmv B is the bank s asset value and change in the asset value respectively, μ, σ B is the bank s asset value drift and volatility, while dz is a Wiener process. Here, we assume that the drift, as in the Merton model, can be approximated by the risk free interest rate. The liabilities consist of the bank debt (D) and equity (E), thus the market value of equity (MV E ) is: MV E = MV E N(d )-De -rt N(d ) (8) ε u v 7 See Berger and Mester (997) for a detailed analysis of the advantages of the alternative profit efficiency concept.

12 where rate. d MVB σ B ln( ) + ( r + ) = D, d = d σ B T, with r being the risk free interest σ T B Now, it can be shown that the volatility of equity and market value of bank are related as follows: σ E 0 = N( d ) σ B (9) E From the above system of equations (8) and (9) we can solve for MV B and σ B, so as to derive the distance to default as: MVB σ B ln( ) + ( μ ) t Dt DD = (0) σ T B The DD measures the number of standard deviations of a bank away from default. B 3.4 Panel VAR Analysis The starting point of our analysis is Sims s (980) Vector Autoregressive (VAR) methodology that fits the purpose of this paper, given the absence of a-priori theory of the relationship between the variables of our model, as it deals with the issue of endogeneity of the variables. This methodology (see Lütkepohl, H., 006) is based on a framework that all variables enter as endogenous a system of equations where the short run dynamic relationships can be subsequently identified. Essentially, the VAR would allow us to explore the underlying causal relationships between our main variables: bank inefficiency and bank risk. It is possible to have one-way causality, i.e. running from the inefficiency to distance to default or vice versa, but also a bidirectional one. Note that a common issue that emerges in panel VAR analysis concerns the heterogeneity across banks (see Arellano and Bover, 995). One way to address this issue is to set individual specific terms. In detail, our panel-data vector autoregression treats all the variables in the system as endogenous, while allowing for unobserved individual heterogeneity. We specify a first order VAR model as follows: w it = i + Φwit + ei, t μ, i =,, N, t=,,t. () where w it is a vector of two random variables, the inefficiency and risk, Φ is an x matrix of coefficients, μ i is a vector of m individual effects and e i,t is a multivariate white-noise vector of m residuals. As with standard VAR models, all variables depend

13 on the past of all variables in the system, the main difference being the presence of the individual specific terms μ i. 8 Regarding estimation and inference, we use a system-based GMM estimator for each equation, as in Arellano and Bover (995). Moreover, we obtain parameters by regressing the endogenous variables on the whole set of lagged endogenous variables. The above system of equations is in reduced form, so that once estimated it can be used to implement dynamic simulations. This analysis would involve the estimation of impulse response functions (IRF) or variance decompositions (VDC) and requires solving a complex identification problem. A commonly used way to tackle this problem is to opt for choosing a preference ordering so as to satisfy that more exogenous variables impact on the more endogenous ones in a sequential order (see Love and Zicchino, 006 and Arias O. and W. S. Escudero, 007). This is the standard identification strategy implicit in the Choleski decomposition, which induces a recursive orthogonal structure on the structure of the shocks e i,t. In this paper we make the plausible assumption that risk, as measured by the distance to default through a Merton s options pricing model, could be relatively more exogenous than efficiency. The distance to default is based on the developments in the stock exchange that are commonly taken as exogenous to the individual bank performance and its efficiency levels (REF+++). Thus, in the model with two variables we assume that the inefficiency affects the distance to default with a lag, while it is simultaneously affected by it own innovation and innovation in the distance to default. The reverse causation will also be tested. Note, though, that the ordering would be irrelevant if there are low estimated covariances between the errors across equations. In detail, we model inefficiency and distance to default in two-equations VAR with the following structure: I it DD = μ it i 0 = μ + μ i0 0t + μ + 0t J j= + a J j= I it j a I + it j J j= + Here, I it and DD it capture the bank inefficiency and distance to default respectively, while μ i0 and μ 0t are the industry and time dummies respectively. a J j= DD a it j DD + e it j i, t + e i, t () 8 In order to impose that the underlying structure is the same for each cross-sectional unit we allow for individual heterogeneity in the levels of the variables by introducing fixed effects, denoted by μ i as in Love and Zicchino (006). In addition, the fixed effects are correlated with the regressors due to lags of the dependent variables and as a result the mean-differencing procedure commonly used to eliminate fixed effects would create biased coefficients. To avoid this problem we use forward meandifferencing, also referred to as the Helmert procedure (Arellano and Bover, 995). This procedure removes only the forward mean, i.e. the mean of all the future observations available for each firmyear. This transformation preserves the orthogonality between transformed variables and lagged regressors, so that we can use lagged regressors as instruments and estimate the coefficients by system GMM. 3

14 4. Data sources and data description Our data comprises listed banks in the 7 Member States of the European Union over the period 998 to 006. The number of listed banks varies widely across countries, ranging from in Estonia to 40 in Denmark. Balance-sheet and income statement data where obtained from the Bankscope database, while data on macroeconomic and banking variables were collected from the World Development Indicators Database and from European Central Bank reports. For the estimation of bank default risk, stock price data were obtained from Datastream, Bloomberg and Bankscope databases. After reviewing the data for reporting errors and other inconsistencies, we obtain an unbalanced panel dataset of,653 observations, which includes a total of 5 different banks. A variety of approaches have been proposed in the literature for the definition of bank inputs and outputs; yet, there is little agreement among economists as to what unequivocally constitutes an acceptable definition, mainly as a result of the nature and functions of financial intermediaries. In this paper we employ the intermediation approach proposed by Sealey and Lindley (977), which assumes that the bank collects funds, using labour and physical capital, to transform them into loans and other earning assets. In order to measure productive efficiency, we specify three inputs, labour, physical capital and financial capital, and two outputs loans, and other earning assets. Due to lack of data on the number of employees, labour is measured by personnel expenses, while physical capital is defined as the bank s fixed assets. Loans are expressed as total loans net of provisions, while other earning assets include government securities, bonds, equity investments, CDs, T-bills, equity investment etc. For the estimation of cost and alternative profit efficiency, input prices are required. The price of financial capital is computed by dividing total interest expenses by total interest bearing borrowed funds, while the price of labour is defined as the ratio of personnel expenses to total assets. In the case of cost and profit function, physical capital is specified as a fixed netput, which is relatively standard in efficiency estimation. Total cost is defined as the sum of overheads (personnel and administrative expenses), interest, fee, and commission expenses, while profit is defined as profit before tax. Another issue in the efficiency literature is the treatment of financial capital, which accounts for different risk preferences. If financial capital is ignored, the efficiency of banks that may be more risk averse than others and may hold a higher level of financial capital would be mismeasured, even though they are behaving optimally given their risk preferences. 9 Apart from this, a bank s capital directly affects costs by providing an alternative to deposits as a funding source for loans (Berger and Mester, 997). Thus, in estimating both the directional distance function and the cost and profit functions, we include equity capital as a quasi-fixed input. In the case of the directional distance function equity capital enters the function with a directional vector value set to zero. Moreover, in the case of the cost and profit functions we include several control variables in order to allow for the effect of country features. These variables include the Herfindahl Index to measure concentration, the ratio of non-performing loans to 9 See also the review of the efficiency literature in section. 4

15 total loans to control for differences in banks loan quality, the share of foreign-owned banks assets as a percentage of total banking assets, the capitalization ratio to control for the part of risk that is attributed to the overall system, the interest rate spread, which is used as a proxy for competition for banking services, the logarithm of total assets to control for size effects, the ratio of bank liquid assets to total assets at the country level to capture liquidity risk, the intermediation ratio, a measure of branch density and two macroeconomic variables, that is GDP per capita and inflation, to control for differences in the macroeconomic environment across countries. 0 Table provides descriptive statistics of the variables used in this study for the overall sample over the period (Please insert Table about here) For the computation of bank default risk, we estimate the annual equity volatility for each bank, based on the daily returns, derived as the standard deviation of the moving average of daily equity returns times 6. All liabilities are assumed to be due in one year, T=, while as risk free interest rate we take the twelve months interbank rates, except for a few countries (Greece, Estonia, Lithuania), for which we opt for the six month interbank rate due to data availability. Liabilities are derived from Bankscope Fitch IBCA and include the total amount of deposits, money market funding, bonds, and subordinated debt. 5. Empirical results 5. Efficiency results Table A in the appendix presents the estimated parameters of the stochastic directional distance function and the cost and profit functions described above, and shows that most of the maximum likelihood coefficients of (3) and (6) are statistically significant. The estimates of λ for all three frontiers are higher than one, suggesting that technical inefficiency, as identified within the composite error term, plays an important role in the analysis of bank performance; the one-sided generalized likelihood ratio tests indicate that λ is statistically significant, thus confirming the importance of technical inefficiency effects. Table presents cost, profit and productive inefficiency scores for each country and for the EU-7 banking industry as a whole. Consistent with the literature, estimated profit inefficiency is higher than cost inefficiency. In particular, we observe an average profit inefficiency of 0.37 for all banks in our sample, compared to a mean cost inefficiency estimate of 0.4, suggesting that there are significant inefficiencies on the revenue side. Considerable variation of inefficiency scores is observed across countries, especially in the case of the profit function. More specifically, profit 0 The Herfindahl Index is defined as the sum of the square of banks market shares in terms of assets in each country. The interest rate spread is defined as the difference between the annual average country-level lending rate minus deposit rate. The intermediation ratio is defined as the country s ratio of total loans to total deposits, while branch density is defined as the number of branches per square kilometre. In order to check for potential multicollinearity correlations among the independent variables of Eq. (6) we calculated variance inflation factors (VIFs) for all independent variables specified. Results are available upon request and indicate no multicollinearity problem. 5

16 inefficiency ranges from 0.87 in Cyprus to 0.5 in the UK. On the other hand, cost inefficiency scores show a higher homogeneity across countries, ranging from 0.07 in the Czech Republic to in Hungary, with the majority of the countries clustering around 0.0 to 0.5. The rank-order correlation between cost and profit inefficiency scores is estimated at about (Please insert Table about here) In the case of productive efficiency, industry inefficiency is measured as the sum of the individual bank directional distance function estimates. Consistent aggregation from firms to industry is facilitated by the use of a constant direction vector. For comparison purposes across countries the figures have been adjusted for the number of banks operating in each country at each time period. Table shows considerable variation of inefficiency scores across countries. Malta appears to have the most efficient banking system, with an average inefficiency score of 0.8, while on the other hand, Netherlands ranks at the bottom of the list, with an average productive inefficiency score of The rank order correlation between productive and cost inefficiency is relatively low (0.30), while it is much higher in the case of profit inefficiency (rank order correlation is estimated at 0.55). Regarding the evolution of inefficiency scores over time (figure ) diverging trends are observed across the three alternative inefficiency concepts. Cost inefficiency exhibits a rather stable pattern over the examined period. On the other hand, profit inefficiency after an initial decline up to 999, presents an upward trend until 00, when profit inefficiency starts decreasing. Nevertheless, during the last year of our sample period profit inefficiency presents an upward trend and reaches its highest average value. In the case of productive inefficiency, an upward pattern is much clearer. With the exception of the sub-period , when a downward trend is observed, productive inefficiency increases over the examined period. (Please insert Figure about here) The Bankscope database also provides information on bank ownership. In light of the growing interest observed in the literature on the relationship between ownership structure and performance, especially in emerging and transition countries, and so as to shed more light on this issue, we present in Table inefficiency estimates of banks with different ownership status. To this end, we divide banking institutions into two categories; namely, majority domestic ownership (when domestic investors, either private or government, hold more than 50% of equity) and foreign ownership (when foreign owners hold more than 50 per cent of the shares). 3,4 Our results suggest that As the Bankscope database reports ownership information only for 006, we follow Bonin et al. (005) and assume that the ownership status of each bank has remained unchanged during the examined period. 3 If the percentages in the data do not add to 00 per cent, we infer the characteristics of the remaining owners, as we are interested only in the type of majority owner. If there is no majority owner and the stakes do not add up to 00 per cent, we assume that there are unreported domestic private owners as long as some private ownership is indicated. If no private ownership is indicated, we attribute the residual to the largest category of owners reported. In this way, we allocate 00 per cent of the banks shares to foreign or domestic owners for each observation (Bonin et al., 005). 4 Our initial aim was to divide banks into three mutually exclusive categories, that is, foreign, stateowned and domestic private banks. However, due to the small number of listed state-owned banks in 6

17 foreign banks are slightly more cost inefficient than domestic banks, while on the other hand foreign-owned financial institutions outperform their domestic counterparts both in terms of profit and productive efficiency. Finally, as part of a sensitivity analysis, we divide our sample into two groups of countries on the basis of the level of financial development and re-estimate inefficiency scores based on separate frontiers. In order to do so, we construct an index of financial development (FD), by combining standardised measures of five indicators proposed by Demirguc-Kunt and Levine (996): market capitalisation over GDP, total value of traded stocks over GDP, turnover ratio, domestic credit to the private sector as a percent of GDP and interest spread. We split countries into two groups based on the median of this indicator. 5 We refer to these two groups as high financial development (HFD) and low financial development (LFD). Nevertheless, we should note that this distinction is relative, as it is based on the median level of financial development among countries in our sample. Table 3 presents the results for cost, profit and productive inefficiency for high and low financial development countries, based on separate frontiers. A direct comparison of inefficiency scores under separate frontiers is not meaningful; nevertheless, some interesting findings arise when comparing the average scores across the two samples. Both groups of countries exhibit similar levels of average cost inefficiency, while on the other hand low financial development countries outperform high financial development countries in terms of profit and productive efficiency. The outperformance of low FD countries is much more evident in the case of productive efficiency. A possible explanation for this finding is that banks in low FD countries that are listed in stock exchanges are usually the largest and best performing banks in their countries. Moreover, given that banks in low financial development play a central role in financial intermediation and in the provision of funds to the economy, they may have some degree of market power and thus earn higher profits. (Please insert Table 3 about here) Another interesting finding is that when estimating separate frontiers for high and low financial development countries, cost, profit and productive inefficiency scores in both samples are much lower when compared to the common frontier. This could indicate that separate frontiers are better able to capture the shape of the true frontier. Nevertheless, the rank-order correlation between the common and separate frontiers is high, especially in the case of profit inefficiency. Among the low financial development countries Estonia appears to be the most cost and profit efficient, while Hungary stands at the other end of the spectrum. In terms of productive efficiency, Slovakia outperforms all low FD countries, while Belgium ranks at the bottom of the list. Looking at the high development countries, Cyprus presents the lowest cost and profit inefficiency scores, while Ireland and the UK rank last in terms of cost and profit efficiency respectively. Moreover, Denmark exhibits the lowest productive inefficiency score, and Netherlands and the UK the highest ones. our sample, we had to merge state-owned and domestic private banks into one category (domestic banks). 5 Given that our sample consists of 7 countries, our sample is split into two unequal subgroups. We chose arbitrarily to place Belgium, which had the median FD index, to the category of low financial development countries, as this subgroup has the lowest number of observations. 7