metadata: authors: 0: author: Calice,Pietro
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docna: 0: docna: Concentration in the Banking Sector and
            Financial Stability : New Evidence
docty: Policy Research Working Paper
subtopic: Economic Growth,Inflation,Macroeconomic Management,Deposit Insurance,Legal Institutions of the Market Economy
teratopic: Public Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: Theory suggests that the effect of
            banking market concentration on financial stability is
            mediated by several competing variables. Using a sample of
            68 countries from 1997 to 2015, this paper proposes a
            unified empirical framework to test for the simultaneous
            presence and impact of the mediators through which
            concentration is expected to impact financial stability. The
            results indicate that the magnitude and net effect of the
            mediators depend upon the level of concentration. At lower
            levels of concentration, increasing concentration improves
            banking system stability via profitability. At higher levels
            of concentration, increasing concentration makes the banking
            system more fragile because of the cost of credit,
            diversification and the ease of monitoring. For intermediate
            levels, concentration has no significant effect on financial
            stability, as the competing moderators cancel each other
            out. The results suggest that an intermediate level of
            concentration may be optimal for welfare.
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            Financial Stability : New Evidence
display_title: Concentration in the Banking Sector
            and Financial Stability : New Evidence
listing_relative_url: /research/2018/10/30501698/concentration-banking-sector-financial-stability-new-evidence
topicv3: Current Account m1326278 1135,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Deposit Insurance m1326722 322,Monetary and Financial Stability m1327169 1098,Financial Institutions m1505015 3797
publishtoextweb_dt: 2018-10-16T00:00:00Z
historic_topic: Public Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 41
author_keys: 0: author_key: 1297294
model_extractions: WPS8615 Policy Research Working Paper 8615 Concentration in the Banking Sector and Financial Stability

# New Evidence

_Pietro Calice Leone Leonida_ Finance, Competitiveness and Innovation Global Practice October 2018
Policy Research Working Paper 8615

# **Abstract**

Theory suggests that the effect of banking market concentration on financial stability is mediated by several competing variables. Using a sample of 68 countries from 1997 to 2015, this paper proposes a unified empirical framework to test for the simultaneous presence and impact of the mediators through which concentration is expected to impact financial stability. The results indicate that the magnitude and net effect of the mediators depend upon the level of concentration. At lower levels of concentration, increasing concentration improves banking system stability via _profitability_ . At higher levels of concentration, increasing concentration makes the banking system more fragile because of the cost of _credit, diversification and the ease of monitoring_ . For intermediate levels, concentration has no significant effect on financial stability, as the competing moderators cancel each other out. The results suggest that an intermediate level of concentration may be optimal for welfare..

This paper is a product of the Finance, Competitiveness and Innovation Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at pcalice@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Concentration in the Banking Sector and Financial Stability: New Evidence**

Pietro Calice<sup>†</sup> and Leone Leonida<sup>‡</sup> JEL: C52; E58; G21; G28.

Keywords: Banking crises; Concentration; Logit model; Interaction effects

> † World Bank Group, Washington DC, USA. Email address: <u>pcalice@worldbank.org</u>

> ‡ King’s Business School, King's College London, London, UK. Email address: leone.leonida@kcl.ac.uk.

We are indebted to Thorsten Beck for his valuable comments. Any error or omission is only ours.
# **1. Introduction**

The relationship between banking market concentration and financial stability, despite a growing body of research, remains ambiguous. Two competing paradigms have come to dominate the theoretical debate:<sup>1</sup> on the one hand, the ‘concentration stability’ view posits that higher market concentration enhances the stability of the banking system; on the other hand, the ‘concentration fragility’ hypothesis maintains that higher concentration destabilizes the banking system and makes it more vulnerable.<sup>2</sup> Theory posits that the effect of banking market concentration on financial stability is mediated by several variables, which may operate in opposite directions, making their magnitude and net effect ambiguous. First is _profitability_ . Proponents of the so-called ‘concentration-stability’ view suggest that concentration may lead to greater market power and profits. Higher bank margins, in turn, boost the charter value of banks, thus decreasing incentives for risk-taking and ultimately making the banking system less prone to crisis (Boot and Greenbaum, 1993; Besanko and Takor, 1993; Hellman et al., 2000; Allen and Gale, 2000; Matutes and Vives, 2000).

A second mediating variable through which concentration affects financial stability is the _cost of credit_ . Advocates of the so-called ‘concentration-fragility’ view acknowledge that concentrated markets lead to higher bank market power and higher profits. However, higher market power allows banks to charge higher interest rates to borrowers, which in turn increases

> 1 For a review and discussion of the different theoretical models see, for example, Allen and Gale (2004), Beck (2008) and Claessens (2009).

> 2 These contrasting effects can be reconciled in models that show a U-shape relationship between concentration and financial stability (see Martinez-Miera and Repullo, 2010; see also De Nicolò and Lucchetta, 2011).

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the incentive of borrowers to assume greater risks and, ultimately, makes the banking system less stable (Boyd and De Nicoló, 2005).

Third, banking market concentration has a bearing on financial stability through the _diversification_ mediating variable. However, the sign of the relationship is ambiguous. On the one hand, concentrated banking systems may entail larger banks with more diversified portfolios due to economies of scale in intermediation, thus increasing stability, in line with the ‘concentrationstability’ view (Diamond, 1984; Ramakrishnan and Thakor, 1984; Boyd and Prescott; 1986; Williamson; 1986; Allen, 1990). On the other hand, larger and more diversified banks may be implicitly protected by ‘too-big-to-fail’ policies that intensify risk-taking incentives and hence increase banking system fragility, overcoming diversification advantages, in line with the ‘concentration-fragility’ hypothesis (O’Hara and Shaw, 1990; Boyd and Runkle, 1992; Mishkin, 1999; Acharya et al., 2012). Further, having larger banks in a concentrated banking system could also increase contagion risk, leading to more instability (Saez and Shi, 2004).

Finally, the effect of concentration on financial stability is mediated by the _ease of monitoring_ . Like the _diversification_ mediator, there is no prior on the sign of the relationship. If a more concentrated banking system implies a smaller number of large banks, this might reduce the supervisory burden and thus enhance overall banking system stability, as suggested by the ‘concentration-stability’ hypothesis (Allen and Gale, 2000). The countervailing argument is that along with a small number of large banks, concentrated markets can also present a large number of small banks that taken together may be systemically important, making more difficult the job of the supervisor and increasing the instability of the system. Moreover, if bank size is positively correlated with complexity then a relatively small number of large banks are harder to monitor 3
than small banks hence increasing the fragility of the banking system, in line with the ‘concentration-fragility’ view (Beck et al., 2007).

The empirical literature, which is mostly concerned with measuring the direct impact of concentration on stability, does not clarify the ambiguity of the theoretical predictions.<sup>3</sup> On the one hand, there is ample evidence that concentrated banking markets may increase financial stability (Keeley, 1990; Demirgüç-Kunt and Detragiache, 2002; Beck et al., 2006; Chang et al., 2008; Evrensel, 2008). The stability effects of higher concentration stem not only from charter values but also from diversification benefits in large banks (Benston et al., 1995; Paroush, 1995; Craig and Santos, 1997; Beck et al., 2006). On the other hand, as theory predicts, concentrated banking markets may also contribute to financial instability (De Nicoló et al., 2003; Boyd et al., 2006; Schaeck et al., 2009; Uhde and Heimeshoff, 2009; Mirzaei et al., 2013; IJtsma et al., 2017). In concentrated markets, as banks get larger and more diversified they may increase the risks of their portfolios, or strategically choose to operate at a closer distance to default (Chong, 1991; Hughes and Mester, 1998; De Nicoló, 2000; Boyd et al., 2006). Larger banks also become subject to internal inefficiencies and increased operational risk (Beck et al., 2006; Cetorelli et al., 2007; Laeven and Levine, 2007).

One possible explanation for the contrasting findings of the empirical literature is that the mediating variables through which concentration can affect financial stability are at work simultaneously, with different magnitudes and net effect on financial stability that crucially

> 3 One related strand of the empirical literature investigates the relationship between competition and financial stability, using primarily measures of market power as opposed to indicators of market structure. However, in line with most recent literature (see, for example, Claessen and Laeven, 2004, and Schaeck et al., 2009), this paper acknowledges that market concentration and competition are two different concepts that are not always related, and accordingly focuses on the former only.

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depends upon the initial degree of market concentration. If this intuition is correct, then, measuring the mediated net effect of concentration on financial stability is an empirical issue. This paper tests this hypothesis thus contributing to shed new light on the complex nexus between banking market concentration and financial stability, and adding to the policy and academic debate.

We propose a unified empirical framework to study whether and the extent to which concentration impacts banking system stability through the competing mediating variables identified in the theoretical literature, namely: (i) _profitability_ , (ii) the _cost of credit_ , (iii) _diversification_ , and (iv) the _ease of monitoring_ . In a seminal paper, Beck et al. (2007) investigate the impact of concentration on stability through _diversification_ and the _ease of monitoring_ , finding evidence for only _diversification_ to play a role. More recently, Bretschger et al. (2012) test for the mediating effect of both _profitability_ and the _cost of credit_ and find evidence for both mediators operating simultaneously. The authors, however, do not measure the net effect of the mediating variables, which is left ambiguous. We build on these results and formally test that the _conditionally offsetting mediators’ hypothesis_ does not hold, i.e. the hypothesis that the mediating variables through which concentration impacts financial stability hold simultaneously with equal strength conditional upon the level of concentration is rejected, and that the degree of concentration does change the effect of the mediators on banking crisis probability. Therefore, we estimate whether the impact of the mediators on financial instability varies at different levels of concentration, and measure their net effect.

Understanding the mechanisms through which banking market concentration affects financial stability is important for the calibration of effective structural policies in the banking system, especially entry/exit rules, consolidation policies and restrictions of activities. Far from being a new question, the global financial crisis (GFC) has reignited interest among policy makers 5
and academics in the relationship between concentration in the banking sector and financial stability, because market concentration may have played a role in the run-up to the crisis, and, more importantly, has tended to increase ever since, raising stability concerns (Committee on the Global Financial System, 2018).

Our empirical analysis rests on a data set comprising available cross-country, annual observations for 68 countries over the period 1997-2015. Financial stability is proxied by the probability of entering both a systemic and a non-systemic banking crisis. Data are drawn from an updated version of the Reinhart and Rogoff (2009) dataset, which gives 42 crisis episodes during the sample period. Crisis data are given by a binary dummy that equals 1 if country _i_ at time _t_ has entered a crisis, and zero otherwise. Concentration is measured by the share of banking assets held by the three largest banks. However, we also study the impact of alternative concentration measures, such as the share of banking system assets concentrated in the five largest banks. We proxy for the mediators through which concentration affects financial stability by using bank return on assets (ROA) for _profitability_ ; real lending rate for the _cost of credit_ ; bank foreign assets plus bank foreign liabilities to banking system assets for _diversification_ ; and the (log) number of banks for the _ease of monitoring._ Following Beck et al. (2006), we estimate a binomial logit model, and control for the following variables: real GDP growth, inflation, nominal exchange rate depreciation, current account balance, real domestic credit growth, and (log) real GDP per capita. In order to disentangle the role of each mediator through which concentration is expected to impact financial stability, we estimate a model where proxies for the mediators are allowed to interact with the level of concentration. This allows us to estimate the marginal effects of the mediators conditional upon selected percentiles of the concentration distribution, and calculate their net effect on crisis probability.

6
Results lend support to our hypothesis. We find that the competing mediators through which market concentration is expected to impact financial stability are at play simultaneously. However, their magnitude and net effect varies with the level of concentration. We find evidence that at lower levels of concentration _profitability_ dominates: increasing concentration increases financial stability. Conversely, at higher levels of concentration, the _cost of credit_ , _diversification_ and the _ease of monitoring_ dominate, and increasing concentration leads to financial instability. For intermediate levels of concentration, which we estimate in the range of 55-66 percent in our sample, the competing mediators cancel each other out, and concentration has no significant impact on banking system stability, suggesting that an intermediate level of market concentration may be optimal for welfare. Several robustness checks, including alternative proxies for the mediators, an alternative measure of concentration, a different subsample, and different econometric models confirm our findings.

This paper is structured as follows. Section 2 provides a description of the data and the econometric methodology. Section 3 discusses our main results, including a battery of sensitivity tests. Section 4 concludes, offering some policy implications.

# **2. Data and methodology**

# **_2.1. Data_**

Our data set is composed of annual observations from 68 countries over the period 19972015. Both the sample composition and time period are driven by data availability. We take information concerning financial stability from an updated version of the Reinhart and Rogoff 7
(2009) database.<sup>4</sup> Reinhart and Rogoff (2009) mark a banking crisis by two types of events: (i) bank runs that lead to the closure, merging or takeover by the public sector of one or more financial institutions, and (ii) in the absence of bank runs, the closure, merging, takeover or large-scale government assistance of an important financial institution (or groups of financial institutions) that marks the start of similar outcomes for other financial institutions. This classification provides us with 42 annual crisis observations, comprising 25 systemic crisis episodes (severe financial distress, in the authors’ definition) and 17 non-systemic crises (milder financial distress) in 38 countries, which gives an in-sample frequency of crises of 3.6 percent, which is in line with similar studies (e.g. Barrell et al., 2010) and within acceptable bounds for the style of analysis.

Dating banking crises is not without drawbacks. Crises can be classified too late, because the financial problems usually begin well before a bank (or a group of banks) is finally closed or merged, or too early, because the worst of a crisis may come later. Moreover, unlike other types of financial crises such as external debt crises, which have well defined closure dates, it is difficult if not impossible to pinpoint the year in which a banking crisis ended. For these reasons, and because we are mostly concerned with investigating the effect of market concentration on the arrival of a banking crisis (i.e. the switch between non-crisis and crisis states), our binary crisis variable takes value of one if country _i_ at time _t_ enters into a crisis and zero otherwise. In other words, as in other studies (see, for example, Barrell et al., 2010), we treat crisis years other than the first (i.e. when the crisis arrives) as tranquil times. Such an approach, as well as the use of lagged control variables (see below) also allows us to control for potential endogeneity between

> 4 Available at <u>http://www.hbs.edu/faculty/initiatives/behavioral-finance-and-financial-stability/Pages/global.aspx.</u>

8
concentration and banking crisis, as bank failures typically modify the structure of the banking sector (Perotti and Suarez, 2002).

Our baseline measure of market structure is the aggregate share of banking assets held by the three largest banks. Market structure should ideally be measured by relevant product and geographic markets; however, such disaggregated data are often not available, and most measures cannot be computed separately for these submarkets. Therefore, as is common in the cross-country literature, we resort to an aggregate measure of concentration. To test the validity of our main findings, we also use an alternative indicator of concentration such as the share of total banking assets held by the largest five banks.

To proxy for the mediating variables through which market concentration affects financial stability, we use several indicators, in line with similar studies (see Bretschger at al., 2012; and Beck et al., 2007). The ‘concentration-stability’ hypothesis assumes that market concentration affects systemic stability or, put differently, the probability of a banking crisis, through higher profits. Therefore, we proxy _profitability_ by a standard measure of bank profitability in the literature: the return on assets (ROA). The ‘concentration-fragility’ view suggests that the effect of higher concentration works through loan rates. Accordingly, we use the real lending rate charged by banks to the private sector as a proxy for the _cost of credit_ . Concentrated banking systems are typically more diversified than diffuse banking systems. Therefore, to proxy for the _diversification_ variable we construct a measure of cross-border financial activity such as the sum of banks’ gross external assets and liabilities relative to total banking system assets. Finally, higher market concentration usually entails a small number of large and diversified banks hence we proxy the 9
_ease of monitoring_ mediator by the (log) number of banks in the country.<sup>5</sup> We provide robustness checks using alternative indicators for the four mediators.

Control variables reflect what the theory of the determinants of systemic banking crises suggests, and include the most common predictors of banking crisis found in the empirical literature (see Kauko, 2014, for a review). A first group of covariates captures macroeconomic developments which can have a direct impact on the performance of the banking system, especially on the quality of assets and the level of nonperforming loans. This group of variables includes real GDP growth and inflation. A second set of control variables reflect structural characteristics of the banking system such as the exchange rate depreciation and the current account balance, which measure the degree of vulnerability of the banking system to currency mismatch and to sudden capital outflows, respectively. Credit growth is also included to reflect the risk that high rates of credit expansion may fuel an asset bubble which can ultimately lead to a banking crisis. Finally, we control for the level of economic development by including the (log) real GDP per capita. To control for potential endogeneity of the regressors, we lag all variables by one year. Moreover, to help interpret how concentration transmits to financial stability through the mediating variables we standardize all variables.

Table 1 provides summary statistics for all variables included in our empirical analysis while Table 2 presents the correlation matrix. Appendix A presents data sources and definitions while Appendix B provides the list of countries with related crisis periods.

> 5 We acknowledge that the number of banks is often used as a proxy for banking market structure. However, given the relatively low correlation between this variable and our baseline concentration measure (-0.26), we retain it as our preferred proxy for the _ease of monitoring_ mediator.

10
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different levels of concentration, i.e. we estimate the marginal effects of the mediators _conditional upon_ different selected percentiles of the concentration distribution.

# **3. Empirical Results**

# **_3.1. Main findings_**

We begin our empirical strategy by employing a binary logit specification as in other studies (e.g., Beck et al., 2006) to estimate the probability of a systemic _and_ non-systemic banking crisis depending on the four mediators, concentration and a standard set of control variables. Results are reported in Table 3, column (1).

The results, computed at the mean, show that all but one of the mediating variables enter the regression significantly. The ROA is negative and statistically significant, in line with the hypothesis that countries with more profitable banks are less prone to financial instability. At the same time, we find that the real lending rate enters positively and significantly, consistently with the view that high lending rates make borrowers riskier, leading to a higher probability of banking crisis. On the other hand, cross-border financial activity (our measure of diversification) enters with a significant positive coefficient, therefore supporting the ‘too-big-to-fail’ argument. Larger and more diversified banks may be induced to take higher risks, leading to higher banking system instability. The (log) number of banks enters with the positive sign, in line with the view that a relatively small number of banks may be easier to monitor, thus enhancing stability. However, this variable is not significant at standard confidence intervals. Interestingly and as expected, we find no evidence for a distinct significative effect of concentration on financial stability.

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Though our variables of interest are the mediators through which concentration is expected to affect financial stability, we find that exchange rate depreciation and current account balance enter negatively and significantly, suggesting that an appreciation of the currency, probably leading to overinvestment in non-tradable sectors, and vulnerability to capital outflows are predictors of banking system instability. We also find that inflation and credit growth enter the regression positively and significantly, suggesting that inflationary bursts and a domestic credit boom are associated with banking problems.

To gauge additional insights on the relationship between our mediators, concentration and financial stability, Table 3, column (1), presents a test for joint significance of the effects of the mediators (ROA, real lending rate, cross-border financial activity and number of banks) as well as a test for joint significance of all these regressors along with our concentration variable. The Wald test for joint significance supports the hypothesis that the mediators have a significant collective impact on banking crisis probability. In Table 4 we present the marginal effects of the mediating variables calculated at selected percentiles of the concentration distribution. One interesting feature of the results reported in Table 4 is that at various levels of concentration the marginal effects of ROA (column (1)), real lending rate (column (2)), cross-border financial activity (column (3)) and (log) number of banks (column (4)) tend to be significant with opposite sign, i.e. the marginal effect of ROA is negative, while the marginal effects of real lending rate, cross-border financial activity and number of banks are positive.

To investigate whether one mediator or group of mediators dominates over the other, Table 4, column (5), reports the LM-type test statistic for the null hypothesis that the sum of the marginal effects equals zero along with the estimated standard errors. Negative and significant values of the test statistic would signal that the null hypothesis can be rejected and that _profitability_ dominates.

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Similarly, positive and significant values of the test statistic would signal that the null hypothesis can be rejected and that the _cost of credit_ , _diversification_ and the _ease of monitoring_ individually or as a group dominate. Results show that the test statistic is never significant along the entire concentration variable distribution, implying that the effects of the mediators with opposite sign cancel each other out with no significant impact on banking system instability.

All in all, we find robust evidence that our mediating variables significantly affect the likelihood of banking crisis in the way suggested by the theory. However, our results also show that no mediator or group of mediators dominates over the other at different levels of concentration so the net effect of the competing mediating variables on financial stability is not different from zero. Our intuition is that the effects of the mediators on banking system instability depend upon the level of concentration, with the magnitude and net effect conditional upon the degree of concentration itself. To test for this, we add to the regression model interaction terms between the four mediators and the concentration variable.

Estimation results for this model, along with a test for joint significance of the effects of concentration working via our proxies for the mediators (ROA, real lending rate, cross-border financial activity and number of banks) as well as a test for joint significance of all these regressors, are reported in Table 3, column (2). Given our interest in evaluating the effects that concentration has on banking instability via the mediators, we calculate the total (i.e. direct and indirect) marginal effects of the four mediating variables computed at different percentiles of concentration (Ai and Norton, 2003). Results, reported in Table 5, suggest that the four mediators are at work simultaneously, and have an impact on the probability of crisis that crucially changes with the level of concentration. Table 5, column (1) shows that the _profitability_ variable, proxied by the ROA, is negatively related to banking system instability: the lower the level of concentration in 14
the banking sector, the higher the positive effect of bank profitability and the lower the likelihood of a banking crisis. The marginal effect of the ROA is always negative, its magnitude decreases with the level of concentration and becomes insignificant at relatively high levels of concentration. Table 5, column (2), shows that the _cost of credit_ mediator is at work as well. The real lending rate is positively related to our banking crisis dummy, implying that more concentrated banking systems lead to a higher cost of money for borrowers, thereby increasing fragility in the system. The marginal effect of the real lending rate is always positive, its magnitude increases with the levels of concentration and is statistically insignificant at relatively low levels of concentration. Table 5, column (3), presents results for the _diversification_ variable. Except for very low levels of concentration, the cross-border financial activity used as a proxy for _diversification_ is positively related to banking instability, implying that the higher the concentration of the banking market, the more banks become diversified and the more likely is the banking system to experience a crisis. The magnitude of this mediator increases with the level of concentration and is significant only at relatively high levels of concentration. Finally, Table 5, column (4), shows that the (log) number of banks, which proxies the _ease of monitoring_ mediator, is positively related to instability: the higher the level of concentration, the more complex it becomes to supervise banks, increasing the likelihood of crisis. The coefficient of the (log) number of banks is always positive, its magnitude increases with the level of concentration, and is always statistically significant, except for very low and very high levels of concentration.

Table 5 also shows that for concentration values between the 30th and the 60th percentile of its distribution ─ corresponding to in-sample concentration ratios of 55 percent and 73 percent, respectively ─ the marginal effects of ROA, real lending rate and number of banks are all significant with opposite sign, i.e. the marginal effect of ROA is positive, while the marginal 15
effects of real lending rate and (log) number of banks are both negative. To gauge a clearer conclusion about what effects dominate, Table 5, column (5), reports the LM-type test statistic for the null hypothesis that the sum of the marginal effects equals zero along with the estimated standard errors. Results show that the test statistic is significant and with the positive sign only at the 60th percentile of the concentration distribution, implying that the _cost of credit_ and the _ease of monitoring_ both dominate over the _profitability_ mediator. For intermediate levels of concentration, i.e. between the 30th and the 50th percentile, the effects with opposite sign cancel each other out with no significant effect of the mediators on banking system instability.

We can also examine how the interaction effect of our mediators with concentration changes the effect of concentration on stability with the help of a chart. Graphical presentations are a very informative adjunct to numerical statistical results in the context of logit models with interactions terms (Greene, 2010). Figure 1 shows the effects of our model for _profitability_ (panel 1), the _cost of credit_ (panel 2), _diversification_ (panel 3), and the _ease of monitoring_ (panel 4). In particular, in Figure 1 the direct and total, i.e. mediated by concentration, marginal effects of the mediators on the probability of banking crisis are plotted on the vertical axis as a function of selected percentiles of the concentration distribution. The interaction effect is the change in the marginal effect of the mediators with respect to changes in concentration levels, which is the distance between the two curves in each of the panels.

Overall, results in Table 5 and reported Figure 1 show that the effects of the mediators through which concentration is expected to affect banking system instability change with the level of concentration, with the net cumulative effect crucially depending upon the level of concentration itself. In the left tail of the concentration distribution (20th percentile and below), further increasing concentration in the banking sector reduces financial instability via _profitability_ .

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When concentration is in its right tail (60th percentile and above), further increasing concentration increases financial instability via the _cost of credit_ , _diversification_ and the _ease of monitoring_ . For intermediate levels of concentration (between the 30th percentile and the 50th percentile), the mediators cancel each other out and the structure of the banking market has no meaningful impact on financial stability. Our results provide, therefore, support for both the ‘concentration-stability’ view and the ‘concentration-fragility’ view: higher concentration enhances stability on the one hand but reduces it on the other, with the net effect of the mediators crucially depending upon the initial levels of concentration.

# **_3.2. Robustness tests_**

Our results may be driven by a number of modeling choices, including the variables used as proxies for the mediators, the measure of concentration used, the sample period and the econometric specification. This section presents results from several robustness checks.

First, we use different proxies for the mediating variables. Our results may reflect the specific variables selected to proxy for the different mediators through which concentration affects banking system instability. Therefore, we run our regression and calculate marginal effects at different values of concentration using the following alternative variables: return on equity (ROE) for _profitability_ ; the deflated lending rate for the _cost of credit_ variable; a measure of income diversification such as the Herfindahl Hirschman Index for _diversification_ (Mercieca et al., 2007);<sup>7</sup> and (log) bank size, a proxy of bank complexity, for the _ease of monitoring_ mediator. Results, which are reported in Tables 6─9, broadly confirm our findings: for relatively low levels of

> 7 A lower HHI of income diversification signals higher diversification and hence we would expect a negative sign for this variable if the results of the baseline proxy for the _diversification_ variable (cross-border financial activity) were confirmed.

17
concentration, increasing concentration reduces the probability of banking crises through _profitability_ ; for relatively high levels of concentration, increasing concentration makes the banking system more fragile. However, while results confirm a strong effect of the _cost of credit_ , they provide somewhat weaker evidence that both _diversification_ and the _ease of monitoring_ are at play as well.

As additional robustness check, we investigate the sensitivity of our results to using an alternative indicator of market concentration: the share of banking system assets held by the five largest banks. Table 10 reports the results, which confirm our findings. We also investigate the robustness of our results to a different sample period. Specifically, given that one-third of crisis episodes in our sample are related to the GFC, we investigate whether our results are driven by the GFC. In Table 11, we run our regression dropping all observations after 2007. We continue to find that _profitability_ is at play for relatively low levels of concentration, while the _cost of credit_ , _diversification_ and the _ease of monitoring_ are at play for relatively high levels of concentration.

A final test concerns the model specification. So far, we have allowed for heteroscedasticity of errors and corrected for it, assuming that errors are independent. However, given that we use panel data, the within-country error terms may be correlated with each other. To control for the fact that omitted country-level characteristics might cause correlation of the error terms withincountries, we allow for clustering within countries. Results, presented in Table 12, confirm our main findings.<sup>8</sup>

> 8 We also estimate a logit model with random country effects and use alternative estimators such as probit, cloglog and LPM. Results, which are not reported for brevity but are available upon request, do not differ significantly from our main findings.

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# **4. Concluding remarks**

This paper presented a unified empirical framework to investigate the mediators through which bank concentration impacts financial stability, and tested for their effects at different levels of concentration. Using data for 68 countries during 1997-2015, we estimated a logit model where interaction effects between our proxies for the mediators and our concentration measure are included and evaluated at different levels of concentration.

Our results show that the mediators through which concentration affects banking system stability operate simultaneously with varying magnitude and net effect that crucially depend upon the initial levels of concentration. For levels of concentration up to the 20th percentile of its distribution, corresponding to a concentration ratio of 47 percent in our sample, _profitability_ dominates and increasing concentration reduces the likelihood of banking crisis. When concentration hits a given threshold, which we estimate at around the 60th percentile of its distribution, or an in-sample concentration ratio of 73 percent, the _cost of credit_ , _diversification_ and the _ease of monitoring_ prevail, and increasing concentration increases crisis probability. For concentration values between these thresholds, corresponding to concentration ratios between 55 percent and 66 percent, the mediators cancel each other out and concentration does not significantly affect financial stability.

Our findings, which are in line with recent studies that have uncovered the presence of nonmonotonicities in the relationship between banking market structure and financial stability (Berger et al., 2009; Bretschger et al., 2012; Beck et al., 2013; Carbó Valverde et al., 2013; Jimenez et al., 2013; Cuestas et al., 2017), suggest that an intermediate degree of concentration may be optimal from a welfare perspective. However, we warn against a normative use. The optimal level of 19
concentration would be subject to significant cross-country heterogeneity (i.e. function of financial development, quality of regulation etc., see Beck et al., 2013), making it hard to make a certain degree of bank concentration as a universal policy objective. Nonetheless, our results suggest that entry/exit rules, merger review processes and activity restrictions should give greater emphasis on profitability, intermediation efficiency, business models and the number of players in the market.

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