THE BANK CAPITAL-COMPETITION-RISK NEXUS – A GLOBAL PERSPECTIVE E Philip Davis, Dilruba Karim and Dennison Noel

The Global Financial Crisis (GFC) highlighted the importance of a number of unresolved empirical issues in the field of financial stability. First, there is the sign of the relationship between bank competition and financial stability. Second, there is the relation of capital adequacy of banks to risk. Third, the introduction of a leverage ratio in Basel III following the crisis leaves open the question of its effectiveness relative to the risk adjusted capital ratio (RAR). Fourth, there is the issue of the relative stability of advanced versus emerging market financial systems, and whether similar factors lead to risk, which may have implications for appropriate regulation. Finally, there is the nature of the relation between bank competition and bank capital. In this context, we address these five issues via estimates for the relation between capital adequacy, bank competition and other control variables and aggregate bank risk. We undertake this for different country groups and time periods, using macro data from the World Bank’s Global Financial Development Database over 1999-2015 for up to 120 countries globally, using single equation logit and GMM estimation techniques and panel VAR. This is an overall approach that to our knowledge is new to the literature. The results cast light on each of the issues outlined above, with important implications for regulation: (1) The results for the Lerner Index largely underpin the “competition-fragility” hypothesis of a positive relation of competition to risk rather than “competition stability” (a negative relation) and show a widespread impact of competition on risk generally. (2) There is a tendency for both the leverage ratio and the RAR to be significant predictors of risk, and for crises and Z score they are supportive of the “skin in the game” hypothesis of a negative relation between capital ratios and risk, whereas for provisions and NPLs they are consistent with the “regulatory hypothesis” of a positive relation of capital adequacy to risk. (3) The leverage ratio is much more widely relevant than the RAR, underlining its importance as a regulatory tool. The relative ineffectiveness of risk adjusted measures may relate to untruthful or inaccurate assessments of bank real risk exposure. (4) There are marked differences between advanced countries and EMEs in the capital-risk-competition nexus, with for example a wider impact of competition in EMEs (although both types of country need to pay careful attention to the evolution of competition in macroprudential surveillance). Similar pattern to EMEs are apparent in many cases for the global sample pre crisis, which arguably are more consistent with normal market functioning than post crisis. (5) Competition reduces leverage ratios significantly in a Panel VAR, with impulse responses showing that more competition leads to lower leverage ratios and vice versa. This result is consistent over a range of subsamples and risk variables. In the variance decomposition, we find that competition is autonomous, while the variance of both risk and capital ratios are strongly affected by competition. The Panel VAR results give some indication of the transmission mechanism from competition to risk and financial instability.

• Our approach enables us to address afresh a number of unresolved empirical issues in the field of financial stability: -The relation of bank capital to risk -The relative importance of the leverage ratio relative to risk adjusted capital adequacy in financial stability -The relation of competition in banking to risk -The differences in financial stability patterns between advanced and emerging market economies -The relation of competition in banking to capital adequacy • We contend that our results using macro data are of particular relevance to regulators undertaking macroprudential surveillance because such data gives a greater weight to large systemic institutions than the more commonly-used bank-by-bank data. • The paper is structured as follows: in Section 2 we provide an overview of the existing literature, Section 3 introduces the data and methodology, Section 4 provides the main results which are summarised in Section 5. Section 6 provides complementary VAR estimates and Section 7 concludes.

Literature
• Our work derives from two distinct strands of the literature. First there are empirical estimates of the effect of capital on risk, which generally does not include competition as a control variable. There are two distinct hypotheses. • According to "skin in the game", a higher capital ratio would be consistent with lower risk as bank managers become prudent and wiser in their investment choices (Bitar et al 2018). Banks hold higher capital to resist earnings shocks and to be able to repay deposits as requested, so obliging banks to hold more capital via regulation improves screening and monitoring and reduces the risk of bailouts (Demirguc Kunt et al 2013). Empirical results supporting this view include Lee and Hseih (2013), Tan and Floros (2013) and Anginer and Demirguc Kunt (2014). • Alternative is the "regulatory hypothesis" suggesting that regulators require higher capital in response to higher risk, and so a positive relation of capital to risk would be expected. This is, for example, found by Iannotta et al (2007) and Bitar et al (2018) • Bitar et al (2018) found risk based capital measures are unrelated to bank risk, whereas unadjusted measures such as the leverage ratio are significantly positively related to risk as shown by loan loss reserves. They suggest that the ineffectiveness of risk adjusted measures may relate to untruthful assessment of bank real risk exposure. • Brei and Gambacorta (2014) tested for procyclicality of capital ratios and found the leverage ratio is significantly more countercyclical than the RAR: it is a tighter constraint for banks in booms and a looser constraint in recessions. • Davis et al (2019) using data from individual banks in Europe and the US found leverage ratios to be more often significant than risk adjusted capital in determination of bank risk. • Berger and Bouwman (2013) looked at the effect of the leverage ratio on survival probabilities and market share and found some differences with results for the risk adjusted capital ratio.
• The competition/risk literature divided between those works which support "competition-fragility" (more competition leads to higher risk) and "competition-stability" which suggests more competition leads to lower risk. Surveys such as Davis and Karim (2018) and Zigraiova and Havranek (2016) show that empirical results are evenly divided between the two hypotheses. • "Competition-fragility" suggests institutions in an uncompetitive banking system have incentives to avoid risk, because a banking licence is valuable in such a context, with restricted entry and probably large capital cushions. When deregulation arises, the value of the licence declines as excess returns are competed away by new entrants and by more intense competition between existing players. This gives incentives to increase balance sheet risk to recover the previous level of profitability, since banks effectively shift risks to depositors (or deposit insurers). Some analyses of the GFC (such as FCIC 2011) give a key role to competition as a causal factor. • According to "competition-stability", whereas lower lending rates in competitive banking markets increase borrower scope for repayment, higher lending rates in uncompetitive markets lead to adverse selection, with only riskier borrowers seeking funds and moral hazard inducing borrowing firms to take greater risks. Large banks may be harder to supervise.
• There are relatively few studies of the capital-competition-risk nexus in its entirety • Freixas and Ma (2015) look at the relation of bank competition to financial stability with a theoretical model and find the effect depends crucially on a bank's type of funding (retail versus wholesale) and whether leverage is exogenous or endogenous. They suggest that "this opens the road for new empirical analysis on the competition-stability link that should depend upon the type of banks and the state of the economy", a path we also follow. • de-Ramon et al (2018) find that higher competition in the UK leads to lower leverage ratios, although the effect on stability measured by the Z-Score may be offset by higher profitability. • Barrell and Karim (2019) found that competition measures such as concentration and the Lerner Index did help to predict banking crises in advanced countries, along with aggregate leverage ratios and property prices. These (along with Berger et al (2009)) are some of the few analyses of capital ratios and risk that take into account competition, which is a paradox given the sizeable literatures on capital and risk, and bank competition and risk cited above.
• Concerning the advanced versus EME issue, most studies of financial stability cited in Davis and Karim (2018) and Zigraiova and Havranek (2016) cover individual countries or only one subgroup (advanced or EME). • The number of studies assessing the differences and similarities between the two groups are relatively sparse. Some recent examples are: • Fratzscher et al (2016) looks at post crisis supervisory changes' effects on risk comparing advanced and emerging market economies • Meng and Gonzalez (2017) looks at differences in credit booms between advanced countries, emerging markets and developing countries. • Finally regarding competition and capital besides the de-Ramon et al (2018) paper cited above, Schaeck and Cihak (2012) look at the effect of competition on capital for 2,600 banks from 10 European countries and find higher competition gives rise to higher capital ratios. This may offer an offset to higher risks taken in highly competitive banking systems.

Methodology
• We undertake an econometric investigation of the relationship of the leverage ratio to risk relative to a risk adjusted measure, with competition as an independent variable as well as standard control variables. • We estimate generally from 1999-2015, using macro data from the World Bank's Global Financial Development Database. • Using logit and panel GMM approaches, we test a global sample and also test for high income countries and emerging market and developing economies separately, as well as before and after the financial crisis. • Thereafter, we present results of simple VARs for the interrelation of competition, risk and capital that casts further light on the interrelationship of these key variables in financial stability analysis.
• Four dependent variables of macroprudential relevance were drawn from the World Bank Global Financial Development Database (GFDD) (Cihak et al (2012), World Bank (2017)) as in Davis (2017). • First, there is the incidence of financial crises per se, as drawn from Laeven and Valencia (2012). It is 1 for each period a crisis lasted, and 0 otherwise. • Second, we use the NPL/loans ratio which may show problems with asset quality in the loan portfolio across the banking sector as a whole. • Third, the Z-Score captures the probability of default of a country's commercial banking system. Z-score compares the buffer of a country's commercial banking system (capitalization and return on assets (ROA)) with the volatility (standard deviation) of those returns. Hence Z-Score = (ROA+(Capital/Assets))/SD(ROA)). As noted by Lui et al (2013), it is appropriate to log the Z score as the level is highly skewed, while the log is normally distributed, so we enter the variable as log (Z-Score). • Fourth, the Provisions/Loans ratio is an indicator of how well protected a banking sector is against future losses. It is a measure of loan quality, being an indicator of a precautionary reserves policy and also an anticipation of high non performing revenue. It takes the past and future performance of the loan portfolio into account (Lee and Hseih 2013).
• Then, we use the leverage ratio and the regulatory capital/risk adjusted assets measures to test for the link of capital ratios to risk. Our key additional variable is competition, which we measure by the Lerner index for bank competition • The Lerner Index is a measure of market power in the banking market. It compares output pricing and marginal costs (that is, mark-up). An increase in the Lerner index indicates a decline in the competitive conduct of financial intermediaries, as reflected in wider margins.
• Other control variables (lagged) were similar to Beck et al (2013), Davis and Karim (2018) and de-Ramon et al (2018): -NONINTSH (share of noninterest income), showing income diversification; -CREDASSET (ratio of bank loans of deposit money banks to assets for deposit money banks), which may link to credit risk -DEPASSET (ratio of deposits of deposit money banks to total assets of deposit money banks) , which shows the dependence of banks on deposits for their funding.

Post-crisis (2008 onwards)
Crisis -*** -*** -*** NPL/loans +*** +*** +* Log Z Score +** Provisions/loans +*** • Regarding the relation of capital to risk, controlling for competition, we have mainly but not solely a negative relation so that more capital leads to lower risk -or conversely less capital leads to higher risk ("skin in the game"). • The leverage ratio is clearly relevant for many cases, as is the regulatory capital ratio, thus justifying the regulatory focus on both measures. In terms of individual regressions, leverage is significant in 16/20 cases, and regulatory capital in 10/20. • From the standpoint of competition and risk, the evidence strongly favours the competition-fragility hypothesis. The implication is clearly that regulators need to take more note of competitive conditions in banking markets when assessing the stance of macroprudential policy and the risk of financial instability. • Finally, we see numerous contrasts between the experience of advanced countries and EMEs in the sample. Results imply, EME regulators should pay particularly close attention to competition, while both groups are justified in a focus on leverage as well as the RAR.

Panel VAR estimation
• To complement our single equation work and investigate further the capital-competition-risk nexus, and in particular the relation of capital to competition, we ran a simple Panel VAR to assess the interrelations of these variables, where risk is measured by the NPL ratio. • Other control variables used in the principal regressions above (the deposit/asset ratio, the credit/asset ratio and the share of noninterest income) are also included but not detailed below. We took two lags of each variable in the VAR. • Impulse responses were run using Pesaran's generalised impulses, the variance decompositions with Cholesky ordering competition, capital, the deposit/asset ratio, the credit/asset ratio and the share of non interest income then risk, but also tested with the reverse ordering, giving similar results.

Panel VAR results
• Impulse responses for NPL ratio and leverage Response of LEVERAGE to LEVERAGE Response to Generalized One S.D. Innovations ± 2 S.E.
• Impulse responses for NPL ratio and RAR Response of REGCAP to REGCAP Response to Cholesky One S.D. Innovations ± 2 S.E.  Response of LEVERAGE to Generalized One S.D. LERNER Innovation

Summary of PVAR results
• In impulse responses, competition drives leverage ratios significantly, with more competition leading to lower capital ratios and vice versa. There is also a significant two way relation between leverage and the NPL ratio, while a shock to Lerner itself does not have a significant direct effect on the NPL ratio. There is no significant impact of competition at 95% on regulatory capital, although there is again an interrelation of regulatory capital and risk. • In the variance decompositions competition is autonomous in both VARs, with over 99% of the variance self-determined even after 10 years. NPLs variance is related to competition albeit not significantly (when leverage is included, 12% after 10 years and 29% with regulatory capital). In contrast, capital (on both measures) is influenced by competition quite significantly (80% with leverage after 10 years and 61% for regulatory capital). • The effect of competition on capital in the impulse responses is quite general, although it is not significant at 95% for emerging market economies. It applies in the cases of advanced countries, pre and post crisis, with the provisions/loans and log Z score measures of risk, and also with the additional macro variables for NPL/loans and for provisions/loans.
• Robustness checks show that the inclusion of key macroeconomic variables and crises do not amend the main results. • We contend that results such as our own using macroeconomic data may in some ways be superior to those with individual bank data which is more typical of the literature. This is the case not least in that the underlying macro data is a weighted average of individual institutions, thus giving implicitly greater importance to large systemic institutions. • Further regulatory implications include: the positive relation of bank competition to risk for most risk measures and subsamples, that has often been disregarded by regulators in the past the widespread importance of the leverage ratio, that underlines the appropriateness of its inclusion in Basel III as a complement to riskadjusted regulatory capital ratios the fact that capital's relation to risk is negative ("skin in the game") for crises and Z score underlines the importance of overall capital regulation the contrasts in some of the results between advanced countries and emerging markets/developing countries underlines that there is no "one size fits all" for regulation the effect of competition on capital indicates that there are indirect as well as direct effects of competition on risk, again emphasising the importance of the monitoring of competition for macroprudential purposes.
• Further research could include: further breakdown of results between emerging market economies against developing countries could also use coefficients that vary over different horizons for example using the functional coefficients approach as in Herwartz and Xu (2010) -since the GFDD is regularly updated, there will in due course be scope to assess robustness including the latest observations. -look at the interaction of the risk adjusted capital ratio and the leverage ratio to see if this enhances stability (as it is expected to). This could be undertaken in future once Basel III is properly in place.