Sophie Brana

Alexandra Campmas

Ion Lapteacru

(Un)Conventional Monetary Policy and Bank Risk-Taking: A Nonlinear Relationship

Keywords: Risk-taking channel, Monetary policy, Asymmetric Z-score, Distance to Default, Shadow interest rate, Panel threshold model. JEL: E4, E5, G21

This paper investigates the effect of monetary policy -especially unconventional monetary policy -on bank risk-taking behavior in Europe over the period 2000-2015. Using a dynamic panel model with a threshold effect, we estimate this effect on two measures of bank risk: the Distance to Default, which reflects the market perception of risk, and the asymmetric Z-score, which corresponds to an accounting-based measure of the risk. We find that loosening monetary policy via low interest rates and increasing central banks' liquidity has a harmful effect on banks' risk, confirming the existence of the risk-taking channel. Moreover, we show that this relationship is nonlinear, i.e., with the sustainable implementation of unconventional monetary policies, the effects are stronger below a certain threshold.

Introduction

Studying the risk-taking channel is a relatively recent area of research that was neglected before the Global Financial Crisis (GFC) for two main reasons.

On the one hand, financial innovation was considered as a stabilizing factor for the financial cycle, under the hypothesis that it permitted better risk sharing.

On the other hand, financial stability was not seen as a threat since most central banks had slowly shifted towards tight inflation-targeting, which they considered their best means of fostering economic growth (Altunbas et al., 2018, Svensson and[START_REF] Svensson | Implementing Optimal Policy through Inflation Forecast Targeting[END_REF].

Recent works argue that the prolonged pre-crisis period of low interest rates under favorable economic and financial conditions encouraged a sense of overconfidence in financial markets and created financial imbalances [START_REF] Taylor | The financial crisis and the policy responses: An empirical analysis of what went wrong[END_REF]. Indeed, persistently low interest rates affected banks' risk perception and valuation, which increased the credit supply (Borio andZhu, 2012, Dell'Ariccia and[START_REF] Dell'ariccia | Lending booms and lending standards[END_REF]. The concerns over this excessive lending supply related not only to the quantity of granted loans but also, and primarily, to these loans becoming riskier. Thus, the risk-taking channel is the impact of a change in interest rates on risk-tolerance and risk perception, triggering a change in credit supply. It began to attract attention only after the fallout had already occurred.

Empirical studies have since rapidly developed and confirmed the existence of this channel1 .

In the aftermath of the GFC, major advanced economies have adopted unconventional tools, including balance-sheet policy, keeping policy interest rates near or below zero and attempting to actively manage agents' expectations. In the short run, the implementation of unconventional monetary policy (UMP) may benefit banks, as the average maturity of a bank's portfolio tends to exceed the average maturity of its liabilities, and when interest rates drop, banks' funding costs fall more quickly than their interest income, and net interest margins rise. Moreover, quantitative easing, or large-scale central bank asset purchases designed to support asset prices, may have positive valuation effects. However, in the medium run, UMP may affect bank risk through the flattening of the yield curve and the cut in the term premium. Hence, banks may rationally take on additional risk and leverage. Ultimately, the overall effects of UMP on bank risk are ambiguous.

As the most of studies focus on the pre-crisis period, our first contribution is to consider the post-crisis period to study the effect of monetary policy on bank risk-taking and, especially, the impact of UMP. Following the Global Financial Crisis, short-and long-term interest rates have been at historically low levels. Thus, concerns have been growing regarding the possible adverse effect of UMP on bank profitability and, hence, on the soundness of the banking sector (Borio et al., 2017).

As a second contribution, we investigate the possibility of nonlinearities in the relationship between UMP and bank risk-taking behavior, an aspect that has been previously neglected in the empirical literature. Many studies support the existence of a regime-dependent effect, as central banks' instruments entail shocks to the monetary policy transmission mechanism, which may, in turn, affect bank profitability, credit supply, inflation or output growth [START_REF] Li | Financial stress, monetary policy, and economic activity[END_REF]St-Amant, 2010, Fry-McKibbin and[START_REF] Fry-Mckibbin | Effects of US monetary policy shocks during financial crises -A threshold vector autoregression approach[END_REF]. Ignoring such nonlinearities may underestimate the effects of very low interest rates (Borio et al., 2017). To investigate the possibility of nonlinearity, we introduce a dynamic panel threshold model, relying on the methodology of [START_REF] Kremer | Inflation and growth: new evidence from a dynamic panel threshold analysis[END_REF], to control for endogeneity and risk persistence. Our approach includes a nonlinear response of bank risk-taking behavior to easing of monetary policy stance. To the best of our knowledge, such an empirical specification has not yet been used. The panel threshold model developed by [START_REF] Hansen | Threshold effects in non-dynamic panels: Estimation, testing, and inference[END_REF] has the advantage of both testing whether a nonlinear relationship exists and identifying the date of rupture without predetermining it. We focus on 20 European countries over the period 2000-2015 to capture the unconventional character of monetary policy.

Since UMP can take many forms, we add a third contribution to the literature when testing for two different aspects, negative interest rates and balance-sheet policy. The last contribution is that we use different complementary measures of bank risk: the asymmetric Z-score, applying the real distribution of the Return on Assets (ROA) variable, and the Distance to Default (DD) measure.

The empirical analysis endorses the existence of nonlinear effects of monetary policy on both bank risk measures. Even though the bank risk-taking channel is at play before the threshold estimated by the model -which confirms previous studies focusing on this issue before the outburst of the GFC -we find that this relationship is even stronger in the aftermath of the GFC. When interest rates are below a certain threshold, we find a positive relationship between both bank risk measures and monetary policy, inducing that bank risk-taking behavior increases after a loosening of monetary policy via lower interest rates. In the end, accounting for central banks' balance sheet policy indicates that additional liquidity encourages banks to take riskier positions with a more critical effect above a specific level of monetary creation for the DD. As robustness checks, we conduct the same analysis with other bank risk measures, the loan-to-asset ratio and the traditional Z-score, and we perform our main regressions with a countrylevel shadow rate, which allows checking the stability of our results. Moreover, splitting the country sample into two regions, Advanced and Emerging Europe, shows that our main findings are mostly driven by advanced European countries.

The remainder of the paper is organized as follows. Section 2 provides an overview of the results in the related literature. The following two sections outline the methodology used to estimate bank risk (Section 3) and UMP (Section 4) measures. Section 5 describes the data, explains the empirical methods and comments the results. Section 6 presents further analysis and robustness checks.

Finally, Section 7 summarizes our main findings and concludes.

Literature Review

The risk-taking channel is justified by several theoretical approaches and operates in several different ways.

The first relevant mechanism, described by [START_REF] Borio | Capital regulation, risk-taking and monetary policy: A missing link in the transmission mechanism?[END_REF], reveals that low interest rates affect risk tolerance through valuations, income and cash flows. This is close in spirit to the financial accelerator developed by [START_REF] Bernanke | The financial accelerator in a quantitative business cycle framework[END_REF]. Indeed, low interest rates increase valuations and boost the net worth of agents, namely their assets and collateral value. Hence, a rise in collateral value, following a policy rate cut, decreases the probability of default of agents, which banks will respond to by granting more loans. However, even if it may stimulate lending, as the risk-bearing capacities of banks (i.e., their net worth) also increase, the financial risk is not necessary worsened. [START_REF] Afanasyeva | Bank market power and the risk channel of monetary policy[END_REF] argue that the effect of a monetary expansion on risk is more complex due to the market power of banks. Following an exogenous increase in the external financial premium, banks may have a keen interest in lending more to obtain a greater "share of the pie". Consequently, agents become more leveraged and, in turn, more likely to default ex-post. However, De Nicoló et al. ( 2010) introduce the skin-in-the-game effect, which predicts that banks will be more cautious in case they engage in highly risky projects. This effect is even more relevant when banks' net worth rises after a policy rate cut because banks with high franchise values have much to lose. [START_REF] Rajan | Has financial development made the world riskier?[END_REF] clarifies a second approach: the search-for-yield mechanism.

The author explains that an expansionary monetary policy decreases the returns obtained from short-term investments composed of risk-free assets. However, if the returns associated with these assets remain low for a long time, these investments will not fulfill the commitments of long-term liabilities. To increase the probability of receiving a higher return, financial institutions are encouraged to invest in risky and high-yield financial assets.

Adrian and Shin (2010) examine a third mechanism relating to leverage and bank's balance sheet. A boom in asset prices encourages financial institutions to expand their balance sheets to maintain their levels of leverage. However, this situation might lead banks to take on more risk. On the liability side, they take on more short-term debts, while on the asset side, they search for potential borrowers, which might have been perceived as riskier in the recent past.

The last mechanism reveals that monetary policy affects the risk-taking channel via its communication policies. A high degree of predictability of future decisions of policymakers can reduce the uncertainty in the market and can lead banks to take risky positions. For instance, a bad economic outcome can affect the agents' perceptions, believing that the central bank will ease monetary policy and cushion the economic risk of slackness. Thus, banks anticipate this insurance effect and take on additional risk [START_REF] Borio | Capital regulation, risk-taking and monetary policy: A missing link in the transmission mechanism?[END_REF].

Many empirical studies confirm the existence of the bank risk-taking channel and provide an interesting background for our analysis. [START_REF] Jiménez | Hazardous times for monetary policy: What do twenty-three million bank loans say about the effects of monetary policy on credit risk-taking?[END_REF] and [START_REF] Ioannidou | Monetary policy and subprime lending: A tall tale of low federal[END_REF] examine the risk-taking channel of monetary policy with micro-level data. By using a duration model, [START_REF] Jiménez | Hazardous times for monetary policy: What do twenty-three million bank loans say about the effects of monetary policy on credit risk-taking?[END_REF] proxy for risk with a loan hazard rate. They control for the macroeconomic environment, country-level risk and for bank, borrower and loan characteristics, and they find that banks relax their lending standards and easily grant new loans to riskier borrowers when interest rates are low. Small banks appear to be more reactive to a monetary policy change. In the same vein, [START_REF] Ioannidou | Monetary policy and subprime lending: A tall tale of low federal[END_REF] compute the probability of default for each loan and conclude that a decrease in the federal funds rate2 prior to loan origination encourages Bolivian banks to take on more risk. In contrast, expansionary monetary policy over the life of a loan lowers the risk. Banks with more liquidity and less equity tend to take on greater risk when interest rates are low. In line with the use of individual loan characteristics, many studies confirm the negative relationship between the interest rate and bank risk during the pre-crisis period in the U.S. [START_REF] Maddaloni | Bank risk-taking, securitization, supervision, and low interest rates: Evidence from the Euro-area and the U.S. lending standards[END_REF][START_REF] Delis | The risk-taking channel of monetary policy in the USA: Evidence from micro-level data[END_REF][START_REF] Dell'ariccia | Bank leverage and monetary policy's risk-taking channel: Evidence from the United States[END_REF] 3 , in Austria [START_REF] Gaggl | Does a low interest rate environment affect risk taking in Austria?[END_REF] and in Colombia [START_REF] Lopez | The risk-taking channel and monetary transmission mechanism in Colombia[END_REF].

Beyond the use of loan-level data, many studies employ measures of risk at the bank level. [START_REF] Altunbas | Do bank characteristics influence the effect of monetary policy on bank risk?[END_REF] focus on quarterly data of 643 European and American listed banks over the period 1987-2008. Risk is measured by the Expected Default Frequency (EDF), a forward-looking and market-based indicator of risk. The GMM econometric model highlights a negative relationship between interest rates and risk. Furthermore, small, liquid and well-capitalized banks seem to take on less risk. Reconsidering their previous paper, [START_REF] Altunbas | Does monetary policy affect bank risk-taking?[END_REF] add institutional variables, such as competition, securitization activity, and intensity of regulation indicators, to disentangle the effect of the bank risk-taking channel from the financial accelerator and the bank-lending channels, and their findings remain unchanged. [START_REF] Gambacorta | Monetary policy and the risk-taking channel[END_REF] provides similar outcomes, focusing on the same regions but a restricted period (2007)(2008). Indeed, his study aims to explain the evolution of bank risk during the financial crisis with EDF as explanatory variable. Finally, [START_REF] Michalak | The Nexus between Monetary Policy, Banking Market Structure and Bank Risk Taking[END_REF] focuses on the relationship between bank risk-taking and banking market structure. His sample covers listed bank holding companies located in Western Europe from 1997 to 2008. The author provides empirical evidence that an extended period of expansionary monetary policy, corresponding to a short-term interest rate below the rate implied by a Taylor rule, has a negative impact on the EDF of European banks.

Other studies use ex-post indicators as explanatory variables for bank risk, such as the risky asset ratio and the non-performing loan ratio, and they focus on the pre-crisis period. By using the GMM4 , although these analyses focus on various countries and/or regions, they all report a negative relationship between bank risk and interest rates [START_REF] Brissimis | Bank heterogeneity and monetary policy transmission[END_REF][START_REF] De Nicoló | Monetary policy and bank risk taking[END_REF][START_REF] Delis | Interest rates and bank risk-taking[END_REF][START_REF] Tabak | The impact of market power at bank level in risk-taking: The Brazilian case[END_REF].

Hence, many studies establish the existence of the risk-taking channel during the pre-crisis period. Nevertheless, only a few recent studies have analyzed the impact of UMP on bank risk-taking behavior. UMP flattens the yield curve and tends to encourage banks to take on greater risk and increase their leverage. [START_REF] Lambert | The effects of unconventional monetary policies on bank soundness[END_REF] and [START_REF] Kandrac | Quantitative easing and bank risk taking: Evidence from lending[END_REF] focus on U.S. banks during the post-crisis period. [START_REF] Lambert | The effects of unconventional monetary policies on bank soundness[END_REF] conduct a panel analysis of bank profitability, balance-sheet repair and risk-taking. They apply the GMM approach and find that UMP has ambiguous effects not only on profitability but also on bank risk because UMP seems to reduce the leverage and short-term debt ratios but increase the ratio of risk-weighted assets to total assets. [START_REF] Kandrac | Quantitative easing and bank risk taking: Evidence from lending[END_REF] analyze Quantitative Easing (QE) transmission and assess the effect of bank level reserve accumulation on lending activity and risk-taking. Their results from the IV method show that reserves created by the Fed, resulting from QE programs, induced higher total loan growth. Consequently, banks' loan portfolios become riskier and led to riskier lending activity.

The previous studies are exclusively based on linear models and neglect the possible existence of a nonlinear relationship between monetary policy and bank risk-taking. Nonetheless, some papers show that monetary policies have different effects between normal and financial stress periods [START_REF] Brana | The effects of global excess liquidity on emerging stock market returns: Evidence from a panel threshold model[END_REF]Prat, 2016, Saldías, 2017), between pre-and post-crisis periods [START_REF] Mallick | Market volatility, monetary policy and the term premium[END_REF], and among different periods of the business cycle [START_REF] Avdjiev | Credit growth, monetary policy, and economic activity in a three-regime TVAR model[END_REF].

Studies that consider the nonlinear effects of monetary policy analyze its impact on its transmission mechanism or on its objectives, but few papers examine its impact on bank behavior. Furthermore, if studies investigating both nonlinearities and financial stress are common, "there is very limited analysis of nonlinearities in monetary transmission linked to the level of interest rates" (Borio and Hofmann, 2017, p.15). Few authors assess the nonlinear relationship while considering periods of low interest rates. [START_REF] Lambert | The effects of unconventional monetary policies on bank soundness[END_REF] find that low interest rates are associated with lower risk-weighted asset ratio in the short term, but a prolonged period of low interest rates may increase risk. [START_REF] Altavilla | Monetary policy and bank profitability in a low interest rate environment[END_REF] find that changes in the level and the slope of the term structure are not associated with lower bank profits. However, maintaining interest rates at a low level for an extended period might reverse the relationship. [START_REF] Claessens | Low-For-Long" interest rates and banks' interest margins and profitability : Cross-country evidence. International finance discussion papers[END_REF] find that the negative impact of the short-term interest rate on banks' net interest margins and returns on assets is significantly larger in low-rate regimes. Borio et al. (2017) conclude that the impact of both interest rates and the yield curve slope on bank asset returns is larger when studies allow for nonlinearities.

Bank risk measures

This section explains the methodology used to estimate our measures of bank risk, namely an asymmetric Z-score and the Distance to Default. We consider two conceptually different risk measures to consider both balance-sheet vulnerability and market perception of bank risk.

The Z-score is the most widely used accounting-based risk measure in the banking literature to identify the balance-sheet vulnerability since it considers a bank's capital being insufficient to cover its losses in case of a default event.

Compared to other accounting-based risk measures, its main advantage is the concept of risk on which it is based, which is not the case of measures such as the ratio of non-performing loans, the ratio of risky assets, or loans loss provisions.

These measures are merely asset quality indicators and are not related to any default event, i.e., a bank may be aware that the quality of its assets is deteriorating without being threatened by default. Moreover, loan loss provisions may be used not only to create reserve cushions for non-performing loans but also as an income-smoothing tool [START_REF] Fonseca | Cross-country determinants of bank income smoothing by managing loan-loss provisions[END_REF][START_REF] Pérez | Earnings and capital management in alternative loan loss provision regulatory regimes[END_REF][START_REF] Bikker | Bank provisioning behaviour and procyclicality[END_REF]. Such income smoothing behavior has been found for both Western [START_REF] Bouvatier | Bank income smoothing, ownership concentration and the regulatory environment[END_REF] and Central and Eastern European (CEE) banks [START_REF] Skala | Does shareholder structure affect income smoothing in Central European banks[END_REF]. However, the probability of default and the default event to which it is related are eliminated in the traditional formula, since it is based on some unrealistic simplifications and assumptions. To avoid such drawbacks, the real distribution of banks' ROA is considered.

The market perception of bank risk is measured by the Distance to Default, which is computed with standard [START_REF] Black | The pricing of options and corporate liabilities[END_REF] and [START_REF] Merton | On the pricing of corporate debt: The risk structure of interest rates[END_REF] option models and is applied to estimate individual [START_REF] Andries | Effects of macroprudential policy on systemic risk and bank risk-taking[END_REF], Vas-salou and Yuhang, 2004[START_REF] Laeven | Bank risk and deposit insurance[END_REF] and systemic bank risks [START_REF] Lehar | Measuring systemic risk: A risk management approach[END_REF].

Other authors, such as [START_REF] Altunbas | Macroprudential policy and bank risk[END_REF], apply the Expected Default Frequency (EDF) to measure the market perception of bank risk, which represents the probability that a bank will default within a given time horizon and is computed only by Moody's KMV and is not publicly available. Aside from the problem of data unavailability, the EDF is measured as a probability of default, in contrast to the DD, which is a quantile in the estimation of the probability of default. As such, it is constrained to take values between 0 and 1, while the DD is not.

The asymmetric Z-score

The original concept of the Z-score issues from the probability of default definition, where the default event occurs when current losses exhaust capital or, equivalently, when the bank's profits, π, are lower than its negative capital, -C : P r[π ≤ -C]. Dividing by total assets, the probability of default is

P r[π ≤ -C] = P r[ROA ≤ -COA],
where ROA is the Returns-On-Assets random variable and COA is the Capital-On-Assets ratio [START_REF] Boyd | Size and performance of banking firms: Testing the predictions of theory[END_REF]Runkle, 1993, Hannan and[START_REF] Hannan | Bank insolvency risk and the market for large certificates of deposit[END_REF]. To provide a simple formula, [START_REF] Boyd | Size and performance of banking firms: Testing the predictions of theory[END_REF] and [START_REF] Hannan | Bank insolvency risk and the market for large certificates of deposit[END_REF] suggested considering a normal distribution for the ROA random variable. Centering and reducing ROA variable, one obtains that the probability of default is N (-COA; µ, σ) = N (-COA+µ σ ), where N (.; µ, σ) is the cumulative distribution function of the normal law with expected value µ and standard deviation σ of ROA, and N (.) is the cumulative distribution function of the normal law with µ = 0 and σ = 1. Thus, the traditional formula of the Z-score, that is Z trad = COA+µ σ , is obtained under the (unrealistic) normal distribution hypothesis. Hence, the negative traditional Z-score is the point at which the normal cumulative distribution function N (.) is equal to the probability of default, as computed with the normal cumulative distribution function,

Z trad = -N -1 (N (-COA; µ, σ)) = COA+µ σ .
Lapteacru (2016) shows that the normal distribution hypothesis is inappropriate for the concept of the probability of default and suggests applying a flexible distribution function that can comprise many other distributions, including the normal one. The stable distribution allows for better consideration of forms of the ROA distribution and thus provides consistent estimates of the Z-score. A random variable is considered stable if its characteristic function can be written as

φ(t; β, α, µ, σ) = exp[itµ -|σt| β (1 -iαsgn(t)φ)],
where:

φ =    tan( πβ 2 ), if β = 1 -2 π log|t|, if β = 1
and β ∈ (0, 2] represents the stability index, α ∈ [-1; 1] the skewness parameter, µ ∈ IR the location parameter and σ > 0 the scale parameter. This very flexible distribution comprises the normal distribution (for β = 2), Cauchy distribution (for β = 1 and α = 0) and Lévy distribution (for β = 1/2 and α = 1) and, hence, can cover the most of real distributions of ROA.

We follow the approach of [START_REF] Lapteacru | On the consistency of the Z-score to measure the bank risk[END_REF] to build our asymmetric Zscore and replace the normal distribution by an estimated stable cumulative distribution function, F StD (.; β, α, µ, σ), as follows:

Zscore = -N -1 (F StD (-COA; β, α, µ, σ)), (1)
where β, α, µ and σ are its parameters to be estimated.

Thus, compared to the traditional Z-score, Z trad , our asymmetric Z-score is computed with stable cumulative distribution function, F StD (.), instead of the normal one, N (.). Because the stable distribution has no analytical functions, we determine its parameters by minimizing the distance between the stable probability density function and that of the smooth kernel distribution. In the literature, the traditional Z-score is computed by applying a three-or fiveyear rolling window to determine the mean and standard deviation of ROA.

However, according to the probability of default concept, this risk measure is linked to the distribution of the random variable ROA. The estimated mean and standard deviation are the parameters of this distribution, but, in our opinion, they cannot be estimated with only three or five observations. Such a small number cannot provide the correct form for the actual ROA distribution, which is why we use a seven-year rolling window to estimate the parameters of our stable distribution function. It is a compromise between having a large number of observations, to correctly draw the distribution function, and the size of our sample. Considering such a number of observations for the rolling window does not affect our sample size since once the stable distribution is estimated, it is applied for all the COA observations that are related to the rolling window.

We do not estimate the stable distribution on the entire time sample because performing a rolling window computation allows us to consider the evolution of a bank's capital-on-assets ratio with respect to the distribution of its returns.

Thus, all distributions are estimated for each year and for each bank.

The Distance to Default

The DD is computed with the [START_REF] Merton | On the pricing of corporate debt: The risk structure of interest rates[END_REF] option model and shows how far a bank is from a default event, i.e., the lower its values, the closer the bank is to insolvency. This measure has been applied to price deposit insurance [START_REF] Ronn | Pricing risk-adjusted deposit insurance: An option-based model[END_REF]Verma, 1986, Duan and[START_REF] Duan | Assessing the cost of Taiwan's deposit insurance[END_REF] and to estimate individual [START_REF] Laeven | Bank risk and deposit insurance[END_REF][START_REF] Vassalou | Default risk in equity returns[END_REF][START_REF] Chan-Lau | Equity returns in the banking sector in the wake of the Great Recession and the European sovereign debt crisis[END_REF][START_REF] Andries | Effects of macroprudential policy on systemic risk and bank risk-taking[END_REF] and systemic bank risk [START_REF] Lehar | Measuring systemic risk: A risk management approach[END_REF].

To derive the DD, the value of bank assets is considered to follow a geometric Brownian motion,

dV t V t = µ V dt + σ V dW t ,
and bank liabilities consist of zerocoupon debt. A bank finances its assets using debt and equity, and the market value of its assets at time t is, therefore, V t = S t + D m t , where S t is the market value of the bank's equity and D m t is the market value of its debt. In a default situation, i.e., when the market value of a bank's assets is less than the market value of its debt, the bank does not reimburse its creditors. A bank's equity is therefore considered to be a call option on the bank's assets, the strike price of which is the book value of the bank's debt, D. The latter is a zero-coupon bond with maturity T, which grows with its interest rate r. Its market value at time t, D m t , and that of its equity, S t , are expressed using the [START_REF] Black | The pricing of options and corporate liabilities[END_REF] model:

S t = V t N (d t ) -De -r(T -t) N (d t -σ V √ T -t), (2)
D m t = V t -S t = V t N (-d t ) + De -r(T -t) N (d t -σ V √ T -t), (3)
where

d t ≡ ln( Vt D ) + (r + 1 2 σ 2 V )(T -t) σ V √ T -t .
Applying Itô's lemma, the market value of the bank's assets at debt maturity

T is V T = V t exp[(µ V -0.5σ 2 V )(T -t) + σ V √ T -tZ t ],
where µ V and σ V are the expected return and the return volatility of the market value of the bank's assets, respectively, and Z t → N (0; 1). The default situation therefore occurs when V T < D and the DD is defined as:

DD t ≡ ln( Vt D ) + (µ V -1 2 σ 2 V )(T -t) σ V √ T -t . (4)
To compute the DD, we apply the [START_REF] Duan | Assessing the cost of Taiwan's deposit insurance[END_REF] and [START_REF] Duan | Correction: Maximum likelihood estimation using price data of the derivative contract[END_REF] estimation approach to estimate µ V and σ V , as explained in Appendix B.

Evolution of bank risk measures

Figure 1 illustrates that both risk measures are different and their pattern also varies. For all regions, the asymmetric Z-score seems to better describe the occurrence of crisis events. In line with section 3.1, the graph clearly indicates that values associated with the asymmetric Z-score are more consistent and meaningful than those associated with the traditional one.

First, the values obtained by the traditional Z-score are inconsistent with the original concept of probability of default. Its lowest average level is for non-euro area banks in 2008, which means, according to the above formulas, a probability of default of N (-8) = 7.62 × 10 -24 . Such a probability does not make sense in terms of the occurrence of a default event, especially during a crisis period. However, with an asymmetric Z-score, the previous probability of default becomes N (-4.75) = 0.0001%. This is still low level, because of the definition of a default event that is too constraining, but has an interpretable meaning.

Second, the evolution of the traditional Z-score does not reflect the main events as well as the asymmetric Z-score. -196 , which makes no sense.

Third, the evolution of the asymmetric Z-score corresponds better to that of the DD.

Finally, there is a much larger difference between these two risk measures across banks, as the Spearman rank correlation coefficient is 0.23 for the entire sample and ranges from very low values to very high correlations as follows:

-0.0056 (for Austria), 0.0022 (for Croatia), 0.82 (for the Czech Republic), 0.61 (for Denmark), -0.45 (for Finland), -0.41 (for France), 0.67 (for Germany), 0.13 (for Greece), -0.66 (for Hungary), 0.45 (for Ireland), 0.39 (for Italy), 0.05 (for the Netherlands), 0.49 (for Norway), 0.56 (for Poland), 0.38 (for Romania), -0.19 (for Slovakia), -0.47 (for Spain), 0.07 (for Sweden), 0.51 (for Switzerland), -0.19 (for the United Kingdom). Thus, the important difference between the asymmetric Z-score and the traditional one may lead to opposite conclusions for countries where Spearman rank correlation coefficient is negative or zero. As one may observe further, for panel data regressions, such a difference leads to very important discrepancies in the results.

We notice that, with very few exceptions, the asymmetric Z-score and the DD follow the same evolution. Both of these measures experienced a sharp decline in all regions of Europe at the time of the GFC, with some delay for the asymmetric Z-score in CEE. It means that the banks of these countries underwent a very gradual worsening of the capitalization profile with respect to the distribution of their returns. However, these banks show a stronger solidity, even during the financial crisis (values of the Z-score are higher).

The evolution of these two measures of risk is driven by different factors.

Being a market-based risk measure, the DD reflects both the evolution of banks' market value and their ability to cover the market value of their total debt. As a result of the collapse of stock markets across Europe, the market value of European banks has fallen, threatening their ability to repay debt. As CEE banks were scarcely affected by the crisis, the minimum level of the DD does not reflect a threat to the stability of these banking systems. The largest decreases were recorded by banks in Austria, Finland, France, Germany and the Netherlands (North Europe zone) and, of course, in Greece, Ireland, Italy and Spain (South Europe zone). As expected, due to the highly indebted profile of these banks, followed by concerns about the sovereign debt crisis, the DD fell sharply until capitalized; thus, their Z-scores increased after that.

Monetary policy tools

To capture the conventional and, primarily, the unconventional character of monetary policy, we rely on four different variables. We first consider an observable interest rate variable, the policy interest rate (i r ), the principal central banks' instrument. However, according to some authors, this variable only allows for the consideration of a conventional monetary policy stance [START_REF] Brissimis | Bank heterogeneity and monetary policy transmission[END_REF][START_REF] Delis | Interest rates and bank risk-taking[END_REF][START_REF] Buch | In search for yield? Survey-based evidence on bank risk taking[END_REF], because of the zero lower bound (ZLB). Furthermore, we rely on the interest rate on the deposit facility (i d ), which may be an indicator of UMP since many European central banks have set this policy rate below zero [START_REF] Borio | Unconventional monetary policies: A re-appraisal[END_REF]. Moreover, to entirely overcome the ZLB constraint, we calculate a shadow short rate (i shadow ). For the countries belonging to the Eurozone, we rely on the shadow short rate estimated by [START_REF] Krippner | Documentation for United States measures of monetary policy[END_REF][START_REF] Krippner | Documentation for measures of monetary policy[END_REF] using the euro-area Overnight Indexed Swap curve. For non-euro countries, we compute a country-level shadow rate.

We apply the [START_REF] Krippner | Documentation for United States measures of monetary policy[END_REF][START_REF] Krippner | Documentation for measures of monetary policy[END_REF] approach to the estimation of the i shadow variable, which is "shortest maturity rate from the estimated shadow yield curve" (Krippner, 2014, p.1). According to the author, the model of [START_REF] Wu | Measuring the macroeconomic impact of monetary policy at the zero lower bound[END_REF], which is a three-factor shadow/lower-bound term structure model (SLM), displays excess sensitivity and can induce a misinterpretation of the policy implications. Krippner relies on a two-factor SLM and uses a continuoustime Gaussian affine term structure model to shape the shadow term structure.

He reproduces the [START_REF] Black | Interest rates as options[END_REF] lower bound mechanism, r(t) = max{r L , r(t)} where r(t) is the lower bound short rate, namely the interest rates on the market, r(t) denotes the i shadow and r L is the lower bound for the interest rate corresponding to a strike price of a call option. The latter is used to impose the ZLB on the shadow bond and is set at 0.00125 in our estimations. The right-hand-side, max{r L , r(t)}, imposes the lower bound. This constraint first entails that the interest rates on the market, r(t), are constrained by a ZLB and, second, that the i shadow cannot be superior to the highest value of r(t).

However, for few countries, higher estimates of the i shadow reflect occasional abnormal economic events before the pre-lower bound (LB) period (e.g., for

Romania, Croatia, Poland, Hungary, Slovak Republic, Greece and Norway) (see

Appendix C).
In an environment where conventional monetary policy prevails, the i shadow may follow the current policy rate because the latter may be close to the data used to estimate the i shadow . Indeed, Krippner uses data from the yield curve with different maturities: 0.25, 0.5, 1, 2, 3, 5, 10, and 30 years. We follow this approach by including the maximum data available per maturity for each country in our sample. The i shadow is very close to the policy interest rate for all countries. However, for some CEE countries (as Romania), the data used for the yield curve and, hence, for the estimation of the i shadow reveal interbank interest rates that are higher at the beginning of the period sample than the policy interest rate (Figure 2).

In a lower bound (LB)/unconventional environment, the i shadow can take on negative values to reflect a global stance of monetary policy that can be more accommodative than the zero-interest rate itself. In other words, the i shadow considers the effects of UMP on the interest rates of securities with longer maturities since it is estimated from the yield curve, and a negative value can be interpreted as the synthesis of a current zero-interest rate policy plus unconventional monetary actions. To estimate the i shadow , Krippner relies on an arbitrage-free model of [START_REF] Nelson | Parsimonious modeling of yield curves[END_REF] with two state-variables that evolve as a correlated vector Ornstein-Uhlenbeck process, which are the Level, L(t), and Slope, S(t), variables. The i shadow is the sum of these statevariables: r(t) = L(t) + S(t). As expected, this unconstrained interest rate is negative during unconventional monetary periods.

Finally, following Lambert and Ueda (2014) and [START_REF] Brana | The effects of global excess liquidity on emerging stock market returns: Evidence from a panel threshold model[END_REF],

we also use the central bank's assets (in log) (CBA) to capture quantitative easing measures. While the policy interest rate indicator might be bounded by a zero lower limit, CBA captures the unconventional monetary stance with an unusually high increase of the central bank's balance sheet (Figure 2).

Monetary policy data are individual to countries, except for the interest rate variables, which are identical for euro area members after their accession. The CBA data are individually collected for all countries.

Evolution of monetary policy instruments

Since the GFC, all policy interest rates and deposit facility rates have sharply declined (Figure 2).

Empirical model and results

This section firstly presents our database. Then, it describes the econometric model used to assess the impact of monetary policy on European banks' risk and provides results and comments.

Data description

Our data cover 126 banks6 in 20 European countries and span from 2000 to 2015. To make our analysis comparable between our two bank risk measures, Figure 3 provides information about European banks' market shares in terms of total assets in each country of our sample and on average for over 2000-2015.

which
On average, our data cover 50% of the total banks' market shares in the sample period. However, CEE countries have few listed banks, and their particular banking structure explains why their bank market shares in our sample are rather low. Indeed, there is a high proportion of foreign banks, mainly from Western Europe. Moreover, the German tiered banking market involves numerous banks. Even though our data include the largest German banks in terms of assets, this complex structure underlines the difficulty of obtaining a high market share for Germany. Finally, Finnish banks in our sample represent only approximately 11% of the total market share of the country. This small percentage is explained by the presence of Nordea Bank, a Swedish bank that accounts for an enormous market share. However, this is accounted for in our sample. Table 2 provides some summary statistics. The data cover listed banks with different characteristics regarding equity, liquidity and size and various banking markets in terms of concentration, real GDP growth and banking supervision and regulation. One may notice that very high interest rates correspond to the crisis periods of the 1990s in many CEE countries. The highest values for the interest rates correspond to Romania. Similarly, and as explained previously, the maximum value for the i shadow also corresponds to Romania and is greater than the policy interest rate. Negative values reflect unconventional monetary events. Note that the very negative and very high values of the GDP rate correspond to the effects of the GFC in 2009 and the very high and recent Irish economic boom, respectively. We include a regulatory index, as bank risk-taking may also be driven by the regulatory environment that prevails in each country [START_REF] Laeven | Bank risk and deposit insurance[END_REF]Levine, 2009, Barrell et al., 2010). This may exert an influence on the level of risk a financial institution may take, i.e., strengthened banking regulation is expected to discourage risk-taking behavior. The construction of this index is in Appendix A. Global Macroprudential Policy Instruments Database [START_REF] Cerutti | The use and effectiveness of macroprudential policies: New evidence[END_REF] Notes: This table reports summary statistics of all variables. The DD is the Distance to Default and describes the distance of banks' balance-sheet structure from a structure that corresponds to the default event: the higher the Distance to Default, the lower is the bank risk. The Z-score describes the capitalization profile of banks with respect to the distribution of their returns: the higher the Z-score, the lower is the bank risk. All bank control variables are collected at each annual closing date.

Dynamic panel model with threshold effect

In this section, we follow [START_REF] Kremer | Inflation and growth: new evidence from a dynamic panel threshold analysis[END_REF] and introduce our dynamic panel model with the threshold effect. Then, we present our results and comments.

Econometric methodology

As we suspect a nonlinear response of bank risk-taking behavior to eased monetary policy, we follow and apply the methodology of [START_REF] Kremer | Inflation and growth: new evidence from a dynamic panel threshold analysis[END_REF] to run the dynamic panel threshold estimations. First, based on a static crosssectional balanced panel threshold model introduced by [START_REF] Hansen | Threshold effects in non-dynamic panels: Estimation, testing, and inference[END_REF], this methodology determines an optimal threshold and estimates a coefficient for each regime. The panel threshold regression model with individual specific effects is given by the following equation:

y i,t = µ i + β 1 x i,t I(q i,t ≤ γ) + β 2 x i,t I(q i,t ≥ γ) + i,t , (5)
where I(.) is the indicator function, which takes the value of 1 if true, 0 otherwise.

These same indicators are used as their own regime-dependent variable. q i,t is the threshold variable and γ is the optimal threshold value. The subscripts i and t stand for the cross-sectional and time dimensions, respectively. The dependent variable y i,t and the threshold variable q i,t are scalar matrices. The regressor x i,t is the vector of explanatory variables, and i,t is the error term.

The observations are divided into two regimes depending on whether the threshold variable q i,t is smaller or larger than the threshold value γ. The individual effects µ i are assumed to be the same in both regimes. Thus, the two regimes are distinguished by different regression slopes β 1 and β 2 .

However, growing empirical literature on bank risk-taking supports many arguments in favor of a dynamic model. It allows for mitigating the potential endogeneity problem the equation might face between risk and monetary policy.

Two main problems are underscored:

(i) Omitted variables: bank risk and interest rates might be endogenous to the local macroeconomic conditions [START_REF] Ioannidou | Monetary policy and subprime lending: A tall tale of low federal[END_REF][START_REF] Jiménez | Hazardous times for monetary policy: What do twenty-three million bank loans say about the effects of monetary policy on credit risk-taking?[END_REF][START_REF] Maddaloni | Bank risk-taking, securitization, supervision, and low interest rates: Evidence from the Euro-area and the U.S. lending standards[END_REF][START_REF] Gaggl | Does a low interest rate environment affect risk taking in Austria?[END_REF].

(ii) Reverse causality: a future higher risk might entail current monetary expansion [START_REF] Ioannidou | Monetary policy and subprime lending: A tall tale of low federal[END_REF][START_REF] Delis | The risk-taking channel of monetary policy in the USA: Evidence from micro-level data[END_REF].

Even though [START_REF] Delis | Interest rates and bank risk-taking[END_REF] Finally, using a dynamic model is a principal advantage given the dynamic nature of bank risk (i.e., it includes the lagged dependent variable as an explanatory variable). The literature provides some reasons to explain risk persistence. [START_REF] Delis | Interest rates and bank risk-taking[END_REF] argue that the relationship between a risky borrower and the bank has a lasting effect on the level of risk despite the historic relationship, which improves efficiency. Moreover, they suggest that bank regulation leads to risk persistence, and coercive measures (e.g., capital requirements) may exacerbate the moral hazard issue by encouraging riskier investments over a considerable period. Finally, as bank risk is associated with the business cycle, banks may need time to smooth the effect of macroeconomic shocks.

To introduce the dynamic nature of bank risk in the estimation, we follow the methodology of [START_REF] Kremer | Inflation and growth: new evidence from a dynamic panel threshold analysis[END_REF]. In a first step, we estimate a reduced form regression for the endogenous variable z i,t (i.e., our lagged dependent variable) as a function of instruments x i,t , which includes a set of explanatory variables.

The regression includes time and bank fixed effects and is estimated with panelcorrected standard errors, robust to heteroscedasticity, at the bank and annual level, and to autocorrelation. Then, the endogenous variable is replaced by its predicted values z i,t in the structural equation. In step two, we estimate Eq. ( 6) via least squares for a fixed threshold, where Risk i,k,t , which denotes our two bank risk measures, the Z-score and the DD, for bank i in the country k at time t, is replaced by z i,t , as follows:

Risk i,k,t = µ i + θ 1 Risk i,k,t-1 + λ 1 M P k,t I(q k,t ≤ γ) + δ 1 I(q k,t ≤ γ) + λ 2 M P k,t I(q k,t > γ) + θ 2 EQU IT Y i,k,t-1 + θ 3 LCR i,k,t-1 + θ 4 SIZE i,k,t + θ 5 M C k,t + θ 6 RGDP G k,t + θ 7 GDP/capita k,t + θ 8 ST OCKIN DEX k,t + θ 9 M P I k,t + i,t . (6)
MP captures a set of four monetary instruments for each country k at time t (i r , i d , i shadow and CBA), considered as regime-switching indicators to test whether central bank instruments have a nonlinear effect on bank risk-taking behavior. The model estimates two coefficients: λ 1 and λ 2 . The index 1 denotes the effect of the instrument of UMP below the optimal threshold level, while the index 2 denotes the effect of the instrument of UMP when it exceeds the optimal threshold level.

We control for a set of bank-specific factors for bank i in year t and country k. We include three individual bank characteristics: the equity to total assets ratio (EQUITY), which controls for banks' capitalization, the liquidity coverage ratio (LCR), which controls for banks' liquidity and the natural logarithm of the banks' total assets, which controls for banks' size (SIZE). These three measures are widely used in the literature [START_REF] Akinci | Monetary policy and the banking sector in Turkey[END_REF][START_REF] Apergis | The behaviour of the bank lending channel when interest rates approach the zero lower bound: Evidence from quantile regressions[END_REF][START_REF] Boateng | An analysis of involuntary excess reserves, monetary policy and risk-taking behaviour of Chinese banks[END_REF][START_REF] Lapteacru | Market power and risk of Central and Eastern European banks: Does more powerful mean safer?[END_REF], because of their appraisal of bank risk. Capitalization (proxied by EQUITY) and liquidity (proxied by LCR) are treated as endogenous variables and, consequently, are lagged. Banks are expected to provide a higher level of capital for riskier assets. The level of risk undertaken by banks may affect the level of liquidity. The effect of bank size is more ambiguous, but according to [START_REF] Delis | Interest rates and bank risk-taking[END_REF], at any given time, banks are aware of their size when they make risk decisions. Hence, this variable is not treated as endogenous.

The level of capitalization should reduce the risk of banks for the Distance to Default because the financial market may positively react to a better capitalization profile. The correlation between the level of capitalization and the Z-score depends on whether the distribution of returns may compensate for a decrease in terms of equity. Moreover, the low liquidity level makes banks fragile, and the recent financial crisis, as was the case in the 1990s for the CEE economies, revealed once again that banking institutions with low liquidity levels are the first to fail. Banks' risk also depends on their size. On the one hand, large banks can be perceived by the market as less risky because they should always be secured. On the other hand, the latter feature may encourage them to take on more risk and accumulate less capital [START_REF] Brown | Too many to fail? Evidence of regulatory forbearance when the banking sector is weak[END_REF]Dinç, 2011, Demirgüç-Kunt and[START_REF] Demirgüç-Kunt | Are banks too big to fail or too big to save? International evidence from equity prices and CDS spreads[END_REF].

We include a set of country-specific factors that controls for the characteristic of country k at time t. We introduce the real GDP growth rate (RGDPG) for each country in the sample to control for the business cycle [START_REF] Jiménez | Hazardous times for monetary policy: What do twenty-three million bank loans say about the effects of monetary policy on credit risk-taking?[END_REF][START_REF] Brissimis | Bank heterogeneity and monetary policy transmission[END_REF][START_REF] Delis | Interest rates and bank risk-taking[END_REF][START_REF] Lapteacru | Market power and risk of Central and Eastern European banks: Does more powerful mean safer?[END_REF]. We also include the GDP per capita expressed in natural logarithm to capture the development gap effects that may exist between advanced and developing countries.

Since many studies [START_REF] Berger | Bank competition and financial stability[END_REF][START_REF] Tabak | The impact of market power at bank level in risk-taking: The Brazilian case[END_REF][START_REF] Michalak | The Nexus between Monetary Policy, Banking Market Structure and Bank Risk Taking[END_REF][START_REF] Schaeck | Competition, efficiency, and stability in banking[END_REF] have addressed the effect of market power on bank risk-taking and have shown that risky behavior might depend on the competitive structure of the market, we also add the Herfindahl index as a proxy for market concentration (MC) within each country. Due to the tightening of prudential policy after the GFC, which may have modified bank risk-taking behavior and its relationship with monetary policy, we include a regulatory variable (MPI).

We decide to rely on the measure developed by [START_REF] Cerutti | The use and effectiveness of macroprudential policies: New evidence[END_REF] because it includes a large range of instruments of macroprudential policies (see Appendix A). Finally, to control for financial instability, we also introduce a stock market index per country, normalized at 100 in 2005 (STOCK INDEX). All bank and country characteristics are treated as regime-independent variables.

Results

Table 3 presents the results of Eq. ( 6). First, our results strongly support the existence of a nonlinear relationship between bank risk-taking and monetary policy. The significance of the thresholds confirms the nonlinear structure of the model. The coefficients of all variables become significant or stronger above (for CBA) or under (for interest rates) the threshold when monetary policy becomes unconventional.

Then, the persistence of bank risk is well captured by the model for the DD.

The different values of these coefficients entail that bank risk displays persistence with a moderate speed of adjustment.

When the interest rate variables are over the thresholds, or when the creation of a monetary base is below a certain threshold, which globally corresponds to the pre-crisis period (see Figure 4), we observe that, for both bank risk measures, expansive monetary policy is likely to encourage risk-taking behavior. In line with many studies that conclude that before the emergence of UMP policy, interest rates were too low and encouraged risk accumulation, our results confirm this finding during this period through the policy interest rate.

Thus, our work confirms that the bank risk-taking channel influences central banks' key interest rates during the period of conventional monetary policy, but as a new contribution, we reveal that this is also the case after the GFC. We

show that this relationship between interest rate indicators, as well as other instruments of UMP, and both bank risk measures, is even stronger when these indicators fall below a certain threshold. Under a UMP regime, all monetary policy instruments, including the central bank deposit rate and the shadow interest rate, have an impact on bank behavior, which was not the case for conventional monetary policy. Monetary policy variables that were not significant become so (i d and i shadow for the DD), while monetary policy variables that were significant (i r ) exhibit coefficients which have sharply increased.

According to the definition of the Z-score, low interest rates are not com-pensated by higher financial returns (or a better distribution of ROA), which in turn encourages banks to take on more risk. As the DD is a wide measure of risk that incorporates a high quantity of information, the lasting positive effect between the DD and monetary policy indicators may be motivated by market perception, which may have integrated unfavorable macroeconomic news flows throughout the studied period (e.g., the Dotcom crisis, the GFC, the sovereign debt crisis and bank frauds and fines).

All thresholds associated with policy and shadow interest rate variables for the DD and the Z-score correspond to the prevailing values during the GFC event (2008)(2009). For the Z-score, the threshold values intervene later for the deposit interest rate, during the 2011-2012 period of the European debt crisis.

For the DD, whose threshold is slightly higher, it is interesting to note that the threshold had also been reached for key interest rates during the period of great moderation, between 2003 and 2006. This result confirms that monetary policy has been too accommodating over this period. The threshold differences between the Z-score and the DD can be explained by the different natures of the two measures. Hence, the DD, which is a market indicator, had a faster and sharper decline during the outburst of the GFC for all the regions in our sample. For the Z-score, the threshold is later, which is due to the partly structural content of this indicator (level of capitalization). This indicator was also more sensitive to the sovereign debt crisis (2011)(2012).

To take into account non-conventional monetary policy, and more particularly quantitative easing programs, we also look at the impact of the central bank monetary creation (CBA). The results obtained with interest rates are confirmed. The creation of a monetary base has a positive impact on banks' risk-taking. This effect becomes significant above a certain threshold for Z-score (although the estimated threshold is not significant). This threshold corresponds to the year 2003 for the Z-score (date from which monetary policy is considered to become too accommodating), and to May 2009 for the Distance to Default, which corresponds to the implementation of quantitative easing policies in Europe.

Due to our measures of bank risk, which are conceptually different, the control variables may affect them differently. However, for both measures, the bank capitalization ratio reduces the probability of default: the more capitalized the bank, the lower the risk of default. Similar to [START_REF] Altunbas | Do bank characteristics influence the effect of monetary policy on bank risk?[END_REF], we find that well-capitalized banks are also considered less risky by the market. This result is expected because the market may integrate favorable information when a bank is well-capitalized since a higher level of capitalization may serve as a stronger buffer and enhance the risk profile. In the same way, the more liquid banks are also perceived as less risky by the market (but the variable LCR is not a significant determinant of the Z-score).

While the size of banks displays a negative sign on the Z-score equation, it is rather the concentration (MC) of the banking system that weighs negatively on the risk for the market. The larger the institutions, the more concentrated the banking system and the more likely banks are to take risks.

Shifting to country-control effects, we observe that, regardless of the risk measure, the tightening of prudential policy (MPI) restricts banks from accumulating risk. Similarly, an increase in real GDP growth reduces the probability of default, whether one considers an accounting-based or market-based risk measures. The good economic situation improves the banks' financial condition, which reduces their risk of default. Notes: λ1 and λ2 are the coefficients estimated for each regime. The DD is the Distance to Default and describes the distance of banks' balance-sheet structure from a structure that corresponds to the default event: the higher the Distance to Default, the lower the bank risk. The Z-score is in logarithm and describes the capitalization profile of banks with respect to the distribution of their returns: the higher the Z-score, the lower the bank risk. CBA denotes central banks' total assets expressed in natural logarithm. i r , i d and i shadow represent the policy interest rate, the interest rate on the deposit facility and the shadow short interest rate, respectively. EQUITY is the ratio equity on total assets. LCR is the liquidity coverage ratio, computed as total liquid assets on total liquid liabilities. SIZE is the natural logarithm of banks' total assets in millions of dollars. All bank control variables are collected at each annual closing date. RGDPG denotes the real GDP growth rate for each country. GDP/capita is the real GDP per capita expressed as natural logarithm. MC is the Herfindahl index and describes the concentration of European banking markets. STOCK INDEX is the stock market index per country, normalized at 100 in 2005. MPI is a macroprudential index included as a differenced variable.

Robustness check

To refine our conclusions, we conduct further analyses and robustness checks.

First, we verify whether our results differ when considering the traditional formula to compute the Z-score, that is,

Z trad = COA+µ σ
, where µ and σ are the empirical mean and standard deviation of ROA, respectively, which are estimated on the same seven-year rolling window. Second, we perform our analyses with the loans-to-assets ratio, as an alternative risk measure. Third, to provide a more thorough analysis of the economic mechanism behind our findings, we split the country sample between Advanced Europe and Emerging Europe.

Since the impact of the recent financial crisis was different in these two regions, one may expect that the effect of monetary policy will also have a different impact. Finally, although the monetary policy is the same within the Eurozone, its effect on the interbank and money markets may be very different among the member countries of the Eurozone. Therefore, we compute a shadow interest rate at the country level for each member country of the Eurozone, which is based on the interbank and sovereign debt interest rates. Hence, our main regressions are performed with a country-level shadow rate, which allows us to check the stability of our results.

Estimation with the traditional Z-score

Although the traditional Z-score has important drawbacks, it has been and continues to be a prevailing risk indicator in the banking literature. It is therefore important to check whether this standard risk measure provides different results with respect to our asymmetric Z-score. The results with the traditional Z-score are presented in Table 4, which also indicates the extent to which they differ with respect to our main findings. First, the tests confirm the existence of non-linearities between monetary policy instruments and banks' risk-taking behavior, as well as the sign and significance of the different explanatory variables. However, the thresholds for interest rates (shadow interest rate and central banks' interest rates) are relatively higher than those obtained with our asymmetric Z-score (see Table 3). This means that the regime changes earlier than with the asymmetric Z-score, i.e., between the 2003-2006 period and after the beginning of 2008 for the main refinancing rate and the deposit facility interest rate. Second, the impact of the monetary policy instruments is much lower compared to that obtained with the asymmetric Z-score. The unrealistic assumption of a normal distribution for the ROA of banks, on which the traditional formula of the Z-score is based, does not only take into account the asymmetry of the distribution, but it also leads to much lower kurtosis than is the case in practice.

Consequently, the traditional Z-score is often much higher than the asymmetric measure.

Alternative risk measure

We complement our analysis with the loans-to-assets ratio, as an alternative measure of bank risk. One may suppose that loans are the part of a bank's assets that can be the most affected by a crisis event. Thus, the higher this ratio is, the more vulnerable a bank is. The results are presented in Table 4 and show that our qualitative results remain unchanged. Every time monetary policy eases above a certain threshold, the credit-to-assets ratio rises sharply, increasing banking risks. The estimate confirms the nonlinear relationship between monetary policy and risk of banks. The other explanatory variables have the expected sign. In particular, a tightening of prudential policy reduces the share of credit in bank balance sheets.

Which region drives the main results?

It [3.21 ; 3.46] [2.15 ; 2.25] [3.40 ; 3.46] [11.65 ; 11.75] [3.08 ; 3.46] [2.96 ; 3.10] [4.55 ; 4.80] [10.85 ; 10.96 Notes: λ1 and λ2 are the coefficients estimated for each regime. The Loans/Assets is the loans-to-assets ratio: the higher the ratio, the higher the bank risk. The traditional Z-score is in logarithm and describes the capitalization profile of banks with respect to the distribution of their returns: the higher the Z-score, the lower the bank risk. CBA denotes central banks' total assets expressed in natural logarithm. i r , i d and i shadow represent the policy interest rate, the interest rate on the deposit facility and the shadow short interest rate, respectively. EQUITY is the ratio equity on total assets. LCR is the liquidity coverage ratio, computed as total liquid assets on total liquid liabilities. SIZE is the natural logarithm of banks' total assets in millions of dollars. All bank control variables are collected at each annual closing date. RGDPG denotes the real GDP growth rate for each country. GDP/capita is the real GDP per capita expressed as natural logarithm. MC is the Herfindahl index and describes the concentration of European banking markets. STOCK INDEX is the stock market index per country, normalized at 100 in 2005. MPI is a macroprudential index.

United Kingdom, and the second sub-sample includes Croatia, the Czech Republic, Hungary, Poland, Romania, and Slovakia. We thus run Eq. ( 6) for each of the two sub-samples, and the results are presented in Tables 5 and6. We can confirm without any ambiguity that our main results are mostly driven by the behavior of banks and by the monetary policy stance in Advanced European countries, since the threshold remain statically significant only for this region of Europe and take values very close to those of the global sample (see Table 3).

The effects of the monetary instruments are also similar, especially during the crisis period (λ 1 for interest rates and λ 2 for CBA), leading to the same conclusions as for the global sample. Indeed, the strengthening of quantitative easing is associated with the worsening of Western European banks' capitalization with respect to the distribution of their returns-on-assets ratio. In the same period, the market value of these banks was too low with respect to their indebtedness, such that their Distance to Default decreased. Moreover, the impact of other variables explains also our global results. The findings for Eastern European banks are very different: most of the thresholds are not statistically significant and most of the coefficients change, especially for the Z-score. The impact of monetary policy instruments is also found to be different (see Table 6). All of this allows us to conclude that our main findings are mostly driven by the results obtained for Western European banks. One must also mention that the sample of Eastern European banks is much smaller, which places these results into perspective.

What is the effect of a country-level shadow interest rate?

The shadow rate computed and applied in our main estimations is the same for all countries that are members of the Eurozone. Although the monetary policy is the same for all these countries, its effects may be very different. Since the shadow interest rate expresses the effects of a monetary policy stance, it can be computed separately for each country using the interest rates on the interbank market and sovereign debt market, which reflect country-level effects.

Therefore, we computed a country-level shadow interest rate for all members of [2.27 ; 3.46] [-0.11 ; 0.13] [3.07 ; 3.16] [10.82 ; 11.00] [3.69 ; 3.88] [2.94 ; 2.98] [3.40 ; 3.47] [11.34 ; 11.77 Notes: λ1 and λ2 are the coefficients estimated for each regime. The DD is the Distance to Default and describes the distance of banks' balance-sheet structure from a structure that corresponds to the default event: the higher the Distance to Default, the lower the bank risk. The Z-score is in logarithm and describes the capitalization profile of banks with respect to the distribution of their returns: the higher the Z-score, the lower the bank risk. CBA denotes central banks' total assets expressed in natural logarithm. i r , i d and i shadow represent the policy interest rate, the interest rate on the deposit facility and the shadow short interest rate, respectively. EQUITY is the ratio equity on total assets. LCR is the liquidity coverage ratio, computed as total liquid assets on total liquid liabilities. SIZE is the natural logarithm of banks' total assets in millions of dollars. Notes: λ1 and λ2 are the coefficients estimated for each regime. The DD is the Distance to Default and describes the distance of banks' balance-sheet structure from a structure that corresponds to the default event: the higher the Distance to Default, the lower the bank risk. The Z-score is in logarithm and describes the capitalization profile of banks with respect to the distribution of their returns: the higher the Z-score, the lower the bank risk. CBA denotes central banks' total assets expressed in natural logarithm. i r , i d and i shadow represent the policy interest rate, the interest rate on the deposit facility and the shadow short interest rate, respectively. EQUITY is the ratio equity on total assets. LCR is the liquidity coverage ratio, computed as total liquid assets on total liquid liabilities. SIZE is the natural logarithm of banks' total assets in millions of dollars. All bank control variables are collected at each annual closing date. RGDPG denotes the real GDP growth rate for each country. GDP/capita is the real GDP per capita expressed as natural logarithm. MC is the Herfindahl index and describes the concentration of European banking markets. STOCK INDEX is the stock market index per country, normalized at 100 in 2005. MPI is a macroprudential index.

the Eurozone. Since Greece has very low shadow interest rates (reaching -90%)

and Romania very high (up to +90%), we decided to exclude these countries from our sample 7 . Figure 5 shows that although interest rates in Europe have similar trends, differences can be observed across countries. In particular, the shadow rate falls much more sharply in euro area countries than in other countries during the debt crisis. Countries whose banking systems are most affected by this crisis are experiencing the largest decline. The results presented in Table 7 are qualitatively very similar to those obtained with the same shadow rate for all members of the Eurozone (see Table 3), i.e., the thresholds are the same and all variables retain their signs. Thus, considering a country-level shadow interest rate does not change our main findings nor our conclusions.

7 All estimates in Table 7 are performed without these two countries. Notes: λ1 and λ2 are the coefficients estimated for each regime. As Greece presents very negative i shadow we drop Greek banks from the sample for the regressions of i s hadow. The DD is the Distance to Default and describes the distance of banks' balance-sheet structure from a structure that corresponds to the default event: the higher the Distance to Default, the lower the bank risk. The Z-score is in logarithm and describes the capitalisation profile of banks with respect to the distribution of their returns: the higher the Z-score, the lower the bank risk. CBA denotes central banks' total assets expressed in natural logarithm. i r , i d and i shadow represent the policy interest rate, the interest rate on the deposit facility and the shadow short interest rate, respectively. EQUITY is the ratio equity on total assets. LCR is the liquidity coverage ratio, computed as total liquid assets on total liquid liabilities. SIZE is the natural logarithm of banks' total assets in millions of dollars. All bank control variables are collected at each annual closing date. RGDPG denotes the real GDP growth rate for each country. GDP/capita is the real GDP per capita expressed as natural logarithm. MC is the Herfindahl index and describes the concentration of European banking markets. STOCK INDEX is the stock market index per country, normalised at 100 in 2005. MPI is a macroprudential index.

Conclusion

We examine the effect of several monetary policy indicators on bank risk across the European banking sector over the period 2000-2015. This period allows us to capture the unconventional character of European monetary policy through negative interest rates and balance-sheet policy. Indeed, we use four monetary policy variables: the policy interest rate, the interest on the deposit facility, the shadow interest rate, which is a good proxy for unconventional monetary policy (UMP), and the logarithm of central banks' total assets. More precisely, we aim to investigate whether monetary authorities' instruments have a non-linear effect on bank risk-taking behavior. We rely on both the asymmetric Z-score and the Distance to Default (DD), an accounting-and a market-based bank risk measures, which provide complementary information.

We build our work on a dynamic panel model with threshold effect as introduced by [START_REF] Kremer | Inflation and growth: new evidence from a dynamic panel threshold analysis[END_REF]. Indeed, as it is widely argued in the literature that bank risk has a lasting effect, this model permits us to take this dynamic feature into account and to mitigate potential endogeneity issues. In addition, this empirical methodology also allows testing the existence of non-linearity.

The model provides interesting results when taking into account threshold effects. We find a nonlinear effect for both measures. The decline in central bank rates, or the rise in the monetary base, reflect riskier banks' behavior.

This result is in line with the literature and suggests that the bank risk-taking channel was at play before the emergence of the GFC. More important, our second contribution indicates that when interest rate indicators are low and below the threshold, the negative relationship between bank risk measures and monetary policy is stronger. Accounting for the central banks' balance sheet policy indicates that additional liquidity encourages banks to take riskier positions.

Their behavior becomes even riskier after the implementation of UMP. These findings are confirmed when (1) using the loans-to-assets ratio as a measure of risk, (2) using the traditional Z-score and (3) using the shadow short rate for each country as a monetary policy variable.

These results indicate that monetary policy does have an impact on banks' risk-taking and that monetary authorities should be concerned about this. They cannot set monetary conditions only on the basis of the final objectives of monetary policy. They must also take into account their effect on financial stability.

A too accommodating monetary policy can contribute to the accumulation of financial imbalances and difficulties in banking industry. Prudential regulation, while reducing these risks, is not when monetary policy is too accommodating.

sider the debt interest rate r i to be specific to each bank i. Even if in the case of economy-wide troubles, banks are subject to the same conditions in the market, and the effects on their own economic and financial situation could be and are, in most cases, different. Employing own interest rate for each bank allows us to account for each bank's debt and its evolution and to be more precise regarding its risk.

  For example, although both measures of bank risk indicate a low risk for banks in North Europe, the asymmetric Z-score reflects a steady increase of risk until 2008 while the traditional Z-score remains more or less constant until 2007. This latter experienced a sharp increase following the GFC, corresponding to a decline of bank risk and, thus, ignoring the sovereign debt crisis while this event is well-caught by the asymmetric Z-score. A similar difference is depicted for the non-euro area. For South Europe, after a period of decline in the traditional Z-score (increased risk), it suddenly increases after 2007, which means that the financial crisis has a positive effect on the capitalization of banks in South Europe with respect to the distribution of their returns. As for the asymmetric Z-score, it decreases continuously after 2007 till 2011 and increases thereafter, which corresponds to different capitalization programs that benefited the banks from Greece, Ireland, Italy and Spain. This decrease from 2007 to 2011 is explained by the harmful effects of the 2007-2008 GFC but also by those of the 2010-2011 sovereign debt crisis in Europe which mainly affected the countries of this zone. For CEE, the asymmetric Z-score decreases from 2004 till 2013, which means that the risk of CEE banks increases throughout the period, whereas the traditional Z-score, as for other European zones, increases from 2008. In the end, the developments in asymmetric and traditional Z-scores are similar after 2008 only for European countries outside of the euro area. However, there is a high difference between their values. The most striking contrast is for banks from North Europe zone. The minimum value of the asymmetric Z-score is around 3, which corresponds to the probability of default of N (-3) = 0.13%, whereas the minimum value of the traditional Z-score is about 30, which means a probability of default of N (-30) = 4.91 × 10

Figure 1 :

 1 Figure 1: Evolution of bank risk in Europe described by the traditional Z-score (Z trad ), the asymmetric Z-score (Z st ) and the Distance to Default (DD). North Europe: Austria, Finland, France, Germany and the Netherlands. South Europe: Greece, Ireland, Italy and Spain. Central and Eastern Europe: Croatia, the Czech Republic, Hungary, Poland, Romania and Slovakia. Non-euro Europe: Denmark, Sweden, Switzerland and the United-Kingdom.

Figure 2 :

 2 Figure2: Evolution of monetary policy rates described by the interest policy (i policy ), the interest on the deposit facility (i f acility ) and the shadow short rate (i shadow ). CBA is in logarithm. North and South Europe: Austria, Finland, France, Germany, the Netherlands, Greece, Ireland, Italy, and Spain. Central and Eastern Europe: Croatia, the Czech Republic, Hungary, Poland, Romania and Slovakia. Non-euro Europe: Denmark, Sweden, Switzerland and the United-Kingdom.

  are conceptually different, we reduce our sample to listed banks only. Indeed, as the market capitalization of banks determines the market perception of their risk, the DD (i.e., the market-based risk measure) can only be estimated for listed banks, while the Z-score (i.e., the accounting-based risk measure) covers banks with very different risk profiles. Considering the largest listed banks from each European country under the condition that the data are available, we obtain a sample of approximately 200 listed banks. However, the necessity to have a balanced panel of the period sample constrains us to eliminate banks with missing data between 2000 and 2015.

Figure 3 :

 3 Figure 3: European banks' market shares in terms of total assets in each country of our sample and in average for the period 2000-2015.

Figure 4 :

 4 Figure 4: Evolution of monetary policy indicators over the time and threshold value for bank risk measures.

Figure 5 :

 5 Figure 5: Evolution of country-level shadow interest rates (i shadow ). North Europe: Austria, Finland, France, Germany and the Netherlands. South Europe: Ireland, Italy and Spain. Central and Eastern Europe: Croatia, the Czech Republic, Hungary, Poland, and Slovakia. Non-euro Europe: Denmark, Sweden, Switzerland and the United-Kingdom.

Table 1 :

 1 Countries and number of banks included in the sample

		List of countries	# of banks	Monetary authority
	1	Austria	5	ECB
	2	Croatia	2	Hrvatska Narodna Banka
	3	The Czech Republic	1	Česká Národní Banka
	4	Denmark	16	Nationalbanken
	5	Finland	2	ECB
	6	France	14	ECB
	7	Germany	6	ECB
	8	Greece	5	ECB
	9	Hungary	1	Magyar Nemzeti Bank
	10	Ireland	3	ECB
	11	Italy	12	ECB
	12	The Netherlands	3	ECB
	13	Norway	15	Norges Bank
	14	Poland	9	Narodowy Bank Polski
	15	Romania	2	Banca Nat ¸ionalǎ a României
	16	Slovak Republic	2	ECB
	17	Spain	5	ECB
	18	Sweden	4	Sveriges Riksbank
	19	Switzerland	14	Swiss National Bank
	20	The United-Kingdom	5	Bank of England
		Total	126

Table

1

and Figure

3

present further details about the structure of our database.

Table

1

describes the number of listed banks for each country. Our database includes 10 euro area members and 10 non-euro countries, allowing us to study the effect of UMP in terms of risk across European banks.

Table 2 :

 2 Definition and descriptive statistics of risk measures and explanatory variables.

	Variables	Description	Nr. of obs.	Mean (SD)	Min	Max	Source
	Risk measures (Risk)
	DD	Distance to Default estimated with Duan's approach, Eq. (4) and Appendix B	2014	2.44 (2.62)	-5.07	17.18	Datastream and authors' computations
	Asymmetric Z-score	Z-score in logarithm estimated with stable cumulative distribution function, Eq. (1)	2016	8.78 (18.98)	-1.90	378.61	BankScope and authors' computations
	Traditional Z-score	Z-score in logarithm estimated with Z trad = COA+µ σ	2016	28.22 (34.72)	-1.67 402.3386	BankScope and authors' computations
	Loans/Assets	Loans to total assets ratio (%)	2016	58.87 (21.98)	0.21	93.25	BankScope and authors' computations
	Monetary policy variables (MP)
	CBA	Central banks' total assets expressed in natural logarithm	2016	11.88 (1.13)	8.19	14.09	Datastream and central banks' annual reports
	i r	Policy interest rate	2016	2.78 (3.08)	-0.75	35	Datastream and central banks' annual reports
	i d	Interest rate on the deposit facility	2016	1.68 (1.76)	-1.1	11.5	Datastream and central banks' annual reports
	i shadow	Shadow short interest rate of Krippner (2014, 2015)	2016	2.44 (4.79)	-5.55	87.71	Datastream, authors' computations and Krippner estimations
	Bank control variables (X)
	EQUITY	Equity to total assets ratio (%)	2016	7.86 (3.52)	-3.93	21.58	BankScope, banks' annual reports and authors' computations
	LCR	Liquidity coverage ratio, estimated as total liquid assets on total liquid liabilities (%)	2016	23.86 (23.04)	0.62	212.33	BankScope, banks' annual reports and authors' computations
	SIZE	Size of banks, expressed as natural logarithm of banks' total assets expressed in millions of USD	2016	9.85 (2.30)	3.79	15.15	BankScope, banks' annual reports and authors' computations
	ACTIVITY	Loans to total assets ratio	2027	58.94 (21.94)	0.21	93.25	BankScope, banks' annual reports and authors' computations
	Country control variables (Y)
	MC	Market concentration, computed with Herfindahl index	2016	0.07 (0.04)	0.02	0.37	Bankscope, Datastream and authors' computation
	RGDPG	Real GDP growth rate (%)	2016	1.64 (2.63)	-9.13	26.28	Datastream
	GDP/capita	Real GDP per capita expressed as natural logarithm	2016	10.55 (0.66)	8.41	11.42	Datastream
	STOCK INDEX	Stock market index per country, normalized at 100 in 2005	2016	105.01 (54.28)	9.03	805.83	Datastream
	MPI	Macroprudential Index (Appendix A)	2016	1.33 (1.33)	0	5

  [START_REF] Altunbas | Do bank characteristics influence the effect of monetary policy on bank risk?[END_REF] claim that this endogeneity problem is less significant in European countries, financial stability has become a major issue for central banks. Indeed, before 2008, there is no evidence that European monetary authorities had set policy rates by looking into bank risk because the main objective was to target price stability. Never-

theless, the failure of Lehmann Brothers triggered tensions in the credit market and raised the European central banks' concerns about financial stability at the end of 2008. For this reason, our study considers potential endogeneity, as our sample considers the crisis period.

Table 3 :

 3 Dynamic panel threshold estimations: nonlinearity between monetary policy indicators and bank risk-taking.

			Z-score			Distance to Default
		i r	i d	i shadow	CBA	i r	i d	i shadow	CBA
	Threshold estimate	2.27**	0.40***	3.15*	10.77	3.22***	2.95***	3.45***	11.76***
	95% confidence	[0.03 ; 2.29]	[0.13 ; 0.43]	[2.45 ; 3.16]	[10.63 ; 10.78]	[3.21 ; 3.46]	[2.94 ; 2.98]	[3.40 ; 3.46]	[11.72 ; 11.77]
	interval
				Regime-dependent coefficients
	λ1	0.132***	0.485***	0.048***	-0.038	0.667***	0.548***	0.291***	-1.962***
		(0.020)	(0.075)	(0.007)	(0.111)	(0.072)	(0.068)	(0.030)	(0.163)
	λ2	0.042***	0.019**	0.020***	0.058*	0.119***	-0.020	0.015	-1.875***
		(0.008)	(0.009)	(0.005)	(0.049)	(0.035)	(0.044)	(0.020)	(0.154)
			Regime-independent coefficients: Impact of covariates
	Riskt-1	-0.112*	-0.100	-0.099	-0.094	0.504***	0.505***	0.490***	0.374***
		(0.065)	(0.067)	(0.065)	(0.065)	(0.042)	(0.046)	(0.039)	(0.041)
	EQU IT Yt-1	0.011*	0.013*	0.014**	0.013*	0.086***	0.119***	0.106***	0.150***
		(0.007)	(0.007)	(0.007)	(0.007)	(0.027)	(0.028)	(0.027)	(0.027)
	LCRt-1	8.65e-4	5.8e-5	-6.15e-4	-5.12e-06	0.010***	0.012***	0.012***	0.014***
		(0.001)	(0.001)	(0.001)	(0.001)	(0.003)	(0.003)	(0.003)	(0.003)
	SIZE	-0.080*	-0.143***	-0.087*	-0.118**	0.171	0.087	0.053	0.581***
		(0.047)	(0.046)	(0.046)	(0.048)	(0.167)	(0.161)	(0.164)	(0.169)
	MC	0.278	0.092	0.241	1.907**	-24.742***	-22.341***	-24.626***	-9.604***
		(0.807)	(0.809)	(0.804)	(0.838)	(2.943)	(2.906)	(2.941)	(2.972)
	RGDPG	0.014***	0.018***	0.015***	0.009*	0.130***	0.114***	0.137***	0.091***
		(0.005)	(0.005)	(0.005)	(0.005)	(0.020)	(0.020)	(0.020)	(0.020)
	GDP/capita	-0.130	-0.161	-0.053	0.056	-1.889***	-1.674***	-0.977***	0.992**
		(0.100)	(0.100)	(0.099)	(0.107)	(0.376)	(0.378)	(0.385)	(0.386)
	STOCK INDEX	0.002***	0.002***	0.001***	0.001**	-0.002**	-0.004***	-0.005***	-0.004***
		(4.22e-4)	(4.25e-4)	(4.12e-4)	(4.11e-4)	(0.001)	(0.001)	(0.001)	(0.001)
	MPI	0.026	0.042	0.044*	0.060**	0.296***	0.376***	0.437**	0.620***
		(0.029)	(0.028)	(0.028)	(0.029)	(0.113)	(0.112)	(0.110)	(0.109)
	δ1	3.966***	4.895***	3.32***	3.078***	19.628***	18.305***	11.849***	7.616**
		(1.035)	(1.039)	(1.039)	(1.070)	(3.377)	(3.384)	(3.520)	(3.552)
	Obs.	1764	1764	1764	1764	1764	1764	1764	1764

Table 4 :

 4 is quite interesting to determine which region of Europe drives our main findings. Since European central banks conducted different monetary policies and to different extents in Western and Eastern European countries, and since the European banks were also affected in different ways, we decided to divide Dynamic panel threshold estimations, non-linearity between monetary policy indicators and bank risk-taking: alternative risk measures

	our country sample into two sub-samples, i.e., Advanced Europe and Emerging
	Europe. The first sub-sample comprises Austria, Denmark, Finland, Greece,
	Ireland, Italy, the Netherlands, Norway, Spain, Sweden, Switzerland, and the

  ]

				Regime-dependent coefficients
	λ1	0.037***	0.059***	0.020***	-0.032	-1.531***	-0.459**	-0.056	-2.475***
		(0.013)	(0.015)	(0.006)	(0.030)	(0.246)	(0.199)	(0.093)	(0.540)
	λ2	0.005	-0.009	0.009**	-0.052*	-0.446***	0.426***	-0.446***	-1.930***
		(0.006)	(0.007)	(0.004)	(0.028)	(0.119)	(0.152)	(0.085)	(0.517)
			Regime-independent coefficients: Impact of covariates
	Riskt-1	0.030	0.023	0.035*	0.015	0.255***	0.265***	0.344***	0.315***
		(0.022)	(0.022)	(0.022)	(0.021)	(0.084)	(0.086)	(0.085)	(0.086)
	EQU IT Yt-1	0.057***	0.060***	0.057***	0.059***	0.204**	0.172*	0.226**	0.195*
		(0.005)	(0.005)	(0.005)	(0.005)	(0.106)	(0.107)	(0.106)	(0.064)
	LCRt-1	5.86e-4	7.31e-4	3.73e-4	8.76e-4	-0.163***	-0.170***	-0.147***	-0.164***
		(7.97e-4)	(7.87e-4)	(8.01e-4)	(7.79e-4)	(0.016)	(0.016)	(0.015)	(0.015)
	SIZE	-0.286***	-0.290***	-0.268***	-0.256***	-6.178***	-5.110***	-5.288***	-4.186***
		(0.038)	(0.036)	(0.037)	(0.038)	(0.704)	(0.694)	(0.689)	(0.746)
	MC	-3.088***	-2.710***	-3.170***	-2.822***	-0.788	-6.890	-7.613	-7.490
		(1.431)	(0.599)	(0.608)	(0.632)	(10.951)	(10.938)	(10.964)	(11.269)
	RGDPG	0.008**	0.008**	0.009**	0.003	-0.413***	-0.433***	-0.464***	-0.426***
		(0.004)	(0.004)	(0.004)	(0.004)	(0.076)	(0.077)	(0.076)	(0.077)
	GDP/capita	0.313***	0.382***	0.341***	0.436***	15.147***	14.472***	12.113***	12.813***
		(0.082)	(0.081)	(0.081)	(0.083)	(1.888)	(1.942)	(1.896)	(1.837)
	STOCK INDEX	0.002***	0.002***	0.002***	0.001***	0.013***	0.018***	0.009*	0.010**
		(2.94e-4)	(2.93e-4)	(3.00e-4)	(2.96e-4)	(0.005)	(0.005)	(0.005)	(0.005)
	MPI	0.077***	0.072***	0.086***	0.109***	-1.325***	-1.067***	-1.148***	-0.461**
		(0.012)	(0.011)	(0.012)	(0.012)	(0.220)	(0.220)	(0.226)	(0.236)
	δ1	2.135***	1.431**	1.660**	1.137	-49.255***	-55.154***	-32.638**	-26.252*
		(0.726)	(0.735)	(0.739)	(0.733)	(13.783)	(14.040)	(14.049)	(13.986)
	Obs.	1764	1764	1764	1764	1764	1764	1764	1764

Table 5 :

 5 Dynamic panel threshold estimations, non-linearity between monetary policy indicators and bank risk-taking: Advanced Europe.

				Z-score			Distance to Default
		i r	i d	i shadow	CBA	i r	i d	i shadow	CBA
	Threshold estimate	3.22***	0.05***	3.15***	10.97	3.84***	2.95***	3.45***	11.76***
	95% confidence
	interval

  ]

				Regime-dependent coefficients
	λ1	0.076***	0.283***	0.643***	-0.002	0.261***	0.653***	0.334***	-2.403***
		(0.018)	(0.013)	(0.031)	(0.043)	(0.016)	(0.077)	(0.033)	(0.190)
	λ2	0.015	0.048***	-0.009*	-0.026	0.025	-0.029	-0.003	-2.331***
		(0.010)	(0.005)	(0.005)	(0.041)	(0.016)	(0.052)	(0.030)	(0.183)
			Regime-independent coefficients: Impact of covariates
	Riskt-1	-0.146**	-0.132*	-0.123**	-0.170**	0.450***	0.480***	0.470***	0.339***
		(0.070)	(0.008)	(0.070)	(0.070)	(0.052)	(0.052)	(0.045)	(0.045)
	EQU IT Yt-1	0.017**	0.015*	0.017**	0.019**	0.112***	0.099***	0.094***	0.119***
		(0.008)	(0.008)	(0.008)	(0.008)	(0.032)	(0.032)	(0.032)	(0.032)
	LCRt-1	-6.60e-4	-4.24e-4	-7.50e-4	-5.14e-4	0.014***	0.014***	0.014***	0.015***
		(0.001)	(0.001)	(0.001)	(0.001)	(0.004)	(0.004)	(0.004)	(0.004)
	SIZE	-0.174***	-0.230***	-0.174***	-0.147***	0.387**	0.076	-0.069	1.029***
		(0.053)	(0.051)	(0.051)	(0.057)	(0.192)	(0.187)	(0.186)	(0.207)
	MC	1.383	0.609	1.087	2.245***	-20.307***	-21.000***	-23.579***	-6.418**
		(0.863)	(0.875)	(0.865)	(0.881)	(3.074)	(3.125)	(3.125)	(3.183)
	RGDPG	0.012**	0.013**	0.014**	0.011**	0.130***	0.112***	0.135***	0.090***
		(0.005)	(0.005)	(0.005)	(0.006)	(0.022)	(0.022)	(0.022)	(0.022)
	GDP/capita	0.087	0.095	0.140	0.050	-0.393	-1.069**	-0.172	1.310**
		(0.132)	(0.130)	(0.132)	(0.139)	(0.489)	(0.479)	(0.503)	(0.566)
	STOCK INDEX	0.002***	0.002***	0.001***	0.001***	-0.004***	-0.005***	-0.006***	-0.006***
		(4.47e-4)	(4.63e-4)	(4.43e-4)	(4.44e-4)	(0.001)	(0.001)	(0.001)	(0.001)
	MPI	-0.019	-0.021	0.002	-0.023	0.225*	0.381***	0.458***	0.294***
		(0.016)	(0.016)	(0.016)	(0.017)	(0.123)	(0.121)	(0.120)	(0.064)
	δ1	2.624**	3.189**	2.105	3.144**	1.081	12.308***	4.684	5.228
		(1.330)	(1.322)	(1.335)	(1.363)	(4.673)	(4.334)	(4.587)	(4.273)
	Obs.	1526	1526	1526	1526	1526	1526	1526	1526

  All bank control variables are collected at each annual closing date. RGDPG denotes the real GDP growth rate for each country. GDP/capita is the real GDP per capita expressed as natural logarithm. MC is the Herfindahl index and describes the concentration of European banking markets. STOCK INDEX is the stock market index per country, normalized at 100 in 2005. MPI is a macroprudential index.

Table 6 :

 6 Dynamic panel threshold estimations, non-linearity between monetary policy indicators and bank risk-taking: Emerging Europe.

			Z-score			Distance to Default
		i r	i d	i shadow	CBA	i r	i d	i shadow	CBA
	Threshold estimate	1.25	0.75	-1.29	9.61	9.68	6.10	3.45***	11.52**
	95% confidence	[1.00 ; 1.28]	[0.40 ; 0.94]	[-2.45 ; -1.06]	[0.60 ; 9.62]	[9.66 ; 11.44]	[4.25 ; 6.50]	[2.83 ; 3.46]	[11.44 ; 11.55]
	interval
				Regime-dependent coefficients
	λ1	0.541***	0.532***	0.187***	0.404***	-0.246***	-0.292***	-0.339***	-0.624
		(0.186)	(0.184)	(0.058)	(0.147)	(0.083)	(0.111)	(0.096)	(0.537)
	λ2	0.050***	0.021	0.020*	0.377***	0.028	0.048	0.054	-0.547
		(0.018)	(0.029)	(0.011)	(0.143)	(0.067)	(0.140)	(0.040)	(0.531)
			Regime-independent coefficients: Impact of covariates
	Riskt-1	0.440*	0.390	0.357	0.531*	313***	0.309***	0.256**	0.276**
		(0.278)	(0.287)	(0.282)	(0.057)	(0.126)	(0.128)	(0.125)	(0.129)
	EQU IT Yt-1	-0.001	0.017	0.021	-0.003	0.004	0.114**	0.071	0.124**
		(0.015)	(0.015)	(0.015)	(0.016)	(0.062)	(0.054)	(0.054)	(0.062)
	LCRt-1	-0.001	2.23e-4	5.31e-4	0.001	0.013	0.004	0.005	0.002
		(0.003)	(0.003)	(0.003)	(0.003)	(0.011)	(0.011)	(0.011)	(0.012)
	SIZE	0.370***	0.326***	0.347***	0.361***	0.439	-0.033	-0.015	0.228
		(0.114)	(0.114)	(0.118)	(0.115)	(0.425)	(0.404)	(0.414)	(0.418)
	MC	-2.972	-0.160	-4.527	-4.065	-27.508***	-19.274**	-24.188**	-25.154**
		(2.834)	(2.738)	(2.924)	(2.863)	(10.208)	(9.955)	(10.475)	(10.294)
	RGDPG	-0.008	0.006	0.007	-8.09e-4	0.104**	0.120***	0.142***	0.130**
		(0.012)	(0.013)	(0.012)	(0.012)	(0.050)	(0.050)	(0.050)	(0.051)
	GDP/capita	-0.600***	-0.409**	-0.434**	-1.113***	-4.775***	-3.972***	-3.073***	-3.200***
		(0.191)	(0.201)	(0.191)	(0.300)	(0.845)	(0.775)	(0.732)	(1.147)
	STOCK INDEX	0.002**	3.31e-4	0.001***	0.001	0.012***	0.011**	0.018***	0.010**
		(0.001)	(0.001)	(0.001)	(0.001)	(0.004)	(0.004)	(0.005)	(0.004)
	MPI	-0.166***	-0.241***	-0.241***	-0.261***	-0.090	-0.135	0.095	-0.219
		(0.056)	(0.052)	(0.054)	(0.047)	(0.208)	(0.198)	(0.201)	(0.176)
	δ1	3.264**	2.172	2.451	4.470**	43.960***	38.980***	29.417***	35.876***
		(1.914)	(2.015)	(1.924)	(2.066)	(7.335)	(7.176)	(6.724)	(7.627)
	Obs.	238	238	238	238	238	238	238	238

Table 7 :

 7 Dynamic panel threshold estimations, non-linearity between monetary policy indicators and bank risk-taking with country-level shadow rate.

			Z-score			Distance to Default
		i r	i d	i shadow	CBA	i r	i d	i shadow	CBA
	Threshold estimate	2.27*	0.05***	2.44	10.81	3.22***	2.95***	3.59***	11.76***
	95% confidence	[2.22 ; 2.39]	[-0.37 ; 0.13]	[2.00 ; 2.67]	[10.57 ; 10.82]	[3.21 ; 3.46]	[2.94 ; 2.98]	[3.48 ; 3.60]	[11.72 ; 11.77]
	interval
				Regime-dependent coefficients
	λ1	0.113***	0.589***	0.046***	0.020	0.812***	0.623***	0.328***	-2.316***
		(0.021)	(0.102)	(0.010)	(0.038)	(0.081)	(0.070)	(0.036)	(0.181)
	λ2	0.031***	4.39e-4	0.015**	0.006	0.219***	0.004	0.054**	-2.228***
		(0.009)	(0.010)	(0.006)	(0.037)	(0.046)	(0.046)	(0.028)	(0.173)
			Regime-independent coefficients: Impact of covariates
	Riskt-1	-0.201***	-0.159**	-0.167***	-0.167**	0.422***	0.470***	0.491***	0.339***
		(0.067)	(0.066)	(0.065)	(0.066)	(0.048)	(0.047)	(0.040)	(0.042)
	EQU IT Yt-1	-0.001	-0.004	-0.002	-0.004	0.139***	0.158***	0.135***	0.159***
		(0.007)	(0.007)	(0.008)	(0.008)	(0.031)	(0.031)	(0.032)	(0.031)
	LCRt-1	-0.001*	-0.001	-0.001	-0.001	0.013***	0.013***	0.014***	0.013***
		(9.89e-4)	(9.84e-4)	(9.92e-4)	(9.91e-4)	(0.003)	(0.003)	(0.003)	(0.003)
	SIZE	-0.094**	-0.129***	-0.103**	-0.122**	0.233	0.231	-0.030	0.973***
		(0.047)	(0.047)	(0.047)	(0.052)	(0.174)	(0.173)	(0.175)	(0.191)
	MC	2.354***	1.815**	1.904**	3.087***	-23.419***	-21.399***	-25.626***	-6.461**
		(0.825)	(0.840)	(0.852)	(0.838)	(3.093)	(3.075)	(3.206)	(3.141)
	RGDPG	-0.001	-0.002	-7.87e-4	-0.001	0.125***	0.108***	0.126***	0.088***
		(0.005)	(0.005)	(0.005)	(0.005)	(0.022)	(0.021)	(0.023)	(0.061)
	GDP/capita	-0.165*	-0.203**	-0.129	-0.094	-1.710***	-1.670***	-1.381***	0.959**
		(0.100)	(0.100)	(0.100)	(0.106)	(0.404)	(0.403)	(0.409)	(0.446)
	STOCK INDEX	0.002***	0.002***	0.002***	0.001***	-0.003***	-0.005***	-0.005***	-0.006***
		(4.28e-4)	(4.33e-4)	(4.19e-4)	(4.19e-4)	(0.001)	(0.001)	(0.001)	(0.001)
	MPI	-0.023	-0.020	-0.010	-0.037**	0.056	0.021	0.127**	0.238***
		(0.014)	(0.014)	(0.015)	(0.021)	(0.056)	(0.056)	(0.058)	(0.061)
	δ1	4.747***	5.589***	4.512***	4.264***	16.641***	16.647***	16.534***	8.106**
		(1.024)	(1.024)	(1.039)	(1.056)	(3.661)	(3.611)	(3.726)	(3.679)
	Obs.	1666	1666	1666	1666	1666	1666	1666	1666

Except Buch et al. (2014),[START_REF] Lambert | The effects of unconventional monetary policies on bank soundness[END_REF].

The federal funds rate is taken as a proxy for monetary policy because the Bolivian currency was pegged to the dollar during the period of study.

[START_REF] Maddaloni | Bank risk-taking, securitization, supervision, and low interest rates: Evidence from the Euro-area and the U.S. lending standards[END_REF] analyze the effect of monetary policy on lending standards in the Eurozone(2002)(2003)(2004)(2005)(2006)(2007)(2008) and in the U.S.(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008).

Except De Nicoló et al. (2010), who use the GLS method and[START_REF] Brissimis | Bank heterogeneity and monetary policy transmission[END_REF], who more precisely use a local GMM.

Until Mario Draghi's speech on 26 July 2012, which pledged to do "whatever it takes" to save the Eurozone.

Commercial banks, saving banks, cooperative banks, investment banks, specialized government credit institutions, bank holding and holding companies and multi-lateral government banks.

Appendix A. Methodology to compute Macroprudential Index (MPI)

This appendix provides details on the construction procedure of the regulation indicator used in the empirical analysis. We rely on the results of [START_REF] Cerutti | The use and effectiveness of macroprudential policies: New evidence[END_REF] who analyse a recent survey which includes detailed information on macroprudential policies in 119 countries. This survey is called the Global Macroprudential Policy Instruments (GMPI) and was carried out by the IMFs Monetary and Capital Department during 2013-2014. The authors focus on 12 different macroprudential instruments: loan-to-value ratio caps (LTV CAP), debt-to-income ratio (DTI), time-varying/dynamic loan-loss provisioning (DP), general countercyclical capital buffer/requirement (CTC), leverage ratio (LEV), capital surcharges on SIFIs (SIFI), limits on interbank exposure (INFER), concentration limits (CONC), limits on foreign currency loans (FC), FX and/or countercyclical reserve requirement (RR REV), limits on domestic currency loans (CG) and levy/tax on financial institutions (TAX). They assign to each instrument the number of 1 if it was implemented, 0 otherwise. The MPI index is the sum of the scores on all 12 policies. Hence, the higher the MPI, the more strength the regulation is.

Appendix B. Duan estimation approach to compute the Distance to

Default

Unlike the bank's assets V t , the equity market values S t are observed every trading day. Given the book value of bank debt D, eqs. ( 2) and ( 4) represent a one-to-one relationship between asset values and equity prices, which allows for the estimation of the state variable V t . The asset value is computed daily through eq. ( 2), where debt value D p is constant during month p. The maturity of debt T is equal to one year (T = 1), and estimations are made on a six-month rolling window.

Let m denote the number of months in our entire sample and n j the number of days within the estimation window j, where j = p -5 and p = [6, ..., m]. We therefore express the time series of n j daily observations within the estimation window j of the bank's market capitalization by {S 1,j , , S nj ,j }, considering 260 trading days per year. For each trading day of a given month p and of the last five months, we compute the implicit market value of the bank's assets using month p's level of debt. For this month p, we then estimate the expected return and the volatility of the bank's asset returns. Finally, we roll the estimation window forward by one month and estimate all unknown model parameters, µ V and σ V , for all months of our sample period, except for the first five months.

The Distance to Default is also computed for each month -specifically, for the last trading day of the month. [START_REF] Duan | Correction: Maximum likelihood estimation using price data of the derivative contract[END_REF][START_REF] Duan | Correction: Maximum likelihood estimation using price data of the derivative contract[END_REF] develops a maximum likelihood estimator of the model parameters µ V and σ V , which is maximized considering the values of the banks' assets:

for each trading day i of the estimation window j using equation ( 2) and where, di,j (σ V ) ≡ ln Vi,j (σ V ) Dp,j

Vi,j (σ V ) determined from equation ( 2), which is slightly transformed to take into account the rolling window procedure:

For both equations p = [1, ..., m]. For all days i belonging to month p, D p,j is constant and t i,p = (i -1) 260 where i = [1, ..., np] has a one-to-one relationship with i, and np is the number of trading days within month p.

To compute the parameters µ V and σ V , an iterative optimization procedure is applied. Using the expected asset returns and asset return volatilities of the first approach as the starting values for µ V and σ V , respectively, and given data on the values of equity S i,j and debt D p,j , Eq. (B.3) is solved to yield the sample of bank asset values Vi,j . Eq. (B.1) is then used to find the values of μV and σV that maximize this likelihood function. These two parameters are computed for each estimation window, and as we roll this window forward by one month, we obtain monthly estimations for annual values of μV and σV for the entire sample except for the first five months.

Because the amount of debt is known only for the end of month, the Distance to Default is estimated monthly on an annual basis with the end-of-month asset value: