The slope of the yield curve and bank risk taking:
Rhineland vs. Anglo-Saxon model
O.L. Tuin
S1905015
University of Groningen
MSc Finance
Supervisor: dr. P.P.M. Smid
14 January 2016
Abstract:This study examines the effect of the yield curve on bank risk taking. We compare the effects of two governance models: the Rhineland- and the Anglo-Saxon model. Three large data samples are used with bank data from Germany and the Unites States in the period from 2001 until 2014. We conclude that there is a significant positive effect between the yield spread and bank risk taking when we measure bank risk taking as the risky assets ratio or the Z-score. The relation is negative in the United States when we measure bank risk taking as the non-performing loans ratio. We find empirical evidence that the degree of capitalization has a moderating effect on the nexus between the yield spread and bank risk taking. No empirical evidence is found for a significant stronger relation in the United States compared to Germany.
Field key words: Yield curve, yield spread, interest rates, bank risk taking, panel data, governance model, Rhineland model, Anglo-Saxon model.
1. Introduction
The theory of financial intermediation attributes a number of activities as core functions to banks (e.g. Bhattacharya and Thakor, 1993). One of the core activities of commercial banking is the maturity transformation: obtain short term deposits to invest in long term fixed rate loans. Transforming these debts with short maturities into credits with long maturities can be a source of a positive net interest margin when long term rates are higher than the short term rates (Entrop, Memmel, Ruprecht & Wilkens, 2015). The yields for similar debt contracts across different contract lengths can be found in the yield curve. Obviously, the term structure of interest rates is a meaningful variable for the business of banks. This study examines the effect of changes in the yield curve on risk taking behavior of banks.
Regularly, the yield curve shows an upward slope as a result of the liquidity preference theory. In principle, long term rates are higher than short term rates because wealth holders demand a premium for exchanging highly liquid assets like cash into non-liquid securities with longer maturities. Moreover, the risk of depreciation due to future inflation should be built in. Even if the current inflation is low, the uncertainty about the future inflation development generally provides a slightly rising slope of the yield curve. When the difference between the short term rate and the long term rate (and thus the yield spread) increases, the profitability of the maturity transformation increases (Alessandri & Nelson, 2015).
When the yield on short term loans is higher than the long term yield, we speak of an inverted yield curve. This situation can occur when the monetary policy of central banks leads to an increasing short term rate. Central banks can have multiple reasons to rise the short term rate, for instance to fight inflation, to slow down a fierce growing economy or to limit overall lending of banks. When the inversion occurs, banks will have an incentive to raise their long term lending rates to keep up their net interest margin. Higher long term rates result in increasing credit costs which has a negative effect on the economic growth. When banks cannot raise their lending rates, for instance due to competitive reasons, their interest rate margin and thereby their profitability decreases.
around the crisis as well. Figure 1 shows that just before 2008, the yield spread becomes zero. This represents a perfectly flat yield curve: there is no difference between 2- and 30-year yields. Interestingly, the chart shows that the spread even takes negative values, which represent an inverted yield curve sloping downward instead of upward.
Figure 1. Treasury Yield Spread of the United States, 2-30 years.
Source: Bloomberg
Some authors describe a causal relation between the low interest rate environment in the middle part of the recent decade and the credit boom and the following crisis in 2008 (e.g. Brunnermeier, 2009; DellʼAriccia, Laeven & Marquez, 2014; Holt, 2009; Wang & Zhang, 2014). Dell’Ariccia et al. (2014) argue that because of the low short term rates, banks took excessive risks by fueling asset prices and promoting leverage. Moreover, they state that the impact of the crisis would have been much less severe when monetary authorities had raised interest rates earlier and more aggressively. The question remains whether banks change their behavior in case of a significant change in the yield spread. Will banks expand their risky investments in search for a higher yield if the slope becomes flatter or inverted?
The primary research question of this study is: Does bank risk taking change when the slope
of the yield curve changes?
As a proxy for measuring the slope of the yield curve we use the yield spread. In recent literature, the yield spread is defined as the 10‐year government bond yield less the 3-month treasury yield (Chinn & Kucko, 2015). For the analysis of bank risk taking behavior we use the ratio of risky assets to total assets, the ratio of non-performing loans to total loans and the Z-score. To examine the effect of the yield spread on bank risk taking, we perform several linear regressions on three large balanced panel datasets of all commercial, savings and cooperative banks in Germany and the United States dated from 2001 until 2014.
cultural aspects of populations as individualism and uncertainty avoidance have a respectively positive and negative effect on bank risk taking. Next to this, it is known that economic and regulatory factors of a country like the deposit insurance system and regulatory capital requirements could influence bank risk taking (Anginer, Demirguc-Kunt & Zhu, 2014;
Yagcilar, 2014). These empirical findings indicate that country specific characteristics influence bank risk taking and, through this influence, may also influence the effect of the yield spread on bank risk taking.
This study focuses on the difference between the Rhineland and the Anglo-Saxon model. The corporate governance system could have a confounding effect on the nexus between yield spread and bank risk taking, because the two economic systems differ in orientation and goals. In their theoretical study Weimer & Pape (1999) suggest that the Rhineland model is a stakeholder oriented system where intermediaries predominate. In contrast, the Anglo-Saxon model is a shareholder oriented system where financial markets play the major role. Furthermore, Osborne & Lee (2001) find empirical evidence that the two models differ in deposit insurance and bank assistance when banks have solvency problems. According to Allen & Gale (2001), Germany and the United States seem to be ideal countries to represent these models.1 In Germany, intermediaries play a dominant role and financial markets are relatively less important. On the other hand, financial markets are determinative in the United States. Moreover, these countries have a comparable structure of the banking sector with thousands of separate banks and bank branches.
The secondary research question of this study is: Is there a significant difference in the
relation between the slope of the yield curve and bank risk taking between Germany and the United States?
To examine the secondary question, we use the same proxies and datasets that are used for the primary research question. After the regression analysis, we compare the results of Germany with the results of the United States.
behavior and risk taking decisions. Furthermore, Delis & Kouretas (2011) focus on the effect of the short interest rate itself on risky investments of banks, without considering the gap between short and long term rates. This gap, the yield spread, is seen as the main driver of the profitability of the bank in its simplest form. Taking the yield spread as independent variable is therefore probably more appropriate than using only the (monetary policy influenced) short term rate. Moreover, the yield curve is an important predictor of a future recession (Estrella & Mishkin, 1998; Özturk & Pereira, 2013). Taking the yield spread as the main independent variable is likely to be more useful than using only the short term rate and it adds value to implications of this research.
Second, further research on the yield spread as causing variable might be useful for central banks. After this study, we might understand and even predict banks' risk behavior. If the relation between yield spread and bank risk taking is significant the behavior of a bank might be predicted based on the yield spread at that time. It is clear that this knowledge can be very useful for financial supervisory bodies: policy makers can adjust their interest rates and take the expected future risk behavior of banks into account. The Federal Reserve and in the recent past also the European Central Bank (ECB) use the forming of short term rates as an instrument to affect the performance of the banking sector and the degree of bank risk taking activities (Delis & Kouretas, 2011). Lower policy rates of central banks will cause lower short term interest rates and consequently steepen the yield curve directly. When policy rates stay low for a longer time, rising inflation expectations might cause increasing long term interest rates and thus increase the term spread further. Borio & Zhu (2008) and Adrian & Shin (2009) speak of the ‘risk taking channel’ of monetary policy: the policy affects the effective risk appetite of banks and the supply of credit to the economy. Empirical research of Gertler (2015) shows that unconventional monetary policy could affect the shape of the yield curve and hence the risk behavior of banks if our examined relation is significant.
Lastly, it is useful to compare Germany and the United States since these countries represent respectively the Rhineland and the Anglo-Saxon model. If there is a significant difference in effect and we can localize the drivers of this difference, we are one step further in understanding and predicting risk behavior of banks based on the governance model of the country.
Section 4 contains the data and the descriptive statistics. In Section 5 the empirical results are presented and in Section 6 the concluding remarks are given.
2. Literature
Interest rates and bank risk taking
In the literature there is theoretical evidence of a systematic effect of market interest rates on bank profitability. Very low nominal rates are usually coupled with a reduction in the margin between the long and the short term rate of banks (Dell’Ariccia and Marquez, 2006). In contrary, high nominal rates will usually be linked to a yield curve with a steeper positive slope. In the long run, high yields and a steep yield curve boost banks' income margins (Alessandri & Nelson, 2015). However, an increase in short term yields depresses income in the short run. Banks have to pay more for deposits while they don’t get more from outstanding loans immediately. There is a presence of frictions affecting the repricing of banks' assets and liabilities in an asymmetric way.
Theoretical literature shows that low interest rates cause an increase in bank risk taking. Rajan (2006) states that a source of risky behavior of financial institutions could be an environment of low interest rates. He explicates a mechanism that banks may be forced to switch to riskier assets when a monetary easing lowers the yield on their short term assets in relation to the expenditures on their long term liabilities. If yields on safe assets stay low for a certain period, prolonged investing in these safe assets means that a financial institution will not be able to satisfy its long term commitments. The probability that banks nonetheless will be able to match its obligations will increase when banks switch to riskier assets and associated higher expected yields. This mechanism works the other way around as well. When there is a high interest rate environment, banks move from risky to more saver assets: there is a ‘flight to quality’. Moreover, Rajan (2006) argues that investment managers have an incentive to switch to riskier investments as well. Nowadays the remuneration of investment managers is often based on returns. Investors are attracted by higher expected returns for the benefit of their own welfare.
the Euro area. Other authors (e.g. Brissimis and Delis, 2009; Ioannidou et al., 2014; Jiménez et al., 2014;) relate expansionary monetary policy to increased bank risk taking. Ioannidou et al. (2014) find a strong relationship between monetary policy and bank risk taking in Bolivia between 1999 and 2003. They find that a lower US federal funds rate increases the lending to borrowers with a lower credit rating or a poor performance in the past.2 Jiménez et al. (2014) agree with these empirical findings about the relation between monetary policy and bank risk taking. In their research they use quarterly data from Spanish banks in the period 1984 until 2006. They state that when expansionary monetary policy is employed, there is an increase in money supply and the short term interest rate will go down. As a result of this low short term interest rate, financial intermediaries will soften their lending standards. Especially commercial banks take more risk when interest rates are low. When the monetary policy affects the effective risk appetite of banks and the supply of credit to the economy, Borio & Zhu (2008) and Adrian & Shin (2009) speak of the ‘risk taking channel’ of monetary policy.
Yield spread and bank risk taking
The literature discussed above, shows that short term interest rates (potentially set by monetary policy) could have considerable effects on bank risk taking. However, this research focuses on the effect of the difference between the short term rate and the long term rate: the yield spread. The arguments for the relation between the short term rate and bank risk taking could be applicable for the relation between the term spread and bank risk taking as well. Adrian and Shin (2010) find an almost perfect negative correlation between the Federal Funds Target rate and the term spread in the United States (see Figure 2). They argue that the banks' costs of borrowing are tightly linked to short term interest rate since a lot of liabilities are short term borrowing arrangements.
Figure 2. Correlation between yield spread and Federal Funds Target rate.
Source: Federal Reserve Board
Mink (2011) provides theoretical evidence that bank risk taking intensifies when the yield curve becomes steeper. When the gains from the maturity transformation increase, banks have an incentive to lower their lending standards. Due to these lower lending standards, it is likely that the ratio of risky assets to total assets increases and one can conclude that the bank shows risky behavior. Risk taking increases and the bank will use more leverage since engaging in maturity transformation causes a larger borrowing cost advantage. However, Mink (2011) argues that regulatory liquidity requirements can reduce certain forms of risk taking.
Adrian, Estrella & Shin (2010) make the connection between the yield curve and financial intermediary balance sheet management. They confirm empirically that an increasing term spread can make lending more profitable for financial institutions in the United States and may form an incentive to expand their lending positions. On the other hand, they find that when the slope of the yield curve flattens, the banks’ profitability is compressed and forces banks to reduce lending. Besides that, Adrian and Shin (2010) argue that a bigger yield spread could be an incentive for banks to engage more in maturity transformation. This corresponds with the empirical findings of Maddaloni and Peydró (2011) that a steeper yield curve leads to a softening of lending standards. The empirical findings of the previous researchers all indicate that a higher yield spread causes an eagerness of banks to lend money. Even though softened lending standards will not immediately cause more bank risk taking, it is in line with expectations that this ‘eagerness to lend’ leaves room for more risk taking.
: The yield spread has no relation with bank risk taking.
: The yield spread has a positive relation with bank risk taking.
Capitalization as moderator
DellʼAriccia et al. (2014) introduce a theoretical model where they show that the degree of capitalization can moderate the effect of interest rate levels on bank risk taking. A decreasing risk free rate could have contrary effects on risk taking and monitoring by the bank itself depending on the degree of leverage. The theory of Dell’Ariccia et al. (2014) works as follows: consider a fully leveraged bank which has no bank capital and is financed only through deposits and debt. When the short term interest rates decline, the funding costs decline as well because of the lower rate they have to pay on their short term deposits. Since the interest income of long term loans remains initially the same, a drop in the cost of its liabilities will increase the bank’s expected net return on all assets. The bank can maximize this effect by reducing the risk of its assets in order to increase the probability of repaying depositors. Now consider a bank which has no leverage. The bank only suffers from the interest rate drop in the long run: the interest income declines at long last if the rates remain low. They will try to compensate lower returns by investing in riskier assets with higher expected returns. Concluding, poorly capitalized banks will generally increase monitoring and reduce risk taking at low interest rates, whereas well capitalized banks will reduce monitoring and increase risk taking. As earlier mentioned, even though the short term interest rate is not a perfect equivalent of the yield curve, the intuition mentioned is also likely to be applicable when the yield spread is low or even negative (Adrian & Shin, 2010).
: The yield spread has no relation with bank risk taking.
: The yield spread has a positive relation with bank risk taking for highly capitalized
banks.
: The yield spread has a negative relation with bank risk taking for highly levered banks.
Rhineland- versus Anglo-Saxon model
As mentioned in the introduction section, the relation of the yield spread with bank risk taking can be influenced by a lot of characteristics of the banking sector and is therefore likely to vary across countries (Anginer et al., 2014; Yagcilar, 2014). Examples of these characteristics are deposit insurance systems, banking competition, contestability of the bank market (ease of access to the market), country specific cultural aspects and regulatory capital requirements.
In general, the remuneration of the board is more performance based in the Anglo-Saxon system than in the Rhineland system (Weimer & Pape, 1999). This indicates that US bank managers might take more risk when the yield spread harm their profits, because they have a direct wage incentive.
Kanagaretnam, Lim & Lobo (2013) found in their empirical research that certain cultural aspects of the whole population can have a positive or negative effect on bank risk taking. They focused on two dimensions of national culture identified by Hofstede (2001): individualism and uncertainty avoidance. Since Kanagaretnam et al. (2013) state that the United States have a very high level of individualism and a low level of uncertainty avoidance, it is likely that the influence of the yield spread on bank risk taking is stronger in the United States than in Germany. Therefore, we test the following hypotheses:
: There is no significant difference between the United States and Germany in the relation between yield spread and bank risk taking.
: The relation between the yield spread and bank risk taking is stronger in the United States than in Germany.
3. Methods
To measure the effect of a change in the slope of the yield curve, we use a research framework that is based on the formula of Delis & Kouretas (2011). The general empirical model to be estimated is of the following form:
Equation 1:
specific spreads, a dummy (D) is inserted. When D=0 the model measures the effect of the German spread, when D=1 the model measures the effect of the United States spread and also adds a constant to . Finally, a set of j bank level control variables ( and k
macroeconomic control variables ( are included. Because the macroeconomic control variables are also country specific we separate the macroeconomic variables in for the United States and for Germany and add a dummy (D) as well. Since we want to measure the moderating effect of the capitalization ratio of a specific bank, two interaction terms are included. The interaction term consist of the capitalization ratio of the bank ) times the yield spread in the specific country. The first interaction term with coefficient measures the interaction effect in the United States, the second one
with coefficient measures the interaction effect in Germany. There are dummies (D) added to these terms as well to measure only the interaction effect with the yield spread of the home country.
Since we use dummies (D) for every country specific variable, there arise actually two different models: one for Germany if D=0 and one for the United States if D=1. We only analyze the effect on bank risk taking of variables in the country of origin of the bank. In fact, Equation 1 contains two empirical models written in one equation.
The data analysis starts with the descriptive statistics where we show the correlation matrices and check for multicollinearity. Then, we perform a pooled Ordinary Least Squares (OLS) analysis. After that, we do a Hausman test to check for endogeneity and we perform several regressions on the datasets (fixed effects and/or time fixed effects). In order to analyze the difference in effect between Germany and the United States we compare the outcomes of the empirical estimations. When there is a significant difference in betas, we can conclude that the difference in the effect of yield spread on bank risk taking between Germany and in the US is significant. The added constant gives also information about the difference between the two governance models. When this added constant is positive, we can conclude that the average level of risk taking is higher in the United States than in Germany.
Bank risk taking
information about the volatility of bank portfolios at any point in time. Risky assets are defined as the total assets minus cash, government securities (at market value) and balances due from other banks. An increase of the risky assets ratio results in a riskier position of banks.
The ratio of non-performing loans to total loans measures the quality of bank assets and serves as a proxy for credit risk. Ioannidou et al. (2014) use this proxy in their research on the Bolivian financial market as well. A loan is non-performing when the debtor does not pay his scheduled payments because he is either in default or close to being in default. The non-performing loans ratio reflects the potential harmful exposure to earnings and asset market values due to decreasing credit quality. Since a portfolio with a lot of non-performing loans will result in decreased earnings, a high value for this ratio is coupled with higher credit risk (Delis & Kouretas, 2011).
Finally, The Z-score is used as a risk measure of banks because it measures the inverse of the probability of default of the bank. Lepetit & Strobel (2013) compare in their research the different existing approaches to the construction of time-varying Z-score measures and conclude that the following definition fits the data the best:
Equation 2:
Z-scor
The Z-score for bank i at time t is the natural logarithm of the original Z-score formula (Lepetit & Strobel, 2013), the ROAA is the annual return on average assets, the CAR is the capital to assets ratio and the is the standard deviation of the annual return on average assets
calculated over all yearly observations in the dataset.
The ROAA is an indicator used to assess the profitability of the bank’s assets and is measured over the period of one year. The CAR is a ratio that measures how capitalized or levered a certain bank is. The capital in the CAR includes reserves, funds contributed by owners, retained earnings, general and specific reserves, provisions and valuation adjustments. Following Lepetit & Strobel (2013), the standard deviation of the ROAA is calculated based on all yearly observations of a bank’s ROAA in the dataset.3 The original Z-score measures the number of standard deviations the return of a bank can fall without exceeding the amount
3 A downside of this way of calculating
is that the variation of the volatility over time is not taken into
of equity. Laevan & Levine (2009) find in their empirical research that the Z-score turns out to be skewed. Following these authors, we take the natural logarithm to solve this problem which leads to a more normally distributed variable. In the following parts of this paper, the term ‘Z-score’ refers to the ln-transformed value of the Z-score.
Since we use three separate proxies for bank risk taking, further robustness of the results regarding the specification of this variable seems not to be necessary.
Yield spread and control variables
The yield spread is defined as the 10-year treasury yield less the 3-month treasury yield, or the closest equivalent for that (Chinn & Kucko, 2015). There are other specific maturities are used as well in empirical literature, but empirical evidence of Ang, Piazzesi & Wei (2006) suggests using the 3-month and 10-year maturity yield to measure the slope of the yield curve is the most appropriate.
Further, a set of bank-level control variables is included in the model: size, capitalization and profitability of the bank. In succession these constructs are measured as the natural logarithm of total assets, equity capital to total assets and profits before tax to total assets.4 Not incorporating these variables can cause the omitted variable bias because empirical researchers suggest a correlation with bank risk taking: Osborne & Lee (2001) state in their research in cross sections of US banks that bank size is positively associated with bank risk taking. Apergis (2014) suggests that profitability can have an impact on risk taking in US financial institutions. Looking at the literature section, it is clear that also capitalization may be strongly correlated with the dependent variable (Delis & Kouretas, 2011; DellʼAriccia et al., 2014; Jiménez et al., 2014). Because these variables may be important drivers of (the difference in) the relation between term spread and risk taking, we include them as control variables.
(2013) find in their empirical analysis of the Spanish financial market that these variables can have a reasonable effect on bank risk taking. Because GDP-growth and the inflation may correlate with the dependent variable, it is necessary to control for them in order to solve the omitted variable bias.
Besides GDP-growth and inflation, deposit insurance systems can also be seen as a country specific macroeconomic variable that can influence bank risk taking. In the United States, the Federal Deposit Insurance Corporation (FDIC) is responsible for the deposit insurance. Nowadays, the safety of a depositors account up to $ 250.000 for each deposit ownership is guaranteed. The German government implemented the European rules: the first € 100.000 of the banks client savings deposit is insured. Osborne & Lee (2001) show in their empirical research on US banks, that introducing an extensive deposit insurance system can have a significant effect on the bank risk taking. Because both systems guarantee a lump sum per account, Germany and the United States could be seen as comparable and it does not make sense to see this factor as a driver of a potential difference between them. Therefore, we do not add a deposit insurance as a control variable.
For measuring the moderating effect of the leverage of the bank, two interaction variables are added.5 One interaction variable is the equity to total assets ratio times the yield spread of the United States (CapSpread US), the other one is idem for Germany (CapSpread Germany). Following the existing literature (Delis & Kouretas, 2011; DellʼAriccia et al., 2014; Jiménez et al., 2014) it is important to add this interaction term because the amount of capitalization can change the direction of the effect of the yield spread on bank risk taking. When no interaction variable is used, the calculated beta of the yield spreads only gives the average effect while the effect of leverage is ignored. When the interaction variables are significant, we can conclude that there is a moderating effect of the capitalization ratio. Comparing these two coefficients ( and in Equation 1) with the coefficients of the yield spreads ( and in Equation 1) can tell us in which direction the leverage moderates the main effect. The total effect of the yield spread on bank risk taking is (after adding the interaction term) given by Equation 3 for Germany and Equation 4 for the United States.
5
Equation 3:
is the difference in bank risk taking for bank i at time t, is the difference in yield spread of Germany at time t and is the
capitalization ratio (equity to total assets) of bank i at time t.
Equation 4:
is the difference in bank risk taking for bank i at time t, is the difference in yield spread of the United States at time t and
is the capitalization ratio (equity to total assets) of bank i at time t.
4. Data
In this section, the process of collecting data is described supplemented by the descriptive statistics and the correlation matrices.
First, a large unbalanced dataset from all German and US active banks from 2001 until 2014 is imported from Bankscope. This sample consists of yearly observations of commercial, savings and cooperative banks that were operating in the United States and Germany over the period 2001 until 2014.
Analyzing this data we conclude that there are some structural gaps in the data. There is hardly any data for the risky assets ratio before 2009 for both US and Germany. This could be related to the financial crisis of 2008 and the fact that banks are not very willing to provide their (indecent) financial decisions at that time. Using the whole sample of 2001 till 2014 including the systematically absent data before 2009 harms the exogeneity assumption of the analysis. Further, for some reason there is no data at all for German banks concerning the non-performing loans ratio.
behavior of banks may have been changed after the crisis (Dataset 1).7 For the second risk proxy (non-performing loans ratio) only banks from the United States are used (Dataset 2). This regression does not contribute to the investigation of the difference between the Rhineland and the Anglo-Saxon model. The Z-score dataset contains data of both German and US banks for the whole period 2001-2014 (Dataset 3). Table 1 shows the descriptive statistics of the three datasets.
Table 1. Descriptive statistics
Dataset Variable Observations Mean Std. deviation Min Max Year
1 Risky assets ratio 44,988 0.798 0.157 0.001 1 ’09-’14 Spread Germany 6 1.725 0.437 1.223 2.390 ’09-’14 Spread United States 6 2.573 0.526 1.720 3.110 ’09-’14 Bank size (thousand $) 44,988 6,267,176 83,400,000 1,567 3,270,000,000 ’09-’14 Bank size (ln) 44,988 12.619 1.660 7.357 21.908 ’09-’14 Capitalization 44,988 0.112 0.085 -0.121 1 ’09-’14 Profitability 44,988 0.009 0.027 -0.338 1.373 ’09-’14 GDP-growth Germany (%) 6 0.688 3.501 -5.638 4.091 ’09-’14 GDP-growth United States (%) 6 1.381 2.061 -2.776 2.532 ’09-’14 Inflation Germany (%) 6 1.319 0.680 0.313 2.075 ’09-’14 Inflation United States (%) 6 1.600 1.139 -0.356 3.157 ’09-’14 CapSpread Germany 6,006 0.133 0.069 0.011 1.136 ’09-’14 CapSpread United States 38,982 0.300 0.240 -0.304 3.110 ’09-’14 2 Non-performing loans 83,776 0.017 0.027 0 0.784 ’01-’14 Spread United States 14 2.093 1.063 -0.060 3.110 ’01-’14 Bank size (thousand $) 83,776 3,642,102 62,000,000 2,157 3,270,000,000 ’01-’14 Bank size (ln) 83,776 12.087 1.462 7.676 21.908 ’01-’14 Capitalization 83,776 0.109 0.041 -0.340 0.962 ’01-’14 Profitability 83,776 0.011 0.033 -0.590 3.409 ’01-’14 GDP-growth United States (%) 14 1.796 1.651 -2.776 3.786 ’01-’14 Inflation United States (%) 14 2.305 1.077 -0.356 3.839 ’01-’14 CapSpread United States 83,776 0.228 0.145 -1.016 2.950 ’01-’14 3 Z-score (ln) 100,590 3.427 0.901 -7.066 7.609 ’01-’14 Spread Germany 14 1.229 0.899 -0.697 2.390 ’01-’14 Spread United States 14 2.093 1.063 -0.060 3.110 ’01-’14 Bank size (thousand $) 100,590 4,262,774 56,200,000 928 2,750,000,000 ’01-’14 Bank size (ln) 100,590 12.375 1.651 6.833 21.734 ’01-’14 Capitalization 100,590 0.110 0.082 -0.006 1 ’01-’14 Profitability 100,590 0.011 0.040 -1.658 3.409 ’01-’14 GDP-growth Germany (%) 14 1.074 2.463 -5.638 4.091 ’01-’14 GDP-growth United States (%) 14 1.796 1.651 -2.776 3.786 ’01-’14 Inflation Germany (%) 14 1.576 0.610 0.313 2.628 ’01-’14 Inflation United States (%) 14 2.305 1.077 -0.356 3.839 ’01-’14 CapSpread Germany 14,812 0.088 0.100 -0.599 2.195 ’01-‘14 CapSpread United States 85,778 0.244 0.229 -0.060 3.110 ’01-‘14 The variables used are calculated as follows: the risky assets ratio is the ratio of risky assets to total assets; non-performing loans is the ratio of non-performing loans to total loans; the Z-score is the natural logarithm of the annual return on average assets plus the capital to assets ratio divided by the standard deviation of the return on average assets (see Equation 2); the spread is the 10-year treasury yield less the 3-month treasury yield; the bank size is the natural logarithm of the total assets; the capitalization is the ratio of equity to total assets; the profitability is the ratio of profit before tax to total assets; the GDP-growth is the economic growth of the country and the inflation is the inflation of consumer prices of the country concerned. To calculate the interaction term (CapSpread), the capitalization ratio of a German bank is multiplied by the yield spread of Germany and the capitalization ratio of a US bank is multiplied by the yield spread of the United States. Because of the use of dummies in the regression formula (see Equation 1), interaction terms of banks calculated with foreign spreads do not take part in the analysis. Only the spread of a banks country of origin is used. Therefore it is more appropriate to show in Table 1 only the banks with matched country spreads.
For the first regression concerning the risky assets ratio, a balanced dataset of 7,498 banks with 44,988 observations from 2009 until 2014 is used (Dataset 1). This sample consists of 1,001 German banks and 6,497 US banks. For the second regression, the non-performing
loans ratio, a balanced dataset of 5,984 US banks with 83,776 observations from 2001 until 2014 is used (Dataset 2). The third balanced datasheet containing the Z-score measures bank data of 7,185 banks with 100,590 observations from 2001 till 2014, including 1,058 German banks and 6,127 US banks (Dataset 3).
The unbalanced samples are transformed to balanced data sheets by deleting banks with one or more missing observations or banks that contain extreme and unlikely values for certain variables. Balanced data gives less efficiency loss and it can add value to the exogeneity of the analysis. However, a selection bias can occur by deleting banks with missing observations. This could be the case when for instance only highly levered banks, only risky behaving banks or only smaller banks have missing data. To check the representativeness of the datasets and the exogeniety assumption we compared the means of different variables of the balanced sample with the unbalanced data sample. No significant deviations are found, the supporting data is available on request.
In this research only active banks are used. One can say that doing so, the ‘survivorship bias’ appears in the analysis because only the banks that are still active are measured. We overlook those that are not visible because of mergers, acquisitions, or defaults. In this specific research, this will not lead to false conclusions. Assuming that more risk taking leads to more bankruptcy in general, the defaulted banks might have taken even more risk based on the term spread at that time. If we find a significant effect of yield spread on bank risk taking, the effect can at most be understated and might be even stronger when we include inactive banks. This intuition is empirically confirmed by Delis & Kouretas (2011) in their research on European banks. Although magnitude of the survivorship bias in their sample is about 10% (10% of the banks does not exist anymore at the end of the sample period), changes in the results of the main variables are negligible.
Bankscope has a function that provides a consolidation code for each bank. This function gives information about certain parent holding- and subsidiary constructions. For this research comparing the US and Germany, it is appropriate to use the unconsolidated accounts because doing so we maximize the sample size and bank data is not influenced by foreign subsidiaries.
spread of Germany is gathered from the database Eurostat.9 Yearly data from 2001 until 2014 concerning 10-year German government bond rate minus the 3-month interest rate is used. Further, a set of country specific macroeconomic variables is extracted from the World Bank database.10 We use yearly observations from 2001 until 2014 of the GDP-growth and inflation (consumer prices) of both Germany and the United States.
Correlation
Table 2 shows the correlation matrix of Dataset 1. The strong correlation of the risky assets ratio with bank size (35.7%), capitalization (-28.6%) and profitability (-14.6%) confirms the need to include these variables as control variables. It is also worth mentioning that the macroeconomic control variables within and between Germany and the US are relative strongly correlated. This has to do with the fact that during a global change of economic growth, the GDP-growth and inflation are likely to go hand in hand in both countries. However, this correlation brings no multicollinearity problems because of the use of dummies in our model (see Equation 1).
Further, the positive correlation of the risky assets ratio with the German (6.4%) and US spread (6.7%) is congruent with the expectations that the yield spread has a positive relation with bank risk taking (hypothesis ). Moreover, the correlation of the risky assets ratio with the added interaction variables (CapSpread) is even higher. The German interaction variable shows a correlation of 25.3% and the US interaction variable show a correlation of -26.1%. Comparing the positive yield spread correlation coefficients with the negative coefficients of the interaction variables strengthens the intuition that the amount of capitalization can cause a change in direction of the effect between yield spread and bank risk taking (see hypothesis and ). It is in line with previous researchers (DellʼAriccia et al., 2014; Jiménez et al., 2014) that the influence of yield spread on bank risk taking becomes negative for highly levered banks.
At last, Table 2 shows that there is a relatively high correlation between the CapSpread-variable and the capitalization CapSpread-variable itself (Germany: 93.5% and US: 95.6%). Regularly, such a strong correlation between two independent variables gives severe multicollinearity
9
Source: http://ec.europa.eu/eurostat.
problems. In this case, the correlation deals with an interaction variable correlating with one of its constituents. Then, the multicollinearity is not a problem according to Brambor, Clark, and Golder (2006). In their research about interaction models, they argue that even when the size of standard errors increases due to multicollinearity, including both the interaction term and its constituents in the formula is the most proper way of analyzing.
Table 2. Correlation matrix Dataset 1: Risky assets ratio.
The variables are calculated similar to Table 1 (see comment at Table 1). In contrast to Table 1, the interaction term (CapSpread) is also calculated by multiplying the capitalization ratio of a German bank with the spread of the United States and vice versa. A matching number of interaction term observations and total observations is necessary in order to make proper correlation calculations over the datasets containing both countries. However, this country ‘mismatches’ do not take part in the regression analysis because of the use of dummies in the regression formula (see Equation 1). Because of the use of dummies, only the spread of the banks country of origin is used for calculating the interaction variable.
Table 3 shows the correlation matrix of Dataset 2. Besides the things that are already mentioned at Table 2, it stands out that the non-performing loans ratio is positively correlated with the spread of the United States (15.7%). This is congruent with the hypothesis ( ) that a higher yield spread goes hand in hand with higher bank risk taking. Further, it is worth mentioning that the non-performing loans ratio is negatively correlated with the GDP-growth (-11.2%) and the inflation (-16.3%). This corresponds to the empirical findings of Jiménez et al. (2013) concerning the influence of macroeconomic variables on bank risk taking in the Spanish financial market. Looking at these relative high correlation coefficients, it is important to control for these variables.
Table 3. Correlation matrix Dataset 2: Non-performing loans ratio.
Non-perf. loans
Spread US
Bank size Cap. Profitb. GDP US Infl. US
CapSpr US Non-performing loans 1.0000
Spread United States 0.1572 1.0000
Bank size 0.0292 0.0029 1.0000 Capitalization -0.0383 -0.0123 -0.0316 1.0000 Profitability -0.1369 -0.0381 -0.0031 0.1510 1.0000 GDP-growth US -0.1120 -0.2104 -0.0022 0.0082 0.0602 1.0000 Inflation US -0.1631 -0.5168 -0.0051 0.0036 0.0410 0.4403 1.0000 CapSpread US 0.0905 0.7655 -0.0169 0.5600 0.0554 -0.1557 -0.3943 1.0000 The variables are calculated similar to Table 1 (see comment at Table 1).
Risky assets Spread Germany Spread US
Bank size Cap. Profitb. GDP Ger GDP US Infl. Ger Infl. US CapSpr GER
CapSpr US Risky assets ratio 1.0000
Looking at Table 4, it stands out that there is a minimal negative correlation between the Z-score and the yield spreads (-0.04% for Germany and -0.9% for the US). The fact that these correlations are close to zero can maybe be explained by the moderating effect of the capitalization ratio. The correlation coefficients of both interaction terms are -0.9% for Germany and -1.5% for the US. Because the sample consists of both highly and lowly levered banks, the overall correlation can be zero. The negative effect on the Z-score of highly capitalized banks might compensate the positive effect on the Z-score of lower capitalized banks.
Table 4. Correlation matrix Dataset 3: Z-score.
The variables are calculated similar to Table 1 (see comment at Table 1). In contrast to Table 1, the interaction term (CapSpread) is also calculated by multiplying the capitalization ratio of a German bank with the spread of the United States and vice versa. A matching number of interaction term observations and total observations is necessary in order to make proper correlation calculations over the datasets containing both countries. However, this country ‘mismatches’ do not take part in the regression analysis because of the use of dummies in the regression formula (see Equation 1). Because of the use of dummies, only the spread of the banks country of origin is used for calculating the interaction variable.
5. Results
Fixed or Random effects
To analyze the effects of the yield spread on bank risk taking, we perform linear regressions on the panel data. It seems to be appropriate for this research to use the fixed effects model. Each bank has its own individual characteristics that may or may not influence the results. Although we added a few control variables, there is a high suspicion that there is unobserved heterogeneity across banks. When we use the bank fixed effects model, we assume that something within the bank may impact the independent and dependent variables. Related empirical articles gives us no definite answer regarding whether or not to use the bank fixed effects model. Delis & Kouretas (2011) use the random effects model in their research because a Hausman test reveals that the difference in coefficients between fixed and random
Z-score Spread Germany
Spread US
Bank size Cap. Profitb. GDP Ger GDP US Infl. Ger Infl. US CapSpr GER
CapSpr US Z-score 1.000
Spread Germany -0.0004 1.000
Spread United States -0.0094 0.6728 1.000
effects is not systematic. However, Jimenez et al. (2014) use a comprehensive variant of the bank fixed effects model because they prove in their research that the individual-specific effects were strongly correlated. To find whether to use fixed or random effects in our research, we run a Hausman test at all three datasets. For all datasets the Hausman test confirms that the bank fixed effects model is the best fitting model. The exact outcomes of the Hausman tests are available at request.
In our model, it is arguable that certain time specific effects can cause unexpected variation over time in the outcomes. Global changes in the economy (i.e. the crisis of 2008) and changing laws and regulations over time can influence the results. We try to capture a part of these effects with adding the control variables but it is evident that we maybe overlook some time dependent effects. Therefore, we also perform a regression controlling for time fixed effects.
Results Risky Assets Ratio
Table 5 shows the results of the analyses of Dataset 1, where bank risk taking is proxied by the risky assets ratio. A basic pooled Ordinary Least Squares (OLS) regression with all control variables is performed on data from Germany (regression I) and the United States (regression II) followed by a regression with bank- and time fixed effects on both countries (regression III and IV). The positive estimated coefficients of the yield spread are in line with the expectations that the yield spread has a positive effect on bank risk taking (hypothesis ).11 Even the degree of capitalization cannot change this positive effect into a negative total effect for the fixed effects regressions (regression III and IV).12 However, the results concerning this effect are not convincing in Germany because the coefficients are not significant at all significance levels. The yield spread coefficients of the United States are significant in both regressions (II and IV) and show bigger values than Germany. An increase of the US yield spread with one percentage point causes an increase of 0.021 in the risky assets ratio according to the pooled OLS and a increase of 0.016 according to the regression with time- and bank fixed effects. The fact that the term spread coefficient decreases after adding time- and bank fixed effects, suggests that unexpected time-varying variation and/or
unobserved heterogeneity across banks has an impact on bank risk-taking and/or the yield spread. Therefore, we can conclude that the use of the time- and bank fixed effects model adds value to the analysis with respect to Dataset 1.
The included interaction variable (CapSpread) to measure the moderating effect of the capitalization shows a significant beta in the pooled OLS of Germany and no significance at all significance levels in the other regressions in Table 5. Based on this sample, there is no empirical evidence that leverage has a moderating effect on the nexus between the yield spread and the risky assets ratio (hypothesis H2).
In the literature review, we hypothesized that the effect of the yield spread on bank risk taking is stronger in the United States than in Germany (hypothesis ). Although the betas of the yield spread point in the same direction, we cannot make proper conclusions based on this results since Table 5 shows that the spread coefficients of Germany are not significant at all significance levels.
The results of Dataset 1 do not confirm the theory that the level of risk taking in the United Stated is significant higher than in Germany. The constants of regressions III and IV shows that the level of bank risk taking measured as the risky assets ratio is higher in Germany than in the United States.
Regarding the betas of the control variables in Table 5, it stands out that the profitability and the capitalization of banks have a reasonable impact on bank risk taking. For instance, by increasing capitalization ratio with 0.1, the risky assets ratio will decrease with 0.023 (-.226/10) in Germany (regression III). This is an intuitive result since higher equity capital, maybe due to strict capital requirements, implies less risky bank behavior. The GDP-growth shows a negative beta which means that a higher real GDP-growth rate reduces the bank risk. Gambacorta (2009) explains that as a consequence of higher GDP-growth levels, an increasing number of projects becomes profitable. As a result of these more profitable projects, the risky assets ratio decreases. The significant betas of control variables in regressions III and IV confirm the importance of adding control variables.
Table 5. Results pooled OLS and linear regression Dataset 1: Risky assets ratio.
Risky assets ratio Pooled OLS
Risky assets ratio Linear regression GER US GER US Regression nr.: I II III IV Spread 0.005 0.021*** 0.013 0.016*** CapSpread -0.152*** -0.025 0.029 0.003 Size -0.006*** 0.026*** -0.002 0.027*** Capitalization -0.295*** -0.250*** -0.226*** 0.035 Profitability 1.368*** -0.185*** -0.323*** 0.182*** GDP-growth 0.0001 -0.003*** 0.0001 -0.011*** Inflation -0.002 -0.002 0.005 0.014*** Constant 1.067*** 0.440*** 0.972*** 0.387*** Observations 6,006 38,982 6,006 38,982 R-squared (overall) 0.128 0.142 0.072 0.083 Number of banks 1,001 6,497 1,001 6,497 Time period 2009/2014 2009/2014 2009/2014 2009/2014 Fixed effects No No Yes Yes Time fixed effects No No Yes Yes
The variables are calculated similar to Table 1. The R-squared gives the explanatory power of the independent variables. ***,**, And * are the statistical significances at the 1%, 5% and 10% level, respectively.
Results Non-Performing Loans
government securities). As a result of less risky behavior, the quality of bank assets will rise and the non-performing loans ratio will decline.
The interaction variable (CapSpread) shows a significant beta of -1.339 in the linear regression (VI) of the non-performing loans. This implicates that when the capitalization ratio of a bank rises with 0.1, the total effect of yield spread on the non-performing loans ratio decreases with 0.1339 (1.339/10) (see Equation 4). Although we can conclude that there is a significant moderating effect of the capitalization on the nexus between yield spread and bank risk taking, we cannot confirm both hypotheses. Hypothesis can be rejected based on this sample, where hypothesis can be confirmed. The total effect of the yield spread on
bank risk taking given by Equation 4 is negative for both highly capitalized and highly levered banks because of a negative and .
Looking at the betas of the control variables, it stands out that the profitability has a reasonable significant influence on bank risk taking. Bearing in mind that the influence of profitability was also reasonable for the risky assets ratio regressions (I, II, III and IV) it is not only justified to add this variable as a control variable but we can also have a legitimate suspicion of endogeniety. Especially for the non-performing loans regressions, endogeniety can be expected because the amount on non-performing loans relative to total loans is closely related to profitability. The non-performing loans ratio measures the potential adverse exposure to earnings and asset market values due to deteriorating loan quality (Delis & Kouretas, 2011). The macroeconomic control variables show the following betas in regression VI: 1.421 for the GDP-growth and -1.216 for the inflation. Since these variables turn out to be influencing on bank risk taking proxied as the non-performing loans ratio, adding these variables as control variables seems to be appropriate.
The R-squared value of the fixed effects regression is 9.1% for the United States. This low rate implicates that the goodness of fit of the model is critical. But as earlier mentioned, this low R-squared value is common in panel data analysis since variations in individual bank behavior are difficult to explain (Gambacorta, 2009).
Results Z-score
(VII and VIII). The fixed effects regressions seem to be the more appropriate analysis method. For both Germany and the United States, the effect of the yield spread on the ln-transformed Z-score is positive: 0.748 for Germany and 0.029 for the United States. Important to notice is that looking at the interaction term betas, even a very high or low degree of capitalization (0 or 1) cannot change this positive effect into a negative total effect in both Germany and the United States (see Equation 3 & 4). This result is in line with the hypothesis that a steeper slope of the yield curve leads to more bank risk taking in general (hypothesis ).
Since we use the natural logarithm of the Z-score, drawing economic conclusions based on the regression results has to be done carefully. When for instance the yield spread in Germany rises with one percentage point, the ln-transformed score rises with 0.748 but the actual Z-score rises with = 2.096. An increase in the Z-score of 2.096 means a change in probability of default of 2.1% which seems to be considerable. In the United States, a rise of the yield spread with one percentage point means a change in probability of default of =
1.0%. Comparing these two effects, it stands out that effect of the yield spread on the probability of default is stronger in Germany than in the US. This in not in line with the expectations (hypothesis ). Moreover, the constant of the German regression (IX) is also bigger in than the constant in the US regression (X): 4.569 against 2.050. This implicates that the overall level of risk taking of banks, proxied by the Z-score, is higher in Germany than in the United States. The influence of the yield spread on bank risk taking proxied by the Z-score is significant and economic relevant.
The betas of the interaction variable (CapSpread) of Germany (IX) and the United States (X) in Table 6 are significant but do not point in the same direction. In Germany, the capitalization is negative related with the effect of the yield spread on bank risk taking with -0.261. If a bank is highly capitalized, the total effect of the yield spread on bank risk taking decreases. For the United States, the opposite situation occurs. The interaction variable shows a positive beta of 0.068, which means that highly capitalized banks take more risk where highly levered banks take less risk given a certain yield spread level.
Table 6: Results pooled OLS and linear regression Dataset 2 and 3: Non-performing loans ratio and Z-score. Non-perf. loans pooled OLS Non-perf. loans linear regression Z-score pooled OLS Z-score linear regression US US GER US GER US Regression nr.: V VI VII VIII IX X Spread 0.470*** -1.845*** 0.015 -0.019*** 0.748*** 0.029*** CapSpread -1.907*** -1.339*** 0.211 0.078** -0.261*** 0.068*** Size 0.236*** -0.403*** 0.017*** -0.051*** -0.140*** 0.040*** Capitalization 4.008*** -1.236*** -0.824*** 0.289*** 5.002*** 4.669*** Profitability -10.689*** -17.183*** -1.633*** 0.016 3.191*** 1.883*** GDP-growth -0.075*** 1.421*** 0.015*** 0.011*** 0.088*** 0.013*** Inflation -0.214*** -1.216*** -0.031 -0.006* 0.192*** 0.051*** Constant -1.443*** 10.917*** 3.970*** 3.900*** 4.569*** 2.050*** Observations 83,776 83,776 14,812 85,778 14,812 85,778 R-squared (overall) 0.069 0.091 0.004 0.014 0.001 0.003 Number of banks 5,984 5,984 1,058 6,127 1,058 6,127 Time period 2001/2014 2001/2014 2001/2014 2001/2014 2001/2014 2001/2014 Fixed effects No Yes No No Yes Yes Time fixed effects No Yes No No Yes Yes The variables are calculated similar to Table 1. The R-squared gives the explanatory power of the independent variables. ***,**, And * are the statistical significances at the 1%, 5% and 10% level, respectively.
6. Conclusion & Discussion
Conclusion
The aim of this study is to analyze whether or not the yield spread in a certain country has a significant influence of the risk taking of banks. According to previous literature, an environment of low short term interest rates has a positive effect on bank risk taking. The difference between the long term rate and the short term rate, the yield spread, is seen as the main driver of the profitability of the bank in its simplest form. Because the yield spread has a direct effect on the business model of banks, taking this variable seems to be appropriate and contributes to existing literature regarding the nexus between the interest rate and bank risk taking. Moreover, we examine the moderating effect of the degree of capitalization and we compare the effect of the yield spread on bank risk taking of two different governance models.
The empirical analysis conducted on the risky assets ratio13 and the Z-score confirms that there is a positive relation between yield spread and bank risk taking in Germany and the United States. As we hypothesized, a higher yield spread incentivize banks to take more risk in search for a higher yield. This result seems to be valuable for central banks. By conducting their monetary policy, monetary authorities could influence the risky behavior of banks. However, the analysis on the non-performing loans dataset gives evidence for a negative effect instead of a positive effect. A possible explanation for this negative effect could be the fact that banks might be somehow incentivized to reach a certain minimum amount of return on equity or another comparable return measure. Due to intern or extern imposed return goals, the banks' investing behavior might be driven by a desire to reach a certain minimum value of a return measure. If the yield spread increases, banks can achieve the imposed minimum with relatively less risky investment decisions. The non-performing loans ratio will decline.
Concerning the moderating effect of the degree of capitalization, we can conclude that there is a moderating effect following the non-performing loans and the Z-score analysis. The capitalization ratio is an important moderator on the nexus between the yield spread and bank risk taking, because the interaction term showed significance and an economic relevant beta on both regressions. However, the found moderating effect does not point in the expected direction. We expected that a high degree of capitalization could change a negative relation into a positive total relation between the yield spread and bank risk taking. This expectation cannot be confirmed based on the results. The analysis conducted on the risky assets ratio does not show significant betas for the interaction term at all.
Discussion
Looking at the results of the analysis, it stands out that there is a reasonable difference between the three different datasets. Firstly, a reason for this discrepancy can be found in the fact that we measure the dependent variable on three different ways. The robustness of the proxies could be problematic and a driver of the difference. Secondly, we perform regressions based on three different datasets. The difference in datasets (time, country and deleted banks) could be a cause of the conflicting results. In general, it is desirable to regress on the three proxies based on one sample: by comparing the results you can check the robustness of the proxies. Since there was considerable structural omitted data and we want to maximize the sample size for each way of measuring the dependent variable, we were forced to split up the total data. We also deleted banks with missing data to make the sample balanced. We checked for a selection bias by comparing several means of variables of the unbalanced datasheet with the balanced datasheet. However, unobserved difference in datasets could have caused the difference in results between the three proxies of bank risk taking.
A suggestion for further research could be to replicate this research but instead of splitting the dataset for the different proxies, reduce to data to one small dataset. The big disadvantage is that the dataset becomes small and the representativeness of the research might become problematic. The advantage of using one dataset is that is easier to compare the proxies and to check the robustness of the dependent variable.
When interpreting the results of the different regressions, it is important to bear in mind for which period the analysis is performed. The risky assets ratio is performed on a dataset from 2009 until 2014. The crisis of 2008 may have had a significant influence on risky behavior of banks. Even though the time fixed effects model is expected to take this into account, fundamental changes in risk appetite of banks may have influenced the results. It is also worth mentioning to wonder why there is no data available about risky assets before the crisis of 2008. It might be obvious that banks are not very willing to display their pre crisis risky behavior. A suggestion for further research can be to split up the sample in a pre-crises and a post-crisis period and to analyze the differences.
supplement to the Rhineland model data, whereas bank data from the United Kingdom could be added to the Anglo-Saxon model data.
Another suggestion for further research could be an addition of a lagged variable. Delis & Kouretas (2011) find empirical evidence in the Euro area that bank risk taking can be predicted by past values of the profitability. Although it might not be essential to add lagged terms of the independent variables, doing so might provide interesting new insights.
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