* University of Groningen, Faculty of Economics and Business Student number: 2026198
E: lennartdekker1@gmail.com T: +31 (0) 640248914
Influence of the yield curve on bank risk-taking in the US
Lennart F. Dekker*
Supervisor: Dr. A.A. Tsvetkov Thesis, MSc in Finance January 2016
Abstract
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1.
Introduction
In the early 2000s, the financial world survived the burst of the dot-com bubble and the terrorist attacks of 9/11, after which the nominal interest rates were set at a historical depth in order to boost the economy. According to Maddaloni and Peydró (2011), these subsequent periods of low interest rates have brutally softened the pre-crisis lending standards of banks. What followed was a period of inordinate bank risk-taking due to the enhanced activity in the securitization of subprime mortgages. Then, in August 2007, the Federal Reserve released a statement about the current financial turmoil stating that the downside risk of the economic growth had increased substantially. It became clear that the financial markets were at the beginning of what we would later call the financial crisis. Consequently, the financial crisis gave rise to a severe public and scientific discussion about the excessive risk-taking of banks, which led to an explanation for the behavior of these banks. Borio and Zhu (2008) were among the first researchers that identified the role of the monetary policy of central banks in the years preceding the crisis. Their theory of a “risk-taking channel of monetary policy” inspired researchers to investigate the influence of primarily the short-term interest rates on the increasing bank risk-taking. Not surprisingly, they found proof for the existence of a risk-taking channel1, meaning short-term interest rates indeed affect the risk-taking of banks as a result of the softening of lending standards.
However, as can be seen in Fig. 1, the Federal Reserve’s short-term interest rate fell to an even lower point at the end of the financial crisis in 2009. This new period of highly unusual low interest rates
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See, e.g., Gambacorta (2009); Altunbas, Gambacorta and Marqués-Ibáñez (2010); Delis and Kouretas (2011); Maddaloni and Peydró (2011); Dell’Ariccia, Laeven and Suarez (2013); Jiménez, Ongena, Peydró and Saurina (2013); and Ioannidou, Ongena, and Peydró (2015).
Figure 1
Development of short-term interest rate
This figure presents the annual average of the Federal Funds effective overnight rate in the period 2000-2014. Data has been obtained from Datastream.
3 has not been reviewed yet by previous studies. The Federal Open Market Committee (FOMC) sets the target for the federal funds rate based on their monetary policy strategy of maximized employment and 2% annual inflation (FOMC, 2015), which is empirically supported by Kesselring and Bremmer (2011). Surprisingly, no evidence has been found yet that the FOMC takes into account the risk-taking of banks. Did the federal government learn from the risky behavior of banks as a result of the low interest rate environment in the years preceding the financial crisis? It would be interesting to investigate if banks engaged in the same risky behavior as before the financial crisis.
Furthermore, since the profitability of banks is partly determined by the long-term rate (Alessandri and Nelson, 2015), and since banks engage in more risk-taking activities due to the search for yield (Rajan, 2006), it would be interesting to examine the combined impact of the interest rates on the risk-taking of banks. The impact of the combination of long- and short-term interest rates – referred to as the slope of the yield curve or the term spread – can be best explained through the concept of maturity transformation, in which banks convert short-term deposits into long-term loans (Dell’Ariccia and Marquez, 2006). That is, banks demand a higher interest rate on long-term loans than they manage to compensate for the short-term deposits. Mink (2011) argues that the term spread could be an additional element in the risk-taking channel of monetary policy by Borio and Zhu (2008). Next to the level and slope of the yield curve, the curvature of the yield curve is seen as another component of the yield curve by Diebold, Rudebusch and Aruoba (2006). It would be rational to incorporate all three yield curve movements in the regressions on bank risk-taking.
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2.
Literature review
The yield curve is a graphical expression of the term structure of interest rates and is a renowned index of the business cycle (Estrella and Mishkin, 1997). In addition, Diebold et al. (2006) have proven that the yield curve is highly influenced by inflation, real economic activity and monetary policy. The yield curve plays a central role in forming monetary policy, interest rate policy by banks and investment decisions. For example, Litterman and Scheinkman (1991) showed that the yield curve explains on average 97% of the variance of excess bond returns. Furthermore, they found strong evidence for three principal factors that explain the movements of the yield curve: the level, the slope2 and the curvature. Diebold et al. (2006) support the relevance of the three factors. However, these studies did not mention any influence of the yield curve on bank risk-taking, even though their factor approach clears the way for further studies relating the impact of the yield curve. For instance, Alessandri and Nelson (2015) made use of the factors of the yield curve to examine its influence on a bank-related subject. They found strong evidence for a relation between the level and slope of the yield curve and the profitability of banks. Therefore, it is clear that researchers should incorporate all three components of yield curve movements when looking at the influence of the yield curve. This paper will make a first step into using slope, level and curvature movements in relation to bank risk-taking. In addition, this paper will examine the effect of solely the short-term interest rate on bank risk-taking to be able to compare the results to prior empirical research. The rest of this section lists the theoretical and empirical evidence concerning the effect of interest rates on the risk-taking of banks.
2.1 Maturity transformation
One of the core functions of banks is related to the maturity transformation principle, in which banks use the short-term deposits of firms and consumers to finance longer-term loans, including mortgages (Dell’Ariccia and Marquez, 2006). In general, the yield curve is upward sloping, meaning that the short-term rate is at a lower level than the long-short-term rate. This assumption relies on the liquidity preference theory, stating that consumers want to be compensated for the illiquidity of their long-term assets (Hull, 2012: 161). The resulting difference between the long- and short-term rate (i.e., the term spread) can be rather alluring for banks (Entrop, Memmel, Ruprecht and Wilkens, 2015). For instance, when the yield curve steepens the term spread increases, resulting in a relatively higher long-term rate and a lower short-term rate. Consequently, the interest income on longer-term loans increases and at the same time the interest expense on the shorter-term deposits decreases, resulting in a higher interest margin. With
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5 a flattening of the yield curve this process is inverted. Alessandri and Nelson (2015) support this statement, since they found that both the level and the slope of the yield curve have a significant impact on the interest rate margin (i.e., profitability) of banks. To conclude, it is clear that the yield curve plays a big role in determining the profitability of a bank. However, the connection between the yield curve and the risk-taking of banks has been researched to a much lesser extent.
2.2 Interest rates and bank risk-taking
Borio and Zhu (2008) came up with the idea that the risk-taking activity of banks should be taken into account when forming monetary policy. They introduce the term “risk-taking channel of monetary policy”, meaning the risk-taking of banks is influenced by monetary policy. Their main explanation is that monetary policy rates have an impact on the measurement of valuations, incomes and cash flows, which in turn influences the risk perception and risk-tolerance of banks. In addition, Rajan (2006) mentions the term “search for yield” which is a possible reason for the existence of a risk-taking channel. When interest rates are low, banks engage in higher yielding and more risky projects in order to yield the predefined target rates set by long-term contracts. The theoretical implications by Borio and Zhu (2008) and Rajan (2006) are endorsed by a number of empirical studies investigating the relationship between (short-term) interest rates and bank risk-taking. The most important studies are summarized below.
Firstly, Delis and Kouretas (2011) examined the risk-taking activity of banks in the Euro area during the period 2001-2008. They focused on the relatively long period of low levels of interest rates after the terrorist attack at 9/11 in 2001. In their empirical model, bank risk-taking is determined by the ratio of risky assets to total assets and non-performing loans to total loans. The latter reflects the quality of bank assets and is a direct measure of credit risk. They controlled for a set of bank-specific, regulatory, macroeconomic and structural control variables and for time effects. A highly significant and inverse relationship between several types of interest rates (e.g., short- and long-term) and bank risk-taking was found. This is robust to the dynamics of bank risk and the use of yearly instead of quarterly data.
Secondly, Maddaloni and Peydró (2011) analyzed the lending standards of banks in the Euro area and the US. They found robust evidence that subsequent periods of a low interest rate environment soften the lending standards for firms and households. On top of that they stated that this was a key factor that caused the financial crisis. Their result is strengthened for banks with high securitization and weak supervision for bank capital. This did not hold for low long-term interest rates.
risk-6 taking is the ratio of non-performing loans to total loans. They found that a lower US federal rate3 significantly increased the risk-taking of banks, even after controlling for bank-specific and macroeconomic variables. Additionally, Ioannidou et al. (2015) found that a lower US federal rate increases the likelihood of banks to grant loans to riskier borrowers with a less preferable past performance. Hence, banks softened their lending standards.
Fourthly, Jiménez, Ongena, Peydró and Saurina (2013) researched the impact of the overnight monetary policy rate on bank risk-taking in Spain from 2002 up to 2008. Their main measure of credit risk is based on the existence of non-performing loans. They identified that a lower short-term interest rate resulted in heavier risk-taking of banks. Moreover, a lower interest rate encourages lowly capitalized banks to engage in lending activities with formerly inefficient firms. After granting the loan to these riskier borrowers, the lowly capitalized banks have a higher possibility of default. At last, Jiménez et al. (2013) found reason to believe that the long-term rate has an insignificant impact on bank risk-taking, as opposed to the short-term rate, which is in line with Maddaloni and Peydró (2011).
Fifthly, Altunbas, Gambacorta and Marqués-Ibáñez (2010) analyzed the monetary policy-bank risk nexus by looking at the expected default frequency (EDF) of listed banks in 15 developed European countries and the US. They measured the stance of monetary policy by using the Taylor rule and compared this benchmark rate with the real interest rates. They found that consecutive years of low short-term interest rates (i.e., monetary policy rates under the benchmark rates) had an increasing impact on the risk-taking behavior of banks.
Lastly, Dell’Ariccia, Laeven and Suarez (2013) used a large survey of the Federal Reserve over the period 1997 to 2011 to investigate whether banks soften their lending standards due to lower short-term interest rates. They found a significant relationship where bank risk-taking is measured by the bank’s internal risk rating of new loans. The result of this measure of risk-taking is very similar to the use of non-performing loans and is less pronounced for poorly capitalized banks.
All in all, these studies agreed on two things. First of all, as a consequence of low interest rates banks softened their lending standards through which firms and households were granted a loan that would not have been granted if the interest rates would have been at a normal level. Second of all, lower interest rates had a significant and negative impact on risk-taking by banks. Following this line of reasoning, the first hypothesis of this research can be formulated as:
H1: the level of the yield curve has a negative impact on the risk-taking behavior of banks
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7 2.3 Term spread and bank risk-taking
It should be noted that the aforementioned studies focused on short-term interest rates rather than long-term interest rates. Some of these studies did not find a significant relationship for long-term rates (Maddaloni and Peydró, 2011; Jiménez et al., 2013), although Delis and Kouretas (2011) do find a significant effect. However, this paper focuses on yield curve moments, that is, the combined impact of different interest rates with different maturities. Maddaloni and Peydró (2011) used the term spread as a macroeconomic control variable in their regression. They presented evidence that an increase in the term spread had a significant impact on the softening of lending standards. However, the main task of their paper was to look at the low long-term versus low short-term rates, therefore the impact of the term spread have not been studied in depth.
Mink (2011) analyzed this relation from a theoretical point of view. He stated that banks are provided with a larger borrowing cost advantage as opposed to the shareholders of the bank when engaging in maturity transformation. Since banks can borrow at a lower cost than their shareholders, financing projects with bank leverage is preferred over financing with equity. Hence, projects lean more heavily on bank leverage and banks become more risky. On top of that, Mink (2011) argues that the enhanced risk-taking behavior due to a larger term spread can be thought of as an additional element of the risk-taking channel of monetary policy, as established by Borio and Zhu (2008). This leads to the following hypothesis:
H2: the slope of the yield curve has a positive impact on the risk-taking behavior of banks
Furthermore, no prior research exists regarding the effect of the curvature of the yield curve on bank risk-taking. Consider an increasing yield curve in which interest rates are higher when maturity increases. In this case, the medium-term rates are at a lower level when the curve is convex rather than concave. This implies that rates are overall at a lower level and it was already proven that lower levels of interest rates are negatively affected with bank risk-taking. Furthermore, a more convex yield curve means higher long-term rates and lower medium rates. Hence, the maturity transformation mechanism could be more profitable in this case. Therefore, the following statement can be hypothesized:
H3: the bank risk-taking behavior of banks increases, when the yield curve becomes more convex
3.
Methodology
8 set in which bank risk-taking has been regressed on interest rates and an array of control variables. To illustrate, Delis and Kouretas (2011) used control variables concerning country-specific effects (supervisory power, capital stringency, market discipline and GDP growth) and bank-specific effects (bank size, profitability and degree of capitalization). They highlight that control variables are needed to avoid the omitted-variable bias. This means that it is likely that yield curve moments have the features of explaining some variance in the risk-taking of banks, even though it is possible that alternative variables are explanatory as well. Not including these variables could result in a model that under- or overestimates the true impact of yield curve movements on the risk-taking behavior of banks.
In contrast to Delis and Kouretas (2011), this paper does not add a set of regulatory and structural control variables to the model due to the fact that these have been used solely to control for the country-varying supervisory policies in the Euro area. Moreover, constructing these regulatory control variables for the US yielded a variable without any variance across several points in time. Another drawback is the method of constructing the variable as the survey database on bank regulation around the world by Barth, Caprio and Levine (2001, 2006 and 2008) and Čihák, Demirgüç-Kunt, Martínez Pería and Mohseni-Cheraghlou (2012) is available at four points in time only, meaning that the years in between have to be interpolated. Čihák et al. (2012) found that the financial crisis did not bring about a major change in the regulatory environment. For example, crisis countries regulated non-performing loans inadequately (Čihák et al., 2012). Additionally, they claim that regulation and supervision still needs some improvement. Therefore, the regulatory control variables are not used in this model. Then, following up on Delis and Kouretas (2011), a first representation of the empirical model can be viewed as follows:
𝑟𝑖𝑡 = 𝛼 + 𝛽1𝑦𝑡+ 𝛽2𝑏𝑖𝑡+ 𝛽3𝑚𝑡+ 𝑢𝑖𝑡 (1)
where 𝑟, the risk-taking of banks i at time t, is regressed on the bank-invariant yield curve movements, 𝑦, displayed by the factors level, slope and curvature; a set of bank-specific control variables, 𝑏; a set of macroeconomic control variables, 𝑚; a constant, 𝛼; and an error term, 𝑢. See Appendix A for a list of variables.
3.1 Fixed effects model
9 banks in the Euro area and strengthened for European banks with more untraditional activities. Additionally, Maddaloni and Peydró (2011) argued that high securitization activities by banks have magnified the softened effect of low interest rates on the lending standards of the bank. Likewise, Jiménez et al. (2013) claim that lowly capitalized banks in Spain have allocated more loans to riskier borrowers in the case of a more tolerant monetary policy environment. These results imply that bank heterogeneity has to be taken into account when regressing interest rates on bank risk-taking. This can be accomplished by keeping the bank-specific effects constant. This is displayed in Eq. (2), where 𝜆 represents the bank-fixed effects. Whether a fixed effects model is more appropriate than a random effects model will be examined with the Durbin-Wu-Hausman test4.
𝑟𝑖𝑡 = 𝛼 + 𝛽1𝑦𝑡+ 𝛽2𝑏𝑖𝑡+ 𝛽3𝑚𝑡+ 𝜆𝑖+ 𝑢𝑖𝑡 (2)
3.2 Generalized Method of Moments
The study of bank risk-taking in relation to interest rates raises two econometrical identification problems (Delis and Kouretas, 2011). In the first place, some of the control variables can be endogenous in the risk-taking decisions of banks. Besides that, the risk-taking behavior of banks is proven to be highly dynamic and persistent. A dynamic panel data model, such as the Generalized Method of Moments (GMM hereafter), takes these problems into consideration by including a lagged dependent variable and by instrumenting the endogenous control variables with its own lags (Arellano and Bover, 1995). Furthermore, Woolridge (2001) states that GMM is very useful for estimating extensions of the basic fixed effects model5. However, Roodman (2006) warns for the use of GMM without proper knowledge of when and how to use GMM. Roodman (2006) listed several basic requirements that together form the econometric environment in which GMM is most reliable and efficient.
Firstly, GMM estimations are typically used in case of a dynamic dependent variable in which current values are influenced by past realizations. According to Delis and Kouretas (2011), bank risk-taking is highly persistent. This is among other things due to the tendency for banks to invest in relationships with their borrowers, including the risky ones, which will have a persisting effect on the risk-taking. The inclusion of a lagged dependent variable on the right-hand side of the equation to control for the persistent character of bank risk is appropriate.
4
All regressions and tests will be performed with StataCorp’s Stata/SE 14.
10 Secondly, GMM favors a fixed effects panel setup allowing variation over time to be used to establish the regression coefficients. Furthermore, regarding the form of the panel data set, GMM is most efficient in case of a small time dimension and a relatively large cross-sectional dimension, meaning the panel is “small T, large N”. With 15 years and 5,471 banks, the use of GMM tends to be well-justified. Thirdly, GMM can be used to solve the endogeneity problem of certain variables by using lagged values as instruments (Arellano and Bover, 1995). Endogenous variables are assumed to be correlated with current errors and earlier disturbances but uncorrelated with future shocks and following disturbances (Delis and Kouretas, 2011). As will be explained in Section 4.4, capitalization, lagged profitability and efficiency will be viewed as endogenous in this paper. Moreover, GMM can be very helpful in the presence of predetermined variables that are not strictly exogenous, like the size of a bank. Banks are assumed to be aware of their relative size when determining the level of risk-taking (Delis and Kouretas, 2011). The use of lagged values as instruments is legitimate only when no external instruments can be found. Since many researchers (e.g., Gambacorta, 2009; Altunbas et al., 2010; Delis and Kouretas, 2011; Alessandri and Nelson, 2015) use GMM to investigate the risk-taking behavior of banks, there is reason to believe that valid external instruments are absent.
Fourthly, Woolridge (2001) points out that the fixed effects estimator assumes constant variances and no correlation across variables to ease the calculations of standard errors. Hence, if either heteroskedasticity or serial correlation exists, a GMM estimator could be more efficient than the fixed effects model (Woolridge, 2001). Accordingly, the Breusch-Pagan test of heteroskedasticity and the Woolridge test for serial correlation in the idiosyncratic errors will be performed to check if these conditions are present in the data set of this paper.
Fifthly, Roodman (2006) states that the idiosyncratic errors are uncorrelated across individual banks. Akbar and Jamilov (2015: 230) argue that this assumption is not realistic, though it can be solved when the GDP growth and the inflation rate are included in the model to cover the relevant time-effect. Then, the impact of time-specific disturbances is taken out of the idiosyncratic error term into the systematic part of the model. Since each of the foregoing requirements of Roodman (2006) has been satisfied, it can be concluded that the use of GMM is well-founded. As opposed to Eq. (2), the use of the GMM estimator alters the model as follows:
𝑟𝑖𝑡 = 𝛼 + 𝛿(𝑟𝑖,𝑡−1) + 𝛽1𝑦𝑡+ 𝛽2𝑏𝑖𝑡+ 𝛽3𝑚𝑡+ 𝑢𝑖𝑡 (3)
11 pace of convergence to the steady-state (Delis and Kouretas, 2011). A statistical value of 0 indicates a low level of persistence and a value equal to 1 suggests an environment in which adjustment to the equilibrium is very slow. Finally, a negative value would imply that convergence to the steady-state cannot be accomplished (Delis and Kouretas, 2011).
3.3 Robustness checks
Several robustness checks will be performed to make the inferences as reliable as possible. First, the data set will be divided into two periods to account for the possible effect of the financial crisis on the data. Irresberger, Mühlnickel and Weiß (2015) already found that investors’ crisis sentiment is a driver of the performance of a bank, irrespective of the size of the bank. Hence, the critical public opinion concerning the risk-taking of banks could have altered the actual risk-taking. In order to capture these uncertainties, the data set will be split up in two groups: before the crisis (2000-2006) and from the start of the crisis onwards (2007-2014). Dewally and Shao (2014) examined the effect of liquidity shocks during the financial crisis on bank lending. They defined the start of the crisis to be in the second quarter of 2007, which is the same period as the statement of Federal Reserve as mentioned in the introduction (August 2007). Since annual data of 2007 is already affected by the financial crisis, the end of the pre-crisis period in this paper is in 2006. Secondly, Delis and Kouretas (2011) discuss the “survivorship bias”, which indicates that some samples could be affected because some banks may not exist in the full period due to bankruptcy or other types of dissolution. A combined data set of active and inactive banks will be constructed to rule out this statement. Lastly, several interest rates will be used to measure the yield curve movements.
4.
Data
The financial crisis of 2007-2009 has put an emphasis on the function of US banks in the worldwide economy. The burst of the US housing bubble in 2007 and the bankruptcy of Lehman Brothers in 2008 both had a big impact on the economy and stock markets in the rest of the world. Hence, for a first step into the analysis of yield curve moments in relation to banks, the use of US data is a reasonable start. In addition, the US has a vast amount of reliable and profound information and unlike Europe, the sample is not affected by country-varying characteristics. Therefore, a large balanced panel data set of United States banks is built to perform the fixed effects model and the GMM estimation.
12 Bureau van Dijk. The measures of yield curve movements have been obtained from Thomson Reuters’ Datastream and the macroeconomic control variables GDP growth and inflation have been acquired through the database of the World Bank and the International Monetary Fund. An overview of the sources and construction of the variables can be found in Appendix A.
Bankscope offers a comprehensive search option through which different types of banks from several geographical areas can be selected. As Delis and Kouretas (2011) point out, investment banks cannot be put in the maturity transformation framework. As a result, investment banks will be excluded from the data set. Furthermore, there was an insufficient amount of data (i.e., only one bank after the selection criteria) for cooperative banks. The selection started with 13,843 active and inactive US banks. After specifying the bank type (i.e., commercial and savings banks) only 10,406 banks were left. Then, I selected banks with at least one annual value for each variable in the period 2000-2014: 9,670 active (69.8%) and inactive (30.2%) banks remained. The main part of this paper will make use of the data set with active banks only, which contains 6,747 banks that are currently in business. The final active sample has been reduced to 5,471 banks after dropping banks for which data is unavailable for at least one year. This final sample involves active commercial (90.4%) and savings (9.6%) banks in the US over the period 2000-2014. Unfortunately, Bankscope did not provide data before 2000 and data of 2015 was available for just a few banks. The total number of bank-year observations is 82,065.
Although a highly balanced data set is preferred, there is a major drawback when using active banks only. Delis and Kouretas (2011) address the “survivorship bias”. That is, banks that went bankrupt during the sample period could have defaulted due to the effect of yield curve movements on bank risk-taking. Inactive banks might have been affected more heavily by a change in the yield curve, leading to engagement in more risky portfolios and as a consequence filing for bankruptcy. On top of that, some banks were left out of the sample due to mergers or acquisitions. The statistical results could be more efficient and representative if inactive banks are included in the data set. A combined data set of active and inactive banks has been constructed to control for this, which consist of 8,394 banks with a total number of 105,727 bank-year observations.
13 4.1 Descriptive statistics and correlation
The summary statistics of all the variables are presented in Table 1. In addition, the descriptive statistics of the underlying interest rates used for the construction of the main independent variables are displayed as well. No outlier rules have been applied since no excessive values were documented. In Table 1 the bank-specific control variable size depicts the natural logarithm of total assets, hence it does not give a good representation of the true descriptive statistics of total assets, which are: a mean of 1.5 billion US dollars with a corresponding standard deviation of 31.4 billion in a range of a minimum of 0.001 billion to a maximum of 2,070 billion US dollars. Furthermore, for a first analysis of the relation between the variables, a correlation matrix is provided in Table 2. Please note that all correlation coefficients are significant. Both Table 1 and Table 2 will be explained in further detail in the next section in which the choices for the dependent, independent and control variables will be clarified.
Table 1
Descriptive statistics.
This table depicts the descriptive statistics of the regression variables. The sample includes annual data of 5,471 US banks in the period 2000-2014. Non-performing loans is the ratio of non-performing loans to gross total loans. Level is the equally weighted average of the 3 months LIBOR, 5 years treasury yield and the yield on 10 year US government bonds. Slope is the yield on 10 year US government bonds minus the 3 months LIBOR. Curvature is two times the 5 years treasury yield minus the 3 months LIBOR and the yield on 10 year US government bonds. Size is the natural logarithm of total assets. Capitalization equals equity capital divided by total assets. Profitability is measured as the share of pretax income to total assets. Efficiency is calculated as total revenue over total expenses. GDP growth is the annual growth of the real gross domestic product. Inflation is the change in consumer prices as measured by the consumer price index. Short-term rate is the 3 months LIBOR. Medium-term rate is the 5 years treasury yield. Long-term rate is the 10 years yield on US government bonds.
Variable Observations Mean Standard
deviation Minimum Maximum
14 Table 2
Correlation matrix.
This table reports correlation coefficients for all the variables used in the model. The sample includes annual data of 5,471 US banks in the period 2000-2014. Non-performing loans is the ratio of non-Non-performing loans to gross total loans. Level is the equally weighted average of the 3 months LIBOR, 5 years treasury yield and the yield on 10 year US government bonds. Slope is the yield on 10 year US government bonds minus the 3 months LIBOR. Curvature is two times the 5 years treasury yield minus the 3 months LIBOR and the yield on 10 year US government bonds. Size is the natural logarithm of total assets. Capitalization equals equity capital divided by total assets. Profitability is measured as the share of pretax income to total assets. Efficiency is calculated as total revenue over total expenses. GDP growth is the annual growth of the real gross domestic product. Inflation is the change in consumer prices as measured by the consumer price index. *, ** and *** denote significance of the correlation coefficient at the 10%, 5% and 1% levels, respectively.
NPL Level Slope Curvature Size Capitalization Profitability Efficiency GDP growth
15 4.2 Bank risk-taking
The dependent variable bank risk-taking is measured by the ratio of non-performing loans to gross loans (NPL), as this is a proxy of the most important risk of banks: credit risk (Delis and Kouretas, 2011). Some studies used the distance to insolvency, e.g., Z-scores (Laeven and Levine, 2006), to measure bank risk-taking. However, as Delis and Kouretas (2011) point out, insolvency risk is not directly related to the maturity transformation framework. Delis and Kouretas (2011) use another measure of bank risk-taking: the ratio of risky assets to total assets. The limitation of this measure is that it does not take into account the riskiness of different bonds and therefore is not able to correctly estimate the risk-taking of banks. Other studies have used the expected default frequency (Gambacorta, 2009) or the risk ratings of banks (Dell’Ariccia et al., 2013) as a proxy for bank risk-taking. These risk measures focus on future risk or default, whereas NPL is a measure of risk taken in the past. The latter introduces a major drawback of using NPL: it is possibly better at measuring risk-taking in the past instead of measuring changes in the riskiness of the bank (Delis and Staikouras, 2010). However, in their study on bank loans in the US-based Bolivian economy, Ioannidou et al. (2015) showed that a loan defaults in the median time of 4 months. With annual data, a leaded NPL ratio for one time period could be out of proportion and leading can be more reasonable with the use of quarterly data. Jiménez et al. (2013) define a loan to be non-performing when interest payments or repayments are 90 days overdue. Since non-performing loans have a negative impact on the income statement of banks, a higher value of NPL indicates that banks behaved more risky (Delis and Kouretas, 2011). As can be found in Table 1, the NPL in this sample has an average value of 1.5%. Fig. 2 displays the graph of the average NPL over the sample period. The rise of NPL in the
Figure 2
Evolution of average NPL
This figure presents the annual means of the ratio of banks’ non-performing loans to gross loans over the period 2000-2014 in the US.
16 period 2007-2011 can be addressed to the financial crisis with a peak in 2011 of 3.2%. Table 2 shows a highly significant positive correlation coefficient of 17.6% between NPL and the term spread, which supports the hypothesis of Mink (2011) as described in Section 2.3. Moreover, the correlation coefficient of NPL and level of the yield curve (-32.2%) also show the expected sign, implying that lower interest rates indeed lead to more bank risk-taking, which is in line with the first hypothesis of this paper.
4.3 Yield curve movements
The main independent variable entails three components: level, slope and curvature of the yield curve. These components have been constructed in accordance with Diebold et al. (2006). Firstly, the level of the yield curve is computed as the equally weighted average of the annual averages of the 3 months London interbank rate (LIBOR), the 5 years treasury yield rate and the yield rate on 10 years US government bonds. In this paper these rates will also be labeled as the short-, medium- and long-term rate, respectively6. The rates are obtained from Datastream. Secondly, the slope is constructed as the difference between annual averages of the long- and the short-term rate, as in Altunbas et al. (2010) and Maddaloni and Peydró (2011). Thirdly, the curvature of the yield curve is calculated as twice the annual average of the medium-rate minus the annual averages of the long- and the short-term rate. The following set of equations summarizes these calculations:
𝐿𝑒𝑣𝑒𝑙𝑡 = 13 (𝑟𝑡3𝑀+ 𝑟𝑡5𝑌+ 𝑟𝑡10𝑌) (4)
𝑆𝑙𝑜𝑝𝑒𝑡= 𝑟𝑡10𝑌− 𝑟𝑡3𝑀 (5)
𝐶𝑢𝑟𝑣𝑎𝑡𝑢𝑟𝑒𝑡= 2𝑟𝑡5𝑌− 𝑟𝑡10𝑌− 𝑟𝑡3𝑀 (6)
where 𝑟𝑡3𝑀, 𝑟𝑡5𝑌 and 𝑟𝑡10𝑌 are the short-, medium- and long-term interest rate at time t, respectively. A
positive value for curvature is associated with a concave yield curve. Since a decreasing curvature value makes the yield curve more convex, a negative relation is expected between curvature and NPL. This is supported by the correlation coefficient of -5.9%. Table 2 shows correlation coefficients higher than acceptable levels between the three components. Also, the variance inflation factor test, which is a measure of multicollinearity, shows values higher than the acceptable level of 10 (Kutner, Nachtsheim and Neter, 2004: 927). Therefore, in modelling bank risk-taking the three yield curve factors enter the
6
17 equation separately. In addition, regressions using only the short-term interest rate (3 months LIBOR) have been performed in order to better compare the results to previous research. To further analyze the yield curve movements, Appendix B provides a view at the change over time for every component in relation to NPL. The increase of NPL from 2007 to 2009 can be assigned to the freefall of the short-term interest rate in this period. After 2009, the short-term interest rate remained close to zero, however the medium-term and long-term interest rate continue to fall, which is reflected by the decreasing level factor of the yield curve. Overall, the level of the yield curve seems to be the most important factor in explaining the risk-taking of banks, which is in accordance with Litterman and Scheinkman (1991) and Diebold et al. (2006).
4.4 Control variables
18 is estimated by the ratio of total revenue to total expenses. Banks with better efficiency ratios are assumed to have better software and other diversification techniques. These tools might give more efficient banks an advantage in managing risks (Delis and Kouretas, 2011). Efficiency is assumed to be an endogenous variable due to the fact that higher risk-taking can result in higher interest income, hence a higher efficiency ratio.
Furthermore, at the country-level, two macroeconomic control variables are included in the model. The macroeconomic data has been retrieved from the database of the World Bank. First of all, the annual growth rate of the real GDP represents the change in the economic environment. When the economic circumstances are more favorable, the credit risk of banks shrinks since an increasing amount of project has a higher possibility of becoming profitable (Kashyap, Stein and Wilcox, 1993). This is endorsed by the negative correlation coefficient of -14.0% between GDP growth and NPL. In addition, inflation, estimated by the change in consumer prices as measured by the consumer price index, is covered in the model. The negative correlation of -18.8% with NPL is in line with Maddaloni and Peydró (2011).
5.
Results
This section provides the main results of the analysis of the yield curve movements on bank risk-taking. First the fixed effects model (FE) of Eq. (2) is estimated and the GMM estimation of Eq. (3) is carried out thereafter. Lastly, additional checks have been performed to make the results more robust.
5.1 Fixed effects results
Firstly, the results of the simple OLS regressions can be found in Appendix C. The OLS output shows that incorporation of the control variables did not alter the significance and sign of the main independent variables. Secondly, to control for the unobserved bank heterogeneity as described in Section 3.1, a fixed effects and random effects model were employed. Then, the Durbin-Wu-Hausman test indicated that the fixed effects model would be more appropriate7. Therefore, the use of a fixed effects model is both theoretically and empirically justified. The results of the fixed effects model can be found in Table 3. Thirdly, the Breusch-Pagan test of heteroskedasticity was performed and the null hypothesis of homoskedasticity was rejected8. Fourthly, the Woolridge test for serial correlation9 showed that serial
7
Hausman test-statistic 𝜒2 = 738.1, with a corresponding p-value of 0.000. 8
19 correlation is indeed present in the data set. Not controlling for heteroskedasticity leads to an inefficient and biased estimation (White, 1980). According to Rogers (1993), in the situation of both heteroskedasticity and serial correlation, standard errors clustered on the panel identifier (i.e., banks) give consistent results. Consequently, the Rogers or clustered standard errors are adopted in regressions 1 to 4. The dependent variable in these regressions is the non-performing loans ratio. Regression 1 Table 3
Fixed effect regression results.
This table presents regression results of the effect of yield curve movements and a set of control variables on bank risk-taking, measured by the ratio of non-performing loans to gross loans. The sample includes annual data of 5,471 US banks in the period 2000-2014. Short interest rate is the 3 months LIBOR. Level is the equally weighted average of the 3 months LIBOR, 5 years treasury yield and the yield on 10 year US government bonds. Slope is the yield on 10 year US government bonds minus the 3 months LIBOR. Curvature is two times the 5 years treasury yield minus the 3 months LIBOR and the yield on 10 year US government bonds. Size is the natural logarithm of total assets. Capitalization equals equity capital divided by total assets. Lagged profitability is measured as the delayed share of pretax income to total assets. Efficiency is calculated as total revenue over total expenses. GDP growth is the annual growth of the real gross domestic product. Inflation is the change in consumer prices as measured by the consumer price index. Bank-clustered standard errors are provided in parentheses. Adjusted R-squared measures the percentage of variance of the dependent variable that is explained by the variance of the model. F-statistic denotes the goodness of fit. *, ** and *** denote significance of the coefficient at the 10%, 5% and 1% levels, respectively.
Variables (1)
Short interest rate
(2) Level (3) Slope (4) Curvature
20 considers the short-term interest rate as main independent variable, followed by the level factor of the yield curve in regression 2, the slope in regression 3, and curvature in regression 4. Firstly, with respect to the results in Table 3, regression 1 and 2 present the expected negative signs for the short-term interest rate and the level factor, respectively. Hence, the short-term interest rate and the level factor are both negatively related to bank risk-taking, which is in line with the theoretical explanations of Rajan (2006) and Borio and Zhu (2008) that lower interest rates incentivize banks to engage in more risky behavior in search for yield. Moreover, these results conform to the empirics of for example Gambacorta (2009), Altunbas et al. (2010) and Dell’Ariccia et al. (2013). Secondly, in regression 3, the coefficient of the slope of the yield curve is highly significant and positive, meaning that an increase of the term spread of 1% causes the NPL ratio to increase by approximately 0.307%. This outcome justifies the theoretical considerations of Mink (2011) and is in line with the results of Maddaloni and Peydró (2011). Hence, the maturity transformation principle appears to encourage banks to engage in more risky lending activities. Lastly, in regression 4 the curvature of the yield curve seems to influence the risk-taking behavior of banks significantly as well. The negative sign implies that a more convex yield curve could lead to more bank risk-taking. Convexity indicates a lower medium rate in contrast to the long-term rate, meaning banks have even more opportunities to engage in maturity transformation. It can be concluded that the yield curve factors have a significant impact on the risk-taking of banks. Until recently, only the level of short interest rates was found to provoke more risky behavior, however this paper adds the importance of the level, slope and the curvature factor. Hence, the Federal Reserve System of the US should take the effect of all three yield curve movements on bank risk-taking into account when forming their monetary policy, rather than solely the effect of a low interest rate environment as suggested by Delis and Kouretas (2011).
21 Kouretas (2011). Moreover, more efficient banks appear to behave less risky due to their ability to manage risks more adequately, which is in accordance with Delis and Kouretas (2011). Finally, the macroeconomic controls present significant coefficients in all specifications. The negative sign of GDP implies that a growing economic environment decreases the NPL ratio. This can be due to a growing amount of projects that becomes successful in an environment with expanding GDP levels (Gambacorta, 2009). Next to GDP, the regression shows a positive effect of the inflation rate on bank risk-taking.
5.2 GMM results
Although the fixed effects estimator gives the expected results of the yield curve factors, it does not take into account the dynamic character of bank risk and the endogeneity of certain control variables. As explained in Section 3.2, a Generalized Method of Moments (GMM) estimation as presented by Arellano and Bover (1995) and Blundell and Bond (1998) resolves these econometrical issues. The GMM model is estimated in Stata via the user-written program xtabond2 of Roodman (2006). The one-step estimator is used in this paper since it provides smaller standard deviations and a smaller bias than the two-step procedure (Athanasoglou, Brissimis and Delis, 2008). Table 4 presents the results of the GMM model. All GMM estimations contain three tests: a test for first order serial correlation (AR(1)), a test for second order serial correlation (AR(2)) and the Hansen test of overidentifying restrictions. The first two are performed to ensure that there are enough lags of the dependent variable in the model to account for the dynamic character of bank risk (Wintoki, Linck and Netter, 2012). Since only one lag is included, the p-value of AR(1) should be lower than the significance level of 10% to reject the null hypothesis of no first order serial correlation. Subsequently, the p-value of AR(2) should not reject the null hypothesis of second order serial correlation. Then, the Hansen test of overidentifying restrictions tests the validity of the moment conditions and can be performed when multiple lags are used as instruments for the endogenous variables (Wintoki et al., 2012). According to Roodman (2006), the Hansen test should not be given too much attention, since the test weakens in the presence of more moment conditions. Lastly, based on Roodman (2006), for the endogenous variables (capitalization, efficiency and lagged profitability) lags two and up are used and for the predetermined variable (size) also lag one is included.
22 Table 4
Generalized Method of Moments (GMM) estimation results.
This table presents regression results of the effect of yield curve movements and a set of control variables on bank risk-taking, measured by the ratio of non-performing loans to gross loans. The sample includes annual data of 5,471 US banks in the period 2000-2014. Short interest rate is the 3 months LIBOR. Level is the equally weighted average of the 3 months LIBOR, 5 years treasury yield and the yield on 10 year US government bonds. Slope is the yield on 10 year US government bonds minus the 3 months LIBOR. Curvature is two times the 5 years treasury yield minus the 3 months LIBOR and the yield on 10 year US government bonds. Size is the natural logarithm of total assets. Capitalization equals equity capital divided by total assets. Lagged profitability is measured as the delayed share of pretax income to total assets. Efficiency is calculated as total revenue over total expenses. GDP growth is the annual growth of the real gross domestic product. Inflation is the change in consumer prices as measured by the consumer price index. Wald-test denotes the goodness of fit of the regressions. AR(1) and AR(2) are the tests for the first and second-order serial correlation. Hansen stands for the test of overidentifying restrictions. Bank-clustered standard errors are provided in parentheses. *, ** and *** denote significance of the coefficient at the 10%, 5% and 1% levels, respectively.
Variables (1)
Short interest rate
(2) Level (3) Slope (4) Curvature
23 behavior of banks too, as explained in Section 2. Furthermore, the relatively high coefficient of lagged NPL indicates that adjustment to the steady state is very slow. Hence, the environment of bank risk-taking is highly persistent, which is in line with the results of Delis and Kouretas (2011). Adding another lag of NPL resulted in a negative coefficient, therefore no persistence was found further than one year in the past. Due to the dynamics of bank risk-taking the sign of the size of a bank became negative, meaning large banks are more risk-averse (Delis and Kouretas, 2011). The effect is however extremely small. In contrast to the fixed effects results, efficiency lost its significance. It can be concluded that the role of the bank-specific control variables is neither significant nor important. This suggests that bank characteristics do not play a role in determining the level of bank risk-taking, which is in contrast to what was expected based on existing literature. Whether these relations are affected by for example the financial crisis will be explored in the next section.
5.3 Robustness checks
The first robustness check concerns the effect of the crisis. Appendix D displays the fixed effects regressions of the short interest rate and the yield curve components, where each regression has been performed twice: in the period before the crisis (pre: 2000-2006) and from the crisis onwards (2007-2014). All regressions account for unobserved heterogeneity and have bank-clustered standard errors in order to solve the heteroskedasticity and serial correlation issues. Three major differences between the two periods can be distinguished. Foremost, the effects become stronger in the second period, which implies that banks partook in even riskier behavior due to the crisis. Secondly, the bank control variables turn into significant explanatory variables of bank risk-taking in the second period. It seems that banks became more aware of their characteristics as a result of the crisis and integrated these aspects into their lending policies. Thirdly, the influence of the macroeconomic control variables changed from a negative to a positive relation in the second period. According to Dewally and Shao (2014), banks grant more loans in a growing economic climate. All in all, the sign and significance level of the short-term interest rate, the level and the slope factor do not change. However, the coefficient of the curvature component of the yield curve is strongly positive in the period 2007-2014, meaning that a more concave yield curve enhances the risk-taking of banks. This could imply that maturity transformation between medium-term loans and short-term deposits has become more alluring due to the crisis.
24 and this could lead to contradicting inferences. Appendix E exhibits the regressions of a data set with both active and currently inactive banks. Again, all regressions include bank-clustered standard errors. Regressions 1, 3, 5 and 7 are performed with solely inactive banks, whereas regressions 2, 4, 6 and 8 are carried out combining both active and inactive banks. The results are robust to the results of the active data set in Table 3. Therefore, it can be concluded that the survivorship bias is not applicable to the sample in this paper.
After analyzing the output of Table 3 and 4, it is clear that the model cannot explain the sharp increase of NPL (0.8% in 2007 to 3.2% in 2011) during the crisis. A variable is missing which is able to account for the financial turmoil and which influences the ability of people to pay off their loans. Due to the financial crisis many companies defaulted and people lost their jobs, which resulted in people not being able to pay off their loans anymore. Therefore, adding the unemployment rate might result in different outcomes. The similarities in the graphs of the unemployment rate and the mean of NPL over time in Appendix F support the expected positive relation. The seasonally adjusted unemployment rate is measured as the number of unemployed people as a percentage of the total labor force and has been obtained from the US Bureau of Labor Statistics.
25 (2011) and Ioannidou et al. (2015) since they did not control for the unemployment rate. Nevertheless, a legitimate explanation of these altered results is still missing and needs to be studied more thoroughly.
6.
Conclusion
The main objective of this paper is to examine the impact of the level, the slope and the curvature of the yield curve on the risk-taking of banks. The low level of interest rates after 9/11 and the financial crisis of 2007-2009 triggered many researchers to investigate the effect of a low level of interest rates on the risk-taking behavior of banks. This has been initiated by Borio and Zhu’s (2008) seminal paper about the “risk-taking channel of monetary policy”. Various papers, including Delis and Kouretas (2011), have found evidence for the existence of this channel, however few studied the impact of the combined effect of interest rates on risk-taking, which can be proxied by the yield curve. Mink (2011), for example, states that banks take on more risk when the slope of the yield curve steepens. Furthermore, according to Litterman and Scheinkman (1997) and Diebold et al. (2006) the movements and variance of the yield curve can be explained by three factors: the level, slope and curvature. Consequently, this paper made a first step in examining the effect of the slope, the level and the curvature of the yield curve on bank risk-taking. In order to meet the objectives of this study, a large panel data set of 5,471 active US banks is constructed over the period 2000-2014, which resulted in a total of 82,065 bank-year observations. The regression model contains the three yield curve factors and a set of bank-specific and macroeconomic control variables. The dependent variable bank risk-taking is measured by the ratio of non-performing loans to gross loans, as in Delis and Kouretas (2011) and Ioannidou et al. (2015). First, a fixed effects regression dealt with the unobserved bank heterogeneity problem. Then, a GMM estimation accounted for heteroskedasticity, serial correlation, the endogeneity of bank-specific control variables and the persistent character of bank risk-taking.
26 level and slope factor change in an unexpected way. Similarly, the curvature factor is not robust to the effect of the crisis. This needs to be considered when interpreting the results of this paper. Likewise, the results of Delis and Kouretas (2011) and Ioannidou et al. (2015) could be biased since they did not control for the unemployment rate.
The significant relation of the yield curve and the risk-taking of banks again confirms the existence of Borio and Zhu’s (2008) risk-taking channel of monetary policy. Most papers found evidence in the years preceding the crisis, however this paper also found proof in the years 2007-2014. The effect of interest rates appears to have become even stronger. It can be concluded that the Federal Reserve System did not take into account the risk-taking of banks when forming their monetary policy, although some lessons could have been learned from the pre-crisis period. Furthermore, the results of this paper suggest that next to the level of interest rates, the Federal Reserve should also consider the slope and to a lesser extent the curvature of the yield curve when forming their monetary policy.
27 Appendix A Overview of variables
Table 5
Overview of variables
This table provides a clear overview of the measurement, source and assumptions of the variables in this paper.
Variable Measurement Source Assumptions
Dependent
Non- performing loans (NPL)
The ratio of non-performing loans to gross total loans
Own calculation on the basis of Bankscope data
Independent
Short-term interest rate
Annual average of the 3 months LIBOR* Own calculation on the basis of Datastream data
Exogenous Level The equally weighted average of the 3 months
LIBOR, 5 years treasury yield and the yield on 10 year US government bonds*
Own calculation on the basis of Datastream data
Exogenous
Slope The difference between the yield on 10 year US government bonds and the 3 months LIBOR*
Own calculation on the basis of Datastream data
Exogenous Curvature Two times the 5 years treasury yield minus the 3
months LIBOR and the yield on 10 year US government bonds*
Own calculation on the basis of Datastream data
Exogenous
Control
Size The natural logarithm of total assets Own calculation on the basis of Bankscope data
Predetermined Capitalization The ratio of equity capital to total assets Own calculation on the
basis of Bankscope data
Endogenous Profitability The ratio of profits before tax to total assets Own calculation on the
basis of Bankscope data
Lagged once and endogenous Efficiency The ratio of total revenue to total expenses Own calculation on the
basis of Bankscope data
Endogenous GDP growth The annual growth of the real gross domestic
product (GDP)
World Bank national accounts data
Exogenous Inflation The change in consumer prices as measured by the
consumer price index
International Monetary Fund via the World Bank
Exogenous Unemployment
rate
The number of unemployed people as a percentage of the total labor force, seasonally adjusted
US Bureau of Labor Statistics
Exogenous * All interest rates are annual averages
28 Appendix B Dynamics of NPL and yield curve factors
Figure 3
Development of yield curve components and NPL
This figure presents the annual means of the ratio of banks’ non-performing loans to gross total loans over the period 2000-2014 in the US and the annual values of the computed level, slope and curvature components of the yield curve. Level is the equally weighted average of the 3 months LIBOR, 5 years treasury yield and the yield on 10 year US government bonds. Slope is the yield on 10 year US government bonds minus the 3 months LIBOR. Curvature is two times the 5 years treasury yield minus the 3 months LIBOR and the yield on 10 year US government bonds.
29 Appendix C OLS regressions with and without control variables
Table 6
OLS regression results with and without controls.
This table presents regression results of the effect of yield curve movements on bank risk-taking, measured by the ratio of non-performing loans to gross total loans. The sample includes annual data of 5,471 US banks in the period 2000-2014. Short interest rate is the 3 months LIBOR. Level is the equally weighted average of the 3 months LIBOR, 5 years treasury yield and the yield on 10 year US government bonds. Slope is the yield on 10 year US government bonds minus the 3 months LIBOR. Curvature is two times the 5 years treasury yield minus the 3 months LIBOR and the yield on 10 year US government bonds. Robust standard errors are provided in parentheses. Adjusted R-squared measures the percentage of variance of the dependent variable that is explained by the variance of the model. F-statistic denotes the goodness of fit. *, ** and *** denote significance of the coefficient at the 10%, 5% and 1% levels, respectively.
Variables (1) Short rate (2) Short rate (3) Level (4) Level (5) Slope (6) Slope (7) Curvature (8) Curvature
30 Appendix D Fixed effects regressions in different time periods
Table 7
Regression results in different time periods.
This table presents regression results in the years before the crisis (pre: 2000-2006) and during and after the crisis (post: 2007-2014) of the effect of yield curve movements and a set of control variables on bank risk-taking, measured by the leaded value of the ratio of non-performing loans to total loans. The sample includes annual data of 4938 US banks in the period 2000-2014. Level is the equally weighted average of the 3 months LIBOR, 5 years treasury yield and the yield on 10 year US government bonds. Slope is the yield on 10 year US government bonds minus the 3 months LIBOR. Curvature is two times the 5 years treasury yield minus the 3 months LIBOR and the yield on 10 year US government bonds. Size is the natural logarithm of total assets. Capitalization equals equity capital divided by total assets. Lagged profitability is measured as the delayed share of pretax income to total assets. Efficiency is calculated as total revenue over total expenses. GDP growth is the annual growth of the real gross domestic product. Inflation is the change in consumer prices as measured by the consumer price index. Bank-clustered standard errors are provided in parentheses. Adjusted R-squared measures the percentage of variance of the dependent variable that is explained by the variance of the model. F-statistic denotes the goodness of fit. *, ** and *** denote significance of the coefficient at the 10%, 5% and 1% levels, respectively.
Variables (1) Short rate Pre (2) Short rate Onwards (3) Level Pre (4) Level Onwards (5) Slope Pre (6) Slope Onwards (7) Curvature Pre (8) Curvature Onwards
31 Appendix E Fixed effects regressions including inactive banks
Table 8
Regression results including inactive banks.
This table presents regression results of the effect of yield curve movements and a set of control variables on bank risk-taking, measured by the leaded value of the ratio of non-performing loans to total loans. Two samples are compared: one with inactive banks only and one with both active and inactive banks. The inactive sample includes annual data of 2,883 US banks in the period 2000-2014. The combined set consists of 8,354 US banks. Level is the equally weighted average of the 3 months LIBOR, 5 years treasury yield and the yield on 10 year US government bonds. Slope is the yield on 10 year US government bonds minus the 3 months LIBOR. Curvature is two times the 5 years treasury yield minus the 3 months LIBOR and the yield on 10 year US government bonds. Size is the natural logarithm of total assets. Capitalization equals equity capital divided by total assets. Lagged profitability is measured as the delayed share of pretax income to total assets. Efficiency is calculated as total revenue over total expenses. GDP growth is the annual growth of the real gross domestic product. Inflation is the change in consumer prices as measured by the consumer price index. Bank-clustered standard errors are provided in parentheses. Adjusted R-squared measures the percentage of variance of the dependent variable that is explained by the variance of the model. F-statistic denotes the goodness of fit. *, ** and *** denote significance of the coefficient at the 10%, 5% and 1% levels, respectively. Variables (1) Short rate Inactive (2) Short rate Combined (3) Level Inactive (4) Level Combined (5) Slope Inactive (6) Slope Combined (7) Curvature Inactive (8) Curvature Combined
32 Appendix F Dynamics of NPL and unemployment rate
Figure 4
Evolution of mean NPL and unemployment rate
This figure presents the unemployment rate next to the annual means of the ratio of banks’ non-performing loans to gross total loans over the period 2000-2014 in the US. Unemployment is the number of unemployed people as a percentage of the total labor force.
33 Appendix G Fixed effects and GMM regressions including the unemployment rate
Table 9
Fixed effect (FE) and Generalized Method of Moments (GMM) regression results with unemployment.
This table presents regression results of the effect of yield curve movements and a set of control variables on bank risk-taking, measured by the ratio of non-performing loans to gross loans (NPL). The sample includes annual data of 5,471 US banks in the period 2000-2014. Short interest rate is the 3 months LIBOR. Level is the equally weighted average of the 3 months LIBOR, 5 years treasury yield and the yield on 10 year US government bonds. Slope is the yield on 10 year US government bonds minus the 3 months LIBOR. Curvature is two times the 5 years treasury yield minus the 3 months LIBOR and the yield on 10 year US government bonds. Size is the natural logarithm of total assets. Capitalization equals equity capital divided by total assets. Lagged profitability is measured as the delayed share of pretax income to total assets. Efficiency is calculated as total revenue over total expenses. GDP growth is the annual growth of the real gross domestic product. Inflation is the change in consumer prices as measured by the consumer price index. Unemployment is the number of unemployed people as a percentage of the total labor force. Standard errors are provided in parentheses. Adjusted R-squared measures the share of variance of NPL that is explained by the variance of the model. F-statistic (with FE) and Wald-test (with GMM) denote the goodness of fit of the regressions. AR(1) and AR(2) are the tests for the first and second-order serial correlation. Hansen stands for the test of overidentifying restrictions. *, ** and *** denote significance of the coefficient at the 10%, 5% and 1% levels, respectively.
Variables (1) Short rate FE (2) Short rate GMM (3) Level FE (4) Level GMM (5) Slope FE (6) Slope GMM (7) Curvature FE (8) Curvature GMM
34
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