Bank Profitability and Risk-Taking under Low Interest Rates

The aim of this paper is to investigate the impact of the unusually low interest rate environment on the soundness of the US banking sector in terms of profitability and risk-taking. Using both dynamic and static modeling approaches and various estimation techniques, we find that the low interest rate environment indeed impairs bank performance and compresses net interest margins. Nonetheless, banks have been able to maintain their overall level of profits, due to lower provisioning, which in turn may endanger financial stability. Banks did not compensate for their lower interest income by expanding operations to include trading activities with a higher risk exposure.


Introduction
Since the start of the financial crisis, concerns have arisen about the soundness of the financial sector. The current macroeconomic conditions and the unseen low interest rates present a challenging environment for financial institutions. Due to weak economic growth and lower expected real returns on investment, interest rates have been falling since the early 2000's all over the world. Moreover, as central banks attempt to meet their inflation target levels in order to ameliorate the economic conditions, an expansionary monetary policy has been exercised in the US, Europe and Japan, maintaining short-term policy rates at near zero levels. By means of large-scale asset purchases, the long-term interest rates have fallen to historically low levels too. Firstly, this paper aims to contribute to the literature by further exploring the relationship between bank profitability and the low interest rate environment. It is generally supposed that, in the long term, falling interest rates have a negative effect on bank profits. At first glance, banks might be able to compensate for lower lending rates by correspondingly lowering their funding rates. However, the funding rate is constrained to a zero lower bound, as customers are not expected to accept a negative deposit interest rate.
Profit margins are squeezed along with the net interest margin, and as bank profits largely determine bank capital, lower profit margins could put pressure on the bank's capital position and thereby on its solvancy. This should also be seen in light of the increasing stringency of capital requirements under Basel 3.5.
Secondly, the issue of bank risk-taking will be addressed. Banks may have increased their risk appetite due to the low interest rate environment, yet the extent to which banks increase their risk exposure through risky investments in search for higher profits is hardly investigated. Thus far, this potential development has merely been suggested by, e.g., Weistroffer (2013) and Genay & Podjasek (2014). In the short run banks may benefit from lower loan loss provisions as a result of a reduced default probability on outstanding loans due to low interest rates for lenders. In the medium term, low interest rates might trigger banks to lower their lending standards which could cause a deterioration in the quality of the loan portfolio, raising credit risk. This paper explores the impact of the low interest rate environment on both bank profitability and bank risk-taking by analyzing a dynamic panel model which considers persistence effects, bank-specific and macroeconomic determinants, as well as the interest rate environment. In order to account for the dynamic structure and the potential endogeneity, a system GMM estimator is used. Alternatively, a static modeling approach is employed to expose relationships of interest.
The remainder of this paper is structured as follows: the next section provides an overview of the literature on determinants of bank profitability and on risk-taking behavior of banks. Section 3 presents the data and the relevant variables for the empirical study on the US banking sector. Also, the initial models are specified. Section 4 describes the methodology and the econometric techniques used to estimate these models in search for consistent and reliable estimates. Subsequently, the empirical results are presented, interpreted and discussed. Section 6 provides a conclusion.

Bank profitability
Identifying the determinants of bank profitability is an important field of research. Demirgüç-Kunt & Huizinga (1999) were among the first to explain differences in bank profitability and net interest margins. Athanasoglou et al. (2008) made the popular, more parsimonious decomposition of determinants into bank-specific, industry-specific and macro economic categories. They adopted a dynamic model and found significant profit persistence. Many papers take this profit persistence into account in accordance with Firstly, numerous bank-specific factors may affect the profits of a bank. Commonly used variables are size, bank capital, the level of (credit) risk, lending, revenue diversification, the business model or type of bank, efficiency and shares of publicly owned banks, see Athanasoglou et al. (2008). Based on the existing literature, this paper illustrates how these bank-specific factors affect bank profitability. Trujillo-Ponce (2013) find an insignificant effect and suggest a non-linear relationship such that profitability initially increases with size and then declines. Berger et al. (1994) remark on the consensus in the literature that the average cost curve in banking has a relatively flat U-shape with medium-sized banks being slightly more scale efficient than either large or small banks. Others such as Shehzad et al. (2013) find that larger banks are more profitable than small banks, but grow at a slower pace. Larger banks may benefit from economies of scale while smaller banks may try to grow faster at the expense of their profitability.
Capital: Bank capitalization, measured as the ratio of equity to assets, is another factor influencing bank profitability. Relying on the effects of the Basel Accords which require banks to have a minimum level of capital as a percentage of risk-weighted assets (RWA), Iannotta et al. (2007) state that higher capital levels may denote banks with riskier assets. This at least holds for a given RWA leverage ratio, i.e. the ratio of capital to RWA. Through higher returns, higher capital ratios could yield higher profits. Athanasoglou et al. (2008) found a positive relationship as bank capital acts as a safety net in the case of adverse developments, so they can maintain their profitability in economically difficult times. Generally, empirical evidence suggests a positive relationship between capital and profitability, see also Demirgüç-Kunt & Huizinga (1999), Borio et al. (2015) and ECB (2015).
Credit risk: Bikker & Hu's (2002) finding that higher credit risk exposure via loans is associated with lower profit margins is widely validated in the literature. Higher credit risk directly affects profits as the amount of provisioning for expected loan losses is deducted from net profits. In the medium term, a lower quality of the loan portfolio also reduces profits as loan losses are actually incurred. Credit risk is found to be pro-cyclical (Bikker & Hu [2002]) and asymmetric (Marcucci & Quagliariello [2009]): during economic downturns, this cyclical effect is even more pronounced. Hence, credit risk and thus the higher level of provisioning has a negative impact on bank profitability, see Athanasoglou et al. (2008) and ECB (2015) as well.
Lending: The ratio of total loans over total assets represents a bank's relative lending size. A larger loan portfolio generates the vast majority of net interest income, obviously determining profit positively, but is also subject to higher credit risk which may, in turn, deteriorate profits. Based on empirical evidence, ECB (2015), Dietrich & Wanzenried (2011) and Trujillo-Ponce (2013) find that, on balance, lending positively affects profitability. Bikker & Hu (2002) find that lending is pro-cyclical and that banks with higher profits will lend more generously.
Diversification describes the ratio of non-interest income over total income. Non-interest income is generated via fee and commission income or trading activities. Stiroh (2004), Demirgüç-Kunt & Huizinga (1999) and ECB (2015) found that greater reliance on non-interest income is associated with weaker bank profitability. The converse has been found by Dietrich & Wanzenried (2011) in the case of Swiss banks and by Elsas et al. (2010) who argue that non-interest businesses yield higher margins and thus enhance profitability. Related to lending and diversification, Roengpitya et al. (2014) identify three different business models by classifying balance sheet compositions and find that profitability and efficiency vary markedly across business models and over time.
A second class of profitability determinants described by Athanasoglou et al. (2008) are those specific to the industry. Herewith, two factors are commonly considered.
Ownership, the shares of publicly-owned banks. Empirically, no clear relationship with profitability is found: Bourke (1989) and Molyneux & Thornton (1992) even claim that this variable is unimportant in explaining profitability.
Concentration, as measured by the Herfindahl-Hirschman index (HHI), is frequently studied by means of two theoretical models. On the one hand, the structure-conduct-performance hypothesis states that highly concentrated markets positively impact bank profitability through greater market power and therewith the ability to charge relatively high rates for loans and low rates for deposits. Empirical evidence for the structure-conduct-profit hypothesis is found in Goddard et al. (2004) for Europe. On the other hand, the efficient-structure theory claims that greater market shares are gained from higher efficiency which increases profitability, see Berger (1995). Athanasoglou et al. (2008), Berger (1995) and Garca-Herrero et al. (2009) do not find a clear relationship between sector concentration and bank profitability, leaving room for the efficiency-structure hypothesis.
Thirdly, the macroeconomic environment is greatly determinative for bank profitability. The business cycle, as approximated by real GDP growth, has a significantly positively impact on profitability, see Demirgüç-Kunt & Huizinga (1999), Albertazzi & Gambacorta (2009) and Bikker & Hu (2002). This pro-cyclicality of bank profits is mainly explained by the influence of the business cycle on lending and provisioning, see Bikker & Hu (2002). In favorable economic conditions, the demand for credit by households and firms is higher, which improves the profitability of traditional interest practices. Bolt et al.
(2012) also link bank profits and economic activity, detecting that the pro-cyclicality is stronger in deep recessions than under normal conditions. Furthermore, in economic booms the level of credit risk is estimated to be lower, and the quality of the lending portfolio is considered to be higher, which lowers credit loss provisions and directly boost profits. Marcucci & Quagliariello (2009) describes the asymmetric relationship of the business cycle and bank credit risk. Athanasoglou et al. (2008) also find an asymmetric effect: only in the upper phase of the business cycle this pro-cyclicality effect is found to be significant.
They also note that net provisioning is a large source of the variability in profits.
Inflation also reflects aspects of the business cycle. Generally, empirical evidence asserts a positive inflation impact on profits, but this coefficient is difficult -if not impossible -to interpret. Demirgüç-Kunt & Huizinga (1999), for instance, find a positive relationship between inflation and net interest margin, giving the interpretation that high inflation translates into higher income from bank float. Besides, as policymakers only have the nominal interest rate in hand, inflation is determinative for the resulting real interest rates. In fact, inflation directly and indirectly affects profitability. Conflicting theories exist and for a full discussion Perry (1992) should be consulted.

Bank profitability and interest rates
The interest rate levels are also part of the macroeconomic environment. The short and long-term interest rate as well as the slope of the yield curve determine bank profitability. The existing bank profit literature mainly considers these factors as a by-product, such as Borio et al. (2015). The literature on monetary policy provides more detailed analyses on the impact of low interest rates, because the nominal interest rate is the main instrument central banks possess to stimulate the economy. So, it is important to take this field of research into consideration. Borio et al. (2015) investigated the influence of monetary policy on bank profitability. They analyzed the effect of interest rates on the different profit components, i.e. net interest income, non-interest income and the level of provisions, as well as on overall profitability, as measured by return on assets. Firstly, net interest income increases with short-term interest rates (which act as proxy for all interest rates). Also, a positive relationship with the slope of the yield curve is found, which corresponds to the findings of Albertazzi & Gambacorta (2009). The relationship is found to be concave, both for interest rates a yield curve slope, so the effect is even more pronounced when interest rates are at low levels. Secondly, Borio et al. (2015) find that higher interest rates lower non-interest income. The short-term interest rate and the yield curve slope both have a positive effect on loan loss provisions. Again, Albertazzi & Gambacorta (2009) arrive at a similar result. Ultimately, the positive effects of interest rate and the slope of the yield curve on net interest income more than offsets the negative effects on non-interest income and provisions. Hence, the effect of higher interest rates on overall profitability is found to be positive and concave. This concave relationship is especially alarming as the present, almost zero interest rates and the flat yield curve have an amplified negative impact on overall profitability. Bolt et al. (2012) is closely related to Borio et al. (2015). They also find that the effect of the short-term interest rate and the slope of the yield curve for loan loss provisions is positive. However, the other effects differ. They conclude that the short-term interest rate negatively affects net interest income (for long-term interest rate, however, they do find a positive effect). For the non-interest income an insignificant effect of short-term interest rate is found.
Alessandri & Nelson (2015) find evidence of a systematic effect of market interest rates on bank profitability. The net interest margin increases with the short-term interest rate. In response to higher interest rates, banks raise their lending rates and reduce their lending volume, potentially by strengthening their lending standards (this will be addressed in the following subsection), and vice versa. Regarding the yield curve, it is found that a steep yield curve boosts bank income margins, evidently as banks borrow short and lend long. An interesting point in Alessandri & Nelson (2015) is that banks in their UK sample take positions in interest rate derivatives. This follows from the finding that the level of interest rates and yield curve slope affect the net interest margin and trading income in opposite directions. English (2002) addresses the issue of interest rate risk and net interest margins by inspecting interest rate volatility. He expects that a steeper term structure increases net interest margins and that interest rate volatility negatively affects net interest margins. A popular explanation is that maturity mismatch and repricing frictions are responsible for squeezed profits.
Since December 2008, the Federal Open Market Committee kept its short-term policy rate at nearly zero. This was combined by large-scale asset purchases aimed at lowering long-term interest rates and boosting economic activity. Genay & Podjasek (2014) examined the impact on bank profitability of this low interest rate environment, caused by expansionary monetary policy. In line with the previously mentioned papers as well as Demirgüç-Kunt & Huizinga (1999), a positive effect of short-term interest rates on the net interest margin is found. This effect is stronger for smaller banks. Although their analysis suggest that low short-term interest rates and a flat term structure squeeze profits, they propose that the net effect of low interest rates on profits turns out to be positive because of the positive contribution to the business cycle.
Apparently, the macroeconomic environment carries a higher weight in determining profitability.
Additionally, Genay & Podjasek (2014) suggest that banks were able to compensate the negative low interest rates effect on profits by altering their business practices, potentially through higher fee income and lowering loan loss provisions. A correlation in the above two channels of risk-taking can be considered, as Delis & Kouretas (2011) found that banks engaging in more non-traditional activities, i.e. higher risk exposure, also tend to take on higher risks in their traditional activities, i.e. higher level of credit risk.

Data
We collect data on all US commercial and savings bank insured by the Federal Deposit Insurance Corporation (FDIC) from 2001 to 2015, stemming from the Call Reports. 3 This allows us to consider the years before and after the crisis, and fully capture the evolution of the low interest rate environment. The quality and completeness of these US data is better than what is available for other regions. The data on GDP growth, CPI inflation and long-term interest rates are acquired from the OECD Main Economic Indicators (MEI) database. The short-term interest rates are attained from Eurostat. Yearly averages are used for all variables. After omitting extreme values and undefined ratios from the sample, the resulting unbalanced sample contains 100,479 bank-year observations, 4 whereas the balanced sample, which is used in the empirical analyses, consists of 3,582 individual banks (see Table 1). In the empirical models, all level variables are divided by total assets in order to make them stationary and comparable. The following variables are adopted in the empirical analysis of this paper.

Dependent variables
Our first model investigates bank profitability (Model I) and the second model bank risk-taking (Model II).
Several measures of profitability are used for Model I. (c) Return on equity (ROE), the ratio of net income over total equity, is another performance indicator, reflecting the bank's return on shareholders' investments.
(d) Profit as reported on the bank's balance sheet is also investigated (as a ratio of total assets).
For Model II two different measures of risk are used in line with the two risk exposure channels described in Section 2.3.
(a) Total capital ratio (TCR), defined by the ratio of Total Risk-based Capital over Risk-weighted Assets. A higher risk exposure, resulting from more risky investments in a banks' search for yield, would translate into a lower ratio.
(b) Credit loss provisions to total loans ratio (PCL) describes the level of credit risk. A more risky loan portfolio, i.e. relatively larger share of NPLs, translates into higher credit risk and therefore more provisioning.

Explanatory variables
Taking the existing literature on the determinants of bank profitability into account as well as the particular interest of this paper concerning the low interest rate environment, the following variables are used. The set of explanatory variables barely differs between the two models. We provide an expected sign and, insofar as is lacking in Section 2, a rationale behind the usage of the variables provided.

Bank-specific variables
Size is approximated by the logarithm of total assets. The effect on profitability is ambiguous as stated in Section 2. For risk-taking the expected effect is negative as larger banks may have a more developed risk management and more diversification benefits and thus a lower risk exposure. Alternatively, smaller banks may be inclined to take higher risks in order to grow. A priori, the effect of size on risk-taking is unclear.
Lending affects bank profitability via its effect on net interest margin and it affects riskiness via the quality of the loan portfolio. We do not have any a priori sign for its effect on risk-taking.
Capitalization, the ratio of total equity capital over total assets, represents a bank's overall soundness and is expected to have a positive impact on both profitability and risk-taking.
Diversification, the ratio of total non-interest income over total income, expresses the bank's reliance on traditional intermediation practices. The effect on profits and risk-taking is ambiguous.
PCL and TCR ratio are explanatory variables in Model I but in turn dependent variables in Model II.
PCL, the ratio of loan loss provisions to total loans, represents the quality of the loan portfolio and impairs profits directly. PCL may affect the TCR ratio as banks with a problematic loan portfolio might attempt to offset this by pursuing higher returns from trading, assuming more risk. A lower TCR reflects a higher risk exposure, and is expected to translate into higher returns.

Macroeconomic environment
The macroeconomic variables take account of the business cycle effect on bank profitability and bank risk-taking. Real GDP growth is expected to have positive coefficients. CPI inflation reflects that income margins are partly driven by inflation expectations through the income from bank float and has a priori a positive effect.

Interest rate environment
As short-term interest rate we take the 3-month money market rate. It is expected that lower interest rates impair the bank's profit margins (making the same assumption as in the literature that the short-term interest rate reflects the general interest rate level) and increase risk exposure. It is assumed that the interest rates' impact on the bank profitability and risk-taking are stronger where interest rates are already low. These concave relationships are studied by including a quadratic term of the short-term interest rate, which is thus expected to have a negative coefficient. As long-term interest rate we take the 10-year government bond yield. In this way, we can evaluate the yield curve slope, as approximated by the difference between longand short-term rates. Analogous to Alessandri & Nelson (2015)

Model specifications
Model 1 explains bank profitability from interest rates and other profit determinants: Π is the profitability measure for bank in year . Like in many other studies, a dynamic model is adopted, as bank profitability tends to persist over time, see Berger et al. (2000). The level of persistence is captured by the lagged dependent variable coefficient . For a value of between 0 an 1, profits show persistence but they will return to their normal level. For a value close to zero, persistence is low and the industry is quite competitive as the speed of adjustment is high. If is close to 1, persistence is strong pointing to absence of competition, see Athanasoglou et al. (2008). The bank-specific determinants are captured by , the macro economy is represented in the term and the interest rate environment is expressed by . The composite error is given by = + , where is the unobserved bank-specific effect, which is time-invariant, and the idiosyncratic error.
Model II describes bank risk-taking as a function of interest rates level and other determinants: is  (1) and (2), therefore, constitute a legitimate starting point for the estimation of the relationships of interest.
Three precarious issues should be taken into account in the empirical estimation of these models.
Firstly, some bank profitability and bank risk-taking determinants are, potentially, of endogenous character.
This either follows from omitted variable bias or from a loop of causality between the independent and dependent variables. A clear example is provided by García-Herrero et al. (2009): more profitable banks may be able to increase their equity more easily by allocating part of their profit to reserves. They could also spend more on advertising and increase their size, which in turn might affect profitability. The causality could also be reversed as more profitable banks may employ more personnel, which could reduce their operational efficiency.
Additionally, it is presumable that there are some fixed effects specific to each individual bank that impact the bank's profitability or risk-taking which are not captured in the model. This is also known as This is in contrast with the related empirical studies on bank profitability and bank risk-taking which claim to find consistent estimates while adopting a similar modeling approach, estimation strategy and instrument set. In section 5, we find some degree of robustness as the estimates of the lagged dependent variable lie well inside the credible range for most models, as explained above.

Static modeling approach
As the lagged dependent variable in the previous modeling approach may cause inconsistency in the estimates, we chose to exclude this dynamic effect and continue to study the relationships of interest by means of a static model.
We start with the pooled OLS estimator. This specification not only omits the dynamics of bank profitability and bank risk-taking by assuming α in Eq. (1) is equal to zero, it also disregards the fixed, individual bank-specific effects by assuming with respect to the error term that η i = η. From the Hausman specification test it could be concluded that such bank-specific effects are present and that the latter assumption is incorrect. The fixed-effects estimator is therefore preferred over the pooled OLS estimator.
In this static modeling approach the possible presence of endogeneity needs still to be solved. A common strategy to work around endogeneity is the use of instrumental variables. Analogous to the system GMM estimator in the dynamic modeling approach, the endogenous, bank-specific variables are instrumented by their own lagged values. This choice for the instrument set provides relevant instruments, as they are indeed correlated with the endogenous variables. As seen before, related empirical studies use a comparable set of instruments.
Whether these instruments are also valid, i.e. uncorrelated with the error term, remains a precarious issue. The Hansen J test of over-identifying restrictions is rejected for all models. It should therefore be concluded that instrumenting the bank-specific, endogenous variables by their own lagged values yield weak instruments. Potentially, a high persistence of the bank profit and risk-taking determinants and the lack of exogenous variation cause the violation of the exogeneity assumption. This is a similar conclusion to the one we have drawn from the dynamic modeling approach. Again, this casts some doubt on whether the research approaches in the literature effectively models bank profitability and bank risk-taking determinants.

Empirical Results
As we have failed to find appropriate instruments and therefore could not work around the endogeneity problems in the two modeling approaches, the within estimator without instrumental variables is considered in order to expose the (static) relationships of interest.

Bank profitability model
The first model exposes the impact of the low interest rate environment on bank profitability. To this end four different profitability measures of profit are examined. See Table 3 for the empirical results.  (1999). As the coefficient of the quadratic term of the short-term interest rate has a negative sign, the relationship is found to be concave, so the effect of a change in interest rates is even more pronounced when interest rates are already low. Also, for the long-term interest rate a small positive effect is found.
From these results it can be concluded that the persistently low interest rate environment leads to a decline in the net interest margin, which is the bank's main source of profitability, see Fig. 1. This is in line with the presumption that as a consequence of the low interest rate environment banks struggle to generate profits from their traditional lending and funding practices. We also found that as credit risk increases, the level of provisioning is raised which leads to a higher lending rate, which in turn boosts the NIM. This positive effect of provisioning is also found by

Profit
For the effects on overall bank profits see the second column of Table 3. A one percentage point increase in the short-term interest rate is associated with a 1.54 basis point decrease in profits. The quadratic term has a negative sign indicating an asymmetric effect of the short-term interest rate on profits. The effect of the long-term interest rate is significantly negative as well. So, overall profits are not hurt as a results of the low interest rate environment. This outcome is somewhat surprising, but in line with the suggestions of Genay & Podjasek (2014). Apparently, banks are able to compensate for the decline in the NIM in such a way that the overall profits are not impaired, see Fig. 2. Whether or not banks did this by making more risky

Fig. 2. The evolution of profits, on average
investments and thereby increasing their non-interest income, will be discussed in the succeeding section.
Genay & Podjasek (2014) suggest that banks maintained their overall level of profits through higher fee income or through lowering provisions. This latter effect will also be addressed in the subsequent section.
Furthermore, they state that, in the US, the net effect on profits might be positive as the low interest rate environment led to better economic outcomes via a lower unemployment rate, higher house prices and faster GDP growth.
The effect of bank size is found to be positive, but insignificant. The very strong positive effect of capitalization is mainly due to the definition of the variable profit as it comprises capital and reserves.
Nevertheless, further evidence is provided that better capitalized banks are associated with higher profits.

Return on Assets
For the results of this commonly used profitability measure, see Column 3. The relationship to the short-term interest rate is positive which is in accordance with the existing literature. Corresponding to a one percentage point increase, the return on assets is found to be 1.17 basis points higher. This finding implies that the low interest rate environment weakens bank performance. The negative sign of the quadratic term implies that this relationship is concave and thus the impact on profitability is even more severe when interest rates are already at low levels. For the long-term interest rate an insignificant effect is found.

5.2
Bank risk-taking model Table 4 presents the results regarding the effects of the low interest rates on bank risk-taking.

Total capital ratio
The first column describes the bank's search-for-yield. It is found that the capital ratio is negatively related to the short-term interest rate: a one percentage point decrease in the short-term interest rate is associated with a 6.28 basis point increase in the capital ratio. This implies that banks have a relatively lower risk exposure at lower interest rate levels. This relationship cannot be concluded to be asymmetric as the quadratic term is insignificant. For the long-term interest rate, a significantly negative relationship is also found. Hence, no evidence is found that as a consequence of the persistently low interest rates banks expand their risky investments. Thus far, banks were able to maintain their overall level of profits without appealing to a search for yield. Note: t statistics in parentheses; * < 0.05, ** < 0.01, *** < 0.001 From the negative effect of bank size it could be inferred that larger banks are more risk-taking, as they may be engaged in more trading activities compared to smaller banks which typically are more traditional in their business practices. The results confirm that better capitalized banks are safer and have a lower risk exposure, see Delis & Kouretas (2011). This sizeable effect of capitalization can be explained from the definition of the capital ratio: for a given level of risk exposure, a higher level of capital directly increases this ratio. The negative effect of diversification is consistent with the expectation that more diversified banks will have more risky assets and thus a lower capital ratio. The higher risk related to a larger loan portfolio greatly impacts the overall risk exposure of the bank. The level of provisioning is positively related to the capital ratio through its effect on the bank's capital position. However, this is an indirect effect as it is found to be insignificant. A slightly pro-cyclical effect of the capital ratio is found. So, in more favorable economic conditions banks tend to increase their risk appetite, which is in line with Manganelli & Wolswijk (2009) who find lower risk aversion under such circumstances.

Provisions for Credit Losses
The second column describes the bank's attitude towards credit risk. It is found that a one percentage point decrease in the short-term interest rate is associated with a 2.78 basis point lower provisioning. This implies that banks expect lower loan losses in the low interest rate environment, potentially because of lower default probabilities on outstanding loans. Moreover, this relationship is found to be concave. These findings are analogous to Borio et al. (2015). Similarly, the effect of the long-term interest rate is significantly positive.
The finding that banks take on a smaller cushion against credit losses in a low interest rate environment could endanger the stability of the bank if credit losses prove to be higher than expected. In combination with the lower lending standards, as found by Maddaloni & Peydró (2011), and higher risk-taking on new loans through the risk-taking channels, see Borio & Zhu (2008), this might be a worrying development. On the other hand, by effectively lowering the provisioning, banks boosted their profits, at least in the short-run. Our analysis confirms the suggestion of Genay & Podjasek (2014) that banks were able to maintain their overall profits through lower levels of provisioning.
No significant impact of bank size is found. Moreover, better capitalized banks are associated with lower credit loss provisions as the negative coefficient indicates. Provisions represent the link between credit risk and capital as provisioning made to absorb (expected) loan losses directly lowers profits before they are allocated to capital and reserves, see Bikker & Hu (2002). So, well-capitalized banks already have a sufficient safety net to absorb credit losses. The diversification of income negatively affects provisioning (-0.0043). This is because in case of greater reliance on interest income, credit risk is a more predominant source of risk and thus more provisioning is needed to manage this. Analogously, the size of lending positively affects provisioning as a larger loan portfolio with potentially higher credit risk needs a higher level of provisioning. Whereas the level of provisioning had a negative impact on the capital ratio, the opposite effect is positive. So, banks that take on lower risks in their lending practices, through a larger buffer for credit losses, also tend to have less risky assets. Furthermore, the effect of the business cycle on provisioning for credit losses is found to be slightly positive as both the effect of real GDP growth and inflation are significantly positive. This slight pro-cyclicality contrasts with Bikker & Hu (2002) and Marcucci & Quagliariello (2009), who find a counter-cyclical behavior of provisions.

Dynamic estimation results
In Section 4.1 we discussed the dynamic modeling approach which is commonly used in the literature. The results from this system GMM estimator are presented in Table A However, for some models we do not see an improvement in the estimation result. Firstly, according to our credibility range, the estimate of Profit is overestimated as the coefficient of the lagged dependent variable is higher than the estimate of the pooled OLS estimator. This coefficient of lagged Profit is very close to 1, which denotes a high level of persistence of overall profits. Probably, by means of adjustments in the level of provisioning or capital reserves the overall level of profits in the balance sheet is often kept fairly constant. In the literature profit measures such as ROA and ROE are more common, so that it is also possible that 'overall profit' is not a suitable bank profitability measure.
Secondly, the estimates for the TCR are underestimated as the coefficient of the lagged dependent variable lies below the estimate of the within estimator. A coefficient close to zero indicates absence of persistence.
All in all, the estimation results from our dynamic modeling approach could be considered as reasonably robust despite the possible lack of consistency of the estimators. Interestingly, the related empirical literature does not come across our estimation issues of invalid instruments, and thus inconsistent estimates. Most of the aforecited papers claim to find consistent estimates and clear persistence effects for both bank profitability and risk-taking, even where a corresponding set of explanatory variables, a similar estimation strategy and an analogous instrument set are used.

Static estimation results
In a second robustness test we use instruments in our static modeling approaches, in order to find consistent estimates (see Table A

Conclusion
The aim of this paper is to investigate the impact of low interest rates on the profitability of banks as well as on the degree of risk-taking by banks. By means of a large panel data set consisting of macroeconomic indicators, interest rate variables and bank-specific balance sheet variables, these relationships are analyzed for the U.S. banking sector.
The presumption that the low interest rate environment deteriorates bank profitability is partly confirmed by this paper's analysis. It is found that bank performance is indeed impaired as a consequence of low interest rates. Moreover, the ability of banks to generate profits from their traditional lending and funding practices is reduced as the net interest margin is being compressed by persistently low interest rates.
Nonetheless, the US banks were able to maintain their overall level of profits. This could have been achieved by effectively lowering their level of provisioning as the default probabilities on outstanding loans are smaller in a low interest rate environment.
With regard to the effects of the low interest rate environment on bank risk-taking, two risk-taking channels are considered. On the one hand, no clear evidence is found that banks increased their risk exposure in a search for yield. Until now, banks were able to maintain their overall level of profits and hence did not compensate for a reduced net interest income by making more risky investments through trading.
Over time, however, banks might alter their business models and expand their trading activities in order to be less dependent on their lending and funding practices. On the other hand, it is found that banks significantly lowered their level of credit loss provisioning in the low interest rate environment.
Consequently, the buffer against unexpected credit losses has shrunk. Banks have thus maintained their overall level of profit at the expense of a smaller cushion against credit losses.   Note: All correlation coefficients with a significance level of 5% or better are indicated with a star (*).   Notes: t statistics in parentheses; * < 0.05, ** < 0.01, *** < 0.001; Notes; t statistics in parentheses; * < 0.05, ** < 0.01, *** < 0.001; # Ho: variables are exogenous