Master Thesis International
Economics and Business
An analysis of the relationship between the deposit rate and
bank risk-taking in the United States
Arjen Kemper (S2229714)
a.j.j.kemper@student.rug.nl
Supervisor: Dr. M.J. Gerritse
University of Groningen
Faculty of Economics and Business
Abstract
This paper examines the relationship between the deposit rate and bank risk-taking in the United States. A low interest rate environment might induce increased risk-taking when rates put pressure on the banks’ margin, the margin between the lending and the deposit rate of a bank. The extensive RateWatch deposit database is employed to estimate the relationship between the deposit rate and bank risk-taking which is measured as risk-weighted asset intensity. The findings provide additional evidence for the relationship of a low interest rate environment and increased bank risk-taking.
Keywords; deposit rate, bank risk-taking, low interest rate environment
Introduction
The global financial crisis has brought the relationship between interest rates and bank risk-taking to the forefront of the economic policy debate. Many observers have blamed the low interest rate environment for the credit boom and the ensuing crisis in the late 2000’s. Dell’Ariccia and Marquez (2006), for instance, argue that low interest rates and abundant liquidity led financial intermediaries to take excessive risks by fuelling asset prices and
promoting leverage. Both theoretical and empirical scholars have provide evidence that banks, when faced with a low interest rate environment, soften their lending standards which raises the level of risk assets in their portfolio and worsening the equilibrium risk of failure as a reaction to reduced bank margins and information asymmetries (Delis and Kouretas, 2010). However, later on some scholars have criticized the idea that low interest rate necessarily lead to higher risk-taking by banks. Dell’Ariccia et al. (2013) state that theoretical foundations for these claims have not been studied enough and hence are not well understood.
Macroeconomic models have typically focused on the quantity rather than the quality of credit (bank lending channel) and have mostly abstracted from the notion of risk. Papers that
consider risk (financial accelerator models) explore primarily how changes in interest rates affect the riskiness of borrowers rather than the risk attitude of the banking system. The banking literature focusses on excessive risk taking by financial intermediaries operating limited liability and asymmetric information. However, this literature largely ignored the role of real interest rates and its determinants, such as monetary policy (Dell’Ariccia et al., 2013 and references therein).
This paper aims to provide additional evidence regarding the relationship between the deposit rate and bank risk behaviour. The idea in this paper is that banks, on aggregate, have different deposit rates which, in turn, determine their risk-weighted asset intensity. The presented research will draw on the work of Rajan (2006) and Dell’Ariccia and Marquez (2006). Both papers have provided a theoretical framework in which bank behaviour in low interest rates environment is explained. A prolonged period of low rates reduces the volatility of these rates which opens up the possibility and encourages riskier positions for banks (Delis, 2010). Rajan (2006) argues that financial institutions may be induced to switch to riskier assets when monetary easing lowers the yield on their short-term assets relative to that on their long-term liabilities. If yields on safe assets remain low for a prolonged period, continued investment in safe assets will mean that a financial institution will need to default on its long-term
Dell’Ariccia and Marquez (2006) find that factors that lead to reductions in banks’ funding costs, such as international capital inflows or monetary expansion, may lead to a credit boom and lower lending standards. This is due to the fact that banks face an adverse selection problem selecting borrowers and reduced costs decrease the banks’ incentive to screen out bad borrowers.
The results of Martinez-Miera and Repullo (2017) provide a theoretical explanation for the relationship noted by Rajan (2006) between high savings, low real interest rates, and the incentives of financial intermediaries to search for yield. The model also provides an
explanation why factors leading to a reduction in real interest rates can be associated with an increase in financial instability. For a good state of nature of the risk factor, aggregate savings will accumulate, leading to lower interest rates and spreads, which translate into higher risk-taking and a fragile financial system. In this situation, the economy is especially vulnerable to a bad state of nature of the risk factor, which can lead to a crisis. The occurrence of a crisis results in a reduction in aggregate savings, leading to higher interest rates and spreads, which translate into lower risk-taking and a safer financial system. Then savings will grow,
restarting the process that produces another boom. In this manner, the model generates endogenous boom and bust cycles. The results provide a rationale for a number of empirical facts in the run-up of the 2007–2009 financial crisis.
(Graph 1; Net interest margin of small banks (<$50B) and large banks (>$50B) Source; Federal Reserve)
Graph 1 shows the decline of the interest rate margin leading up to the financial crisis. Net Interest Margins (NIMs) are constructed as banks' net interest income expressed as a share of interest-earning assets. Net interest income accounts for about half of bank revenues and is defined as the difference between interest income earned on loans and securities and interest
paid on deposits and other sources of bank funding.1
— 1 https://www.federalreserve.gov/econresdata/notes/feds-notes/2015/why-are-net-interest-margins-of-large-banks-so-compressed-20151005.html 2 2,5 3 3,5 4 4,5
NET INTEREST MARGIN
(PERCENTAGE POINTS
)
Scholars, such as Dell’Ariccia and Marquez (2006), have argued that the low interest rate environment, among other things, led to excessive risk taking which ultimately fuelled the global financial crisis. Graph 1 shows that interest margin indeed declined until 2007.
However, in the wake of the financial crisis the low interest environment has increasingly put downward pressure on the NIMs of banks, especially on those of large banks. This could indicate that banks are likely are more susceptible to excessive risk-taking to counter this downward pressure.
Low short-term interest rates may influence banks’ perceptions of, and attitude towards, risk in at least two ways: through their impact on valuations, incomes and cash flows which in turn can modify how banks measure risk; through a more intensive search for yield process,
especially when nominal return targets are in place. These two ways may be amplified if agents perceive that monetary policy will be relaxed in the case of decreasing asset prices in a financial downturn (the so-called insurance effect) causing a classic moral hazard problem (Altunbas et al. 2010).
While many papers focused on the effect of the interest rate on bank risk-taking (i.e. Altunbas et al., 2014, Delis and Kouretas, 2010), this paper will focus on the other determinant of the bank margin, the deposit rate. The bank margin is defined as the difference between the lending (interest) and deposit rate. The wider the margin the more profit a bank is making. Drechsler et al. (2016) state that deposits are the main source of funding for banks. Their stability makes them particularly well-suited for funding risky and illiquid assets. The authors provide a model that predicts that that the contraction in deposits induced by a rate increase causes a contraction in lending as banks cannot costlessly replace deposits with wholesale (non-deposit) funding. This assumption that deposits are special is standard in the banking literature. It can arise from the unique stability and dependability of deposits, or from an increasing marginal cost of wholesale funding (Drechsler et al., 2016 and references
therein).Hence, a change in the pricing of deposit, the rate, can have significant consequences for bank behaviour.
This paper will investigate the relationship between the deposit rate and bank risk-taking. A key question in this field relates to the effect of a low interest rate environment on bank risk-taking. This paper contributes to the existing literature by identifying exogenous shocks to the deposit rate of a bank group and subsequently estimating the impact on the banks’ risk taking behaviour. This study focuses on the United States as the RateWatch deposit database has captured the rates of virtually all deposit products for all banks and their branches in the United States. Furthermore, analysing one country ensures that estimated relationship is not influenced by other variables, the macro-economic conditions are the same for each bank in the sample. Moreover, Laeven and Levine (2009) show that banking structure, regulation, and supervision differ in each country and these factors affect bank (loan) risk-taking.
However, when accounting for endogeneity the results are either insignificant or likely invalid. The results from the robustness tests indicate that banks have a lower ratio of impaired loans to gross loans when the deposit rate increases. This indicates a decrease in bank risk-taking when the deposit rate increases.
The remainder of this paper is structured as follows. Section 2 discusses relevant literature. Section 3 states the hypothesis regarding the relationship between the deposit rate and bank risk-taking. Section 4 presents the econometric model and the data. Section 5 discusses the methodology. Section 6 demonstrates the results and Section 7 concludes.
Section 2 Literature
In this literature review the relationship between the deposit rate and bank risk-taking will be examined more deeply.
Empirical evidence lends support to the notion that low interest rates may help fuel increases in bank leverage and risk-taking. (Dell’Ariccia and Marquez, 2013). These authors provide a clear overview of the multiple strands of literature regarding factors that influence bank decisions with respect to risk-taking. They point what kind of relationship has been established and what gap still exists. Especially, they focus on the role of low real interest rates and bank risk-taking. A theoretical model is presented to illustrate a channel through which changes in real interest rates affect bank risk-taking and leverage with a very simple, static model. First, there is a pass-through effect through the loan rate. To the extent that increases in real interest rates may be passed on, at least partly, to bank customers, increases in reference rate provide greater incentives to reduce risk (i.e., to increase loan monitoring) through increases in the loan rate. Second, there is a standard risk-shifting effect through the costs of depositors which are repaid only when the banks’ projects are successful. Increases in the costs of funds, such as what would likely follow an increase in real interest rates, reduce banks’ return conditional on success and thus encourages greater risk-taking. Finally, there is a leverage effect through the fraction of banks’ portfolio financed by deposits. All things equal, the greater the fraction the lower the incentive banks have to monitor and thus maintain safe portfolios (More deposits reduces incentive to monitor).
Dell’Ariccia and Marquez (2013) mention that financial intermediaries can react immediately on both the asset and liabilities side to changes in the real interest rate environment. Yet, some financial intermediaries may find themselves locked into contractual obligations on either side of their balance sheets that constrain their ability to adjust to changes in market rates. These constraints are at the core of the search-for-yield mechanism through which changes in reference rates may affect risk-taking (Rajan 2006). Financial institutions may be induced to switch to riskier assets when, for instance, a monetary easing lowers the yield on their short-term assets relative to that on their long-short-term liabilities. If yields on safe assets remain low for a prolonged period, continued investment in safe assets will mean that a financial institution will need to default on its long-term commitments. A switch to riskier assets (and higher yields) may increase the probability that it will be able to match its obligations.
Because of severe agency problems in banking (due to bailouts and liquidity assistance), low interest rates may induce banks to soften their lending standards by improving banks’
liquidity and net worth. Since banks rely mostly on short-term funding, low short-term rates may spur risk-taking more than low long-term rates.
Additionally, Maddaloni and Peydro (2011) provide evidence that suggest that securitization activity, weak supervision and extended periods of low short-term rates amplify the softening of lending standards. These findings are supported by Altunbas et al. (2010) who investigate the relationship between short-term interest rates and bank risk in the United States and Europe. Using expected default probabilities of individual banks to measure risk they show that ‘unusually’ low interest rates over an extended period of time contribute to an increase in bank’s risk-taking.
By performing a quasi-natural Experiment in Bolivia, which is a dollarized country, Ioannidou et al. (2014) find that a lower policy rate spurs the granting of riskier loans, to borrowers with worse credit histories, lower ex-ante internal ratings, and weaker ex-post performance. More precise, they find robust evidence that a lower federal funds rate increases banks’ appetite for risk: banks grant new loans to ex-ante less creditworthy borrowers and with a higher ex-post default rate, yet with both lower expected returns and lower loan spreads. The reduction in credit risk for existing loans due to an expansionary shock of monetary policy reduces the capital constraints for banks, thus allowing them to take on higher risk.
In similar fashion, Jiménez et al. (2014) use an extensive database with Spanish borrower quality to find a positive relationship between loan extension to bad borrowers and low
interest rates. They find that a lower overnight interest rate induces banks to higher risk-taking in their lending. Moreover, a lower overnight interest induces lowly capitalized banks to grant more loan applications risky firms than highly capitalized banks and that, when granted, the committed loans are larger in volume and are more likely to be uncollateralized.
Dell’Ariccia et al. (2013) show, by using confidential loan-level data on the internal ratings of US banks on loans to businesses, that ex ante risk-taking by banks (as measured by the risk rating of the bank’s loan portfolio) is negatively associated with increases in real policy rates. These findings on the average relationship between the policy rate and bank risk-taking are consistent with those of Jiménez (2014). The findings in this paper are consistent with these papers. In the robustness analyse a negative relationship between the deposit rate and bank risk-taking is established, an increase in the deposit rate reducing bank risk-taking.
Endogeneity of the interest rate
In the literature that has been discussed multiple approaches have been used to deal with the endogeneity of the interest rate that banks face. It is likely that more risky banks are, a priori, more willing to pay a higher rate as their increased riskiness provides a higher pay-off in case of success. The other way around, depositors might require a higher rate from more risky banks to cover for the banks’ risk position. The bank-level lending rates may be endogenously determined with the level of bank risk-taking if one considers that banks shape their own lending rate by discounting the expected level of risk in their portfolios (Delis and Kouretas, 2011). Altunbas et al. (2010) use the change in expected default frequency of a bank where all bank-specific characteristics refer to t-1 in order to avoid endogeneity bias. Ioannidou et al. (2009) guarantee the exogeneity of interest rate by using the U.S. federal funds rate to determine the relationship of bank risk-taking in Bolivia. Delis and Kouretas (2011) use the German short-term nominal interest rate as an instrument for the interest rates of other euro area countries. They argue that the German interest rate plays an important role in the reaction function of major euro area countries which should make it a suitable instrument for the Euro Area interest rate.
This paper makes use of banks’ exposure to different markets to capture exogenous variation in the deposit rate. This approach is similar to that of Goetz et al. (2016). Goetz et al. (2016) show that for the average Bank Holding Company (BHC), their instrumental variable results suggest that geographic expansion materially reduces risk. Geographic diversification does not affect loan quality. These results imply that geographic expansion lowers risk by reducing exposure to idiosyncratic local. Since BHCs choose both whether and where to expand endogeneity and selection might provide biased estimates for their regular regression. To correctly estimate this relationship the authors develop a BHC-specific instrumental variable for the diversity of BHC deposits across the United States based on twenty years of interstate bank deregulation. By using instrumental variables, the authors provide an estimate of the impact of geographic diversity on risk for a randomly selected BHC.
Section 3 Hypothesis
On the other hand, the deposit rate of a bank can be seen as the (re)-financing rate for the banks’ investments. It’s is the price a bank has to pay to acquire funds. From the same example it can be seen that bank group A might increase its risk-taking as it has to pay a lower (re)-financing rate than bank group B. The punishment for faulty investments is less harsh for bank group A than for bank group B. Logically, it can assumed that a lower deposit rate will induce banks to increased risk-taking as their refinancing costs have become lower. Following from these arguments the relationship between the deposit rate and bank risk-taking can be negative or positive. A cheap (re)-financing rate reduces the downside risks of an investment Higher deposit rates could also induce banks to increase their risk-taking since their bank margin is being pressured. To examine the existence of a search-for-yield
mechanism the following hypothesis is postulated.
H1; an increase in the deposit rate will result in an increase of the risk-weighted assets intensity of a bank.
Section 4 Econometric model and Data
To test the hypothesis the econometric model that will applied is represented by the following equation;
𝑅𝑊𝐴𝑝𝑡= 𝛼 + 𝛽1𝐷𝑅𝑝𝑡+ 𝑢𝑝𝑡 (1.1)
Where the risk variable, RWA, of bank group p at year t is written as a function of the deposit rate, DR. The dependent variable measures the risk behaviour. The explanatory variables quantifies the aggregated deposit rate of bank group p in year t. This aggregated rate is an average of the rates of the two deposit products used in this research. Descriptions of the variables employed in this paper are presented in Appendix 1.
Following from Delis and Kouretas (2010) the ratio of risk weighted assets to total assets, also known as risk weighted assets intensity is used as proxy of bank risk-taking. This measure reflects the riskiness of bank portfolios at any point in time and corresponds directly to the term “bank risk-taking”. Bank risk assets include all bank assets except cash, government securities (at market value) and balances due from other banks. In other words, all bank assets subject to change in value due to changes in market conditions or changes in credit quality at various re-pricing opportunities are included as risk assets. Hence, an increase in risk assets demonstrates a more risky position of banks. Risk-weighted asset intensity is preferred over a measure such as non-performing loans since it captures more than just loans. Also, opposed to the non-performing loans measure, risk-weighted asset intensity reflects both credit and market risks. The dataset includes commercial banks, savings banks, cooperative banks and bank-holding companies. Investment banks are not included as do no not take deposits.
(Graph 2; Risk-Weighted Asset Intensity; Risk-Weighted Assets as percentage of Total Assets, data obtained via Orbis Bankscope)
The reported graph 2 corresponds to risk-weighted asset intensity of banks in the sample. The sample mean value of risk assets equals 69.18%. The lowest value is reported in 2012 (65.41%) and the highest value in 2008 (72.84%). This drop of 7% cannot go unnoticed, as it represents a substantial shift in the average risk-taking behaviour of banks due to the financial crisis. Via the extensive RateWatch database I obtained all the weekly deposit rates for two products which are representative for the market, the 12 months Certificate of Deposit 10K (12MCD10K) and the Money Market 25K deposit (MM25K) (Drechsler, 2016). The weekly rates on these products were then used to produce a yearly rate for each individual bank and or branch in the sample. Only banks that offered these products for at least half year (>26 weeks) were collected in the sample. Eventually, a yearly rate was computed for each bank in the sample which is an average of all its branches weighted equally. The sample contains nine yearly rates starting in 2006 and ending in 2014. The database consists of 1698 banks and
15,252 observations.The summary statistics of both product rates are presented in appendix 2
and 3. The mean deposit rates for the two products are 1,74 for Certificate of Deposit and 0,82 for Money Market. The standard deviations for the average rate of both products between banks is quite reasonable (0,24 and 0,32). More surprising are the standard deviations within banks (1,47 and 0,77). The within numbers refer to the deviation from each banks its average.
65% 66% 67% 68% 69% 70% 71% 72% 73% 74% 2 0 0 5 2 0 0 6 2 0 0 7 2 0 0 8 2 0 0 9 2 0 1 0 2 0 1 1 2 0 1 2 2 0 1 3 2 0 1 4 2 0 1 5
(Graph 3; average Money Market 25K deposit rate, obtained via RateWatch)
(Graph 4; Average 12 months 10K Certificate of Deposit rate, obtained via RateWatch) Both the average of the Money Market deposit and the average of the Certificate of Deposit rate indicate a significant drop after 2007. In the sample period the average rate for the Money Market product decreases from 2.05% in 2007 to 0.18% in 2014. The average rate for the Certificate of Deposit product dropped from 4.27% in 2007 to 0.36% in 2014. This indicates that the average rate for the Certificate of Deposit decline faster, comparatively. This drop in the average rate for both products indicates that banks had to pay less for the funds they attracted in the sample period. Lower rates lead to lower (re)-financing costs for banks which can induce increased risk-taking.
However, graph 2 illustrates simultaneous drop in the average risk-weighted asset intensity of banks. This points towards the rejection of the idea that banks will increase risk-taking when faced with lower costs. The increase after 2012, however, could mean that banks first reacted to the financial crisis and decreased their share of risk-weighted assets as a percentage of their total assets. 0,00% 0,50% 1,00% 1,50% 2,00% 2,50% 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Money Market deposit rate (25K)
After 2012 an environment of even lower deposit rates could give some room for increased bank risk-taking. It is to be expected that banks will adjust their appetite for risk according to changes in the deposit rates over the whole sample period.
Section 5 Methodology
Certain areas of the United States have different intensities of competition. Together with different lending possibilities in the operating locations of bank group this will, among other things, influence its overall deposit rate. It is to be expected that this aggregated rate will, in turn, determines the banks’ risk-weighted asset intensity. To empirically test the relationship between the deposit rate and bank risk-taking a two-stage least squares regression is
performed which will employ an instrumental variable. The instrumental variable is designed around the idea that banks, due to geographical dispersion, are exposed to different rate in their operating locations. This exposure provides exogenous variation needed to establish the causal relationship of deposit rates influencing bank risk-taking. This approach is used in order to deal with the issue of dual causality in the relationship between the deposit rate and bank risk-taking. Customers, when faced with a more risky bank, might a priori require a higher deposit rate to pay for the higher risk position of the bank. Conversely, risk-averse banks are likely reluctant to pay a higher deposit rate as it requires a higher interest loan, i.e. more risk-taking, rate to acquire the same bank margin. The risk attitude of a bank can, therefore, already be captured in the level of the rate. Hence, bank behaviour regarding risk-taking does not necessarily evolves from the deposit rate it has to pay. Thus, it would be appropriate to use an instrument for the dual causality issue. This instrument has two conditions it has to satisfy. First, the instrument has to be relevant which means it has to
explain the deposit rate, 𝐷𝑅𝑝𝑡. Second, the instrument has to be exogenous which means that
it should not explain the risk measure other than by affecting the deposit rate. This paper employs two instruments to deal with the possible endogeneity of the deposit rate.
Locational rate shifters
The first step involves regressing the bank fixed-effects and location fixed-effects on the deposit rate of a bank branch. After that, a location-specific rate shifter can be computed. The rate shifter in each operating location, when aggregated, determines the overall influence of location on the deposit rate of a bank group. The resulting instrument is constructed from a variable that has been cleared of bank-specific variables and represents exogenous shocks to the deposit rate that a bank faces.
𝑍𝑙𝑝𝑡 = 𝐹𝐸𝑝𝑡+ 𝐹𝐸𝑙𝑡+ 𝜇𝑙𝑝𝑡 (1.2)
Where 𝑍𝑙𝑝𝑡 is the aggregation of each bank branch deposit rate. 𝐹𝐸𝑝𝑡 are the bank
fixed-effects on a bank group level, 𝐹𝐸𝑙𝑡 are the location-specific rate shifters, l equals all the
locations where bank group p has a presence and 𝜇𝑙𝑝𝑡 the error term.
The location-specific rate shifter, 𝐹𝐸̂ , can be then be used to construct a bank-group specific 𝑙𝑡
exposure to a locational rate shifters.
𝑍̂𝑝𝑡 = ∑𝑙∈𝑝𝐹𝐸̂𝑙𝑡
Appendices 3 and 4 provide histograms of the location rate shifters. The histogram of the Money Market deposit rate shows that more than 50% of the individual locational rate shifters are zero or close to zero. This indicates that this instrumental variable might not possess the desired characteristics to be employed in a two-stage least squares regression. The histogram of the Certificate of Deposit rate shifters are also close to, but necessarily equal to, zero. Hence, this instrumental variable might provide better results.
Locational average instrument
Banks operate in certain locations and different deposit rates in each location determine, on aggregate, the deposit rate a bank group is facing. In each location, among other things, competition determines the local deposit rates. The same market conditions apply to all banks in a location which will be captured via the location average. The average deposit rate of the other banks operating in each location is calculated which then is used to create an instrument which exogenously influences the deposit rate for a bank operating in that location and does not necessarily influences its risk behaviour on a bank group level.
To determine the location of a bank its Core-Based Statistical Area (CBSA) code is used. Core Based Statistical Areas consist of the county or counties or equivalent entities associated with at least one core (urbanized area or urban cluster) of at least 10,000 population, plus adjacent counties having a high degree of social and economic integration with the core as
measured through commuting ties with the counties associated with the core.2
Appendix 6 provides a correlation matrix with the correlations between both the instruments and the deposit rates. The correlations of the locational average instruments are quite high (around 0,98 for Certificate of Deposit and around 0,88 for Money Market). This indicates that these instruments are very relevant. On the other hand, the correlations for the location rate shifters (around -0,04 for Certificate of Deposit and around -0,02 for Money Market) imply very weak relevance for this instrument.
Section 6 Results
Continuing, both instruments are employed in the regression equation 1.1 in order to estimate the relationship between the deposit rate and bank risk-taking. First the result of the locational rate shifter regressions are discussed. This approach reduces the number of observations and banks in the sample. This is due to the fact that this sample only collects banks that are exposed to differential location rate shifters. For the Money Market sample the number of observations is reduced to 1377 which corresponds to 153 banks. The Certificate of Deposit sample now consists of 1467 observations which corresponds to 163 banks. These banks have multiple branches and, thus, are subject to locational rate shifters. This indicates that the sample probably consists of larger, more efficient banks which have been able to branch out. Hannan and Prager (2004) find that, on average, multimarket banks offer lower deposit interest rates than do single-market banks operating in the same market. Hence, a sample consistent only of multimarket banks may influence the results.
—
Table 1. Ordinary Least Squares (OLS) regression and two-stage least squares regressions
(2SLS). First, a location rate shifter is computed which is used as an instrument for the second stage regression. The second stage instrument is an aggregation of a banks’ exposure to locational rate shifters in each operating location. RWA/TA is a proxy for bank risk-taking, measured as the percentage risk-weighted assets of total assets.
Locational Rate
Shifters OLS 2SLS 2SLS 2SLS
RWA / TA RWA / TA RWA / TA RWA / TA
Average yearly rate 0,022*** -0,380 -0,009 -0,022
(0,001) (0,537) (0,054) (0,057) Constant 0,664*** 1,196* 0,738*** 0,754*** (0,001) (0,663) (0,067) (0,070) Observations 15,252 1467 1377 1359 Number of banks 1698 163 153 151 Fixed Effects No No No No First Stage of 2SLS
Rate Shifter CoD -0,263 -0,068
(0,346) (0,393) Rate Shifter MM -0,531* -0,512* (0,279) (0,300) Constant 1,234*** 1,232*** 1,234*** (0,029) (0,029) (0,030) F 678 0,58 3,62 1,81 Prob > F 0,0000 0,446 0,057 0,164 Wald chi2 0,5 0,03 0,15 Prob > chi2 0,48 0,87 0,70
Instrument Rate Shifter
CoD Rate Shifter MM Both Sargan p-value 0,025 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
From Table 1 one can conclude that for the regular OLS the yearly average rate is positive and significant at the 1% level. This provide evidence for the search-for-yield mechanism describe by Rajan (2006). Higher deposit rates induce banks to increase their risk-taking as their margin is under pressure. However, as discussed earlier, the regular OLS regression might suffer from an endogeneity bias. Hence, instruments are used to estimate the
In the two-stage regression with both instruments the yearly average deposit rate loses its significance. Moreover, the Sargan p-value of 0,025 leads to the rejection of the null
hypothesis of correctly identified instruments. This rejection indicates that this regression is over-identified and thus, one should strongly doubt the validity of these estimates.
Table 2. Ordinary Least Squares (OLS) regression and two-stage least squares fixed-effects
regressions (2SLS). First, a location rate shifter is computed which is used as an instrument for the second stage regression. The second stage instrument is an aggregation of a banks’ exposure to locational rate shifters in each operating location. RWA/TA is a proxy for bank risk-taking, measured as the percentage risk-weighted assets of total assets.
Locational Rate
Shifters OLS 2SLS 2SLS 2SLS
RWA / TA RWA / TA RWA / TA RWA / TA
Average yearly rate 0,022*** -0,120 0,047* 0,0346
(0,001) (0,122) (0,024) (0,022)
Constant 0,664*** 0,875*** 0,669*** 0,683***
(0,001) (0,150) (0,030) (0,027)
Observations 15,252 1467 1377 1359
Number of banks 1698 163 153 151
Fixed Effects No Yes Yes Yes
First Stage of 2SLS
Rate Shifter CoD -0,581 -0,244
(0,476) (0,538) Rate Shifter MM -0,878** -0,8262** (0,362) (0,387) Constant 1,232*** 1,229*** 1,230*** (0,030) (0,031) (0,031) F 678 1,49 5,86 3,06 Prob > F 0,0000 0,223 0,02 0,047 Wald chi2 26813 163381 188319 Prob > chi2 0,00 0,00 0,00
Instrument Rate Shifter
CoD Rate Shifter MM Both Sargan p-value 0,002 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
The fixed effect estimator removes the panel-level means from each variable which means that only changes over time within a unit matter. Comparing the results to those of Table 1, one can see that this approach did not yield much different results. The yearly average rate is still not significant and the Sargan p-value of 0,002 also indicates that this regression is over-identified.
Summarizing, the regular OLS regression provides some early indication of a search-for-yield mechanism as the co-efficient for the deposit rate is positive and significant. An increase in the deposit rate will result in increased risk-taking. However, when both accounting for endogeneity of the deposit rate and using fixed-effects in a two-stage least squares regression this result does not hold up. The significance of the yearly average deposit rate is dropped and the model is over-identified when both locational rate shifting instruments are used.
Table 3. Ordinary Least Squares (OLS) and Two-stage least squares fixed effects regression
(2SLS) for locational average instrument. First, an average of other banks operating in the same location is computed which is used as an instrument for the second stage of the regression. The second stage instrument is deposit rate which is exogenously influenced by the prevailing average in the locations a bank is operating. RWA/TA is a proxy for bank risk-taking, measured as the percentage risk-weighted assets of total assets.
Locational
Average OLS 2SLS 2SLS 2SLS
RWA / TA RWA / TA RWA / TA RWA / TA
Average yearly rate 0,022*** 0,022*** 0,022*** 0,022*** (0,001) (0,0005) (0,0005) (0,0005) Constant 0,664*** 0,664*** 0,663*** 0,664*** (0,001) (0,0007) (0,0008) (0,0007) Observations 15,252 14931 14904 14895 Number of banks 1698 1659 1656 1655
Fixed Effects No Yes Yes Yes
First Stage of 2SLS Other bank average CoD 0,717*** 0,663*** (0,002) (0,007) Other bank average MM 1,472*** 0,126*** (0,004) (0,015) Constant 0,047*** 0,044*** 0,041*** (0,004) (0,005) (0,004) F 678 202121 120228 101663 Prob > F 0,00 0,00 0,00 0,00
Wald chi2 2.12e+06 2.11e+06 2.11e+06
Instrument Other bank average CoD
Other bank
average MM Both
Sargan p-value 0,0001
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
First, it can be concluded from the OLS regression that increase in the yearly average deposit rate has a significant and positive effect on bank risk-taking, measured as risk-weighted asset intensity. However, due to the potential endogeneity issue one should be careful with
interpreting this co-efficient. Multiple 2SLS regressions are also presented. Fixed effects are employed to only use the variation of one bank over time. This eliminates the possibility that one bank can, a priori, be inclined to risk-taking than another bank in the sample. The first two 2SLS regression are with the separate instruments. The regression on the right
incorporates both instruments to give a full depiction of the relationship. First, it can be seen that the yearly average rate, when instrumented, still is highly significant and positive. There are no changes when compared to the regular OLS regression. However, the Sargan p-value (0,0001) indicates that this 2SLS regression is over-identified. Hence, one should doubt the validity of the estimates.
All in all, it can be concluded the regular OLS regression provided some initial evidence of the existence of the relationship between the deposit rate and bank risk-taking. The co-efficient for the deposit rate is positive and significant at the 1% level. However, due to potential endogeneity issues the deposit rate should be instrumented. The locational rate shifters are very weakly correlated to the deposit rate and also provide insignificant results. On the other hand, the locational average instruments are highly correlated and provide positive and significant co-efficient for the instrumented yearly average deposit rate.
However, the Sargan p-value indicates a strong rejection of the null hypothesis which should make one strongly doubt the validity of these estimates. Hence, with these inconclusive results H1 cannot be rejected nor failed to be rejected.
Robustness test
Table 4. Ordinary Least Squares (OLS) and Two-stage least squares fixed effect regression
(2SLS) for locational average instrument. First, an average of other banks operating in the same location is computed which is used as an instrument for the second stage of the regression. The second stage instrument is deposit rate which is exogenously influenced by the prevailing average in the locations a bank is operating. IML/GL is a proxy for bank risk-taking, measured as the ratio of impaired loans to gross loans.
Locational Average OLS 2SLS 2SLS 2SLS
IML / GL IML / GL IML / GL IML / GL
Average yearly rate -0,003*** -0,004*** -0,004*** -0,004***
(0,0002) (0,0001) (0,0002) (0,0001)
Constant 0,023*** 0,024*** 0,024*** 0,024***
(0,0003) (0,0002) (0,0002) (0,0002)
Observations 15,252 14886 14859 14850
Number of banks 1698 1654 1651 1650
Fixed Effects No Yes Yes Yes
First Stage of 2SLS
Other bank average CoD 0,717*** 0,658***
(0,002) (0,007)
Other bank average MM 1,472*** 0,127***
(0,004) (0,30) Constant 0,048*** 0,045*** 0,042*** (0,029) (0,005) (0,004) F 313 201180 119736 101197 Prob > F 0,00 0,00 0,00 0,00 Wald chi2 15951 15854 15926 Prob > chi2 0,00 0,00 0,00
Instrument Other bank
average CoD
Other bank
average MM Both
Sargan p-value 0.00
Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
The locational average instruments provide a negative and significant co-efficient, in line with the OLS estimate. The significant and negative co-efficients imply that an increase in the deposit rate results in a decrease of the ratio between impaired loans and total loans. This relationship indicates that a decrease in the deposit rate results in a higher percentage of impaired loans compared to gross loans. Hence, banks increase their risk-taking as a result of reduced (re)-financing costs. However, just as with the 2SLS regression in Table 3, the Sargan p-value (0,00) leads to a strong rejection of null hypothesis that the model is correctly
identified. Similar to the previous results, one should strongly doubt the quality of these estimates.
Table 5. Ordinary Least Squares (OLS) regression and two-stage least squares regressions
(2SLS). First, a location rate shifter is computed which is used as an instrument for the second stage regression. The second stage instrument is an aggregation of a banks’ exposure to locational rate shifters in each operating location. IML/GL is a proxy for bank risk-taking, measured as the ratio of impaired loans to gross loans. Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
Locational Rate
Shifters OLS 2SLS 2SLS 2SLS
IML / GL IML / GL IML / GL IML / GL
Average yearly rate -0,003*** -0,010 0,005 0,003 (0,0002) (0,030) (0,013) (0,012) Constant 0,023*** 0,033 0,015 0,017 (0,0003) (0,037) (0,016) (0,015) Observations 15,252 1467 1377 1359 Number of banks 1698 163 153 151 Fixed Effects No No No No First Stage of 2SLS Other bank average CoD -0,263 -0,068 (0,350) (0,393) Other bank average MM -0,531* -0,512* (0,279) (0,30) Constant 1,234*** 1,232*** 1,233*** (0,029) (0,029) (0,03) F 313 0,58 3,62 1,81 Prob > F 0,00 0,45 0,06 0,16 Wald chi2 0,10 0,15 0,08 Prob > chi2 0,75 0,70 0,78
Instrument Rate Shifter
CoD
Rate Shifter
MM Both
Table 5 provides the robustness test for the locational rate shifter instruments. The results are similar to the results of these instruments in Table 1 with original measure of risk. The significance of the co-efficients the yearly average deposit is dropped when instrumented. Hence, nothing meaningful can be concluded regarding the relationship between the percentage of impaired loans and bank risk-taking. It should be noted that, opposed to previous regressions, this 2SLS regression with both instruments provides the first Sargan p-value that does not reject the null hypothesis which implies that instruments are correctly identified.
Table 6. Ordinary Least Squares (OLS) regression and two-stage least squares fixed-effects
regressions (2SLS). First, a location rate shifter is computed which is used as an instrument for the second stage regression. The second stage instrument is an aggregation of a banks’ exposure to locational rate shifters in each operating location. IML/GL is a proxy for bank risk-taking, measured as the ratio of impaired loans to gross loans. Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
Locational Rate
Shifters OLS 2SLS 2SLS 2SLS
IML / GL IML / GL IML / GL IML / GL
Average yearly rate -0,003*** 0,007 -0,018** -0,017** (0,0002) (0,017) (0,009) (0,008) Constant 0,023*** 0,012 0,044*** 0,042*** (0,0003) (0,021) (0,011) (0,010) Observations 15,252 1467 1377 1359 Number of banks 1698 163 153 151
Fixed Effects No Yes Yes Yes
First Stage of 2SLS Other bank average CoD -0,581 -0,244 (0,476) (0,538) Other bank average MM -0,878** -0,826** (0,361) (0,387) Constant 1,232*** 1,230*** 1,231*** (0,030) (0,031) (0,031) F 313 1,49 5,86 3,06 Prob > F 0,00 0,22 0,02 0,05 Wald chi2 1174 967 1030 Prob > chi2 0,00 0,00 0,00
Instrument Rate Shifter
CoD
Rate Shifter
MM Both
Table 6 provides the same OLS regression as Table 4 which indicates that the percentage of impaired loans is significant at the 1% level. The negative co-efficient indicates that an increase in the ratio of impaired loans reduces bank risk taking. However, as discussed, a two-stage least squares regression should be employed to estimate the relationship. Fixed effects are employed to only use the variation of one bank over time. The regression on the right indicates that the yearly average rate, when instrumented, still is significant (at the 5% level). The co-efficient also still is negative which indicates that relationship did not alter when the dependent variable is instrumented. The Sargan p-value (0,58) means that the null hypothesis cannot be rejected and the regression is correctly identified. Hence, it can be assumed that the estimates are valid.
Concluding, the robustness tests with impaired loans as a percentage of gross loans as a risk measure holds mostly the same results as the initial regressions. The locational average instruments provide a significant co-efficient for the yearly average deposit rate but this regression is over-identified. The location rate shifters regression without fixed effects fail to provide a significant co-efficient. However, the locational rate shifter regression with fixed effects does provide a negative and significant co-efficient. This indicates that an increase in the deposit rate of a bank results in reduced bank risk-taking, measured as the ratio of
impaired loans to gross loans. This last regression is correctly identified so these estimates can be assumed to be valid. Thus, when the ratio of impaired loans is used as a measure of bank risk-taking the hypothesis H1 can be rejected.
Validity of instruments
Unfortunately, not every instrument can be tested for validity. The validity of this minimum number of required instruments cannot be tested. In the case in which we have more than one instrument available, we can test the validity of the extra, or surplus, moment conditions. Econometric jargon for surplus moment conditions is ‘‘over-identifying restrictions.’’ A surplus of moment conditions means we have more than enough for identification, hence ‘‘over-identifying’’ (Carter-Hill et al., 2010). This paper employs two instruments for the rates of two deposit products. However, the instruments used in each regression following similar reasoning. This means that ‘over-identification’ for one extra instrument can be tested but the validity of the instrument as a whole cannot be tested. So, because the instruments in the regressions are computed using the same methodology these instruments may very well be either jointly consistent or jointly inconsistent (Woolridge, 2012).
Limitations of this research
Another measurement issue relates the representation of the deposit market via the products used in this paper. In this paper it is assumed that two products will give a satisfying
representation of reality which might not be the case. To give a more concise estimate of the impact of the deposit rate on bank risk-taking more products should be used. This paper employs a two-stage least squares regression to counter some econometrical issues regarding the endogeneity of the relationship between the deposit rate and bank risk-taking. A good instrument has to be both exogenous and relevant. However, the locational rate shifter instruments do not meet the satisfactory conditions regarding relevance. The correlations of these instruments are near to 0 which indicates very low relevance. The location average instruments suffer from possible selection bias, at least theoretically. The average deposit rate in a certain location could be driven by more risky banks settling all in the same location. It is possible that under certain prevailing market conditions only more risky banks could operate in a location. Due their risky nature these banks may reach a desired bank margin even though the local deposit rate is relatively high. This effects can influence the average deposit rate in that location. A selection bias problem impedes the required exogeneity of the instrumental variable.
Section 7 Conclusion
This paper has examined the relationship between the deposit rate and risk-weighted asset intensity as a measure of bank risk-taking. Drawing from the existing literature arguments can be made in favour of both a negative relationship and a positive relationship. Theoretically, a low deposit rate would mean low (re)-financing costs for a bank which could induce risk-taking. When the costs of financing are relatively low, risky investments become more attractive since the costs of bad investments are reduced. On the other hand, relatively high deposit rates, in turn, might induce increased risk-taking by banks via a mechanism which is coined ‘search-for-yield’. Rajan (2006) identifies that a search for yield mechanism comes into play when low nominal rates reduce the banks’ margin, the margin between the lending and the deposit rate of a bank.
In order to determine the causal direction of the relationship that exists between the deposit rate and bank risk-taking this paper employs instrumental variables. The deposit rate might be endogenously determined as customers require a higher deposit rate from more risky banks. The additional riskiness of one bank could therefore be capture in the height of the deposit rate it faces. Vice versa, a risk-averse bank might be reluctant to pay a relatively high deposit rate as this rate will put pressure on its margin. A higher lending rate, and thus more risk-taking, is needed to acquire the same bank margin. Two instruments were designed to deal with this endogeneity issue. The first instrument made use of a banks’ exposure to locational changes in the deposit rate and consisted of locational rate shifters. The second instrument made use of the locational average of the banks operating in the same location. Both instruments were employed to provide exogenous variation in the deposit rate which is not explained by bank risk-taking. The initial Ordinary Least Squares regressions provide evidence for the search-for-yield mechanism as described by Rajan (2006). However, when accounted for endogeneity these results do not hold up. The robustness analyse, which
Furthermore, this additional piece of evidence holds consequences for policymakers and regulators as the current levels of the deposit rates are even below pre-crisis levels.
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Appendices
Appendix 1. Description of the variables
Variable Description Source
RWA/TA
Risk-weighted asset intensity, measured as the percentage risk-weighted of total assets
Orbis Bankscope
Certificate of Deposit 12 Months Certificate of
Deposit 10K RateWatch
Money Market deposit Money Market deposit
25K RateWatch
Locational Rate Shifter Aggregated locational rate shifters used for the two stage
Own
calculations
Year-rate ( per product)
Yearly rate for all banks and its branches in the sample
RateWatch
Other bank average
The locational average deposit of all banks except the bank group or its branch
Own
calculations
Impaired Loans / Gross Loans The ratio of impaired
loans of gross loans
Orbis Bankscope
Appendix 1. Summary statistics of the Certificate of Deposit rate
Variable Observations Mean Standard
Deviation Minimum Maximum
RWA/TA 15282 0,692 0,122 0,159 1,231 between 1698 0,106 0,252 1,071 within 9 0,059 0,105 1,233 Year rate 15282 1,739 1,493 0,040 5,363 between 1698 0,240 0,723 2,828 within 9 1,474 -0,151 5,074
Locational Rate Shifter 1467 -0,005 0,083 -0,794 0,434
Appendix 2. Summary statistics of the Money Market deposit rate
Variable Observations Mean Standard
Deviation Minimum Maximum
RWA/TA 15282 0,692 0,122 0,159 1,231 between 0,106 0,252 1,071 within 0,059 0,105 1,233 Year rate 15282 0,823 0,832 0,009 4,872 between 0,324 0,056 2,103 within 0,766 -0,862 4,232
Locational Rate Shifter 1377 -0,007 0,105 -0,775 0,781
Other bank average 14904 0,840 0,716 0,020 4,454
Appendix 5. Histogram of the locational rate shifters for the Certificate of Deposit (CD) rates
Appendix 3. Correlation Matrix (Observations = 1359)
Rate CoD Rate MM Loc Avg
CoD Loc Avg MM Rate Shifter CoD Rate Shifter MM Rate CoD 1 Rate MM 0,892 1
Loc Avg CoD 0,983 0,887 1
Loc Avg MM 0,974 0,881 0,992 1
Rate Shifter CoD -0,025 -0,016 -0,023 -0,021 1
