Monetary policy, funding cost and banks’ risk-taking: evidence from the USA

Accurately determining the monetary policy transmission channels is crucial to the understanding of the effects of monetary policy. Two of the most discussed of these transmission channels are the bank lending channel (BLC) proposed by Bernanke and Blinder (1988) and risk-taking channel (RTC) emphasized by Disyatat (2011) and Jiménez et al. (2014). Under the former, monetary policy affects the reserves of a bank and tightening monetary policy decreases the deposits a bank has (e.g., an increase in the reserve requirement ratio). Because banks are not able to fully substitute between deposits and funding through the interbank or wholesale market, this reduces the amount of loans that banks can make and hence slows down the economy. Under the latter, tightening monetary policy (e.g., by increasing the Fed Funds rate) makes risky assets less attractive and reduces collateral and asset values. This again reduces the loans banks can make and hence slows down the economy.

An important aspect of these models is the different responsiveness of banks to monetary policy depending on the amount of their deposits. For the bank lending channel this is somewhat trivial. Since monetary policy directly affects deposits, banks with relatively more deposits are more affected and hence should respond more to monetary policy shocks [e.g., see Drechsler et al. (2017)]. This implies that banks without deposits should only have a limited response to monetary policy through the BLC.¹ For the RTC, the role of deposits has to our knowledge not been addressed so far.

This paper addresses the role of deposits for the RTC. Specifically, we use a variation of the Hahm et al. (2013) Value-at-Risk (VaR) RTC model to obtain general relationships between bank lending, capital, and deposits. Our model shows that under monetary tightening, banks can use their non-interest-bearing (NIB) deposits and capital as a buffer and banks with less leverage or more NIB deposits should react less to a monetary policy tightening. The non-interest-bearing part of deposits thus acts as “Pseudo Capital.”² Deposits and equity tend to co-move substantially over the business cycle as shown in Fig. 1 which could be an indicator that they are similar in nature. Intuitively, non-interest-bearing deposits act like an interest-free loan to the bank. The cost of this loan does not depend on the Fed Funds rate, and hence bank lending financed through these deposits should not be affected by interest rate changes. This argument that at least parts of deposits are little affected by monetary policy has become even stronger since banks started to hold substantial excess reserves in 2008 as shown in Fig. 2.

The model in this paper thus allows for high capital banks to be less responsive to monetary policy. This is usually associated with the BLC as supported by Kishan and Opiela (2000), Jayaratne and Morgan (2000), Altunbaş et al. (2002), Gambacorta and Mistrulli (2004), Ashcraft (2006). Banks with more capital can more easily access the wholesale market and more easily use the wholesale market as a substitute for deposits.³ For the RTC, Dell’Ariccia et al. (2014) showed that banks whose capital constraints are binding should react less to monetary policy easing. The main intuition is that the banks cannot expand lending as they are capital-constrained. Subsequently, Dell’Ariccia et al. (2017) provided some evidence on this based on US data. Without a binding capital constraint, we find the opposite for the RTC and are thus removing a key difference between the BLC and the RTC while also allowing for deposits to act as “Pseudo Capital,” an additional testable implication. The key differences between these models are given in Table 1.

We then apply the model to a panel of US banks shows substantial evidence in support of these two key model implications. Specifically, the risk-taking of banks with more equity or NIB deposits react less to monetary policy for a number of risk measures. When comparing different types of deposits, we find that the relationship reverses for interest-bearing deposits.

The remainder of the paper is structured as follows. Section 2 presents a model that lays out the main empirical hypothesis in this paper. Section 3 will present the data and the empirical results are in Sect. 4. Finally, Sect. 5 concludes.

We use the static, two-period model in Hahm et al. (2013) with some small changes. A bank makes loans in period 0 and receives repayment in period 1. The bank’s balance sheet identity in period 0 is total assets or lending (L) which is equal to equity (E) plus liabilities (D). Liabilities are a mix of retail deposits and wholesale funding. Unlike Hahm et al. (2013), we do not differentiate the retail deposits and wholesale funding in the model, but we still take into account the different funding cost as shown below.The bank holds a diversified loan portfolio. Credit risk follows the Vasicek (2002) model in line with the Basel requirements. The default risk for each individual firm is \(\varepsilon \). Borrower j repays the loan when \(Z_{j}>0\), where \(Z_{j}\) is the random variable given bywhere \(\Phi (.)\) is the c.d.f of the standard normal, \(\varepsilon \) is the probability of default on the loan, and Y and \(\{X_{j}\}\) are mutually independent standard normal distribution. \(\rho \in (0,1)\) is the exposure of a loan j to the market risk Y. The loan interest rate is r so that the amount due in period 1 is \((1+r)L\) (notional assets). A banks’ expected wealth in period 1 is a random variable w(Y), defined as:The c.d.f of the realized value of the loan portfolio w(Y) at date 1 is given byThe bank needs to pay its lenders at date 1 (notional liabilities):where f is the risk-free rate and \(\xi \in [1/(1+f),1]\) is the interest distribution parameter of liabilities. It is assumed that deposits have a strictly lower interest rate than the wholesale market.⁴ When \(\xi =1\), the bank’s liabilities are fully financed from the wholesale funding market, and it does not have any deposits. Conversely, if \(\xi = (1/(1+f)\), the bank’s liabilities are fully funded by non-interest-bearing deposits. Most banks are somewhere in between, and it can be motivated in a similar way as in Xiao (2020).

In order to link the lending to the liabilities, we use a Value-at-Risk (VaR) constraint. Suppose a loan’s default probability is less than \(\alpha \) based on the bank’s risk management requirement. So the VaR constraint becomes:Rearranging equation (11), we can obtain the following equation for the ratio of notional liabilities to notional assets:Denote the left side of this equation \(\varphi \):\(\varphi \) is a function of loan default probability \(\varepsilon \), the value-at-risk constraint parameter \(\alpha \) and systemic risk share \(\rho \). Combining equations (12) and (13) with (1) leads to the loan supply equationSolving for L:Note that for the loan supply to be well defined, it is necessary that \(\frac{\varphi (1+r)}{(1+f)\xi }<1\). The market equilibrium condition is that the loan demand is equal to the loan supply. Demand is downward sloping in the loan interest rate r.This leads us to our first proposition:

Reducing \(\xi \) shifts the loan supply curve to the right and increases the risk-taking of the banking sector. Since more non-interest-bearing deposits correspond to a lower \(\xi \), a bank’s risk-taking is elevated if non-interest-bearing deposits are high, given everything else constant. If \(\xi \) is close to the lower bound \(1/(1+f)\), liabilities are essentially non-interest-bearing deposits and bank lending does not react to changes in the risk-free rate. If \(\xi =1\), the bank is fully financed by wholesale funding and its lending is most sensitive to the short-term interest rate. As a result, the lending of banks with larger non-interest-bearing deposits should be less sensitive to changes in the short-term interest rate.

For equity, a similar relationship can be found. \(\varphi \) is the leverage of the bank, and hence capital increases if \(\varphi \) becomes smaller. The lending of banks with a low \(\varphi \) will respond less to changes in the interest rate than the lending of banks with a high \(\varphi \), meaning that banks with a higher leverage react more to changes in the interest rate.

The main data we use are a quarterly panel of bank holding companies from Q1 1996 to Q3 2021. We retrieved the bank holding companies’ financial statement through Federal Reserve Y9-C report. The monthly stock market return data are from the Center for Research in Securities Prices (CRSP). We merge banks’ stock return with FR Y-9C report using the Permanent Company Number - Regulatory identification numbers (PERMCO-RSSD) link table by the Federal Reserve Bank of New York. The summary statistics for our variables are presented in Table 2.

In order to assess whether equity and other liabilities influence the risk-taking of banks, we first need to define the bank asset risk, our dependent variable. We use four measures from the existing literature. The first measure is the ratio of loan loss provisions to the total loans [see Khan et al. (2017)]. This measure is also closely related to the loan level measure used in Dell’Ariccia et al. (2017). The second measure is the minus Z-score defined aswhere \(\sigma _{ROA}\) is the standard deviation of the return on assets (ROA). The third measure is the one-year rolling window standard deviation of the return on assets (ROA) [see Egan et al. (2017)]. Finally, we use a market-based measure of bank asset risk, proxied by the bank holding companies’ quarterly standard deviation of its stock return.

Our main independent variables are the risk-free rate for which we use the Wu and Xia (2016) shadow Fed Funds rate.⁵ For the equity measure, we use the tier 1 ratio and for \(\xi \) we use the non-interest-bearing deposits over total assets.

Our main control variables are taken from (Khan et al. (2017) and Dell’Ariccia et al. (2017)) and include the natural logarithm of total assets, the return on assets (ROA), the share of total loans to total assets, the share of commercial and industrial loans to total loans and the liquid asset ratio, where liquid asset is defined as the ratio of cash and balances due from depository institutions to total assets.

For all variables, we winsorize the data at the 5% level like in Khan et al. (2017) to avoid outliers from driving our results. We also repeated the regressions with trimming at the 5% level, and the results are robust to this alternative.

The empirical prediction from the model is that low funding cost liabilities should play a similar role as tier 1 ratio in the banks’ risk-taking. For readability, we did not list the tier 1 ratio and its interaction with the shadow Fed Funds rate separately in the below equations. To this end, our baseline fixed effects panel specification iswhere \(BankRisk_{i,t}\) is one of the four risk measures, \(SFFR_{t}\) is the shadow Fed Funds rate, \(NIBDep_{i,t-1}\) is the share of non-interest-bearing deposits as a fraction of total assets in period \(t-1\).⁶X are the control variables, \(\nu _i\) are the bank fixed effects and \(\varepsilon _{i,t}\) is the error term. Standard errors are clustered at the bank level.

Our alternative setup also includes time fixed effects \(\mu _t\) which will remove the shadow Fed Funds rate from the regression.As in the previous specification, standard errors are clustered at the bank level.

This paper showed in a value-at-risk risk-taking channel model that the lending for banks with relatively more equity and non-interest-bearing deposits should respond less to monetary policy tightening. This suggests that non-interest-bearing deposits act as “pseudo capital.” The implication for capital in this model is the same as in the bank lending channel; under monetary tightening, well-capitalized banks should reduce their lending by less than less capitalized banks. This is not the case for deposits. The bank lending channel assumes that monetary policy mainly affects deposits and banks with substantial deposits should react strongly to monetary policy changes. Our model suggests that this is not the case for banks with substantial non-interest-bearing deposits.

Our subsequent tests of these implications using a panel of US banks find strong evidence in support of our model for a variety of risk measures. We also find that it is not general deposits that determine the reaction to monetary policy but rather there is a hierarchy. Specifically, lower interest rate deposits reduce the monetary policy reaction, while higher interest rate deposits increase the monetary policy reaction. Further research might be able to address whether this hierarchy of deposits also arises in a bank lending channel model or not.