Bank Market Power and Monetary Policy Transmission: Evidence from a Structural Estimation
银行市场力量和货币政策传导：结构估计的证据

A. Households A. 家庭

In our infinite-horizon equilibrium model, at each time t, the economy contains a mass
在我们的无限时间视野均衡模型中，在每个时间 t，经济体包含一个质量$$W_{t}$$ of households, each of which is endowed with one dollar. Households allocate their endowments in across three investment options: cash, bonds, and deposits. Deposits of each bank constitute a differentiated product. If we index each option by j, the households' choice set is given by
每个家庭都被赋予一美元。家庭将其赋予分配到三种投资选择中：现金、债券和存款。每家银行的存款构成了一种差异化产品。如果我们用 j 来索引每个选项，家庭的选择集由以下给出。$$\mathcal {A}^{d}=\lbrace 0,1,\ldots ,J,J+1\rbrace $$, with option 0 representing cash, option
, 选项 0 代表现金，选项$$J+1$$ representing short-term bonds, and options
代表短期债券和期权$$1, \ldots , J$$ representing deposits in each bank. Because the households' problem is static, we drop the t subscript hereafter for convenience. We further assume that each depositor can choose only one option. This one-dollar, one-option assumption is without loss of generality. For example, we can interpret this setting as if households make multiple discrete choices for each dollar they have, and the probability of choosing each of the options can be interpreted as a portfolio weight.
在我们的无限时间视角均衡模型中，在每个时间 t，经济体包含一群 $$W_{t}$$ 的家庭，每个家庭都拥有一美元。家庭将其资产分配到三种投资选择中：现金、债券和存款。每家银行的存款构成了一个差异化产品。如果我们用 j 索引每个选项，家庭的选择集由 $$\mathcal {A}^{d}=\lbrace 0,1,\ldots ,J,J+1\rbrace $$ 给出，其中选项 0 代表现金，选项 $$J+1$$ 代表短期债券，选项 $$1, \ldots , J$$ 代表每家银行的存款。由于家庭的问题是静态的，为了方便起见，我们在此之后省略 t 下标。我们进一步假设每个存款人只能选择一种选项。这种一美元、一选项的假设并不失去一般性。例如，我们可以将这种设置解释为家庭为每个拥有的美元做出多个离散选择，而选择每个选项的概率可以解释为投资组合权重。

Each option is characterized by a yield, $$r_{j}^{d}$$, and a vector of product characteristics, $$x_{j}^{d}$$, which capture the convenience of each option. For instance, a household might value the number of branches and the number of employees per branch when choosing a bank. The yield on cash is zero, and the yield on bonds is the federal funds rate, f, where we abstract from differences between short-term Treasury yields and the federal funds rate. All interest rates are quoted in real terms, as we assume that inflation expectations are anchored at zero, but in the general equilibrium version of the model in Section XI of the Internet Appendix, we allow for an endogenously determined inflation rate.2

B. Firms B. 公司

There is a mass K of firms, where we again drop the time subscript. Each firm wants to borrow one dollar, so aggregate borrowing demand is K. Firms can borrow by issuing long-term bonds or by taking out long-term bank loans. We assume that each bank is a differentiated lender, given factors such as geographic location and industry expertise. Letting each option be indexed by j, the firms' choice set is given by $$\mathcal {A}^l=\lbrace 0,1,\ldots ,J,J+1\rbrace $$, where option $$J+1$$ represents bonds, options $$1,\ldots ,J$$ represent loans from each bank, and option 0 is the option to not borrow at all.

For tractability, we assume that both bonds and bank loans are long term and that a fraction η of the outstanding balance is due every year. Thus, if the borrower obtains one dollar, this debt has a maturity of $$\frac{1}{\eta }$$ years, on average. If a firm obtains a loan from bank j, it will be charged a fixed interest rate of $$r^{l}_{j}$$. If a firm issues long-term bonds, the interest rate is given by an expected default cost, δ, plus the expected weighted average of future federal funds rates, $$f_t$$, which is given by

(5)

Each of the firm's financing options is characterized by a rate, $$r_{j}^{l}$$, and a vector of product characteristics, $$x_{j}^{l}$$, capturing the convenience of using each of the financing options.

C. The Banking Sector

Similarly, given each bank j's choice of $$, firms solve their profit-maximization problem, which yields the quantity of loans borrowed from bank j, $$, given by equation (9). To simplify notation, we suppress the dependence of loans and deposits on the relevant interest rates, denoting them simply by $$ and $$.

We assume that in each period, a random fraction of maturing loans, $$, becomes delinquent. The bank takes δ as an exogenous state variable in its decision-making problem. We assume that the bank writes off delinquent payments, with charge-offs equal to $$, so default depresses the bank's current-period cash flows. However, defaulting on a payment in one period does not exonerate the borrower from future payments, so delinquency does not affect the evolution of loans in equation (12).

The rest of the asset side of each bank's balance sheet consists of reserves, $$, and holdings of government securities, $$, which the bank can accumulate if the supply of funds exceeds demand from the lending market. These securities earn the federal funds rate, $$.

The cost in equation (13) represents an important friction because, in its absence, banks could always raise nonreservable funding to compensate for any deposit shortfalls. The availability of such funding would disconnect banks' deposit-taking and lending decisions, so changes in bank deposits induced by federal funds rate shocks would have no impact on lending.

D. Monetary Policy

Monetary policy affects banks in two ways. First, from equation (13), the federal funds rate affects the marginal funding costs that banks pay in the nonreservable funding market. Second, the short-term federal funds rate affects long rates through expectations. Thus, both long- and short-rate movements affect banks' market power in the deposit and loan markets.

E. Bank's Problem and Equilibrium

Figure 2 shows the sequence of events in each time period. The bank enters the period and observes both the federal funds rate $$ and the realization of the fraction of defaults $$. Next, banks interact with households and firms by setting the loan and deposit spreads. The loan and deposit demand functions then dictate the amount of deposits from households and the amount of loans to firms. Depending on the extent of these activities, the banks adjust their reserves, holdings of government securities, and nonreservable borrowing. Finally, banks collect profits at the end of the period and distribute dividends to shareholders.

We define equilibrium in this economy as follows.

In solving the model, which we describe in detail in Section I of the Internet Appendix, we ensure that $$ and $$ are consistent with equilibrium bank choices by iterating over their values until we reach convergence. To check the accuracy of our solution, we regress the simulated evolution of the aggregate deposit and loan rates on the perceived law of motion based on banks' beliefs. The R²s for these approximations are over 95% for the deposit market and 97% for the loan market. Thus, although the banks do not consider the full distribution, $$, when making their decisions, their forecasting errors are small. This accuracy stems from two mechanisms in the model. First, without any financial or regulatory constraints, banks have static optimal deposit and loan rates. For example, in the lending market, the optimal level of loans is set to equalize expected marginal interest income and funding costs, which is a function of the current federal funds rate only. Therefore, the static optimal rate depends only on the federal funds rate, not on other aggregate moments. Second, taking the loan market as an example, although banks can deviate from the static optimum by charging higher loan spreads, this behavior is limited by competition from other banks. Thus, banks that deviate from the static optimum introduce only modest distortions into the other banks' rate forecasts.

F. Monetary Policy Transmission in a Static Model

In this subsection, we use a simplified, static version of the model to highlight the intuition behind the effects of frictions on monetary policy transmission. We assume that both deposits and loans have a maturity of one year, thus precluding a maturity transformation. Because the model is then static, we drop the t subscripts. Banks face no idiosyncratic uncertainty, and their ex ante identical problems produce ex post identical solutions. In addition, all depositors have the same rate sensitivities: $$. Finally, we assume that the operating costs, $$ and $$, are zero. Derivations of all of the statements in this subsection can be found in Section II of the Internet Appendix.

A. Estimation Procedure

We estimate the model in two stages. First, we estimate the loan and deposit demand functions. Second, we plug these estimates into the model and use SMD to estimate the remaining parameters that describe banks' balance sheet frictions.

We estimate deposit and loan demand, given by equations (3) and (8), using the methods in Berry, Levinsohn, and Pakes (1995) (BLP) and Nevo (2001), where the set of bank characteristics used in the demand estimation includes the number of branches, the number of employees per branch, bank, and time fixed effects. We provide a brief outline of our implementation of this procedure below. A detailed explanation is in Section III of the Internet Appendix.

We start with the definition of a market. For both our deposit and loan demand estimation, we use the U.S. national market as the market definition, where each year constitutes a separate market. This choice is necessary because data on many types of loans (e.g., commercial and industrial loans) are not available at subnational levels. However, as shown in Section IA.I of the Internet Appendix, our results are robust to estimating deposit demand at the local level.

A key challenge in identifying demand elasticities is the natural correlation between either deposit or loan rates and any unobservable demand shocks $$ that move the error terms in the estimating equations. For example, a positive deposit demand shock can induce banks to lower deposit rates. Therefore, we use a set of supply shifters as instrumental variables. In particular, following Ho and Ishii (2011), we use salaries and noninterest expenses related to the use of fixed assets.

We need to assume that these supply shifters are orthogonal to unobservable demand shocks and thus shift the supply curve along the demand curve, allowing us to trace out the slope of the demand curve. One assumption that supports but does not guarantee identification is that customers do not care about these costs, holding product characteristics constant. Note that our identification of the demand curve does not use variation in monetary policy. In fact, any aggregate shocks are absorbed by time fixed effects, so our identification strategy avoids a common challenge that studies of monetary transmission face, namely, the endogeneity of monetary policy and aggregate bank credit supply.

The final plug-in problem consists of inserting the estimated demand functions described in equations (37) and (38) into the banks' dynamic problem (24). This plug-in problem operationalizes the notion that banks set deposit and loan rates facing the above-specified demand curves for deposits and loans.

In the second stage, we estimate seven additional parameters using SMD, which produces parameter estimates that minimize the distance between moments (or functions of moments) generated by the model and their analogs in the data. We use 10 moments to identify the remaining seven-model parameters. Parameter identification in SMD requires choosing moments whose predicted values are sensitive to the model's underlying parameters. Our identification strategy ensures that there is a unique parameter vector that makes the model fit the data as closely as possible.

First, we use banks' average nonreservable borrowing as a fraction of deposits to identify the cost of holding nonreservables, $$. Intuitively, higher financing costs induce banks to finance loans mainly through deposits, and less via borrowing. Next, we use the average deposit and loan spreads to identify banks' marginal costs of generating deposits, $$, and servicing loans, $$. Higher marginal costs lead banks to charge higher spreads in both deposit and loan markets. Next, we use two moments to identify the net fixed operating cost, ψ. The first is average net noninterest expenses scaled by assets. This moment measures the costs that banks pay outside of their routine deposit-taking and loan-servicing businesses. The second moment is banks' average leverage ratio, which indirectly reflects fixed operating costs, as higher fixed costs induce banks to operate with lower leverage. Next, we use banks' average dividend yield to identify the discount rate γ because a high discount rate makes banks impatient, so they pay out more of their profits to shareholders instead of retaining the funds to finance future business.

Next, to identify the relative size of the deposit market $$ and the value of firms' outside option of not borrowing $$, we include banks' average deposit-to-asset ratio and the sensitivity of total borrowing to the federal funds rate, which we estimate using a vector autoregression (VAR), the details of which are in Section V of the Internet Appendix. These two moments suit this purpose for several reasons. Holding banks' market shares constant, when $$ increases, the value of deposits rises relative to the value of loans, leading to a higher deposit-to-asset ratio. In addition, the deposit-to-asset ratio is positively related to $$ because loan demand falls with this outside option. Fewer loans imply a smaller overall balance sheet, so ceteris paribus, the ratio of deposits to assets rises. The sensitivity of aggregate corporate borrowing to the federal funds rate also helps identify $$ because when the outside option becomes less valuable, its market share remains low regardless of the federal funds rate. Thus, the sensitivity of aggregate corporate borrowing to the federal funds rate falls as $$ falls.

Finally, we include two extra moments that are important for ensuring that our counterfactuals are empirically relevant. To make our model accurately reflect bank valuation, we include banks' average market-to-book ratio. To ensure that our model correctly quantifies baseline monetary transmission from the federal funds rate to bank lending, we include the sensitivity of bank lending to the federal funds rate, again estimated using a VAR. Otherwise, it would be hard to claim that our model provides a sensible decomposition of the various monetary transmission mechanisms.

B. Baseline Estimation Results

Table III presents the point estimates for the model parameters. In Panel A, we start with the statutory parameters. We set the corporate tax rate to its statutory rate of 35% and the capital requirement to 6% according to the Basel III accord. According to the Federal Reserve Board's Regulation D, the reserve ratios are 10% for transaction deposits, 1% for saving deposits, and 0% otherwise. In our model, we include only one type of deposit, so our estimate of the reserve ratio is a weighted average of these three requirements, where the weights are the shares of a particular type of deposit in total deposits. We calibrate the number of representative banks to be six, which matches the average county-level banking concentration in the data.

Panel B presents the parameters that we can directly quantify in the data. Specifically, we obtain the means, standard deviations, and autocorrelations of the federal funds rate and the bank-level loan default rate by direct estimation of equation (22). Next, average loan maturity, defined in Table I, is approximately 3.5 years.

Panel C in Table III provides the demand parameters from the first-stage BLP estimation, with details of the estimation results presented in Table IA.II in Section VI of the Internet Appendix. Not surprisingly, we find that depositors react favorably to high deposit rates, while borrowers react negatively to high loan rates. Both yield sensitivities are precisely estimated, and the economic magnitudes are significant. A 1 percentage point increase in the deposit rate increases a bank's market share by 0.968%, while a 1 percentage point increase in the loan rates decreases its market share by 1.424%. We also find that depositors exhibit significant dispersion in their rate sensitivity. Finally, we estimate depositors' and borrowers' sensitivities to nonrate bank characteristics. The estimates are also both statistically and economically significant. A 1 percentage point increase in the number of branches increases a bank's market share by 0.804% in the deposit market and 0.944% in the loan market. In comparison, the sensitivity to the number of employees per branch is smaller. A 1 percentage point increase in the number of employees per branch increases a bank's market share by 0.714% in the deposit market and 0.630% in the lending market. These estimated yield sensitivities lie close to similar estimates in the literature, with Dick (2008), Ho and Ishii (2011), and Egan, Hortaçsu, and Matvos (2017) finding deposit sensitivity estimates from 0.6 to 1.1. Comparable loan sensitivity estimates can only be found in the mortgage demand literature, which features estimates in the −1.1 to −5.2 range (DeFusco and Paciorek (2017), Buchak et al. (2018)).

One challenge to identification of this demand estimation is the possibility that when banks face more demand, they hire more higher-quality staff. Conversely, hiring higher-quality staff might spur demand. We confront these concerns in two ways. First, we emphasize that this issue is partially alleviated by the inclusion of bank fixed effects, which absorb the heterogeneity in demand in the cross-section of banks. Similarly, time fixed effects absorb the aggregate shocks to deposit demand. Second, because our instruments may nonetheless be correlated with bank-specific, time-varying unobservable demand shocks, as a robustness check, we also use an instrument from Dick (2008) that is less likely to capture bank-specific labor costs, namely, the weighted average of the local bank teller wages from the Bureau of Labor Statistics (BLS) over the markets in which the bank operates, where the weight is the bank's deposit share in each market relative to its total deposits. This instrument addresses the concern that the Call Report salary data likely contain a quality component that might influence demand. The results from using this instrument are in Tables IA.III and IA.IV in Section VII of the Internet Appendix. We find a deposit sensitivity of 0.668 and a loan sensitivity of −0.950. Both estimates are somewhat smaller than those in Table III, but their relative magnitudes remain intact, even though the sample period for the BLS data runs from only 1997 to 2017. Both estimates are also noisier than those in Table III, with the loan sensitivity being insignificantly different from zero, likely because loan markets are less local in nature than deposit markets. Because of the noise in these estimates, for our baseline analysis, we use the estimates in Table III.

Panel D of Table III presents the parameters from our second-stage SMD estimation. We find that banks have a subjective discount rate of 4.8%, which is higher than the average federal funds rate observed in the data. Given the discount rate, banks pay out 3% of their equity value as dividends. Next, the cost of nonreservable borrowing is both statistically and economically significant. At the average level of nonreservable borrowing (30% of total deposits), a marginal dollar of nonreservable borrowing costs a bank 30 basis points (bps) above the cost implied by the prevailing federal funds rate, where we calculate this cost as $$, which implies that banks pay an extra 30 bps on each extra dollar of nonreservable borrowing. This result implies that banks cannot easily replace deposits with other funding sources. Therefore, shocks to bank deposits are likely to be transmitted to bank lending. Finally, we find that banks incur a 1% cost of maintaining deposits and a slightly lower 0.7% cost of servicing their outstanding loans.

In Table IV, we compare the empirical and model-implied moments. The model is able to match closely the banks' balance sheet quantities, the spreads they charge, and their valuations. Banks borrow nonreservable securities that amount to 30% of the deposit intake in the data (versus 26% in the model). In both the model and the data, the spreads that banks charge in the deposit market are significantly smaller than those in the loan market. When the federal funds rate is low, as it is in much of our sample, banks face stiffer competition from cash, so they shrink deposit spreads.

C. External Validity

While Table IV provides evidence of model fit, we now proceed to several external model validation exercises. First, in Figure 3, we plot the relation between banks' deposit and loan rates and the federal funds rate, as implied by our model and as calculated from our data, where we accompany the data calculations with a quarterly scatter plot. Note that we do not use these relations in our moment-matching exercise, as we target only the average levels of these rates. Figure 3 shows that the pass-through of the federal funds rate in both the deposit and loan markets is less than one to one, as indicated by the less than unitary slope of the plots. This result is consistent with the message in Table III and Table IA.II in Section VI of the Internet Appendix, as it suggests that banks have significant market power. In addition, our model-predicted deposit and loan rates track the pattern that we see in the actual data, indicating that our model can quantitatively capture banks' pricing of their products in both the deposit and the loan markets.

Second, we compare our model predictions with the reduced-form evidence in Drechsler, Savov, and Schnabl (2017) on heterogeneity in monetary transmission. In particular, we consider their finding that the sensitivity of deposit spreads to the federal funds rate rises with the local market Herfindahl-Hirschman Index (HHI) by 3 to 4 bps when moving from a local market at the 25^th percentile of the HHI distribution to one at the 75^th (Drechsler, Savov, and Schnabl, 2017, figure IV). Using the summary statistics in Drechsler, Savov, and Schnabl (2017) and assuming that HHIs are normally distributed, we estimate this interquartile range to be (0.15, 0.34). We find quantitatively similar results in our model when we allow the HHI in our model to vary over this range, with Panel A of Figure 4 showing a fall in the deposit rate sensitivity of 3 bps, which implies that the deposit spread sensitivity rises by 3 bps.

Third, Drechsler, Savov, and Schnabl (2017) find that an increase in the deposit market HHI over its interquartile range accompanies a rise in the sensitivity of deposits to the federal funds rate by 66 bps (Table III). Panel A of Figure 4 shows that in our model, an equivalent increase in the deposit market HHI accompanies a rise the sensitivity of deposits to the federal funds rate by 76 bps, which is close to the estimate in Drechsler, Savov, and Schnabl (2017). Panel A also shows that an increase the HHI over its interquartile range raises the sensitivity of deposits to the federal funds rate by 70 bps.

Fourth, our model also generates the pattern in Drechsler, Savov, and Schnabl (2017, figure IV) whereby even in regions with an extremely low HHI, the sensitivity of the deposit spread to the federal funds rate is still significantly different from zero. Drechsler, Savov, and Schnabl (2017) argue that factors beyond market concentration, such as depositor sophistication, also play a role in determining banks' market power. We find a similar pattern in our estimated model—even when the HHI is 0.1, a 100 bp increase in the federal funds rate leads to only a 80 bp increase in the deposit rate, as the deposit spread increases by 20 bps. Our model generates this result through a relatively large estimate of the yield dispersion, $$. High dispersion implies that even in less concentrated markets, a significant fraction of depositors are rate-insensitive. They tolerate higher spreads charged by banks, thus giving banks market power.

Fifth, we compare the results in Scharfstein and Sunderam (2016) with predictions from our model. This comparison cannot be quantitative because Scharfstein and Sunderam (2016) examine the mortgage market, while we examine the total loan market. Nonetheless, as shown in Panel B of Figure 4, we find that the sensitivity of the loan spread to the federal funds rate falls in absolute value as the HHI rises, which implies that the transmission of the federal funds rate to lending rates becomes lower when the market becomes more concentrated. Additionally, Panel B shows that an increase in the loan market HII over its interquartile range decreases the sensitivity of loans to the federal funds rate by 82 bps. In comparison, Scharfstein and Sunderam (2016, figure 3) show that the transmission of changes in yields on mortgage-backed securities, which they use as a proxy for banks' cost of funds, is lower in counties with more concentrated loan markets. Panel B also shows that the sensitivity of the quantity of loans to the federal funds rate decreases in absolute value with the model HHI. Scharfstein and Sunderam (2016) show that the sensitivity of mortgage refinancing to the yield on mortgage-backed securities decreases with market concentration.

Sixth, we check the external validity of the estimation results in Table IV by ascertaining whether our model can match the impulse responses of several variables not used for estimation. To calculate the VARs in our data, we use the high-frequency monetary shocks (Gertler and Karadi (2015)) as external instruments. Details are in Section V of the Internet Appendix. This high-frequency approach is not possible for our actual estimation because our model is not sufficiently rich to produce these shocks. However, using it in our actual data as an external validity check is informative because the federal funds rate in our model is assumed to be exogenous, so it is natural to compare model impulse responses to well-identified data estimates.

Table V presents the simple VAR coefficients generated by our model, along with the well-identified VAR coefficients estimated from our data. Panels A and B of Table V present the impulses of prices and quantities, respectively, over a two-year horizon. We find that we can closely match the sensitivities between the federal funds rate and both deposit and loan spreads. We also find that in the data, net noninterest expense is insensitive to the federal funds rate, which is also consistent with our model because we model this expense as a constant, so its sensitivity to federal funds rate shocks is zero by definition. Finally, our model generates impulse responses that match their empirical counterparts for other important bank balance sheet variables such as deposits, loans, borrowing, and securities.

Finally, we examine how the market value of bank equity reacts to an unexpected federal funds rate shock. In the data, a 1 percentage point increase in the federal funds rate leads to a 1.93% drop in bank equity value. Although our model is not geared to match asset pricing moments, the same magnitude shock generates a 1.44% drop in equity value. This result is important because models without market power can overpredict this response.

This small equity market response occurs in our model because of deposit market power, which makes deposit rates insensitive to the policy rate and thereby implies that deposits effectively have long duration (Drechsler, Savov, and Schnabl (2021)). To emphasize this point, we examine the equity response in our model when we force deposit rates to move one-for-one with the federal funds rate, finding a sharp 11% drop.

A. Decomposing Monetary Policy Transmission

We now examine the quantitative forces that shape the relation between aggregate bank lending and monetary policy, as embodied in the federal funds rate. Table VI depicts, for different versions of our model, the percentage change in aggregate bank lending in response to a 1 percentage point change in the federal funds rate over a two-year horizon. We show the results of an experiment in which we start with our model exactly as specified in Section II, with all frictions as estimated in Table III. We then eliminate from the model regulatory constraints and banks' market power one at a time. As such, we analyze how the absence of each of these frictions affects the transmission of monetary policy.

Row (1) corresponds to the baseline model and shows a response of 1.64%, which is insignificantly different from the response of 1.59% that we find in the data. Row (2) presents the results from a version of the model without the reserve requirement. We find that the sensitivity of bank lending to the federal funds rate decreases by 8.6%. This modest magnitude reflects the small amount of noninterest-bearing reserves held by banks in our sample period.4 As a result, monetary policy has a limited effect on banks' marginal costs of lending through the reserve requirement.

This result provides insights into a recent policy debate over interest on excess reserves. In October 2008, the Federal Reserve started paying interest on reserves. This move spawned worry over the power of monetary policy to affect bank lending. For instance, a January 1, 2019 Wall Street Journal article argues that “by paying banks not to lend, the central bank diminished its ability to control interest rates.5” Also, a June 22, 2019 article in the American Banker states that “It was thanks to interest on excess reserves that the Fed ended up stimulating so little in the economy, despite its efforts to ease so much.6” However, we find that this concern is unwarranted, as the bank reserve transmission channel is not important during our sample period. This result is also consistent with Xiao (2020), who shows that the reserve requirement is not a quantitatively important feature that distinguishes commercial banks from shadow banks.

Row (3) in Table VI presents the results from a version of the model that excludes the capital requirement. We find that the presence of the capital requirement enhances monetary policy transmission by 23.9% $$. This result connects two long-standing sets of reduced-form evidence on the bank capital channel. The first set shows that monetary policy shocks can trigger movements in bank capital because of the maturity mismatch on banks' balance sheets (Flannery and James (1984), English, Van den Heuvel, and Zakrajšek (2018)). The second set shows that bank capital has an economically significant impact on bank lending (Peek and Rosengren (2000), Mora and Logan (2012)). Because bank capital is endogenous, this second literature often exploits exogenous shocks to bank capital instead of directly focusing on the role of monetary policy. Our paper bridges the two bodies of empirical evidence by connecting monetary policy to bank lending through the bank capital requirement. Moreover, we measure the quantitative magnitude of this long-established channel.

Row (4) of Table VI shows the results from removing banks' deposit market power from the model. In this case, banks receive fixed lump-sum profits equal to their oligopolistic profits in the baseline case. They also use marginal cost pricing for deposit-intake decisions, setting the deposit rate equal to the federal funds rate minus the bank's marginal cost of servicing deposits. They then take as many deposits as depositors offer, given the deposit rate.7 Note that we do not change the parameters governing investors' preferences (the yield sensitivities and dispersion) in this counterfactual analysis. We find that once we eliminate market power in the deposit market, bank lending becomes less sensitive to changes in the federal funds rate. A 1% increase in the federal funds rate causes an almost one-to-one decrease in aggregate lending. This sensitivity is 31% $$ smaller than the 1.641% sensitivity observed in the baseline case. Moreover, the change in sensitivity is larger than that observed when we eliminate the capital requirement.

Intuitively, if deposit market power is in place, when the federal funds rate increases, the households' opportunity cost of holding cash rises, making cash less attractive relative to bank deposits and other interest-bearing assets. Banks react by charging higher deposit spreads, so households substitute into other interest-bearing assets and the equilibrium quantity of deposits falls. This fall in deposits impacts banks' lending decisions because they need to use expensive nonreservable borrowing to finance their loans when the amount of loans exceeds deposits. Thus, bank market power, combined with the nonreservable borrowing cost, contributes to a negative relationship between bank lending and the federal funds rate. Finally, this result is important because it highlights the interconnectedness of banks' deposit-taking and lending businesses. Banks' market power in the deposit market is passed on to the loan market and contributes to the sensitivity of bank lending to the federal funds rate.

Row (5) of Table VI shows the results from removing banks' lending market power from the model. To isolate the effect of loan market power, we allow banks to retain their oligopolistic market power in the deposit market, but in the loan market, we assume that banks act as price takers. They adopt marginal cost pricing and set their loan rates equal to the funding cost. We find that the presence of banks' loan market power makes the aggregate quantity of loans less sensitive to the federal funds rate, with the sensitivity changing by −18.9% $$. This result quantifies the intuition in Scharfstein and Sunderam (2016) and Corbae and Levine (2019), who argue and show that loan market power allows banks to cushion the effects of monetary tightening on lending by reducing markups on loans.

In Table IA.VIII in Section X of the Internet Appendix, we present the results of the converse experiment, in which we start with a version of the model without regulatory frictions or market power and then add these frictions back in one at a time. We find that the relative importance of the different channels remains intact, but the quantitative effects of both capital regulation and market power are weaker when we start from the frictionless case, suggesting significant complementarity between the two mechanisms.

Overall, we find that monetary transmission channels based on market power have comparable, if not larger, effects than channels based on regulation. Thus, our findings highlight the importance of accounting for the banking system market structure in assessing monetary transmission mechanisms.

B. Reversal Rate

Does the sensitivity of lending to the federal funds rate depends on its level? In Panel A of Figure 5, we show the amount of bank lending that corresponds to different levels of the federal funds rate, where we normalize steady-state lending to one. We find that aggregate bank lending in the economy is hump-shaped. When the federal funds rate rises above a certain threshold, a further increase has the usual effect of tightening lending. However, when the rate is below 0.9%, a rate increase actually expands lending. We call this region a reversal-rate environment.

To understand the mechanism behind the reversal rate, in Panel B, we plot the amount of desired bank lending in a world with no capital requirements, and in Panel C, we plot the level of bank capital. First, we see that desired lending always falls with the federal funds rate. However, the relation between bank equity capital and the federal funds rate is also hump-shaped, with a 2% turning point at which the relation between bank equity and the federal funds rate flips sign.

Two properties of the relations shown in Panels B and C underlie the reversal rate. The intuition behind Panel B is straightforward, as high funding costs deter firms from borrowing in equilibrium. The intuition behind Panel C is more nuanced and depends on the relative profitability of lending and deposit taking. First, as the federal funds rate rises, depositors find holding cash to be increasingly costly, so banks face weaker competition from cash in the deposit market. Hence, bank profits from the deposit market rise with the federal funds rate. Second, bank profits from lending decrease with the federal funds rate, as higher funding costs make firms' outside option of not borrowing more appealing. Our parameter estimates imply that the deposit market exerts more pressure on profits than the lending market when the federal funds rate is low. Thus, an increase in the rate leads to higher bank profits, which banks use to bolster their equity capital base. Banks accumulate equity capital instead of paying out their profits to shareholders as a precaution against being capital constrained in the future. In contrast, in a region of high federal funds rates, further rate increases erode bank capital via a standard maturity mismatch argument.

The reversal rate in Panel A arises because optimal lending is the smaller of two quantities: desired and feasible lending. The former is the optimal amount of lending in the absence of a capital requirement, and the latter is the maximal lending permitted by a bank's equity capital. When the federal funds rate is low, given firms' equilibrium heavy demand for loans in a low-rate environment, desired lending exceeds the amount allowed by the bank's equity. Thus, the capital requirement binds, and actual lending tracks the bank's equity capital, which increases with the federal funds rate. When this rate is high, the capital requirement is slack, and the actual quantity of lending is the desired amount.

To bolster the intuition that the reversal rate stems from the interaction of deposit market power and capital regulation, in Panel D of Figure 5, we plot the relation between bank lending and the federal funds rate under the assumption that banks face perfectly elastic demand for deposits when deposits are priced at the federal funds rate minus the banks' marginal cost to service depositors. We find no reversal effect in this setting.

To understand more fully the dynamic response of bank lending to monetary policy shocks, in Figure 6, we report the simulated response of bank lending to federal funds rate shocks. The economy starts at time 0 in an initial steady state with the federal funds rate equal to the inflection point of 0.9%. At time 1, the federal funds rate either increases to 2% or decreases to 0.1%, and it stays at that level until the economy reaches a new steady state. Each variable in the graph is scaled by its level in the initial steady state.

Panel A of Figure 6 depicts the response to an increase in the federal funds rate. In this case, banks face less competition from household demand for cash in the deposit market. Thus, they behave more like monopolists by charging higher spreads, which, in turn, lower household deposit demand. Lower deposit intake increases the need for banks to fund their lending by turning to the market for nonreservable borrowing, which carries increasing marginal costs. A positive federal funds rate shock also increases the cost of capital in the corporate sector, making firms more likely to switch to the outside option of not borrowing. Both effects shrink lending. Because deposits have shorter duration than loans, deposits drop sharply and converge almost instantaneously to the new steady state. In contrast, loan quantity converges slowly as the bank replaces only a fraction, η, of its long-term loans in each period. Nonreservable borrowing increases to fill the gap between deposits and loans.

Panel B of Figure 6 depicts the responses to a decrease in the federal funds rate. On the one hand, when this rate decreases, banks profit from having a maturity mismatch on their balance sheets as the rates they pay on short-term liabilities decrease instantly, while most of their long-term assets keep generating higher rates of return. This effect diminishes gradually over time as existing loans mature and are repriced. On the other hand, a lower federal funds rate leads to increasingly intense competition from cash in the deposit market. The effect is especially strong as the federal funds rate approaches the zero lower bound, in which case the spreads that banks can charge in the deposit market are squeezed, leading to a sharp drop in their profits. Given the persistence of the federal funds rate, lower profits translate into slower retained earnings accumulation and, in turn, lower bank capital. In the new steady state, banks take more deposits, which can support increased lending. Indeed, lending increases in the first year. However, banks cannot sustain this higher level of lending, as their capital requirements tighten when the federal funds rate is extremely low. Because total lending decreases, banks need less external financing and thus less nonreservable borrowing.

Note that in Figure 6, lending falls when the federal funds rate changes in either direction. Although lending moves in the same direction, the driving force differs in the two cases. When the federal funds rate increases, loans fall because higher spreads in the deposit market discourage households from making deposits. Banks turn to nonreservable borrowing to fund loans, and because of increasing costs in this market, the amount of lending is highly dependent on the quantity of deposits. Instead, when the federal funds rate decreases, the loan amount decreases because of the binding capital requirement, which, in turn, echoes changes in the banks' profit accumulation.

This discussion highlights two differences between the reversal rate in our model and the reversal rate in Brunnermeier and Koby (2016). First, they assume an exogenous relation between the deposit rate and the federal funds rate, $$, which generates a sticky deposit rate, which, in turn, drives the reversal mechanism. We provide a microfoundation for this assumption by modeling the interaction between imperfect competition in the deposit market and regulatory frictions. Second, Brunnermeier and Koby (2016) calibrate their model, while we estimate ours, thus providing an empirical estimate of the turning point.

The reversal-rate result is informative about the sluggish recovery of bank lending in the United States since the 2008 financial crisis. By the end of 2018, cumulative bank lending had increased only about 25% from its low in August 2009. In contrast, from trough to peak, in all recessions since 1974, bank lending grew by 60% to 120%. Although many factors such as banking regulation may have contributed to this slow recovery, the ultra-low rate policy could be an important factor.

C. External Validation

We check external validation of the reversal-rate prediction in two ways. First, we estimate a reduced-form regression to examine the relation between bank equity returns and monetary policy news on Federal Open Market Committee (FOMC) meeting days. We measure monetary policy news released during FOMC meetings as changes in the two-year Treasury yield on FOMC meeting days, following Hanson and Stein (2015). The advantage of examining the two-year Treasury yield instead of the federal funds rate is that the former captures the effects of “forward guidance” in FOMC announcements, which has become increasingly important in recent years (Hanson and Stein (2015)).8 The identifying assumption is that unexpected changes in interest rates in a one-day window surrounding scheduled Federal Reserve announcements arise largely from news about monetary policy because macroeconomic fundamentals would not change discretely within such a short window. While our sample period runs from 1994 to 2017, we exclude the dot-com bubble collapse (2000 to 2001) and the financial crisis (2007 to 2009) because, in these crisis times, information other than conventional monetary policy news could also be released in FOMC meetings.9

Because Panel C of Figure 5 shows that the relation between bank capital and the federal funds rate changes sign around 2%, we split our data sample using a 2% cutoff for the federal funds rate. In Table VII, we report the regression estimates. As shown in column (1), when rates are high, interest rates and returns are negatively related. However, this conventional negative relation reverses sign in a low-rate environment. As shown in column (2), a rate increase is associated with a positive significant bank equity return, consistent with market expectations that an increase in rates will lead to an increase in bank capital. This result is not driven by a steepening of the term structure, as we control for changes in term spreads. As shown in Figure 7, the contrast between the results in columns (1) and (2) can be seen in a simple scatter plot of bank industry excess returns against monetary policy shocks on FOMC days. To examine the statistical significance of the difference between columns (1) and (2), in column (3), we report results from a regression in which we pool all sample observations and include a term for the interaction between the monetary policy shock and a dummy for a low federal funds rate. We find a highly significant positive coefficient on this interaction term, which is consistent with a strong reversal effect. In summary, we find that monetary policy has a nonmonotonic effect on bank capital. When the federal funds rate is high, the relation between the short-term rates and bank capital is negative, but when this rate is low, the relation is positive.

In columns (4) and (5) of Table VII, we report the results of interacting changes in the federal funds rate with the HHI of the local deposit market (county) in which a bank operates. If a bank operates in several counties, the bank-level HHI is the weighted average of local HHIs, weighted by the deposits of the bank in each county. We find that in a low-rate environment, banks with greater deposit market power experience higher positive returns. Moreover, this evidence that the reversal effect is closely linked to banks' deposit market power is reinforced by the finding in column (6) that the triple interaction between the low federal funds rate dummy, the HHI, and the policy shock is significantly positive.

Next, we explore whether the positive relation between monetary policy shocks and bank stock returns during low-rate environments is driven by the central bank's economic outlook (Nakamura and Steinsson (2018)). In Section VIII of the Internet Appendix, we present returns for all 49 Fama-French industries. We find that the banking industry is the only industry exhibiting a switch from a negative to a positive interest sensitivity in the low-interest environment. Furthermore, we use an alternative measure of monetary policy shocks constructed by Jarocinski and Karadi (2020), who disentangle the potential information shocks from monetary policy shocks. Our results are robust to this alternative measure.

The results are in Table VIII. Columns (1) and (2) show the effects of low interest rates on bank equity, and columns (3) and (4) show the effects of low interest rates on bank lending. Consistent with our model predictions, book equity and lending decrease more for high-HHI banks than for low-HHI banks when the federal funds rate falls into the reversal region.

A. Heterogeneous Transmission through Large and Small Banks

We extend our analysis by examining whether monetary transmission depends on bank size, motivated by the finding in Kashyap and Stein (1995) that monetary policy particularly affects lending by small banks, as they cannot replace deposits with frictionless access to nonreservable funding. However, one limitation of the data they use is the absence of a measure of the actual cost of external finance. While they use bank size as a proxy for this cost, size is correlated with many other bank attributes, whose presence compromises the interpretation of their results. For instance, small banks tend to lend to small firms, whose credit demand is more cyclical. Therefore, the higher sensitivity of smaller bank lending might be driven by demand rather than by financing frictions on the supply side.

To explore this issue, we split our sample at the 10^th percentile of the bank size distribution and estimate a subset of the model parameters separately for the large and small banks. For these estimations, we hold constant across subsamples parameters describing household preferences and macroeconomic conditions. We also fix the banks' discount rate because we cannot identify it in the small-bank sample. Identification using dividend yields is infeasible because many small banks do not report dividends. Also, many small banks are private, so we cannot calculate their market-to-book ratios. We reestimate all of the remaining parameters.

The results are in Table IX. We find that both external financing costs $$ and fixed operating costs ψ are larger for small banks. This result is striking because we do not use bank size as an identifying moment. Instead, $$ is identified from the fraction of assets financed by nonreservables, and ψ is identified from the banks' net noninterest expense and leverage ratios. These parameter differences across samples imply that small-bank loans are 40% more sensitive to the federal funds rate, with a −1.742 sensitivity for small banks and a −1.235 sensitivity for large banks.

Next, we examine how the sensitivity of lending to the federal funds rate depends on the frictions embodied in $$ and ψ. If we increase the big banks' financing cost $$ to the level estimated for the small banks (0.015), the big banks' sensitivity of loans to the federal funds rate rises to −1.471, an increase representing 47% of the difference in loan sensitivity between large and small banks. Because we allow only five parameters to differ across large and small banks, we effectively hold loan demand constant, thus isolating the effect of financial frictions. This result is consistent with the hypothesis in Kashyap and Stein (1995) that large and small banks have different external financing costs, which lead to differences in the transmission of monetary policy to credit supply. The fixed operating cost ψ also contributes to the stronger monetary transmission among smaller banks. Small banks have relatively few sources of noninterest income, so they have higher net operating costs, and they accumulate equity buffers more slowly. As a result, when rate hikes erode bank capital via the maturity mismatch, this effect hits small banks more strongly, leading to a sharper reduction in lending.

B. Changes in Transmission over Time

In this subsection, we examine how the impact of monetary policy on bank lending has changed over time. For example, in the past few decades, the average interest rate has declined substantially, and the banking industry itself has experienced a large volume of mergers, leading to increased concentration. To this end, we split our sample into two subperiods—early (1994 to 2005) and late (2006 to 2017). We then reestimate all model parameters for the two subperiods.10 The parameter estimates in Table X imply that the sensitivity of lending to the federal funds rate has declined from 1.53% to 1.22% over time. This result is consistent with evidence in the literature that monetary policy has had more muted effects on real activity and inflation in recent decades (Boivin, Kiley, and Mishkin (2010)).

To understand the declining impact of monetary policy on bank lending, we categorize our parameters into three groups. The first group characterizes macroeconomic conditions—the federal funds rate and the loan charge-off processes, the regulatory constraints, and the loan and deposit market sizes. The second group consists of measures of bank operating efficiency and financial frictions—discount rates, operating costs, and external financing costs. The last group consists of parameters that govern banks' market power—the number of competing banks in the local market, $$, as well as the rate sensitivities that banks face in the deposit and loan markets, $$ and $$. As seen in Table X, banks' market concentration has risen over time, with the number of competing banks in the local market falling from seven to five. However, both depositors and borrowers have become more rate-sensitive. The adoption of new technology and a surge in Internet and mobile banking has lowered the cost of searching. Thus, deposits and borrowers are more reactive to banks' rate setting. All else equal, this increased sensitivity decreases banks' market power.

To gauge the overall effect of bank market power on the observed change in the federal funds rate sensitivity, we eliminate the difference in bank market power parameters across the two subsamples by setting the late-period values to those from early period. We find that the gap between the early and late sensitivities declines by 34%.

Table X also shows that fixed operating costs have fallen, likely because of bank mergers. The consequent rise in profitability allows banks to accumulate healthier capital buffers that reduce their exposure to monetary policy. Furthermore, the cost of accessing the nonreservable funding market has declined, so banks can better cushion fluctuations in deposits. If we eliminate the difference in bank operating and financing costs, the gap between the early and late sensitivities declines by 22%.

The remaining 44% of the gap is attributable to changes in macroeconomic conditions. In particular, we find that changes in the federal funds rate process play the most important role in explaining the declining trend in the sensitivity of lending to the federal funds rate. In particular, the average federal funds rate is much lower in our late period, so the economy spends more time around the reversal-rate region, where monetary policy has a weaker, or even opposite, effect on bank lending decisions.

C. Model Robustness

In this subsection, we examine the implications of several ingredients that we have left out of the baseline model. First, instead of requiring dividends to be positive, we allow them to be negative, subject to a linear equity issuance cost, $$. We reestimate our model, with the parameter $$ being identified by an additional moment, namely, the ratio of bank equity issuance to total assets. In the data, this moment is 2%. As shown in Table IA.VII in Section IX of the Internet Appendix, we find that matching this moment yields an equity issuance cost of 11%, which is comparable to the estimates for industrial firms in Hennessy and Whited (2007).

Second, we introduce time-varying discount rates. Specifically, we assume that banks apply a discount rate of $$. In our estimation, we identify ω from banks' dividend yields, which is the same moment that we use to identify the constant discount factor in our baseline model. As shown in Table IA.VII in Section IX of the Internet Appendix, we find that $$. As is the case with the baseline estimates, the spread between the federal funds rate and banks' discount rates indicates that banks face substantial frictions in their maturity transformation activity.

Third, we address the concern that agents in our model are risk-neutral, while in reality, loan spreads contain a risk premium. To make the model and data moments comparable, we adjust the data moment by subtracting a risk premium, which we calibrate following Giesecke et al. (2011), who show that the credit risk premium in the bond market roughly equals the expected default loss. After adjusting the data moment, we reestimate the model. As shown in Table IA.VII in Section IX of the Internet Appendix, we find that the only notable difference in the new results lies in banks' estimated cost of servicing loans, which becomes insignificantly different from zero. This result suggests that omitting loan default risk in our original model causes this component to load onto loan servicing costs.

Fourth, we address the functional form of the nonreservable financing cost in equation (13), which is quadratic. We reestimate the model under the assumption that the nonreservable cost takes a more general power-function form: $$. We identify the multiplicative coefficient and the exponent by matching the mean and standard deviation of banks' nonreservable borrowing. We find that the power term, $$, equals 2.177 and is insignificantly different from two, suggesting that our original functional form is a reasonable approximation. All other parameter estimates under this power financing cost specification also remain near the baseline parameter estimates.

Fifth, one simplifying assumption of the model is that the present value of all future interest payments is paid to the bank in the first period in which a loan is issued. Moreover, we implicitly assume that this payment is default free. To address these issues, we extend the model by introducing an additional state variable that represents the average contractual interest rate on outstanding loans. Details are in Section IX of the Internet Appendix. We solve the model using the parameters reported in Table III. In Table IA.VI, we show that the moment conditions are largely unchanged relative to the values in Table IV. In Figure IA.3, we show that the reversal rate result is nearly unchanged.

Finally, in Section XI of the Internet Appendix, we consider an extension of the model in which we endogenize the federal funds rate. Our extended model contains a standard New Keynesian block and a banking block, with the New Keynesian block determining the effects of productivity and monetary policy shocks on the nominal short-term rate and inflation. The banking block determines the transmission of the nominal short-term rate to the lending rate. In this setting, the federal funds rate process is pinned down by a Taylor rule, which depends on the monetary authority's policy as well as aggregate output and inflation.

We assume a continuum of ex ante homogeneous households with separable preferences over real consumption and real money balances. These households face a two-stage decision-making process. First, they choose the quantity of consumption and money holdings given aggregate prices. Second, they allocate their money demand across different options—cash or deposits in any bank. Similarly, firms decide their optimal demand for capital and whether to finance this demand via corporate bonds or bank loans. We model the banking sector as in our baseline partial equilibrium setting discussed in Section II. The detailed model setup and parameter calibrations are discussed in Section XI of the Internet Appendix.

With the calibrated general equilibrium model, we first confirm that the relation between the federal funds rate and aggregate bank lending is nonmonotonic and hump-shaped. We also repeat our decomposition of monetary policy transmission mechanisms using the general equilibrium framework. We find that the sensitivity of loans to the federal funds rate is lower than in our baseline model in Section IV.A because our New Keynesian model implies a much weaker relationship between the federal funds rate and long-term real rate than what we observe in the data. Nevertheless, our main conclusions remain valid. We find that the qualitative effect of the reserve regulation remains limited, while both the deposit and loan market power channels are quantitatively important in explaining monetary transmission.