Abstract
We study the interaction between occasionally binding financial constraints in the traditional (retail) banking sector and banking panics in the shadow banking sector. Shadow banking panics occur when retail banks choose not to roll over their lending to shadow banks. Occasionally binding financial constraints of retail banks increase the likelihood of and amplify boom-bust dynamics around such shadow banking panics. The model can quantitatively match the dynamics of macroeconomic and financial variables around the US financial crisis. We quantify the impact of wholesale funding market interventions akin to those implemented by the Federal Reserve in 2008, finding that they reduced the fall in output by about half a percentage point. The timing of this intervention matters: an intervention before the banking panic would have been more effective and might even have avoided the panic.
1 Introduction
We develop a model of banking panics with financially constrained borrowers and lenders. At the heart of the 2007–2009 financial crisis was the collapse of the shadow banking system.[1] Before the crisis, shadow banks were an integral part of the broader banking system of the US. They provided liquidity and maturity transformation for the US economy. To do so, they securitized illiquid long-term assets like small business loans. They used these as collateral for liquid short-term wholesale borrowing.[2],[3] During the Financial Crisis of 2008, this source of funding collapsed. Because of this, the shadow banking system came under severe stress.
The lenders on the wholesale funding market were traditional financial institutions, like commercial banks or savings institutions. These institutions also came under severe financial stress. Yet macroeconomic studies often abstract from their financial constraints. Here, we study the leverage constraints of lenders and borrowers on the wholesale funding market during a panic.[4] We do this in a quantitative macroeconomic model, which allows us to bring the model’s predictions to the data.
The financial constraints of retail banks and the possibility of a run on shadow banks reinforce each other. The retail banking sector’s leverage constraint is slack during booms. Thus, wholesale funding spreads are low. A low wholesale funding spread increases the profit margin of shadow banks, leading to a build-up of shadow bank leverage. In turn, this increases the likelihood of a shadow banking panic.
When a shadow banking panic hits, asset prices fall. Because of this, the leverage constraint of retail banks becomes binding, which raises the wholesale funding spread. A high wholesale funding spread squeezes the profit margin of shadow banks. In turn, a further shadow banking panic becomes more likely, and this reduces shadow bank leverage capacity. This novel channel amplifies the fall in real economic activity and slows the recovery.
Our model is consistent with many stylized facts about the 2007–2009 financial crisis. These include the significant spike in the wholesale funding spread and the collapse in wholesale funding. Moreover, the model matches the balance sheet dynamics of traditional and shadow banks. Our model produces stronger boom-bust dynamics relative to a model without lender constraints, and it does so by making the wholesale funding costs of shadow banks counter-cyclical.
In Section 2, we show evidence for the financial constraints of retail banks and shadow banks in the data. We show five facts. First, before the crisis, both sectors were highly leveraged. Second, there was a spike in leverage in both sectors during the financial crisis. Third, the shadow banking sector had a high exposure to short-term debt. Fourth, the shadow banking sector saw a decline in short-term liabilities. Fifth, this coincided with a significant decline in the net worth of both sectors. Facts one to four are consistent with findings from the literature. To our knowledge, fact five about the declines in the net worth of both sectors is novel.
We aim to explain these facts and study the role of the retail banks’ leverage constraints in the meltdown of the shadow banking sector. To do so, Section 3 outlines an otherwise conventional business cycle model with a rich financial system. It includes a retail and a shadow banking sector, modeled as in Gertler et al. (2016). In equilibrium, the financial sector reflects many of the attributes of the pre-crisis US financial system. Retail banks borrow deposits from households and have low leverage. Shadow banks borrow wholesale from retail banks and have high leverage. Thus, shadow banks are vulnerable to banking panics. Such panics arise occasionally and endogenously in the form of rollover crises.[5]
We first characterize the equilibrium, proceeding in two steps. First, we discuss the case when the retail bank leverage constraint is slack. In this case, retail bank net worth does not affect the likelihood of a banking panic. Second, we discuss the case when the retail bank leverage constraint binds. In that case, there is an inverse U-shaped relationship between the net worth of retail banks and the likelihood of a banking panic. The mechanism is as follows. An increase in the net worth of retail banks has two effects on shadow banks. First, it reduces the return on shadow banks’ assets, as retail banks lend more to the non-financial sector. We call this the asset channel. Second, it reduces the required interest rate on the liabilities of shadow banks, as retail banks lend more to the shadow banking sector. We call this the liability channel. The asset channel dominates for low values of retail banks’ net worth. Thus, an increase in the net worth of retail banks squeezes the profit margin of shadow banks. This increases the likelihood of a banking panic. The liability channel dominates for high values of retail banks’ net worth. An increase in retail banks’ net worth relaxes the profit margin of shadow banks. This reduces the likelihood of a banking panic.
To what extent was the great recession driven by a panic, as opposed to fundamentals? This question is difficult to answer with aggregate data, as the period of high financial distress coincided with large bank losses. To provide some evidence in favor of a panic, we instead turn to evidence from microdata. Specifically, in Section 4, we investigate whether bank-specific asset return shocks of a given size had larger effects when stress in the wholesale funding market was highest. We interpret such a stronger response to a fundamental shock of a given size as panic-driven. It was indeed the case that fundamental shocks to asset returns were amplified more during the two quarters which saw the highest wholesale funding market distress. Moreover, banks with better higher idiosyncratic asset return shocks substituted away from short-term debt during the crisis. We interpret the fact that banks with good fundamentals turned away from wholesale funding markets as further evidence of a panic-driven disruption in the wholesale funding market.
We next quantify the predictions of the model. To do so, we calibrate the model in Section 5. In Section 6, we show that the model dynamics resemble US data around the financial crisis. Our main experiment works as follows. First, a series of positive shocks slackens the financial constraints of retail banks. This slackening increases credit supply in the wholesale funding market. In turn, this amplifies the shadow banking boom. Then, a series of adverse shocks occur from 2007 onward. These reduce asset prices and tighten the financial constraints of retail banks. The supply of wholesale funding falls, and wholesale funding spreads rise. This increase in spreads squeezes the profit margin of shadow banks. A rollover crisis becomes possible in the fourth quarter of 2008. The result of such a materialized rollover crisis in the model is a drastic reduction in the net worth of banks.[6] A major recession ensues.
The feedback between retail banks and shadow banks plays a key role. At the end of the boom, retail bank net worth is high. Thus, the liability channel is more important. A fall in retail bank net worth lowers the profitability of shadow banks. This fall increases the likelihood of a banking panic and causes a fall in shadow bank leverage. This chain of events resembles the period from August 2007 to September 2008. At that time, the commercial paper market saw a reduction in credit supply (Covitz et al. 2013). After a banking panic, retail bank net worth is low. Thus, the asset channel is more important. As retail bank net worth recovers, the likelihood of a further shadow banking panic increases, and shadow bank leverage decreases. The lower shadow bank leverage prolongs the recovery. These results show that modeling lender financial constraints is important for explaining both the boom and the bust.
We finally discuss policy counterfactuals. The model allows us to analyze the effects of the central bank’s wholesale funding market intervention. These target shadow banks’ short-term liabilities and are thus distinct from direct asset purchases. To do so, we introduce government policy in Section 7. The central bank can raise household deposits and lend them to shadow banks. The benefit of the central bank doing so is that it does not face the same leverage constraint as the retail banking sector. It can thus act as a lender of last resort. That means that it can provide lending to shadow banks when credit supply by retail banks falls. The cost is that the central bank is less efficient than retail banks at lending to shadow banks.
First, we study the short-run effect of an unanticipated ex-post-intervention after a banking panic. As an example, we study the commercial paper funding facility. This facility held around 350 billion US dollars in commercial paper at its peak. We find that the policy reduced spreads on the wholesale funding markets, allowing the shadow banking sector to build its net worth faster. Consequently, the fall in output due to the banking panic was about half a percentage point lower. This effect is large. Ferrante (2019) finds a two percentage point smaller output fall due to mortgage-backed security purchases. Del Negro et al. (2017) finds a 1.5 percentage point smaller output fall due to all liquidity interventions. These policy interventions were much more extensive. MBS purchases amounted to 1.2 trillion US dollars. All liquidity interventions together amounted to 1 trillion US dollars. The commercial paper funding facility was thus particularly effective. Second, we show that the timing of the intervention matters. The intervention would have been more effective if the central bank had announced the intervention before the crisis. If the central bank had even stepped in during the crisis, it could have avoided a panic altogether.
1.1 Related Literature
This paper relates to three strands of literature. The first literature incorporates shadow banks into macroeconomic models. We build on the work of Gertler et al. (2016), from now on GKP2016. They developed a macroeconomic framework that incorporates financial crises as shadow bank runs. They extend Gertler and Kiyotaki (2015) by including a wholesale or shadow banking sector. Shadow banks played an essential part in the onset of the 2007–2009 financial crisis. Our contribution relative to that paper is threefold. First, we embed their model into a conventional New Keynesian model. Doing so allows us to quantify the macroeconomic effects of a banking panic on the wholesale funding market. Second, in our model, retail banks’ financial constraints can occasionally be binding. We can thus study the role of the occasionally binding constraint during a rollover crisis. Third, we use the model to study the effects of central bank interventions on the wholesale funding market.
Begenau and Landvoigt (2022) studies optimal regulation of traditional banks in a model with shadow banking panics. However, they abstract from modeling a wholesale funding market. Ferrante (2018) studies endogenous asset quality in a model with shadow banks, which amplifies business cycles and banking crises. In his model, there is also no wholesale funding market. Thus, the liability channel emphasized in this paper is absent from these studies. Various other papers include shadow banks in macroeconomic models but do not study banking panics. Meeks et al. (2017) study the effects of a shadow banking sector on the propagation of macroeconomic shocks. Durdu and Zhong (2022) investigate the drivers of bank and non-bank credit cycles through the lens of a structural model. Fève, Moura, and Pierrard (2019), as well as Gebauer and Mazelis (2019), study regulatory spillovers in an estimated model with shadow banks.[7]
A second literature studies financial crises in macroeconomic models. The paper closest to this paper is Gertler et al. (2020a), from now on GKP2019. They introduce banking panics into a macroeconomic model. We add another layer of constrained intermediaries. Doing so has three benefits. First, it allows us to study the interaction between retail and shadow banks. Second, we can match the model to novel data. Third, we can study the effects of wholesale funding market interventions by the central bank.[8]
The paper relates to a third literature, which analyses the macroeconomic effects of unconventional central bank policies. Two key papers are Kiyotaki and Moore (2019) and Del Negro et al. (2017). They evaluate the Federal Reserve’s liquidity facilities. Their model is different from ours in several ways. First, the authors do not explicitly model the banking sector, and therefore also not the wholesale funding market. Second, the authors do not model endogenous banking panics. Doing so allows us to discuss the effects of liquidity measures on the likelihood of a financial crisis. Such an effect is a key concern of policymakers.[9]
2 Retail Banks, Shadow Banks, and the Wholesale Funding Market during the Financial Crisis
The breakdown of the wholesale funding market had an especially severe impact on the shadow banking sector. In the first panel of Figure 1, we use data from Compustat to show that the shadow banking sector was especially highly leveraged before the financial crisis compared to the retail banking sector. Our measure of leverage is the market leverage ratio, which we compute as the market value of equity plus the book value of current debt, long-term debt, and deposits, divided by the market value of equity. We focus on market leverage and measure the net worth of the respective banking sectors as the market values of their equity. This approach is consistent with our model and in line with the literature. See, e.g. Gertler and Kiyotaki (2015) and Gertler et al. (2020a).[10] This figure shows the market leverage of retail banks as a blue, solid line and the market leverage of shadow banks as a red, dotted line. In Appendix A.2, we explain which institutions we include in the retail and shadow banking sectors, respectively. We can see that the market leverage of both retail and shadow banks increased during the financial crisis, peaking in the fourth quarter of 2008 and declining rapidly after that.
Capital structure dynamics of retail and shadow banks around the financial crisis. Note: Data source: compustat. Retail banks are companies with SIC codes 602, 603, and 671. Shadow banks are companies with SIC codes 614, 615, 616, 6172, 620, and 6211. Market leverage is the market value of equity plus the book value of short-term debt, long-term debt, and accounts payable (i.e. deposits) divided by the market value of equity. The short-term debt share is short-term debt over short-term debt plus long-term debt plus accounts payable. Market capitalization is the market value of equity, computed as shares outstanding of common stock times the closing price for the quarter. For the last figure, we detrend market capitalization with a linear trend estimated using data from 1986Q1 to 2018Q4. We normalize it to zero in 2007Q3.
In the second panel of Figure 1, we show that the shadow banking sector was primarily exposed to short-term debt and experienced a much stronger outflow of short-term debt during the financial crisis than the retail banking sector. We show the share of short-term debt in total liabilities, which is short-term debt divided by short-term debt, long-term debt, and deposits. Throughout, the short-term debt share of shadow banks is much higher than the short-term debt share of retail banks. Moreover, the short-term debt share of shadow banks started decreasing in 2007, and it continued to do so until the end of the financial crisis. Overall, it decreased by about a third. In comparison, the short-term debt share of retail banks is much more stable.
In the last panel of Figure 1, we show that the spike in leverage and the outflow of short-term debt of shadow banks coincided with a dramatic fall in the net worth of both the shadow banking sector and the retail banking sector. Relative to the beginning of the sample, the net worth of shadow banks, which we again show as a red, dotted line, fell by almost 100 percent. However, the retail banking sector’s net worth decreased by almost 70 percent. This decline indicates that the retail banking sector also experienced substantial financial stress.
3 Model
This section presents a macroeconomic model with a detailed financial sector. The model builds on GKP2016 and GKP2020. The crucial feature of the model is a wholesale funding market, where retail and shadow banks can make loans to each other. Notably, the borrowers and the lenders in the wholesale funding market face financial constraints. There is no deposit insurance for lending on the wholesale funding market. Thus, a loss in lenders’ confidence in the ability of borrowers to repay can lead to a rollover crisis where the wholesale funding market dries up completely. The critical distinction relative to the previous papers is that the leverage constraint of the lenders on the wholesale funding market is occasionally binding.
The rest of the model works as follows: There is a continuum of households, each consisting of a measure φ R of retail bankers, a measure φ S of shadow bankers, and a measure 1 − φ R − φ S of workers. Workers consume, supply labor, invest in mutual funds, and can make deposits at retail banks and shadow banks. Bankers make retail loans to consumption goods producers and wholesale loans to each other. Monopolistically competitive consumption goods producers produce intermediate goods using capital and labor and set prices subject to price rigidities.[11] They finance capital purchases from capital goods producers with retail loans from banks and mutual funds. A competitive final goods production sector repackages intermediate goods. Capital goods producers transform final goods into capital goods subject to a capital adjustment cost.
Time is discrete, with t = 0, 1, …, ∞. We follow the convention that lower case letters for variables denote individual variables, while upper case letters denote aggregate variables.
3.1 Banks – Environment
3.1.1 Objective Function
There are two types of bankers: retail bankers R and shadow bankers S. As we will make clear below, they differ in their cost function for making loans and in their ability to accumulate internal funds. Bankers of type J,
where
3.1.2 Balance Sheet
At time t, banks use deposit funding from households,
In addition to financing retail loans with deposits or equity, banks can borrow and lend on the wholesale funding market. We denote wholesale loans by
The balance sheet of a bank at the end of period t is
3.1.3 Net Worth
In period t, incumbent banks obtain a risky return on retail loans issued in period t − 1,
if the bank lends on the wholesale funding market and
if the bank borrows from the wholesale funding market. Since the banks cannot raise additional equity, their equity at the end of the period is equal to their net worth at the beginning of the period:
3.1.4 Entry and Exit
With probability σ
J
, a banker of type J experiences an exit shock. In the case of such a shock, the banker sells the bank’s assets, repays its liabilities, and returns to being a worker, transferring the bank’s net worth to the household. It is common to introduce such an exit probability in the literature (see, e.g. Gertler and Kiyotaki 2010; Gertler and Karadi 2011) to ensure that banks do not outsave their borrowing constraints. We interpret the payouts from banks to households as dividend payments. To keep the measure of bankers constant over time, a fraction of workers σ
J
become bankers of type J. They receive an exogenous endowment
We make the following assumption regarding the exit probability of retail and shadow banks:
Assumption 1
The exit probability of retail banks is lower than the exit probability of shadow banks, i.e., σ R < σ S .
This assumption is not essential for the qualitative results, but it allows us to quantitatively match the relative size of the retail and the shadow banking sector. An interpretation of this assumption is that retail banks pay lower dividends than shadow banks.
3.1.5 Loan-Servicing Firms
For the retail loans on their balance sheet at the end of the period, banks and households must pay a loan-servicing cost. Households, retail, and shadow banks have access to different loan-servicing technologies. Specialized firms owned by households and operating in a competitive industry provide such loan servicing. Servicing loans requires effort, which we model as a utility cost to the owner of the loan-servicing firm. The effort cost is quadratically increasing in the total amount of loans serviced,
Loan-servicing firms charge a linear fee
where
Regarding the cost of screening, we make the following assumption:
Assumption 2
Shadow banks have lower loan-servicing costs than retail banks. Households have the highest loan-servicing costs: ζ H < ζ R < ζ S .
In the calibrated model, we choose a ζ
S
high enough to ensure that
3.1.6 Moral Hazard Problem
With the assumptions so far, banks would be financially unconstrained, and the capital structure of banks would be indeterminate. To introduce a role for the capital structure of banks in the model, we follow Gertler and Kiyotaki (2010) in assuming the following moral hazard problem: Banks can divert a fraction of their assets after they have made their borrowing and lending decisions. How much they can divert depends on the type of assets. We make the following assumptions regarding the diversion of assets:
Assumption 3
A fraction
ψ, 0 < ψ < 1, of retail loans,
γψ, 0 < γ < 1, of wholesale loans, and
ωψ, 0 < ω < 1, of wholesale funded (securitized) retail loans can be diverted.
Note that these assumptions are specific to the different types of assets, not the different types of banks. Moreover, we make the following assumption about deposit insurance:
Assumption 4
Deposit insurance exists for deposits but not for wholesale loans.
ω < 1 ensures that shadow banks finance their capital holdings with wholesale lending. It moreover helps us to match both the high leverage and the significant holdings of short-term unsecured debt of shadow banks, two of the stylized facts we showed in Section 2. Appendix B lays out a small model with asymmetric information that can rationalize that wholesale loans are uninsured and allow for a loose collateral constraint, while, at the same time, deposits are insured and require a tight collateral constraint. The argument goes as follows. Suppose that banks differ in their type, and that it is costly for their lenders to observe this type. Then, without deposit insurance, lending can break down if the information cost is high. It is plausible that retail depositors like households have high information costs, while wholesale depositors like banks have low information costs. Deposit insurance can overcome this lending breakdown, as insured lenders do not need to know the borrower type. But it comes at the expense of a lower profitability and, therefore, leverage capacity of good borrowers.
γ < 1 ensures that retail banks are willing to lend on the wholesale lending market. This assumption captures the benefits of holding wholesale loans relative to retail loans. It is a simple way to model that wholesale loans on the wholesale funding market trade at a lower premium than even bonds issued by prime borrowers on the retail funding market, as we showed in Section 2. In reality, there are a variety of reasons why wholesale loans allow for more leverage than retail loans. The simplest reason is that regulation gives wholesale loans a lower weight in risk-weighted capital requirements than retail loans. Moreover, there is a higher standardization of wholesale loan contracts compared to retail loan contracts, which means that there is a market and, therefore, a known market price for them. Hence, the potential for diversion is much higher for retail loans than for wholesale loans.
In a more realistic model, γ and ω would be endogenous to the state of the economy and thus depend on aggregate shocks and regulation. For example, Huang (2018) shows that the benefit of operating a shadow bank varies with regulation. We see this paper as complementary, focusing on banks’ endogenous net worth and leverage dynamics instead.
3.2 Banks – Optimality
3.2.1 Incentive Constraint
If a banker diverts assets, he will not repay his bank’s liabilities. His creditors will subsequently force the bank to close down. Diversion occurs at the end of the period before the uncertainty about the next period resolves. Therefore, creditors can ensure that diversion will never occur in equilibrium by imposing an incentive constraint on the banker. This incentive constraint states that the benefit of diversion to the banker must be smaller or equal to the franchise value of continuing to operate the bank. If the bank lends on the wholesale funding market, i.e.
To create
If the bank borrows on the wholesale funding market, i.e.
To create
3.2.2 Occasionally Binding Leverage Constraint
Define the leverage ratio of a bank as
i.e. the fraction of bank assets that require some equity financing divided by the bank’s net worth or equity. Remember that a fraction 1 − γ of wholesale loans is non-divertable and does not require equity financing.
We guess (and verify) that the value function of the bank is linear in its net worth:
If the bank is a wholesale borrower, the incentive constraint is instead
3.2.3 Optimal Retail Banker Decisions
In this section, we show that the occasionally binding leverage constraint of the retail banking sector leads to nonlinear dynamics for the wholesale funding rate. We consider an equilibrium where retail bankers optimally choose to issue deposits and lend on both the retail and the wholesale funding markets. In contrast, shadow banks do not issue deposits and borrow on the wholesale funding market. We also abstract from the default risk of retail banks:
3.2.3.1 Case I: Non-binding Retail Bank Leverage Constraint
The maximization problem of the retail banker is to choose
and
The balance sheet constraint gives
where
3.2.3.2 Case II: Binding Retail Bank Leverage Constraint
Consider next the case of a binding incentive constraint or capital requirement, such that leverage is
It is optimal for retail banks to lend on both the retail and the wholesale funding markets if the following condition holds:
Equation (3.18) states that the excess return for lending a unit of wholesale loans must equal the excess return of lending γ units of retail loans. To finance an additional unit of wholesale loans, the retail bank must give up γ units of retail loans if the leverage constraint binds. Thus, the financial constraints of the retail banks, which are the lenders on the wholesale funding market, will be reflected in the wholesale credit spread. By rearranging Equation (3.18), we can write the wholesale funding credit spread
This spread has two components: As before, in the case of the non-binding incentive constraint, it contains a premium for the risk-adjusted loss in default. Moreover, it contains a liquidity premium reflecting the retail banks’ financial constraints in the wholesale funding market. The parameter γ determines to what extent the wholesale funding credit spread reflects the financial constraints of lenders. For γ = 0, it does not reflect them at all. For γ = 1, it fully incorporates them.
Figure 2 shows the leverage of the retail bank
Policy functions as a function of aggregate retail and shadow bank net worth.
3.2.4 Optimal Shadow Banker Decisions
Next, we show how the wholesale funding spread affects the leverage decision of shadow bankers. Shadow bankers find it optimal not to issue deposits and to borrow on the wholesale funding market.[18] Their maximization problem is to choose
Plugging 3.4, 3.2 and 3.12 into 3.1 and rearranging, Equation (3.20) yields the following expression for shadow bank leverage:
Equation (3.21) implies that shadow bank leverage is increasing in the credit spread for retail loans and decreasing in the credit spread for wholesale loans. An increase in the banking panic probability also lowers leverage by lowering
Summing up, this section shows that if the occasionally binding constraint of the retail banking sector becomes binding, wholesale funding credit spreads will nonlinearly spike up, which leads to a nonlinear fall in the leverage capacity of the shadow banking sector.
3.3 Banking Panics
3.3.1 Optimal Rollover Decision of Shadow Bankers’ Creditors
For ease of exposition, since we abstract from the default risk of retail banks, we only characterize the rollover decision of shadow bankers’ creditors. We focus on the case where a bank that exclusively borrows on the wholesale funding market defaults since these were the more relevant runs in the financial crisis of 2007–2008.[19]
3.3.1.1 Illiquidity and Default
The incentive constraint 3.12 implies that lenders are unwilling to lend to a shadow banker with a negative net worth because any positive amount of lending would violate the incentive constraint. If a creditor would nevertheless lend to such a shadow banker, the shadow banker would choose to divert assets and default on the debt.
By the definition of bank net worth, negative net worth also means that the bank’s assets are insufficient to cover its liabilities:
If a bank defaults, creditors liquidate it. They recover the assets of the bank instead of their wholesale loan. The recovery rate on their lending is
If the bank is illiquid, the creditors do not fully recover their claim:
3.3.1.2 Equilibrium Multiplicity
Since there are no idiosyncratic shocks to bank net worth, all or no incumbent shadow banks default. Consider two returns on retail loans
We can distinguish three situations: If x
t
≥ 1 and
3.3.1.3 Banking Panics and Sunspots
A banking panic is a situation where two things happen. First, all incumbent shadow banks default on their outstanding debt. Second, all shadow bankers having entered the economy in the current period postpone entry until the next period.[20] A banking panic is a situation of coordination failure. By coordinating on not to roll over their debt, creditors drive the shadow banking system into default, even though the shadow banking sector would have been able to service its debt if creditors coordinated to roll it over. This situation may arise if the economy is in the crisis zone or the default zone.
The coordination mechanism of shadow bank creditors is a sunspot shock. If the economy is in the crisis zone, the optimal strategy of each shadow bank creditor is to roll over his debt when all others do so and to not roll over his debt when nobody else does. Agents will decide not to roll over their debt if they observe a sunspot shock, which occurs with probability π. Otherwise, they will roll over their debt. Thus, the probability of a banking panic is the product of two terms. First, the probability of the economy being in the crisis zone, and second, the probability of a sunspot:
While the probability of a sunspot shock is constant and exogenous, the probability of a banking panic is endogenous and state-dependent. We can rewrite
Hence, the probability of a banking panic is increasing in leverage, decreasing in the credit spread on retail loans, and increasing in the credit spread on wholesale loans. Agents will correctly anticipate whether a banking panic can occur or not. The probability of a systemic bank default is the sum of the probability of the economy being in the default zone plus the probability of the economy being in the crisis zone and experiencing a banking panic.
Notice the subtle difference between a systemic bank default and a banking panic. A banking panic occurs only if there is a systemic bank default and newly entering shadow banks decide to postpone entry, which occurs with probability π in both the crisis zone and the default zone. With probability 1 − π, there is a default of incumbent shadow banks in the default zone which does not trigger a banking crisis, as newly entering banks still choose to enter.
3.3.2 Retail Bank Leverage Constraints and the Shadow Banking Panic Probability
The probability of a banking panic is non-monotonic in the net worth of the retail banking sector. For a high net worth of retail banks, an increase in retail bank net worth lowers the probability of a banking panic. It does so because an increase in retail bank net worth reduces the interest rate on shadow banks’ liabilities more than the return on their assets. As we showed in Equation (3.25), a retail bank net worth increase leads to a reduction of the wholesale funding spread, which increases the excess return of shadow banks and thereby reduces the likelihood of a banking panic.
For low values of the net worth of retail banks, an increase in retail bank net worth increases the probability of a banking panic. It does so because an increase in retail bank net worth relaxes the incentive constraint of the retail banking sector, which lowers the return on retail loans, as we showed in Figure 2. The lower return on assets increases the likelihood of a banking panic, as it reduces the excess return of shadow banks.
These two effects lead to the non-monotonic relationship between the net worth of the retail banking sector and the shadow banking panic probability. These effects arise only if retail and shadow banks face financial constraints. The second effect arises if retail and shadow banks are linked through the wholesale funding market, highlighting the importance of these two assumptions.
3.4 Closing the Model
The household sector and the production sector of the model follow GKP2019. We describe them in Appendix C. Here, we briefly summarize the assumptions. Households consume, supply labor, and save in the form of capital and deposits. They have additively separable constant relative risk aversion preferences over consumption and labor. On the production side, there are final goods producers and intermediary goods producers. Final goods producers bundle intermediary goods with an aggregator function with a constant elasticity of substitution across varieties of intermediary goods. Intermediary goods use capital and labor to produce differentiated intermediary goods. When adjusting their prices, they pay a quadratic price adjustment cost. Finally, capital goods producers transform consumption goods into capital goods subject to a quadratic capital adjustment cost.
4 Empirical Evidence
The model predicts that the effects of a shock to banks’ asset return differ across different regimes. In the no-crisis regime, such a shock will only have moderate effects. If the shock instead pushes the economy from the no-crisis regime into the crisis regime, such a shock can have much more significant effects, especially if it triggers a banking panic.
It is difficult to disentangle with aggregate data whether asset return shocks have larger effects during financial distress periods, as bank asset returns tend to experience large adverse shocks during such periods. In this section, we, therefore, use microdata to test this prediction of the model. Specifically, we test whether idiosyncratic shocks to the return on assets of financial intermediaries have stronger effects during times of high financial distress.
The idea is as follows. Consider a set of ex-ante identical banks i which differ only by bank-specific capital quality shocks ω
it
, where ω
it
has a mean of 1. These shocks lead to ex-post variation in the recovery rate x
it
= ω
it
x
t
. If no panic happens, only the banks with realizations of ω
it
such that ω
it
x
t
≤ 1 will default, while all other banks will continue to operate. Therefore, the effect of an idiosyncratic shock is, on average, small. If a panic happens, all banks with realizations of ω
it
such that
4.1 Specification
We describe the data in Appendix A. We estimate the following regression model:
The dependent variable is the log of the net worth of financial intermediary i at time t, NWi,t, measured as the market value of common equity. Net worth is the relevant idiosyncratic state variable of financial intermediaries in the model. The most important independent variable is the interaction between the return on assets of financial intermediary i at time t and an indicator for whether the economy is in a panic at time t, ROAi,t × Panic t . We define the economy as being in a panic during the two quarters where the interbank lending rate spiked, i.e. the third quarter of 2007 and the fourth quarter of 2008. If the coefficient β3 is positive, idiosyncratic shocks are amplified more during financial crisis periods.
The specification includes financial intermediary fixed effects α i that proxy for financial intermediary-specific net worth growth rates. Importantly and crucial for identification, the specification includes time fixed effects α t . These control for all factors that affect the net worth and are common to all financial intermediaries, e.g. the sizeable fall in asset returns during the financial crisis. We also control for the lagged return on assets to isolate the impact of idiosyncratic asset return shocks. Finally, we include financial intermediary-specific lagged covariates that might affect net worth growth. These include the logarithm of total assets, the logarithm of total liabilities, and the market-to-book ratio. The logarithm of total assets proxies for size effects, the logarithm of total liabilities for leverage, and the market-to-book ratio for growth options.
4.2 Results
Table 1 shows that return on asset shocks have stronger effects during banking panic periods. Column 1 displays the baseline specification. The coefficient during normal times is β1 = 0.382, implying that an idiosyncratic quarterly return on assets one percentage point higher than the average return on assets is associated with a 0.382 percent higher quarterly net worth growth. The coefficient β1 significantly differs from zero at the one percent level. During 2007Q3 and 2008Q4, a one percentage point higher return on assets was associated with much stronger net worth growth of 0.382 + 1.269 = 1.651 percent per quarter. The coefficient of β3 = 1.269 is significantly different from zero at the one percent confidence level.
Amplification of idiosyncratic asset return shocks during banking panics.
| (1) | (2) | (3) | (4) | (5) | (6) | |
|---|---|---|---|---|---|---|
| Baseline | Only 2007Q3 | Only 2008Q4 | Sector × time FE | Placebo 1 | Placebo 2 | |
| ROA | 0.404c | 0.432c | 0.433c | 0.439c | 0.461c | 0.470c |
| (3.43) | (3.70) | (3.63) | (3.95) | (3.79) | (4.02) | |
| Panic × ROA | 1.216c | 2.043c | 0.862c | 0.924b | −0.0351 | −0.217 |
| (3.65) | (4.48) | (5.29) | (2.02) | (−0.09) | (−0.46) | |
| R2 | 0.168 | 0.168 | 0.168 | 0.246 | 0.167 | 0.167 |
| Adjusted R2 | 0.145 | 0.144 | 0.144 | 0.190 | 0.144 | 0.144 |
| N | 57,190 | 57,190 | 57,190 | 55,706 | 57,190 | 57,190 |
-
This table shows the results of estimating regression 4.1. The data are from Compustat, from 1973Q1 to 2018Q4. Specification (1) is the baseline specification. In specification (2), the panic dummy is only 1 in 2007Q3. In specification (3) the panic dummy is only 1 in 2008Q4. In specification (4), we include three-digit SIC sector times time fixed effects instead of just fixed effects. Specification (5) defines 2007Q2 and 2008Q3 as placebo panic periods. Specification (6) defines 2007Q4 and 2009Q1 as placebo panic periods. All specifications include financial intermediary fixed effects, time fixed effects, and control variables. We winsorize the return on assets at the 1 percent tails. We doubly cluster standard errors at the financial intermediary and quarter level. t statistics in parentheses. ap < 0.1, bp < 0.05, cp < 0.01.
Columns 2 to 6 contain various robustness checks. First, columns 2 and 3 define only 2007Q3 or 2008Q4 as panic periods, with similar results. If anything, 2007Q3 led to a more considerable amplification of idiosyncratic asset return shocks. Column 4 replaces the time fixed effects with more granular three-digit SIC code times time fixed effects. The results continue to hold. Finally, columns 5 and 6 show important placebo experiments. If we shift the panic periods one period forward to 2007Q2 and 2008Q3 (column 5) or one period back to 2007Q4 and 2009Q1 (column 6), we do not find stronger amplification of asset return shocks. That shocks to asset returns in quarters adjacent to the “panic” quarters do not lead to stronger effects supports the hypothesis that the strong reactions in the “panic” quarters were indeed driven by panic, not by fundamentals.
4.3 Implications for Bank Balance Sheets
How does the stronger response of net worth to asset return shocks affect other financial intermediary balance sheet variables? To test this, we repeat the estimation of Equation (4.1) using the log change of various balance sheet variables as dependent variables. These are total assets, total liabilities, and the three components of the latter, namely short-term debt, long-term debt, and accounts payable. This last category includes deposits. Table 2 shows that an idiosyncratic return on assets one percent higher than the aggregate return is associated with a 0.84 percent higher asset growth and 0.64 percent lower liability growth during normal times. During crises, the coefficient is smaller, indicating that higher asset return shocks are associated with less strong asset growth increases and muted liability growth declines. However, the coefficient that measures the differential crisis response is not statistically significant from zero at conventional levels.
Effects of asset return shocks on bank balance sheet variables.
| (1) | (2) | (3) | (4) | (5) | |
|---|---|---|---|---|---|
| Assets | Liabilities | ST debt | LT debt | Acc. payable | |
| ROA | 0.839c | −0.635c | −0.568b | −0.260 | −0.386c |
| (6.22) | (−6.00) | (−2.47) | (−1.29) | (−3.52) | |
| Panic × ROA | −0.223 | 0.321 | −1.638c | 2.778c | 0.448b |
| (−0.43) | (1.64) | (−2.96) | (4.29) | (2.34) | |
| R2 | 0.086 | 0.127 | 0.119 | 0.104 | 0.159 |
| Adjusted R2 | 0.061 | 0.102 | 0.086 | 0.073 | 0.135 |
| N | 57,732 | 53,710 | 36,860 | 46,440 | 55,749 |
-
This table shows the results of estimating regression 4.1, replacing net worth with various other bank balance sheet variables. The data are from Compustat, from 1973Q1 to 2018Q4. All specifications include financial intermediary fixed effects, time fixed effects, and control variables. We winsorize the return on assets at the 1 percent tails. We doubly cluster standard errors at the financial intermediary and quarter level. t statistics in parentheses. ap < 0.1, bp < 0.05, cp < 0.01.
The dynamics of total liabilities mask substantial heterogeneity across types of liabilities. In particular, during the crisis, financial intermediaries with higher idiosyncratic asset return shocks reduced their short-term debt substantially more than during normal times. Instead, they increased their long-term debt rather than reducing it as they would during normal times. This substitution is consistent with the idea that a disruption in short-term debt markets increased borrowing costs for all borrowers so much that good borrowers moved to other debt markets, particularly the markets for long-term debt and, to a lesser degree, deposits.
5 Calibration
For our main results, we solve the model numerically. To do so, we calibrate the model to match moments of the US economy during the 1986–2018 period at a quarterly frequency.[21] Since we solve a complicated nonlinear model, estimating it is infeasible. We, therefore, divide the parameters into three blocks. Parameters in the first block include the technology, preference, and policy parameters. We use conventional values for those parameters. The second block of parameters is for the financial sector. We set the parameters to match the stochastic steady state of the model to long-run data averages. We target credit spreads and balance sheet variables from the financial accounts and Compustat. The third block of parameters is specific to bank runs or specifies the exogenous stochastic processes. We internally calibrate those parameters to match the business cycle properties and dynamics of the 2008 financial crisis.
5.1 Parameters
5.1.1 Preferences
We list the preference parameters in panel (a) of Table 3. Regarding functional forms, we model the utility of consumption as
and the disutility of labor as
Calibration.
| Name | Value | Role | Target or source |
|---|---|---|---|
| Σ | 2 | Utility of consumption | Risk aversion = 2 |
| Φ | 0.5 | Disutility of labor | Frisch elasticity of labor supply = 2 |
| ̃ | 0.9902 | Household discount factor | Real interest rate 4% p.a. |
| Σ | 1.317 | Disutility of labor | Labor supply = 1 in SS |
| alpha | 0.36 | Capital share in production | Capital income share = 36% |
| Δ | 0.025 | Depreciation rate | Annual deprecation rate = 10% |
| θ 0 | 0.25 | Capital adjustment cost | Elasticity of investment to capital price |
| θ 1 | 0.5302 | Capital adjustment cost | Capital price in steady state = 1 |
| θ 2 | −0.008333 | Capital adjustment cost | X t = I t in steady state |
| ɛ | 11 | Elasticity of substitution btw varieties | Markup = 10% |
| ρ R | 1000 | Price adjustment cost | Elasticity of inflation to marginal cost |
| ρ Z | 0.7 | Autocorrelation, productivity | ρ(Y t , Yt−1) = 0.9 |
| σ Z | 0.005 | Standard deviation, productivity shock | σ(Y t ) = 0.03 |
| G | 0.2474 | Government consumption | Government consumption share in output = 20% |
| κ Y | 0.125 | Weight on output in Taylor rule | Standard value |
| κ π | 1.5 | Weight on inflation in Taylor rule | Standard value |
| Γ | 0.5749 | Diversion benefit of wholesale lending | Change in TED spread in crisis = 1.8% |
| ζ H | 0.1854 | Household bank capital holding cost | AAA-10Y treasury spread = 1.35% |
| ζ R | 0.4429 | Retail bank capital holding cost | BAA-10Y treasury spread = 2.33% |
| σ R | 0.04683 | Retail bank exit rate | K R /K = 0.45 |
| σ S | 0.09406 | Shadow bank exit rate | K S /K = 0.35 |
| Ψ | 0.303 | Asset diversion share | ϕ R = 10 |
| Ω | 0.4619 | Diversion benefit of wholesale funding | ϕ S = 15 |
| Υ | 0.0005682 | Banks’ initial equity | Change in investment in crisis: −32.3% |
| η H | 0.2584 | Household capital holding cost | Change in AAA-10Y spread in crisis: 1.2% p.a. |
| η R | 0.2089 | Retail bank capital holding cost | Change in retail bank net worth in crisis: −68.5% p.a. |
| Π | 0.02819 | Sunspot probability | Crisis freq. of
|
We choose the curvature of the utility of consumption to imply a risk aversion σ of the households of 2. We set the curvature of the disutility of labor ϕ to imply a Frisch elasticity of 2. We set the discount rate of households β to target an annual risk-free real interest rate of 4 percent. We set the remaining labor disutility parameter μ to normalize labor to 1 in the steady state.
5.1.2 Technology
The parameters in panel (b) of Table 3 describe the technology. We set the production function curvature α to match a capital share in GDP of 36 percent. The quarterly depreciation rate of capital δ is set to 0.025, implying an annual depreciation rate of 10 percent. We set the capital adjustment cost parameter θ0 to 0.25, such that the elasticity of the capital price to investment is 25 percent. This elasticity is in line with estimates from, for example, Eberly et al. (2012). We choose the other two adjustment cost parameters θ1 and θ2 such that the price of capital in the stochastic steady state is one and the quarterly investment-to-capital ratio is 2.5 percent per quarter in the steady state. We set the elasticity of substitution across varieties of intermediate goods to imply a markup of 10 percent, which follows Del Negro et al. (2017) and Gertler et al. (2020a). We set the price adjustment cost parameter ρ R to get an inflation elasticity to the marginal cost of 0.1 percent, in line with Gertler et al. (2020a). We choose ρ Z and σ Z to match the conditional volatility and the autocorrelation of detrended GDP for the United States.
5.1.3 Government
We list government and monetary policy parameters in panel (c). We set G to match a share of government consumption in GDP in the steady state of 20 percent and the parameters of the Taylor rule to match an elasticity of the policy rate to inflation of 1.5 percent and the markup of 0.125 percent, in line with Del Negro et al. (2017) and Gertler et al. (2020a).
5.1.4 Financial Sector
The parameters in panel (d) of Table 3 are specific to the financial sector. We target leverage ratios of 10 and 15 for retail and shadow banks to calibrate the diversion parameters ψ and ω. These numbers correspond to the leverage ratios of retail and shadow banks in Compustat before the crisis. We choose the remaining diversion parameter γ to match the increase in the TED spread during the financial crisis. We set the exit shock probabilities σ R and σ S such that the shares of assets intermediated by retail banks and shadow banks in steady state are 45 and 35 percent. The former corresponds to the share of retail bank assets of total assets of the financial sector in Compustat. The latter is higher than the share of shadow bank assets in Compustat but corresponds to the size of the shadow banking sector used by Gertler et al. (2020a) and Begenau and Landvoigt (2022). For the capital-holding cost parameters ζ H and ζ R , we target the spreads of Moody’s BAA and Moody’s AAA yield over a 10-year treasury bond.[22] We map the expected return on assets of retail banks to the return on AAA-rated bonds and the expected return on assets of shadow banks to the return on BAA-rated bonds to capture the fact that retail banks were lending mostly to prime borrowers. In contrast, shadow banks also lent to subprime borrowers (Pozsar et al. 2013). We set the banks’ endowments υ to target the fall in investment during the financial crisis. We set the remaining holding cost parameters η H and η R to match the increase in Moody’s AAA spread and the fall in retail bank net worth during the financial crisis. Finally, we set the probability of the sunspot to target a frequency of financial crises of 4 percent per year, in line with Jordà et al. (2011).
5.2 Solution Method
We solve the model nonlinearly with a projection method on a sparse grid. We use the toolbox of Judd et al. (2014) to construct the sparse grid. Due to the high degree of nonlinearity, we use piecewise polynomials. They differ depending on whether the retail bank leverage constraint binds or the economy is in a banking panic. Solving the model using global methods has three key advantages: First, it allows us to accurately characterize the dynamics of the economy very far away from the steady state. Being able to do so is essential since a financial crisis will wipe out the net worth of the shadow banking sector and substantially reduce the net worth of the retail banking sector below its steady-state level. Second, the nonlinear solution allows us to compute risk premiums in the model accurately. Doing so is crucial since asset price dynamics are essential for generating financial crises in the model. Third, and most importantly, banking panics and the occasionally binding leverage constraint introduce substantial nonlinearity into the model, which perturbation methods cannot capture. We describe the details of the solution algorithm in Appendix G.
6 Quantitative Results
This section illustrates the importance of retail bank constraints for banking panic dynamics quantitatively. First, Section 6.1 shows that including retail bank constraints amplifies the effects of a banking panic relative to a re-calibrated model without retail bank constraints. Second, Section 6.2 compares the effects of the retail bank constraint becoming binding and the effects of a banking panic. Appendix F.1 discusses the model fit. Appendix F.2 discusses untargeted business cycle moments, showing that the model does a good job at matching those.
6.1 Financial Amplification due to Retail Bank Constraints
Figure 3 shows the ability of the model to quantitatively reproduce the dynamics of macroeconomic aggregates, bank balance sheets, and asset prices during the US financial crisis of 2008. The experiment is similar to Gertler et al. (2020a). We start the model in the stochastic steady state in the second quarter of 2004 when the output gap in the data was close to zero. We then feed in a sequence of shocks to match aggregate investment from the third quarter of 2004 to the third quarter of 2008. In the fourth quarter of 2008, an additional shock hits the economy that is just large enough to push it into the crisis zone, where the recovery value on wholesale loans in a panic is below one, such that both the panic and the no panic equilibrium are possible. We then compute the impulse response of the economy if a banking panic occurs (the blue line). The black, solid line represents the data. Appendix F.4 shows the case in which no banking panic occurs.
A banking panic in the model and the data. For this figure, we choose a sequence of capital quality shocks to match the dynamics of aggregate investment between 2005Q3 and 2008Q3. In 2008Q4, a sunspot occurred that led to a banking panic if the economy was in the crisis zone where the panic equilibrium exists. Appendix A describes the data.
The panic probability rises once the adverse shocks start to hit the economy. Even in the fourth quarter of 2008, a banking panic is a tail event: the probability of it occurring is less than 5 percent. The multiplier of retail banks, which measures whether the incentive constraint of retail banks binds, falls to zero after the initial positive shocks and then increases rapidly. The resulting low credit spreads on the wholesale funding market produce an additional build-up of leverage, which increases the likelihood of the banking panic occurring later. Thus, the slackening of the leverage constraint of retail banks amplifies the leverage boom preceding the crisis and makes the bust more likely.
Comparing the model to the data, the model accounts well for the dynamics of the macroeconomic aggregates, banking sector variables, and credit spreads during the crisis. However, it has trouble matching the historically very low AAA-10Y, and BAA-10Y spreads before the crisis. Credit spreads might have been low due to economic mechanisms that we abstract from, for example, due to investor sentiment (López-Salido et al. 2017) or expectational errors (Bordalo et al. 2018; Gertler et al. 2020a). The model does an excellent job at matching the balance sheet dynamics of banks during the financial crisis: it matches the capital ratios and the net worth dynamics of both retail and shadow banks before the crisis well.
The red line in Figure 3 shows impulse responses for the alternative model without the financial constraints of retail banks. We start both models in the respective stochastic steady state, feeding in the same sequence of capital quality shocks and letting a run happen in the fourth quarter of 2008.
We can see that even conditional on a run, output, investment, consumption, and hours fall much less in the alternative model without the financial frictions of retail banks. This weaker fall is because unconstrained retail banks increase lending substantially when the shadow banking sector fails. The positive shocks at the beginning of the sample are also less amplified. That is, however, overshadowed by the crisis dynamics in the figure. Note that the alternative model achieves less amplification even though the leverage of the shadow banking sector is higher in the alternative model. The banking panic probability is much lower throughout the sample. Thus, introducing financial constraints for the retail banking sector amplifies the dynamics around a banking panic. Appendix F.3 shows that capital quality shocks also get amplified by retail banking sector financial constraints.
6.2 Boom-Bust Dynamics Around Financial Crises
The model features two sources of nonlinearity that the academic literature considers important mechanisms during the financial crisis: banking panics and occasionally binding financial constraints. This section compares the average dynamics in the model around each of these events. We proceed as follows: we simulate 1000 model economies for 1000 periods. Then, we identify all events, either banking panics or occasions where the retail leverage constraint becomes binding, and compute the average path of model variables in a window from 50 periods (quarters) before the event to 50 periods after the event. We exclude all events with another banking panic in the event window.
Figure 4 shows the results. The blue line displays the model’s average dynamics around a banking panic. Appendix F.5 compares these to the run experiment conducted in the previous section, showing that the dynamics are similar. Banking panics are preceded by a sequence of small, positive capital quality shocks, followed by a few large, adverse shocks in the periods before the banking panic. In that sense, the boom lays the seed of the bust in this model. How do the positive shocks help to make a banking panic more likely? In response to the positive shocks, the leverage constraint of the retail banks becomes slack, and the wholesale funding spread falls, allowing shadow banks to increase leverage. The higher leverage of shadow banks and the larger exposure of the retail banking sector to shadow bank losses make a banking panic more likely.
Boom-bust dynamics around banking panics. For this figure, we simulate 1000 economies for 2000 periods, discarding the first 1000 periods as burn-in. We then select all events, either the occasionally binding constraint of the retail banking sector becoming binding or a shadow banking panic occurring. We then compute the average path of all variables around the event. We exclude all events where another shadow banking panic occurs during the event window.
In contrast, the average dynamics around episodes where the retail bank leverage constraint becomes binding generate large, nonlinear bust dynamics but no preceding boom. Thus, the combination of panic in the wholesale funding market and the occasionally binding leverage constraint in the retail banking sector leads to boom-bust cycles.
7 The Macroeconomic Effects of Liquidity Interventions
After the collapse of Lehman Brothers in September 2008, the Federal Reserve introduced the Commercial Paper Funding Facility (CPFF) as a liquidity backstop in October 2008. This focus on the role as a liquidity backstop distinguished the CPFF from other programs, like the Asset-Backed Commercial Paper Money Market Mutual Fund Liquidity Facility (AMLF) and the Money Market Investor Funding Facility (MMIFF). In Figure 5, we show that the Federal Reserve’s intervention in the wholesale funding market was quantitatively significant. At its peak, the central bank held more than 20 percent of all outstanding commercial paper. In this section, we investigate the macroeconomic effects of such liquidity interventions.
The commercial paper funding facility. Data source: board of governors of the federal reserve system.
7.1 Modelling the CPFF
We assume the central bank can lend on the wholesale funding market,
The central bank finances its loans on the wholesale funding market by issuing deposits. For simplicity, we assume that the central bank can raise deposits directly from households.[23] The balance sheet of the central bank is then
In contrast to the retail and shadow banks, the central bank does not face a moral hazard problem. Thus, it does not need to finance a fraction of its lending with equity. The central bank can therefore provide lending at a lower rate than the retail banks:
The goal of the central bank is to choose
The central bank intervenes if the intervention implied by 7.5 is non-negative. It sets the interest rate to ensure that it does not make losses in expectation and targets the size of the intervention to trade off the reduction of spreads on the wholesale funding market with the utility cost of lending. We pin down the parameters c0 and c1 to ensure that the central bank does not intervene in the steady state and that the intervention in the period after a banking panic is around 17 percent of outstanding commercial paper, similar to the size of the commercial paper funding facility at its peak.
7.2 The Short-Run Effect of an Unanticipated Intervention after a Run
We first consider an unanticipated intervention by the central bank. For that purpose, we start a simulation of the economy in the fourth quarter of 2008, assuming that a banking panic occurred. We then simulate the model forward using the policy rules and laws of motion of the model with the central bank intervention and compare them to the baseline model without intervention. The blue line in Figure 6 shows the difference in the impulse responses between the baseline model, which are the same as in Figure 3, and the alternative model with the liquidity intervention.
The effects of a central bank intervention on the wholesale funding market. This figure shows the difference in impulse response functions between the baseline model and three interventions: in the first intervention, the central bank introduces a liquidity facility in the period of the run after the run has happened (the blue line). In the second intervention, the central bank introduces a liquidity facility in the period before the run but does not commit to acting as a lender of last resort on the wholesale funding market, which would involve taking over the entire wholesale funding market (the red line). In that case, the panic still occurs. In the third intervention, the central bank introduces a liquidity facility and commits to act as a lender of last resort, in which case the panic does not occur (the yellow line). The black, vertical line denotes Q4-2010 when the CPFF program stopped.
The intervention starts after the banking panic, when the wholesale funding market becomes active again, and stops when credit spreads on the wholesale funding markets return to normal levels. The intervention in the model matches the one in the data very well. The anticipation of the intervention does, however, already have an effect in the period of the banking panic.
As a consequence of the intervention, credit spreads on the wholesale funding market fall by about 1 percent. The AAA-10Y and the BAA-10Y spreads fall by about five basis points. The minor fall in these credit spreads is due to us computing 10-year spreads, which are not very volatile. The effects on the real economy are substantial: Due to the intervention, output and employment rise by about 0.3 percent, consumption by 0.1 percent, and investment by about 1.5 percent.
The capital ratio of retail banks increases temporarily and decreases as the central bank intervention stops. The capital ratio of shadow banks increases at first and then permanently, as the promise of future interventions makes banking panics less likely. The banking panic probability increases temporarily, which is explained by the lower credit spread, which lowers the profitability of shadow banks after a run. We discuss the permanent effects of the liquidity intervention in Appendix F.7, showing that they are successful at increasing the mean and reducing the volatility of macroeconomic aggregates by reducing the likelihood of banking panics.
7.3 The Role of the Timing of the Intervention
The red line in Figure 6 shows the effect of an intervention that the Federal Reserve announces in the period prior to the run. However, the central bank does not commit to lending as the sole lender if a banking panic happens, so it cannot rule out the banking panic equilibrium. Nevertheless, the policy is more effective: credit spreads increase by less and macroeconomic aggregates decrease by less compared to the situation where the intervention is introduced after the run, even though the size of the intervention is smaller than in the first case.
Finally, the yellow line in Figure 6 shows the effect of the policy if the central bank commits to act as a lender of last resort during a potential panic. The central bank can rule out the banking panic equilibrium in this case. Thus, credit spreads increase less and macroeconomic aggregates fall substantially less compared to the intervention after the run. The size of the intervention also becomes substantially smaller. This large effect illustrates that the credibility of lender of last resort policies in models where financial crises arise due to multiple equilibria hinges on the agents’ beliefs about what the central bank will do.
8 Conclusion
We study the macroeconomic effects of a banking panic in a quantitative macroeconomic model with retail and shadow banks connected through a wholesale funding market. In our model, banking panics are rollover crises in the wholesale funding market. Our main contribution to the literature is to investigate the importance of occasionally binding financial constraints in the retail banking sector on the likelihood of financial stress in the shadow banking sector, asset prices, and the macroeconomy. Our main theoretical result is that the retail and wholesale funding spreads are disconnected when the constraint is not binding but become highly correlated when the constraint is binding. Moreover, the effect of retail bank financial constraints on the shadow bank probability has an inverse u-shape. At low retail bank net worth values, an increase in net worth increases the likelihood of a shadow banking panic. At high retail bank net worth values, an increase in net worth reduces the likelihood of a shadow banking panic.
The model is quantitatively consistent with the dynamics of macroeconomic variables and asset prices during the US financial crisis. In particular, due to occasionally binding financial constraints of retail banks becoming binding, the model produces a slow run period with elevated credit spreads on the wholesale funding market, followed by a fast run. We show that the slow run makes the fast run more likely by deteriorating the balance sheets of shadow banks. The model also produces boom-bust cycles amplified by the occasionally binding constraint of retail banks.
We discuss policy implications. A government intervention as a lender of last resort in the wholesale funding market can reduce credit spreads and relax the financial constraints of both retail and shadow banks. Such a policy is similar to the Commercial Paper Funding Facility instituted by the Federal Reserve System in October 2008. This relaxation, in turn, reduces the likelihood and severity of banking panics. The timing of this intervention matters: an earlier introduction can reduce the impact of a banking panic or even avoid it.
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