THERE IS A SURPRISING DISCONNECT between the theory that we teach about financial intermediation and the ongoing debates about how financial institutions ought to be regulated. In this essay, we explore that tension. Throughout, we will refer to these institutions as banks, but understand that non-banks may often also undertake some of these activities, and it is often conceptually hard to explain why regulations are based on organizational form rather than function.
Banking theory suggests that intermediaries arise (and create value) through various channels. One explanation supposes that their purpose is to create claims that can be traded but are backed by illiquid assets.2 Other theories suppose that what makes banks special is their ability to expand credit to certain type of borrowers, in particular because they can more efficiently monitor them and collect on loans granted.3,4 Finally, some theories emphasize the ability of banks to improve risk-sharing by creating securities (for example, deposits and equity) that differ in the risk that the owners of the securities face.
Yet when we look at the major debates regarding regulatory design, and/or the calibration of regulations, these theories tend to be absent from the discussion. For example, consider two of the most contentious aspects of bank capital regulation. One debate regards the level of capital that banks should be required to hold. The other pertains to whether capital ratios should be compared with a risk-weighted concept of assets or with a simple sum of assets. In both debates, theory is rarely invoked and, when it is, the central argument is usually a variant of the Modigliani and Miller propositions applies to banks.5
Alternatively, consider the new liquidity regulations that are coming into effect. Both the net stable funding ratio and the liquidity coverage ratio were designed from scratch without appeal to any particular theory. We will see that in some cases these two regulations are potentially redundant.
This essay is based on a paper (Kashyap, Tsomocos, and Vardoulakis [2019]) that explores what happens when banks do two things. One is to monitor borrowers to support lending, and the other is to offer deposits that provide savers with valuable liquidity services. That paper has gone through several revisions, and in the course of these alterations, we have experimented with different assumptions and found that most plausible ones deliver similar implications. In what follows, we stress implications of our framework that are generic in the sense of holding across several variants of the model.6
We will see that studying environments where banks provide multiple services delivers new insights, especially regarding regulations. The frictions that create a role for banks also naturally create a gap between the choices that banks will make on their own (the privately optimal equilibrium) and what a social planner would prefer. The framework can be used to think about how regulations can interact to close the gap between privately and socially optimal banking allocations.
The remainder of this essay is broken into four parts. We will begin by describing the baseline Diamond and Dybvig model on which our analysis built. After reviewing their classic model, we describe the kind of assumptions that one must make to create the possibility that banks can deliver multiple services to borrowers and savers.
We then describe the deviations between the private allocations chosen by the banks, savers, and entrepreneurs and those that a benevolent social planner would choose. The planner has to trade off fixing various distortions, and the choices will depend on how much the planner cares about the different actors in the economy.
The third section of the analysis explores how regulations can be used to implement the objectives of the social planner. One important finding is that run risk is harmful to banks, savers, and borrowers. However, there are multiple ways to lower the run risk that differ in the incidence across the different actors in the model. For example, alternative strategies for reducing run risk can lower bank profits, reduce deposit services, and/or limit credit extension. Different agents view these outcomes differently and hence have different preferences for how run risk is controlled. Put differently, decreasing run risk or eliminating runs altogether is not the primary social objective; rather, it is a by-product of trying to maximize overall social surplus. The social surplus has two components, the windfall created by reducing run risk and the way that the surplus is allocated across agents (because a planner does not necessarily weight everyone equally). A second important observation is that a regulator will need to use multiple tools jointly to approximate what a planner would like to accomplish.
Finally, we offer some concluding remarks about directions for further research.
BANKING ENVIRONMENT
Our model is a generalization of the classic Diamond and Dybvig (1983) banking model (DD going forward). Their setup was initially stark, designed to emphasize one consideration. So, we begin by reviewing their environment and then explain how and why we amend it.
A REFRESHER ON THE DIAMOND-DYBVIG MODEL
In DD, some people (savers) have money that can be lent but have no investment opportunities. There is an investment opportunity that requires funding and delivers payoffs in two periods. In our rendition of the model, this investment opportunity will be available to entrepreneurs who have no resources. A saver has uncertain needs to consume that are purely idiosyncratic. In particular, some of them will need money after one period, while others can wait two periods. The savers do not know whether they will need liquidity early or not.
Consider two ways to handle the uncertain need for access to funds. Suppose a saver were to make a direct loan to an entrepreneur. If the saver learns that she needs the funds after one period, the loan can be recalled. However, the interest payment in this case is zero; think of this as a technological constraint, where a loan that is liquidated early repays only the principal that was lent. So, direct lending by individuals is a poor way to deal with uncertain liquidity needs because when the savers need to consume early, they receive no interest.
As another alternative, suppose a firm (we will call it a bank) collects deposits from many savers and makes loans to many entrepreneurs. This bank can reduce the idiosyncratic risk that each borrower faces. By diversifying across many savers, the bank can take some of the interest that will arrive in two periods and pay part of it out to the people withdrawing early. This arrangement reduces how much can be paid to the patient savers. However, because savers are not sure whether or not they are patient, they welcome this kind of arrangement.
The amount promised to the early withdrawers will depend on how many of them there are, relative to the patient savers and the profitability of loans (that are not called early). Essentially, the bank is a vehicle by which the savers who are patient end up insuring the savers who wind up being impatient. If there is competition between banks for deposits, it will force bank profits to be very low, so essentially all the interest collected from the loans is paid out to the savers. The central question is how much of this interest is offered to earlier withdrawers.
The banking solution appears to be a better risk-sharing arrangement than having each person self-insure via direct lending. However, the bank is fragile in the following sense. If more people than anticipated request their money back early, the bank may have to liquidate so many loans to satisfy the withdrawals that it cannot fully meet the promised payments that are due to the patient savers. In that case, the patient savers have to make a conjecture about what other patient savers might do. If enough of them opt to ask for their money early, the bank will run out of funds in the course of paying off the early withdrawals.
The problem arises because the only way that the early withdrawals are being paid is by liquidating loans, so there may be insufficient remaining loans to fully pay the patient depositors. This means that it can be individually rational for a depositor who believes others are going to redeem early to do so also, even if that depositor has no immediate need for funds. In other words, a run can be self-fulfilling.
GENERALIZING DIAMOND AND DTBVIG
The DD model brilliantly captures the fragility that is inherent in having the bank provide liquidity services by pooling risk. This is the reason that the model has been so widely studied and is often used as a basis for policy discussions. Nonetheless, in making their point as simply as possible, Diamond and Dybvig intentionally left out many other important aspects of the financial system and the role banks play in the economy. In particular, the DD model presumes that banks do not contribute to credit extension and so the fragility is disconnected from banks’ capital structure and asset composition.
Therefore, we have experimented with various extensions of their framework that create the possibility that banks do not only provide liquidity services but also improve lending outcomes. The benefit of adding such features is that we are able to address a much wider range of issues, while the cost is that the model becomes more complex. Whereas Diamond and Dybvig can solve their model analytically, we have to use numerical examples to characterize the properties.
We make five modifications to their original setup. We assume that banks (and savers) can invest in a riskless, safe asset (not just loans). We also assume loans have an uncertain payoff, rather than being completely safe, as in DD. This pair of assumptions about the assets that are available to the banks introduces a trade-off between safety and profitability. The banks make more money by making loans but are more exposed to run risk when they opt to make more loans and hold fewer safe assets.
Our third change is to suppose that entrepreneurs and banks are subject to limited liability. This assumption is realistic, and accounting for it opens up two interesting possibilities that are absent in DD. First, the banks now have a reason to take excessive risk to exploit the limited liability. In DD, it is well known that offering deposit insurance would eliminate run risk without creating any other problems. With limited liability for the banks, introducing deposit insurance would exacerbate the temptation of banks to gamble by extending even more loans. Our extension allows us to investigate the idea that banks sometimes excessively gamble at the taxpayers’ expense.
The other by-product of assuming that entrepreneurs have limited liability is that it creates a role for banks to monitor borrowers. We assume that banks can audit the entrepreneurs to see whether they have the ability to repay the loan or not. The choice to monitor is endogenous, in that the banks have to expect to receive enough extra in repayment from exerting the effort to undertake the auditing. This makes banks the efficient entities to generate loans and means that their presence in the economy yields more lending than if individuals, who are not good at auditing, had to make direct loans.
Finally, we assume that banks are funded with equity and debt. This change delivers two benefits. First, it means that the price of equity is endogenously determined, so that when capital regulation is contemplated, we have to see whether investors are willing to supply more equity funding. Often it is just assumed that as much equity is needed will be available.
The main difficulty with introducing equity is that it significantly complicates the calculation of the equilibrium. The bank’s solvency is threatened by run risk and the possibility of loans going bad. To simplify the run decision, we suppose that depositors receive a signal about how much the liquidation value of a loan will be if it is recalled by the bank. The liquidation value is random. We make technical assumptions about the nature of the signal so that the depositors follow a threshold rule, and whenever the signal about the liquidation value exceeds a cutoff, patient depositors do not run. If the signal is below the threshold, they do run.7
Inefficiencies
Our modifications to DD not only create more socially valuable roles that banks can play but also lead to reasons why private actors following only their own incentives will make choices that a social planner would seek to improve.
PRIVATE vs. SOCIAL EQUILIBRIA
Rich balance sheets allow banks to perform socially useful services but also expose them to run risk. One of the main points of our analysis is that private banking choice generates run externalities that adversely affect the welfare of savers and borrowers. Run risk is harmful for all agents in the economy: banks, savers, and borrowers. But the trade-offs driving their respective welfare differ. Banks would benefit from low run risk, but not at the expense of substantially lower profits. Savers would prefer lower run risk and more deposit services, while borrowers would benefit from higher investment accompanied by lower run risk.
The private choices that the agents make work as follows. Banks are assumed to internalize how savers and borrowers worry about run risk. Therefore, banks choose the amount to lend and the interest rates on deposits to maximize the value of equity, trading off the structure of the balance sheet against the risk of a run (and accounting for the protection in bankruptcy afforded by limited liability). Importantly, the bank does not directly care about what a run does to the welfare of borrowers and savers.
Savers and borrowers are small actors that ignore their effect on banks’ choices. More specifically, this means they take the loan and deposit schedules that a bank offers as given, although if they were to coordinate, they could influence these choices (and hence the run probability).
These assumptions mean that the private decisions do not fully account for the determinants of a run and the private equilibrium will not coincide with a socially optimal equilibrium. A social planner would care about how runs directly affect banks, savers, and borrowers and would choose allocations accordingly.
A natural way to compare private and social banking choices is to group the deviations into three types. One reflects the asset mix (that is, the proportion of loans and liquid assets). A second accounts for the liability mix (the proportion of deposits and equity). The third is the overall size of the balance sheet. The scale essentially depends on how many deposits savers are willing to supply and how many loans the entrepreneurs take. These decisions can be summarized by the gap between the loan rate and the interest rate offered to patient depositors.
There are other ways to categorize the differences, but this one strikes us as particularly intuitive. Because the bank (or planner) can choose investment, liquid assets, deposits, and equity but makes these choices while respecting the balance sheet identity, we would expect there to be three independent choices. The exception to this rule would be if there is some additional constraint (for example, coming from regulation) that pushes the bank to a corner by pinning down one of the margins. More typically, the social and private deviations differ according to how the run risk distorts each of the three margins and by how the planner weighs the different agents.
Correcting some of these distortions involves trade-offs because the interventions skew allocations that favor borrowers over savers (or vice versa). For instance, if the bank holds more safe assets and makes fewer loans, that marginally helps the savers because it makes their deposits safer. Conversely, the opposite choice of more loans and fewer safe assets creates more opportunities for the borrowers but reduces the buffer that helps mitigate the riskiness of deposits.
We have modeled the banks so that they internalize all the effects of their choices. This means that the social planner can never make the banks better off. In versions of the model where bank contracts with depositors and borrowers are less sophisticated, this need not be true. However, we find it instructive to limit the number of distortions that a planner is worrying about, so we proceed with the assumptions that imply that the banks are also disadvantaged when the planner acts.
RUN RISK
Generically, run risk is different than other types of risk from the perspective of the savers and entrepreneurs. When a bank is subject to a run, some of its borrowers will see their loans liquidated to service the withdrawals. Likewise, some savers may not be fully paid what they were promised. Both borrowers and lenders could be better off if the run could be prevented unless doing so requires a dramatic reduction in the provision of deposit services or loan availability.
The externalities generated from runs play a central role in our analysis. Thus, it is essential to understand their basis in order to study ways to mitigate their adverse effect. Savers decide whether to run based on their conjecture about the bank’s ability to repay. The bank has two sources of funds that can be tapped to service early withdrawals: the liquid assets it holds and the value of loans that can be recovered upon liquidation. The amount that bank has promised (if everyone decides to try to withdraw) is the total value of deposits plus the promised interest on those deposits at date one. If we take the ratio of these two figures, we get the probability for the individual of being repaid. It will be helpful to write out this expression for future reference:
As mentioned earlier, the model has to be solved numerically – that is, picking values for the main parameters and then solving for the agent’s optimal choices conditional on those values. To gauge the robustness of our findings, we experimented with different parameter values, and statements that follow are indicative of the results for many parameter sets.
There are three ways that the planner can raise the probability of that depositors are repaid and hence reduce the risk of a run. One approach is to raise the numerator in the equation by tilting the asset composition to consist of more liquid assets and fewer loans. The second approach is to reduce the denominator of the equation by shifting the liability composition to consist of more equity and less debt. A third, subtler option is to raise the promised return to the patient depositors, so that the gains from not joining a run are higher. Notice that each of these options will also affect the way that the gains from intermediation are divided between the banks, the savers, and the borrowers.
In general, the choices that the planner will make we will depend on the weights that the planner places on the three agents. Nonetheless, there are a couple of generic predictions about how the planner will deviate from the privately optimal choices. First, when the planner cares primarily about savers, then the allocations selected will be twisted to make the asset side of the banks’ balance sheet safer. Raising the percentage of assets that are liquid allows the bank to take more deposits, which is the primary thing that savers crave. The size of the banking sector rises.
Second, when the planner cares primarily about borrowers, the allocations are tipped to generate more lending. This preference means the planner reduces the percentage of liquid assets that the bank holds. There is a limit on how far the planner can go in this direction because as the bank cuts back on liquid assets holdings, the savers will stop making deposits. In this case, the size of the banking sector shrinks.
In arranging allocations, if the planner wants banks to monitor the entrepreneurs, the banks have to conclude that lending is sufficiently profitable to justify the effort. This constraint limits how far the lending can be cut because if lending becomes too low, the profits from lending are not sufficient to justify monitoring borrowers. In this setup, the planner typically does not guarantee that borrowers always be repaid because doing so would limit the banks’ profitability so much that they would stop monitoring. Hence, runs may still occur even when the planner is determining allocations.
When the planner cares equally about the savers and borrowers, then we get a result that is a combination of the more extreme possibilities. Run risk is reduced via all three potential channels. In particular, the asset mix is safer because there is a higher percentage of liquid assets. Deposit rates rise to deter runs and the banks increase their percentage of equity financing so that the liability side of the balance sheet is also safer. The combined changes improve the welfare of borrowers and savers.
REGULATION
The results regarding the planning solution follow from letting the planner simply pick the levels of loans, liquid assets, deposits, and equities subject to the constraints that savers, borrowers, and banks are voluntarily willing to hold these quantities. For example, the promised return on deposits for the patient savers has to be higher than on liquid assets; otherwise, they would just invest directly in liquid assets. The final step in the analysis is to investigate what happens when there is no social planner but a regulator can choose requirements for capital and liquidity ratios to try to mimic what a planner might do.
REGULATORY TOOLS
There are four potential regulatory tools that we focus on: two capital requirements and two liquidity requirements. We view it as a strength of the modeling approach that we can use it to analyze regulations that are similar in spirit to the main banking ratios that were recommended by the Basel Committee on Bank Supervision.
One of the capital regulations is the ratio of equity to total assets. There are no off-balance-sheet assets in our setup, and loans are the only risky, on-balance-sheet asset, so this leverage ratio is very simple. The other capital ratio compares equity to loans, and this is akin to a risk-weighted capital ratio, where liquid assets are given a zero risk weight and loans are given a weight of 1.
The liquidity coverage ratio is aimed at insuring that deposit outflows over a certain period (30 days, in practice) are backstopped with funds that are readily available. In our two-period setup, all deposits could potentially run, so the definition of outflows is clear. To decide on the available funds, there are two potential choices. One would be to count only liquid assets that are currently on the balance sheet. The other alternative is to also include the value of loans that could be used to meet outflows in the very worst case regarding potential liquidation values. It turns out that either definition leads to similar findings.
The net stable funding ratio is essentially the mirror image of liquidity coverage ratio. It requires that illiquid assets are funded with stable liabilities. In our setup, the numerator of the ratio is the combination of equity and the expected amount of patient deposits – though one could include a parameter to use to translate the expected amount of patient deposits into an equity equivalent. The denominator – that is, the illiquid assets – will be loans.
In seeking to approximate the planning solution, a regulator must use multiple tools. It is possible to make the asset side of the balance sheet safer using liquidity regulation. However, in shifting toward liquid assets and away from lending, the entrepreneurs are made worse off. It is possible to raise the proportion of equity financing using either of the capital regulations, which makes the liability side of the balance sheet safer. Increasing the leverage ratio creates an incentive to shift out of liquid assets and toward lending, so the asset side of the balance sheet becomes riskier. Using this tool helps the borrowers because so much more credit is extended, but it reduces the welfare of savers. The risk-weighted capital ratio limits the lending, so it helps savers but hurts borrowers.
Mimicking the planner’s allocations requires using at least one capital regulation and one liquidity regulation. These kinds of combinations can move both the liability side and the asset side of the bank toward the planners’ desired outcome. Importantly, some combinations, such as using both a liquidity coverage ratio and a net stable funding ratio, do not work better as a pair because they operate on the same margins. Any improvements require the tools be distinct enough to fix different distortions.
Given that there are three distortions in the private equilibrium, one might conjecture that the regulator would need to have three tools to fix the three distortions. Our numerical analysis confirms this hunch. However, none of the capital and liquidity regulations are well suited to deal with the distortion in the scale of intermediation. For instance, when the planner weights the savers and borrowers equally, the planner wants a larger-balance banking system (that has a safer mix of both assets and liabilities). In this case, there are other tools that can be used to encourage the banks to expand their balance sheet to the level that the planner prefers. For example, a deposit subsidy (say, through the tax deductibility of interest payments) would work. Likewise, a program that subsidizes certain type of credit extension, such as a funding for lending program, could also be used to change the level of intermediation. When a tool like one of these is combined with a capital and liquidity tool, the regulations can deliver outcomes that mimic the planner’s.
CONCLUSION
Once banks perform multiple services, regulating them becomes more complicated. The frictions that make the services valuable will drive a wedge between private and social objectives. In our framework, banks take more lending risk and prefer to operate with higher leverage than a social planner would prefer. Both considerations make the risk of runs higher. A regulator can use a combination of a capital and a liquidity regulation to correct these two distortions. The regulator will need an additional tool to adjust the overall level of banking activity. Typically, that level will also be distorted. So, to fully replicate a planner’s preferred outcomes, the regulator would need to deploy three tools.
There are two obvious directions of future research that seem particularly promising. One is to extend the analysis so that some form of regulatory arbitrage is possible. This could be modeled in several ways. One approach would be to give banks access to off-balance-sheet assets. In this case, the liquidity and capital regulations that we have studied would be less potent because the banks could try to move some of their risk-taking off of their balance sheets. The actual Basel regulatory ratios recognize that banks have off-balance-sheet activities and seek to account for their presence. Nevertheless, understanding how multiple regulations interact in this environment would be interesting.
Alternatively, we could permit the arbitrage by allowing for additional intermediaries, “shadow banks,” that could partially or perhaps fully evade bank regulations. Obviously, these entities have to be less efficient at banks at some functions; otherwise, they would drive the banks out of business. Exploring how the substitutability of activities across organizations changes the efficacy of regulations also seems like a promising direction for future work.
Finally, because our model was derived from Diamond and Dybvig’s work, it is not well suited for analyzing dynamic issues. Working out what happens in a more dynamic version of the model would also be valuable. For example, in a more dynamic model, we could study the efficacy of both ex ante regulations and ex post ones, such as bailouts. n
ENDNOTES
1 This material is based on our paper, “Optimal Bank Regulation in the Presence of Credit and Run Risk.” All views are our own and do not necessarily reflect the views of the Federal Reserve Board, the Federal Reserve System, or the Bank of England.
2 D.W. Diamond and P.H. Dybvig, “Bank Runs, Deposit Insurance and Liquidity,” Journal of Political Economy 91, no. 3 (1983), 401-419.
3 D.W. Diamond, “Financial Intermediation and Delegated Monitoring,” 51, no. 3 (1984): 393-414.
4 D.W. Diamond and R.G. Rajan, “Liquidity Risk, Liquidity Creation and Financial Fragility: A Theory of Banking,” Journal of Political Economy 109, no. 2 (2001), 287-327.
5 The appeal to Modigliani and Miller is somewhat puzzling since the standard theories of intermediation, such as the ones cited in the prior paragraph, do not satisfy the assumptions required for the capital structure invariance propositions to apply.
6 For instance, in prior versions, we also considered how allowing savers access to bank equity and deposits could offer insurance against aggregate risk. This service is not unique to financial intermediaries and abstracting from this makes the model more tractable. See the following for a version of the analysis that includes this channel: A.K. Kashyap, D.P. Tsomocos, and A.P. Vardoulakis, “How Does Macroprudential Regulation Change Bank Credit Supply?” revision of National Bureau of Economic Research working paper 20165 (2017).
7 This approach was initially proposed by Goldstein and Pauzner, who assumed that the signal concerned the value of the loans in the final period. See I. Goldstein and A. Pauzner, “Demand–Deposit Contracts and the Probability of Bank Runs,” The Journal of Finance, 60 (2005): 1293-1327.
About the Authors:
Anil Kashyap
Anil Kashyap is the Edward Eagle Brown Professor of Economics and Finance at the University of Chicago’s Booth School of Business and an external member of the Bank of England’s Financial Policy Committee. He co-founded the U.S. Monetary Policy Forum, serves as a consultant for the Federal Reserve Bank of Chicago, a research associate for the National Bureau of Economic Research, and a research fellow for the Centre for Economic Policy Research.
Dimitrios P. Tsomocos
Dr. Dimitrios P. Tsomocos is a Professor of Financial Economics at Saïd Business School and a fellow in management at St. Edmund Hall, University of Oxford. He co-developed the Goodhart-Tsomocos model of financial fragility in 2003 while working at the Bank of England. The impact has been significant, and more than 10 central banks have calibrated the model, including the Bank of Bulgaria, the Bank of Colombia, the Bank of England, and the Bank of Korea. Before joining the Saïd Business School in 2002, Dimitrios was an economist at the Bank of England. He holds a B.A., M.A., M.Phil., and a Ph.D. from Yale University.
Alexandros P. Vardoulakis
Alexandros Vardoulakis is a Principal Economist at the Federal Reserve Board. Before joining the Board, he worked as an economist at the European Central Bank and Banque de France. He has participated in various international working groups and is currently a member of the Nonbank Monitoring Experts Group of the Financial Stability Board. His principal areas of research are banking, macro-finance, and monetary theory and policy. Vardoulakis is currently doing research on the effects of financial regulation on financial stability and real economic activity. He received his D.Phil. in Financial Economics from the University of Oxford, Saïd Business School.
