Introduction: Banks have some self-interest to avoid runs. But opaque and imperfect asset information makes it tricky to reassure all depositors. Must regulations demand some unused liquidity? This framework can help future discussions find the optimal level and form of liquidity requirements.
By Douglas W. Diamond and Anil K Kashyap, University of Chicago Booth School of Business
There is little agreement on regulatory goals for bank liquid asset holdings and no benchmark theory on the issue, despite recent regulation in this area. Economists even have competing concepts in mind when discussing liquidity, resulting in no generally accepted empirical measure. Allen (2014), in a literature survey, concludes: “With capital regulation there is a huge literature but little agreement on the optimal level of requirements. With liquidity regulation, we do not even know what to argue about.”
There is an asymmetry in the economic analysis of capital and liquidity regulations. For capital regulation, the pioneering work of Modigliani and Miller (1958) provides a solid theoretical framework. At the international level, capital regulations for banks go back to 1988, and there are many empirical examinations of the impact of these regulations.
Nonetheless, practice is ahead of both theory and measurement for liquidity requirements. The global regulatory community, through the Basel III rules of the Committee on Bank Supervision, agreed on the Liquidity Coverage Ratio (LCR) and the Net Stable Funding Ratio (NSFR), in 2013 and 2014, respectively. Banks will be compelled to meet requirements for these ratios by 2019.
Forming a Framework
In a recent paper, we, Diamond and Kashyap (2016), developed a framework for discussing liquidity and suggested that regulations bearing some resemblance to those in Basel III will improve outcomes relative to an unregulated benchmark. However, the optimal regulations that arise would depend on bank characteristics in ways other than those specified in Basel III, so they do not mimic exactly the ones that are on track to be implemented.
Our analysis assumes that banks create liquid deposits to provide liquidity insurance given the uncertain timing of some customers’ withdrawals. This builds on Diamond and Dybvig’s (1983) model of banking in which banks provide this insurance by relying on the law of large numbers to eliminate idiosyncratic customer liquidity needs.
One modification we made involves the form of run risk that the banks face. Banks are assumed to have a good assessment of the fluctuating aggregate liquidity needs of their customers. This assessment varies over time in ways that outsiders cannot know directly. Given the complexity of modern banks, it seems realistic to presume that most customers can’t precisely determine their bank’s maturity mismatch and hence its vulnerability to a run. The imperfect information creates a challenge for the banks because their customers will not necessarily know if the bank is holding enough liquidity, which reduces the bank’s incentive to hold liquidity.
Our framework allows for the possibility that not all customers seek to withdraw their funds during a run (note: related work includes Ennis and Keister (2006), Cooper and Ross (1998) and Vives (2014)). It is useful to analyze partial runs because in practice there are some sticky deposits that don’t flee even in times of considerable banking stress. It is also usually clear, even before troubles occur, which types of deposits are prone to running. In practice, most runs involve institutional wholesale deposits. In addition to being better informed about a bank’s portfolio than small depositors, they are better at predicting when others might panic. That is, sophisticated or institutional investors would be in the best position to get the information that a run (caused by panic that others might be about to run) could be imminent.
Within this environment, we can assess the vulnerability of the financial system to runs under different regulatory arrangements. It is possible, but not always true, that self-interest will make an unregulated bank run-proof even if depositors have no detailed information about its liquidity holdings. In these situations, liquidity mandates would not be helpful.
Depositors may not be able to interpret disclosures of a bank’s liquidity holdings to determine if the holding is sufficient to allow it to survive a run. Consider whether a bank would choose to hold a sufficient amount of liquidity even if its choice between liquid assets and illiquid loans was completely unobservable. In circumstances where depositors cannot be sure about how changes in liquidity holdings affect the robustness of banks to runs, the banks will typically face a tension in deciding how much to fortify against the risk of a run. They can always choose to be sufficiently conservative to be able to withstand a run on top of the highest possible level of normal withdrawal activity, which is the worst case for the total fraction of withdrawals. But to do that, they will engage in very little lending, and the forgone profits from deterring the run will be high. The added liquidity to survive a run will turn out to be excessive whenever a run is avoided. Hence, it is possible they will make more profits from added lending, which would leave them unable to always be able to sustain a run.
Next we allow regulatory interventions that place restrictions on present and possibly future bank holdings of liquid assets. If future minimum holdings are required, some of a bank’s liquid assets will not be available to meet future withdrawals. Banks turn out to have perfectly aligned incentives to prepare to service fundamental withdrawal needs. So the challenge is to determine whether a requirement that distorts their incentives toward being more robust to withstand a run will improve outcomes.
Our framework specifically addresses regulations based on the two impending Basel rules. One requires an initial liquidity position be established in normal times, before any deposits are withdrawn. This liquidity would not be required to be held at all times and could be used freely for a long period, as long as the liquidity buffer is replenished in the distant future. This regulation, which can be temporarily violated, is similar to what the NSFR proposed as part of the Basel reforms. A second option is a mandate to always hold additional liquid assets beyond those needed for the fundamental withdrawals. This imposes both present and future minimum holdings of liquid assets. This regulation looks like the LCR that is part of the Basel reforms and is similar to a traditional reserve requirement for the bank.
The Last Taxi at the Station
One point of contention regarding the liquidity coverage ratio is whether required liquidity can be deployed in the case of a crisis. Goodhart (2008) framed the issue nicely with an analogy of “the weary traveler who arrives at the railway station late at night, and, to his delight, sees a taxi there who could take him to his distant destination. He hails the taxi, but the taxi driver replies that he cannot take him, since local bylaws require that there must always be one taxi standing ready at the station.”
Stability can be achieved either by having the bank hold the correct amount of liquid assets up-front as with an NSFR, or by imposing restrictions that require liquidity be available even after withdrawals are underway, as with an LCR.
One way to interpret Goodhart is to recognize that, broadly speaking, there are two ways to think about the purpose behind liquidity regulations. One motivation is to make sure that banks can better withstand a surge in withdrawals if one occurs. From this perspective, mandating that the last taxi can’t depart the station seems foolish. Another motivation is to design regulations aimed at reducing the likelihood of a withdrawal surge in the first place. Mandating some unused liquidity in the future could provide beneficial incentives to hold a desirable amount of liquidity in the present.
Our main conclusion from analyzing the two Basel-style regulations is that they may improve outcomes relative to the ones that arise from pure self-interest, but each brings possible inefficiencies. We describe an integration of liquidity requirements with the lender of last resort policy, which can be superior.
Figuring out the Formulas
Mathematical formulas best explain our framework for liquidity requirements. To start, we maintain that there are three dates, 0, 1, and 2. The deposit interest rates that a bank must offer are taken as given. For a unit investment at date 0, the bank offers a demand deposit that pays either a total return (including interest) of r1 at date 1 or r2 in total at date 2. For simplicity, assume that the interest rate offered is zero, which implies that r1=r2=1. We will assume that depositors are sufficiently risk-averse that they would like the banking system to supply one-period deposits that are riskless. Therefore, we consider interventions that will be designed to ensure this outcome.
The residual claim after deposits are paid is limited liability equity retained by the banker. All equity payments are made at date 2. The bank can invest in two assets with constant returns to scale. One is a liquid asset (which we will also refer to as the safe asset) that returns R1, which is more than it pays on deposits over one period (R1>1), per unit invested in the previous period. The other is an illiquid asset for which a unit investment at date 0 returns R2 at date 2, an amount that exceeds the return from rolling over liquid assets (R2>R1*R1). The illiquid asset (which we will also refer to as a loan) can be liquidated for θR2 date 1, which is less than the return from having invested in the liquid asset (that is, θR2<1 and θ≥0). These restrictions imply that when the bank knows it must make a payment at date 1, it will invest in the safe asset rather than planning to liquidate the loan. Runs can make the bank insolvent because each unit of the illiquid asset can be liquidated for less than r1=1, the amount owed depositors at date 1 (θR2<1). If everyone withdrew at date 1 and only illiquid assets were held, the bank would fail. There are many possible reasons to presume that the illiquid asset can be liquidated for only θR2. Nothing hinges on why this discount exists, though we do insist that it is operative for everyone in the economy, including a potential lender of last resort.
There is uncertainty about how many depositors will need to withdraw for fundamental reasons (all reasons other than fear of bank failure). For fundamental reasons, a fraction, ts, of depositors want to withdraw (absent fear of a run) at date 1 and 1-ts want to withdraw at date 2. The variable s in the subscript on ts denotes the state of the economy (which determines how many will want to withdraw). The bank, having the best data on its customers, will make the asset composition choice based on its foreknowledge of ts. For simplicity, we assume the bank knows the exact value of s and of ts. Indeed, some early theories of banking supposed that the advantage of tying lending and deposit making was that by watching a customer’s checking account, a bank could gauge that customer’s creditworthiness (Black, 1975). (note: Mester, Nakamura and Renault (2007) provide direct evidence supporting the assumption that banks can learn about customer credit needs by monitoring transactions accounts).
If there is fear of a bank run, it is possible that more than a fraction of ts deposits will be withdrawn. Let the actual fraction of depositors who withdraw at date 1 be denoted by f1. To understand agents’ incentives, note that if the ex-post state of the economy is s and there is not a run, a fraction f1=ts will withdraw r1 =1 each, requiring ts in date 1 resources.
With complete information, a bank will be forced to hold enough liquidity to deter runs and its desire to maximize profits will assure that it holds no more than this amount. But given the possibility of incomplete information, arriving at a formula for run-free banking can be challenging.
Because we assume that the bank knows ts, its own self-interest will lead it to invest enough in the liquid asset to cover these withdrawals. If actual withdrawals, f1, were known, the bank would choose to hold just enough liquid assets to avoid needing to liquidate any loans. As a result, the bank will always have an incentive to choose to hold enough liquidity to meet normal withdrawals, ts. In symbols, this means that if we let denote the fraction of liquid assets chosen by a bank and as the fraction just sufficient to meet fundamental withdrawals, this means that we know that .
Seeing a Sunspot (anything that might cause fear of a run)
Now consider what might happen in a run. A fixed fraction Δ of depositors potentially will fear that a run might occur, which can be described as “seeing a sunspot.” Everyone knows that the fraction Δ might run based on the sunspot, and those who see the sunspot must decide whether they believe that the others who see it (and thus fear a run) will decide to withdraw their funds early. The sunspot stands in for general fears about the solvency of the bank, so the inference problem relates to their conjecture about whether others investors might panic. As a result, they have to decide whether to join the run. If they join the run, the fraction of withdrawals will be ts+Δ.
If the bank will be insolvent with a fraction of withdrawals of ts+Δ , then each depositor who fears a run will prefer to withdraw, and this will lead to withdrawals of f1=ts+Δ. This will give zero to all who do not withdraw, and the goal of bank or its regulator is to prevent this outcome from ever being a self-fulfilling prophecy. We will refer to a bank as unstable if its asset holdings admit the possibility of a run. Alternatively, we refer to a bank as stable if its asset holdings eliminate the possibility of a run.
We define the minimum stable amount of liquidity holdings, , as the minimum fraction of liquid assets in the state of the economy, s, which eliminates the possibility of a run. This implies that a bank holding the fraction will be run-free. Whenever bank self-interest from funding fundamental withdrawals does not make them stable (i.e., when ), a run will be avoided only if the bank holds more liquid assets than it will need for actual withdrawals, given that a run is avoided.
Information and Disclosures
Depositors desire run-free bank deposits. As a first benchmark, suppose that depositors know all of the choices and information that banks know, and thus observe liquidity, the size of a run, and the fraction who will withdraw for fundamental reasons (αs Δ and ts). In this case, the need to attract deposits will force the bank to make itself run-free. If, given this full depositor knowledge, the bank would remain solvent in a run, then it never pays for any depositor to react to the sunspot that causes a run to be feared and there will be no runs. Our framework shows that it is possible that the bank’s self-interest to choose to hold enough liquid assets to meet just the fundamental withdrawals, ts, will prevent runs even if not all the information is known by depositors. This is the case if the assets are not too illiquid, the run is not too large, and bank is sufficiently profitable.
When these conditions fail, because loans are quite illiquid or the bank is not very profitable, then to deter runs, a bank must hold more liquidity than is needed to meet normal withdrawals and incomplete information of depositors can make then wonder if the bank holds sufficient liquidity to deter a run. Consider what happens when loans are totally illiquid (θ=0). In this case, the bank must always hold enough liquidity to fully finance the run because there is no other way to get access to liquidity, or . Therefore, the bank must always hold more liquidity than is needed for normal withdrawals in order to deter a run. More generally, whenever the loan is sufficiently illiquid, merely preparing to service fundamental withdrawals will not be enough to deter a run.
Alternatively, suppose the depositors do not observe the fraction of normal withdrawals, ts, or the liquidity holdings, αs, but the bank and a regulator do. With full information available to the bank or regulators, a bank (or a regulator) seeking to deter runs will choose to require just enough to avoid a run, or . Note that when some liquidity must be unused even after funding normal withdrawals at date 1 and it will appear that there is an unneeded amount of liquidity (taxis are always remaining at the station). The unused liquidity will look like it is unneeded.
With complete information, a bank will be forced to hold enough liquidity to deter runs and its desire to maximize profits will assure that it holds no more than this amount. But given the possibility of incomplete information, arriving at a formula for run-free banking can be challenging.
Full information would be helpful, but is unrealistic. For several reasons, bank disclosures of liquidity holdings are difficult to interpret. First, if disclosure (or a regulatory requirement) regarding liquidity only applies on some dates (such as the end of an accounting period), the bank can distort the disclosure. Second, even if a liquidity disclosure (or requirement) is on all dates, it is plausible that the bank knows more about its customers liquidity needs than anyone else, which makes it difficult for others to determine if a given level of liquidity is sufficient to make the bank run-free.
One important problem facing depositors is the difficulty in interpreting the kind of accounting data that must be parsed in order to decide whether to join a run. Disclosures that are made on liquidity positions typically occur with a delay and are periodic (such as at the end of a quarter or a fiscal year). The inference problem for depositors can be compounded by the temptation for banks to engage in window dressing of their accounting information. (note: See Munyan (2015) for evidence on window dressing by European banks).
Possible window dressing implies that liquidity disclosures and regulations should hold on all dates rather than being applied periodically. This will mean that it may be difficult to credibly disclose , the initial holding of liquidity, because this could be reinvested in illiquid loans after the disclosure. Requiring liquidity to be held on all dates (even on date 1) will of course limit its use to meet withdrawals of deposits. This unusable liquidity brings back the problem of not allowing the last taxi to leave the station.
The normal fraction of withdrawals, ts, fluctuates. If there is no way to communicate what the bank knows about this, and self-interest does not automatically make it stable, then runs will occur unless the bank discloses enough liquidity to stay solvent even in the worst case: the largest possible fraction of normal withdrawals plus the fraction withdrawn in a run. Depositors will have two reasons to worry. First, for realization of normal withdrawals where it would not be stable, a run would cause the bank to fail and thus would be self-fulfilling, leading to total losses by depositors who did not run. Second, because depositors who do not participate in a run that makes the bank fail lose everything invested, a small chance of a run will cause a depositor to run for sure. This is because a depositor who worries about a run but does not know the fraction of others who will withdraw for normal reasons will have incentives to withdraw rather than face the potential losses. This implies that a liquidity disclosure that is not sufficient to make a bank run-free for the worst-case level of normal withdrawals (the largest possible ts) will lead to runs for all levels of ts. This causes the bank to liquidate loans unnecessarily, even when the run does not leave it insolvent.
Approaches Based on Basel III
Our framework considers two approaches to liquidity regulation that a regulator could pursue. These are inspired by the regulations proposed in Basel III. The analysis supposes that the regulator can credibly certify that the bank has some level of the liquid asset present (as a percentage of deposits). One option is to report on this ratio at the time when the liquid assets are acquired (at date 0). This would amount to regulating initial holdings of liquidity, and allowing the bank to use any of it when needed. This is similar in spirit to the NSFR. The Basel NSFR requires “banks to maintain a stable funding profile in relation to the composition of their assets and off-balance sheet activities.” Loosely speaking, the NSFR can be thought of as forcing banks to match long-term assets with long-term funding. Our interpretation of this requirement is that the bank is free to violate the requirement temporarily in the future (with a long period allowed to rebuild its liquidity holdings), so it is not always a binding restriction. As a result, it is very much like a requirement that the bank chooses a minimum level of liquid holdings at date 0, αs.
Alternatively, a regulator could insist that the bank will always have a certain amount of liquid assets relative to deposits at all times, including after any withdrawals. This requirement can never be violated. This kind of regulation is like the LCR. The LCR requires “that banks have an adequate stock of unencumbered high-quality liquid assets (HQLA) that can be converted easily and immediately in private markets into cash to meet their liquidity needs for a 30 calendar day liquidity stress scenario.”
Our framework shows that in many cases the LCR (which can never be violated) will be superior to the NSFR by providing incentives for banks to economize on liquidity holdings only when their fundamental level of withdrawals is low. Requiring some liquidity that can never be used when some deposits remain (even on date 1) induces the bank to choose to hold enough liquidity to make it stable and free of runs. In addition, the amount of liquidity needed will generally exceed that which would be required if all depositors and regulators had the full information possessed by the bank. The additional liquidity, in excess of what would be required if information was complete, is required because not all of it can be released to meet withdrawals that would occur in a run. It must continue to be held because neither depositors nor regulators can determine if a given amount of withdrawals, for example 15% of deposits, is due to normal withdrawals for fundamental reasons or to a smaller number of withdrawals and a partial run, e.g., 5% of deposits for fundamental reasons and 10% due to a partial run. This lack of information will constrain the efficiency of regulation. If liquidity requirements are the only intervention, excess liquidity must be required – extra taxis must remain.
When the regulator has less information than the bank, additional excess (and unusable) liquidity must be required to provide incentives to hold the proper amount of liquidity. However, integrating liquidity requirements with a lender of last resort policy can do better. The idea is to allow access to the excess liquidity by borrowing against it from the lender of last resort, such as the Federal Reserve discount window in the United States. This borrowed liquidity would be used if a run were to occur, and this could this could deter such a run. Though this would effectively violate the liquidity requirement, a sufficient penalty, such as reduced executive compensation and a limitation on dividends, would still provide incentives to hold extra liquidity. The original Federal Reserve Act had such a dividend prohibition for banks in violation of their reserve requirements. The ability to use the all liquidity subject to a penalty allows incentives to hold sufficient liquidity without leaving any of it unusable in a run. It is similar to allowing the last taxi to leave the station but imposing a penalty on the taxi company. (note: The penalty should not be a high interest rate that would make bank insolvent if paid. If it made the bank insolvent, the ability to borrow would not deter runs).
Liquidity regulation serves a critical function in market stability. Let this analysis serve as a basis for subsequent discussions on designing optimal liquidity requirements. Without such regulation, depositors may have doubts about whether the bank will make choices that lead it to be able to withstand a panic. This lack of confidence arises because banks are opaque and balance sheets can be challenging to assess – even for sophisticated counterparties. When depositors cannot determine if the given amount of liquidity is sufficient to make the bank stable, the bank’s incentive to become super safe is limited because cutting back on lending to hold additional liquidity is not fully rewarded.
The optimal liquidity holding to deter runs requires banks to hold a level of liquid assets tied to the level of anticipated withdrawals. If the regulator is well informed about these withdrawals (and the risk of a run), then there are many equivalent ways to guarantee that the bank makes adequate liquidity choices. In particular, stability can be achieved either by having the bank hold the correct amount of liquid assets up-front as with an NSFR, or by imposing restrictions that require liquidity be available even after withdrawals are underway, as with an LCR. Using combinations of these kinds of policies will work too.
Some liquidity must go unused. Even in the best possible case (i.e., with full information), the last taxi often remains at the station. To use another analogy, by mandating “dry powder,” the regulator preserves solvency in a run and thus removes the depositors’ incentive to run. Optimal regulation prevents runs without mandating more dry powder than needed. Liquidity regulation combined with a lender of last resort policy can realize this goal. The integration penalizes liquidity regulation violations, allowing the bank to borrow against required liquidity. This, at least, leads to fewer taxis remaining at the station.
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This is a summary of the NYU Stern-TCH Gallatin Lecture Series on Banking presented by Douglas Diamond on September 10, 2015.
About the Author:
Douglas W. Diamond specializes in the study of financial crises, liquidity, and financial intermediaries. He is the Merton H. Miller Distinguished Service Professor of Finance at the University of Chicago’s Booth School of Business. Diamond is research associate of the National Bureau of Economic Research and visiting scholar at the Federal Reserve Bank of Richmond. Diamond received the Morgan Stanley-American Finance Association Award for Excellence in Finance in 2012 and the CME Group-MSRI Prize in Innovative Quantitative Applications in 2015.
Anil Kashyap is with the University of Chicago Booth School of Business, and his research focuses on financial intermediation and regulation, the Japanese economy, price setting, and monetary policy. His research has won him numerous awards, including a Sloan Research Fellowship, the Nikkei Prize for Excellent Books in Economic Sciences, and a Senior Houblon-Norman Fellowship from the Bank of England (twice). As of October 1, 2016, he is an external member of the Bank of England’s Financial Policy Committee.
Prior to joining the Chicago Booth faculty in 1991, Kashyap spent three years as an economist for the Board of Governors for the Federal Reserve System. He currently works as a consultant for the Federal Reserve Bank of Chicago and as a research associate for the National Bureau of Economic Research. He serves on the Board of Directors of the Bank of Italy’s Einuadi Institute of Economics and Finance, is a member of the Squam Lake Group, and serves on the International Monetary Fund’s Advisory Group on the development of a macro-prudential policy framework. Kashyap is also one of the academic members of the Bellagio Group (whose non-academic members consist of the Deputy Central Bank Governors and Vice Ministers of Finance of the G7 countries). Kashyap is a member of both the American Economic Association and American Finance Association, and is on the faculty oversight Board of the Chicago Booth’s Initiative on Global Markets and a co-founder of the US Monetary Policy Forum.