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«Douglas W. Diamond Anil K Kashyap University of Chicago Booth School of Business and National Bureau of Economic Research April 22, 2015 Preliminary ...»

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“Liquidity requirements, liquidity choice and financial stability”*

Douglas W. Diamond

Anil K Kashyap

University of Chicago Booth School of Business and National Bureau of Economic Research

April 22, 2015

Preliminary and Incomplete, not for citation or circulation

* Prepared for the Handbook of Macroeconomics. We thank Franklin Allen, Nancy Stokey and seminar participants

at Imperial College and the University of Chicago for helpful comments and Adam Jorring for expert research

assistance. We thank the Initiative on Global Markets at Chicago Booth, the Fama Miller Center at Chicago Booth and the National Science Foundation for grants administered through the NBER for research support. All errors are solely our responsibility.

Introduction In September 2009 the leaders of 20 major economies created the Financial Stability Board (FSB) whose purpose is to “coordinate at the international level the work of national financial authorities and international standard setting bodies (SSBs) in order to develop and promote the implementation of effective regulatory, supervisory and other financial sector policies.” Since that time the financial system has undergone a regulatory overhaul. Much of the public attention has focused on changes to the rules regarding capital requirements for banks. Yet by 2019, via the Basel Committee on Bank Supervision, the major economies have also agreed also to implement new rules governing banks’ debt structures and requirements to hold certain types of liquid assets.

To date there is a remarkable asymmetry in the economic analysis of the capital and liquidity regulations. The pioneering work of Modigliani and Miller (1958) provides a solid theoretical framework for analyzing capital regulation. Any student taking a first course in corporate finance will encounter this theory and there is a massive empirical literature that explores the theory’s predictions. Banking regulations at the international level go back to 1988 and there many empirical examinations of the impact of these regulations.

In contrast, there is no benchmark theory regarding liquidity provision by intermediaries.

Indeed, financial economists even have competing concepts that they have in mind when discussing liquidity. Allen (2014), in his survey of the nascent literature on liquidity regulation, concludes his paper by writing “much more research is required in this area. 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 long tradition of studying bank runs, but there is very little research that tries to measure liquidity or assess whether there might be too much or too little being created by financial institutions. Hence, in implementing the new liquidity regulations it seems fair to say we are in a situation where practice is far ahead of both theory and measurement.

In this paper we survey the existing work on liquidity regulation and develop a framework for discussing the regulation. The theory that we propose suggests, in certain parameterizations, regulations which bear some resemblance to those being proposed by Basel process can emerge as ones which will improve outcomes relative to an unregulated benchmark. However, the regulations that arise in our model would naturally differ across banks, depending on certain bank characteristics, so they do not mimic exactly the ones that are on track to be implemented.

The critical ingredients in our model are the following. First, we consider banks which are spatially separated and hence do not compete aggressively for deposits. Treating the bank as monopolist simplifies the analysis by allowing us to side-step some complications that arise from having to model the deposit market equilibrium. The model can also be interpreted as a description of the aggregate banking system, which for many financial stability and regulatory discussions is the object of primary concern and under this interpretation ignoring the deposit competition is perhaps more natural.

Second, we assume that intermediaries provide liquidity insurance for customers who have uncertain withdrawal needs (or consumption desires). We build on the Diamond and Dybvig (1983), henceforth DD, model of banking in which banks provide this insurance by relying on the law of large numbers to eliminate idiosyncratic customer liquidity needs. For those familiar with DD, we make two modifications. We allow the bank to invest in a liquid asset that has a positive rate of return and can be used to pay customers that need liquidity. This introduces a tradeoff between lending and holding liquidity as in Bhattacharya and Gale (1987) and several papers of Allen and Gale (1997 and others).

The other change from DD is the form of run risk that the banks face. Banks are assumed to have a good assessment of the aggregate needs of their customers for fundamental reasons. But, they also know that some customers will receive a signal about the bank which could lead to a run. The sunspots that we consider are a metaphor for people being concerned with the health of the bank, but not having a fully formed set of beliefs about the bank’s solvency status. In making their decisions we assume that customers are unable to fully evaluate the ability of the bank to honor deposits. Given the complexity of modern banks it seems realistic to presume that most customers cannot 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 prudently holding liquidity or not, which reduces the incentive to hold liquidity.





In the event that a run does occur, we allow for the possibility that not all customers seek to withdraw their funds. We believe it is useful to analyze partial runs for two separate reasons.

One is that in practice there do seem to be some sticky deposits that do not flee even in times of considerable banking stress. In addition, even before troubles occur it is usually clear which types of deposits are prone to running. So this allows us to talk about policies for different types of withdrawal risk.

Within this environment we can assess the vulnerability of the financial system to runs under different regulatory arrangements. In the baseline case, we assume that banks simply maximize their profits and see which types of equilibria arise. As usual in DD style models, the outcomes depend critically on how depositors form beliefs. It is possible, under certain parameter configurations, that the pure self-interest motives of the banks will sufficient to insure that the system will be run proof.

Given that depositors cannot be sure about how robust the banks are, the banks will typically face a tension in deciding how much to fortify themselves against the risk of a run. They can always choose to be sufficiently conservative to be able to withstand a worst case scenario. But in order to do that, they will engage in very little lending, and the forgone profits from deterring the run will be high. Hence, it is possible they will make more profits from taking more risk and living with the consequence that they may be wiped out.

We next allow regulatory interventions that place restrictions on bank portfolio choices. In the baseline set up, the banks have perfectly aligned incentives to prepare to service fundamental aggregate withdrawal needs. So the regulatory challenge is to determine whether a requirement that distorts their private incentives towards being more robust to a run will improve outcomes.

We allow for the regulation that can take several forms.

One possibility is to require an initial liquidity position that must be established before depositors make their intentions clear. This can function like the “net stable funding ratio” that is 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 regulation looks like a traditional reserve requirement for the bank, but can also be interpreted as a kind of “liquidity coverage” ratio that is part of the Basel reforms.

One point of contention regarding the liquidity coverage ratio that has emerged is whether required liquidity can be deployed in the case of crisis. Goodhart (2008) framed the issue nicely with a now famous analogy of “the weary traveller 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.” The model we propose also allows us to address the wisdom of requirements that insist that some liquidity must always be on hand.

The main conclusion from these very simple forms is regulation is that they may improve outcomes relative to the ones that arise from pure self-interest, but each brings potential inefficiencies. Hence, we next solve the mechanism design problem of a social planner who has less information about withdrawal risk than the bank does and seeks to optimally regulate banks to avoid runs. We characterize the optimal form of regulation under different assumptions about the tools available to the planner. We then compare these regulations to the simpler ones that were initially analyzed and to the Basel style regulations.

The remainder of the paper is divided into five parts. Section two contains our selective overview of previous work. As mentioned already, there is enormous and rapidly growing literature on capital regulation. We note several surveys on pure effects of capital regulation.

Our emphasis is instead on papers that focus specifically on liquidity regulation.

Section three introduces the benchmark model. We explain how it works under complete information. We also derive a generic proposition that holds with incomplete information that describes when the bank’s preferred liquidity choice will be sufficient to deter a run.

In section four we analyze the two types of liquidity regulation that are akin to the ones contemplated under the Basel process. We first demonstrate that a particular type of regulation that requires the bank to hold liquid assets equal to a fixed percentage of deposits at all times can potentially deter runs. This works because the liquidity mandate, combined the bank’s selfinterest to prepare to service predictable deposit outflows, leads the bank to hold more overall liquidity than it would otherwise. Because depositors understand this, it removes the incentive to run in some cases. We also consider alternative assumptions about depositors’ knowledge and the information available to regulators and assess the vulnerability of the bank to runs in these scenarios.

In section 5, we pose the regulatory challenge as a problem in mechanism design where the regulator does not have all of the bank’s information. We first solve a case where the social planner has all potential tools needed to implement the best possible outcome given the information constraints. We then turn to the case where the regulator is limited to setting rules based on bank balance sheet characteristics. In this case, the regulation takes the form of an excess liquidity function that ties the level liquidity assets to withdrawals. Runs can be deterred in this case, and this kind of regulation improves on the simpler versions described in the previous section, but will not implement the first best arrangement that is obtainable when the planner has additional tools. One final result shows how a lender of last resort policy, combined an excess liquidity function, can deliver first best allocations.

Section six presents our conclusions. Besides summarizing our findings, we also pose a few open questions are natural next steps to consider in addressing the issues analyzed in this paper.

2. Literature Review In considering capital regulation, the literature can be organized by sorting papers along two dimensions. The first regards what is assumed regarding the Modigliani-Miller (1958) (henceforth MM) capital structure propositions. As in all models of corporate finance, absent failures of one of the MM propositions any choices regarding capital structure will be inconsequential. There have been four primary MM violations that have drawn attention in the literature.

One concerns that existence of deposit insurance. If certain parts of a bank’s capital structure is protected from losses by the government, that can create risk-shifting incentives for equity holders. In many models, bank managers working on behalf of the equity owners face an incentive to gamble after adverse shocks that goes unchecked because depositors are immune from losses that they would suffer if the gamble fails.

A second distortion is concerns over guarantees to protect equity holders of banks from losses.

Usually this is couched as a problem of having some banks that are assumed to be “too big” or “too-interconnected” to fail. But, in the recent global financial crisis, there were also cases in some countries where equity owners of smaller, non-systemic banks were insulated from losses due to political connections.

A third violation regards the MM assumption of complete financial markets. With incomplete markets, an institution that creates new securities could be valuable. In the banking context, deposits are a leading example of special security that banks might create.

Finally, there are many models where either asymmetric information or moral hazard problems are considered. Some of the prominent examples include the possibility that borrowers know more about their investment opportunities than lenders, or that borrowers can shift the riskiness of their investments after receiving funding.

So unlike much of the literature research on non-financial corporations, the trade-off theory of capital structure, whereby firms prefer debt for its tax advantages and balance those benefits against costs of financial distress, has not figured prominently in the banking research on capital regulation. Rather, regulation is usually justified on the grounds of addressing one of these other four problems. The type of regulation that can be welfare improving will differ depending on which of these other frictions is assumed to be present.



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