The Diamond and Dybvig model

The Diamond and Dybvig model was first outlined in a seminal paper from Douglas W. Diamond and Philip H. Dybvig in 1983 in a famous Journal of Political Economy piece, “Bank Runs, Deposit Insurance, and Liquidity.”  You can think of this model as our most fundamental understanding, in modeled form, of how financial intermediation works.  It is a foundation for how economists think about deposit insurance and also the lender of last resort functions of the Fed.

Here is a 2007 exposition of the model by Diamond.  You can start with the basic insight that bank assets often are illiquid, yet depositors wish to be liquid.  If you are a depositor, and you owned 1/2000 of a loan to the local Chinese restaurant, you could not very readily write a check or make a credit card transaction based upon that loan.  The loan would be costly to sell and the bid-ask spread would be high.

Now enter banks.  Banks hold and make the loans and bear the risk of fluctuations in those asset values.  At the same time, banks issue liquid demand deposits to their customers.  The customers have liquidity, and the banks hold the assets.  Obviously for this to work, the banks will (on average) earn more on their loans than they are paying out on deposits.  Nonetheless the customers prefer this arrangement because they have transferred the risk and liquidity issues to the bank.

This arrangement works out because (usually) not all the customers wish to withdraw their money from the bank at the same time.  Of course we call that a bank run.

If a bank run occurs, the bank can reimburse the customers only by selling off a significant percentage of the loans, perhaps all of them.  But we’ve already noted those loans are illiquid and they cannot be readily sold off at a good price, especially if the banks is trying to sell them all at the same time.

Note that in this model there are multiple equilibria.  In one equilibrium, the customers expect that the other customers have faith in the bank and there is no massive run to withdraw all the deposits.  In another equilibrium, everyone expects a bank run and that becomes a self-fulfilling prophecy.  After all, if you know the bank will have trouble meeting its commitments, you will try to get your money out sooner rather than later.

In the simplest form of this model, the bank is a mutual, owned by the customers.  So there is not an independent shareholder decision to put up capital to limit the chance of the bad outcome.  Some economists have seen the Diamond-Dybvig model as limited for this reason, but over time the model has been enriched with a wider variety of assumptions, including by Diamond himself (with Rajan).  It has given rise to a whole literature on the microeconomics of financial intermediation, spawning thousands of pieces in a similar theoretical vein.

The model also embodies what is known as a “sequential service constraint.”  That is, the initial bank is constrained to follow a “first come, first serve’ approach to serving customers.  If we relax the sequential service constraint, it is possible to stop the bank runs by a richer set of contracts.  For instance, the bank might reserve the right to limit or suspend or delay convertibility, possibly with a bonus then sent to customers for waiting.  Those incentives, or other contracts along similar lines, might be able to stop the bank run.

In this model the bank run does not happen because the bank is insolvent.  Rather the bank run happens because of “sunspots” — a run occurs because a run is expected.  If the bank is insolvent, simply postponing convertibility will not solve the basic problem.

It is easy enough to see how either deposit insurance or a Fed lender of last resort can improve on the basic outcome.  If customers start an incipient run on the bank, the FDIC or Fed simply guarantees the deposits.  There is then no reason for the run to continue, and the economy continues to move along in the Pareto-superior manner.  Of course either deposit insurance or the Fed can create moral hazard problems for banks — they might take too many risks given these guarantees — and those problems have been studied further in the subsequent literature.

Along related (but quite different!) lines, Diamond (solo) has a 1984 Review of Economic Studies piece “Financial Intermediation and Delegated Monitoring.”  This piece models the benefits of financial intermediation in a quite different manner.  It is necessary to monitor the quality of loans, and banks have a comparative advantage in doing this, relative to depositors.  Furthermore, the bank can monitor loan quality in a diversified fashion, since it holds many loans in its portfolio.  Bank monitoring involves lower risk than depositor monitoring, in addition to being lower cost.  This piece also has been a major influence on the subsequent literature.

Here is Diamond on google.scholar.com — you can see he is a very focused economist.  Here is Dybvig on scholar.google.com, most of his other articles in the area of finance more narrowly, but he won the prize for this work on banking and intermediation.  His piece on asset pricing and the term structure of interest rates is well known.

Here is all the Swedish information on the researchers and their work.  I haven’t read these yet, but they are usually very well done.

Overall these prize picks were not at all surprising and they have been expected for quite a few years.