A couple of readers asked me if I was familiar with and what I thought about Douglas Diamond and Philip Dybvig’s  Bank Runs, Deposit Insurance and Liquidity paper.  It has been hailed as a seminal paper because of its influence on how both economists and policymakers with an Economics PhD think about bank runs.

The fatal flaw in the article is the authors are unaware of all the assumptions they make in order to create a mathematically solvable model.  Specifically, they don’t recognize their significant assumption about transparency.

The authors create a two period model of a bank.  The assets mature at the end of the second period, but can be sold at par prior to maturity.  The liabilities can be redeemed at any time.  Some depositors having a preference for redeeming in the first period.  Others are willing to defer redemption til the end of period two in exchange for an interest payment.

Then the authors layer on their stated assumptions.  The most important of the assumptions the authors are aware of is the bank invests 100% of the deposits in the two period assets and promise the depositors a return on their deposits even if they withdraw their deposits early.

This is a model of a bank engaged in a risky funding strategy with no slack.  As a result, depositors know if there are early withdrawals they won’t get all their money back.  Hence, they have an incentive to engage in a bank run and get their money back sooner.

The authors then go on to show there are two Nash equilibrium outcomes for their model: bank runs or depositors hold till maturity.

With these two equilibriums, the authors have actually shown funding longer term assets with shorter term debt is a risky funding strategy.  This was well known to anyone involved in the financial markets in the early 1980s.  In the years immediately prior to the publication of this paper in 1983, short term interest rates soared.  It was public knowledge financial institutions like Savings & Loans using this funding strategy lost considerable amounts of money.

What happens to the authors’ model if the assumption of 100% of deposits is invested in loans maturing at the end of period two is relaxed?  There are a number of ways this can be done including investing less than 100% of deposits or adding capital.

Regular readers know I am not a fan of bank capital regulations (having helped to write them so as to hide the true amount of risk the bank is taking on).  However, individuals like Anat Admati are.  One reason they like bank capital is its impact on bank runs.

Adding bank capital or reducing the percentage of deposits invested creates slack.  With slack, early withdrawals become much less problematic for depositors.  It also changes the depositor reaction function to early withdrawals.  In the model, as soon as there might be early withdrawals, all depositors know to run to get their money back.  By adding slack, depositors now get to ask how are the bank’s assets performing and is this performance sufficient to payoff the remaining deposits.  Of course, answering these questions requires transparency.

Assuming away transparency and bank capital also impacts how the authors look at preventing bank runs.  It limits their conclusions.  They discuss how prevention can be accomplished by suspending the ability of depositors to withdraw their money or by deposit insurance.  By definition this is true and has been known since the 1930s.  The former transforms short term funding into long term funding that matches the maturity of the assets.  The latter eliminates the risk of loss and therefore any need for depositors to run to get their money back.

There are some interesting parts to their paper.  To their credit, the authors recognize no one would make a deposit in a bank if they anticipated there would be a run on this particular bank.

The authors also recognize their model doesn’t move us closer to understanding why bank runs occur.  The authors describe the causes of a bank run as a random variable.

Hmmm… I had to read the causes of a bank run several times before it hit me.  The authors have modeled an opaque bank in the Blind Betting quadrant of the Information Matrix.  The authors discussed the information asymmetry with regards to the timing of depositors withdrawing their funds.  The authors didn’t discuss the role information asymmetry with regards to asset and liability performance plays in bank runs.  In fact, they assume this away in constructing their model.  Of course, this assumption, like the lack of slack, limits the generalizability of any conclusions they reach.

	Does Seller Know What They Are Selling?
Does Buyer Know What They are Buying?		Yes	No
	Yes	Perfect Information	Antique Dealer Problem
	No	Lemon Problem	Blind Betting

The Information Matrix shows what prompts a bank run in the Blind Betting quadrant.  It is the “story” about the opaque bank’s fundamental condition and the safety of an investment in its deposits changes.  The run occurs because in the absence of information, there is no logical stopping point in the downward valuation of the bank’s assets other than zero. Hence, the incentive to run to the bank and get the deposits back early.

Regular readers know it is the absence of information that makes bank runs possible.  When depositors have information about the bank’s fundament condition, the facts stop them from engaging in runs.

The Information Matrix easily handles and explains all of the authors’ “commonly observed random variable” causes of bank runs.

The authors do describe the behavior of investors who have an exposure to investments in the Blind Betting quadrant whose value is dependent on a story.

The problem is that once they have deposited, anything that causes them to anticipate a run will lead to a run. This implies that banks with pure demand deposit contracts will be very concerned about maintaining confidence because they realize that the good equilibrium is very fragile.

So what would a bank that is very concerned about maintaining confidence and avoiding a bank run do?

It would provide transparency into its exposure details so depositors would have the facts they need to know there is no reason to engage in a bank run.

A solution the authors of the paper miss.