Bryant (1980) and Diamond and Dybvig (1983) have provided us with the classic benchmark model for a bank run. There, an individual bank engages in maturity transformation, using demand deposits to finance long term loans, which can be liquidated in the short term only at a cost. If too many agents claim short-term liquidity needs and withdraw their demand deposits, the value of the bank assets are thus not sufficient to meet these liquidity demands, in turn justifying even patient depositors to get their money while they can: a bank run ensues. One policy conclusion then is for a central bank to follow the classic Bagehot principle of committing to inject liquidity to illiquid but otherwise solvent bank, in order to stop bank runs.
The financial crisis of 2007 and 2008 is reminiscent of a bank run, but not quite, see Brunnermeier (2008). First, this was (with few exceptions) not a run of depositors on their local house bank, but a run of banks and money funds on some core financial institutions. Second, the health of some core financial institutions (I shall call them “core banks” for the purpose of this paper) was called into question not because of their commitment to costly- to-call long-term loans, but rather because of the questionable value of a variety of “exotic” securities, most notably their guarantees for particular tranches of mortgage-backed security derivatives and credit default swaps. These are assets which could be marked to market at least in principle. So, when a bank cannot repay its depositors because the market value of their assets is below the value of its liabilities, the traditional prescription is to declare the bank to be bankrupt and not to provide it with additional liquidity.
In the current situation, this would mean for the affected banks to mark their assets to market and to sell e.g. their questionable assets, while they can meet withdrawals. There is a widespread perception, however, that current market prices are below fundamental values, and that further sales of these assets are akin to fire sales, leading to further depression of the price of these assets, triggering additional bankruptcies. This conclusion appears unpalatable to many and therefore, the Federal Reserve Bank and the Treasury have instead expanded interventions where these assets will be bought at above laissez-faire prices. There is the perception that current events should be understood as some version of a systemic bank run, despite the inapplicability of the original Diamond-Dybvig framework. This creates a gap in our understanding. A new or at least a modified theory is needed.
This paper seeks to contribute to filling that gap, and provide a model (in two variants) of a systemic bank run. It thereby seeks to provide a framework for analyzing or evaluating policy options in a financial crisis similar to the one experienced in 2007 and 2008. For example, who are the gainers and losers of the March-2009 Geithner plan? Or: is the “plan B” proposed by Zingales (2008) a better alternative to the October-2008 Paulson plan? The model proposed here seeks to be provide one vehicle for answering these questions.
- It seeks to capture the following stylized features of the 2008 crisis:
1. The withdrawal of funds was done by financial institutions at other financial institutions, rather than depositors at their bank.
2. The troubled financial institutions held their portfolio in asset-backed securities rather than being invested directly in long-term projects.
3. These securities are traded on markets. In the crisis, the prices for these securities appears low compared to some benchmark fundamental value benchmark (“underpricing”).
4. There is a large pool of investors willing to purchase securities, as evidenced e.g. by market purchases of newly issued US government bonds or the volume on stock markets.
5. Nonetheless, these investors are only willing to buy these asset-backed securities at additional discounts compared to some benchmark fundamental value calculation.
I describe the model in section 2. A starkly simplified version of the model, that may be useful as a guide to some ideas for the full model is in appendix B. For the full model, I start from an environment inspired by Smith (1991), in which depositors interact with a local bank, which in turn refinances itself via an (uncontingent) deposit account with one of a few core banks, who in turn invest in long-term securities backed by locally run projects (think: mortgage-backed securities). Clearly, the observable world of securities is considerably richer (and harder to describe), but this framework may capture the essence of the interactions. I assume that there are two aggregate states, a “boom” state and a (rare) “bust” state. In the “boom” state, everything follows from the well-known analysis in the benchmark bank run literature, see section 3: essentially, things are fine. More serious problems arise in the bust state. I assume that the long-term securities become heterogeneous in terms of their long-term returns, and that local banks (together with their local depositors) hold heterogeneous beliefs regarding the portfolio of their core bank. Therefore, some local banks may withdraw early, even in the local consumption demands are “late”.
