Bryant (1980) and Diamond and Dybvig (1983) have provided us with the classic benchmark model for a bank run. The financial crisis of 2007 and 2008 is reminiscent of a bank run, but not quite (Brunnermeier 2008; Gorton 2009).
The following six features summarise the prevalent view of many observers:
- The withdrawal of funds was done by financial institutions (in particular, money market funds and other banks) at some core financial institutions (I shall call them “core banks” for the purpose of this column) rather than by depositors at their local banks.
- The troubled financial institutions held their portfolios in asset-backed securities (most notably tranches of mortgage-backed securities and credit default swaps) rather than being invested directly in long-term projects.
- These securities are traded on markets.
- There is a large pool of investors willing to purchase securities. For example, in the 2008 financial crisis, newly issued US government bonds were purchased at moderate discounts and the volume on stock markets was not low.
- Nonetheless, investors were willing to buy the asset-backed securities during the crisis only at prices that are low compared to standard discounting of the entire pool of these securities.
- The larger the market share of troubled financial institutions, the steeper the required discounts.
This perspective has possibly been crucial for a number of policy interventions, 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.
My paper (Uhlig, forthcoming) seeks to contribute to filling that gap. A systemic bank run is a situation in which early liquidity withdrawals by long-term depositors at some banks are larger and a bank run is more likely if other banks are affected by liquidity withdrawals too, i.e. the market interaction of the distressed banks is crucial. This is different from a system-wide run, which may occur if all depositors view their banks as not viable, regardless of whether the depositors at other banks do too.
The goal is for the model to produce the stylised view, i.e. the six items listed above. That stylised view may be entirely incorrect as a description of the 2008 financial crisis. It is possible that the appropriate perspective is one of insolvency rather than illiquidity, and future research will hopefully sort this out. Absent that clarification, it is worthwhile to analyse the situation from a variety of perspectives, including the one described above.
It turns out that items one to three are straightforward to incorporate, merely requiring some additional notation. Item four (large pool of investors) is easy to incorporate in principle, but hard once one demands items five (investors require discounts during crisis) and six (discount-market-share link) as well. Item six turns out to be particularly thorny to achieve and will be decisive in selecting one of two variants for modelling outside investors.
Here is the key argument. Common to both variants, suppose that there are some unforeseen early withdrawals. Therefore, core financial institutions need to sell part of their long-term securities, thereby incurring opportunity costs in terms of giving up returns at some later date. Suppose that the remaining depositors (or depositing institutions) are the more inclined to withdraw early as well, the larger these opportunity costs are. If a larger market share of distressed banks and therefore larger additional liquidity needs drive these opportunity costs up, then a wide spread run on the core banks is more likely; this creates a systemic bank run. Whether this happens depends on the market for the long-term securities, the outside investors, and the reasons for steep discounts of these securities, and it is here where the two variants differ.
- In the first variant, I hypothesise that expert investors have finite resources, while the remaining vast majority of investors are highly uncertainty averse: they fear getting “stuck” with the worst asset among a diverse portfolio and are therefore not willing to bid more than the lowest price.
- For the second variant, I assume that risk-neutral investors together with adverse selection create an Akerlof-style lemons problem; liquid core banks have an incentive to sell their worst assets at a given market price, leading to a low equilibrium price.
Both models generate a downward sloping demand curve or, more accurately, an upward sloping period-2 opportunity cost for providing period-1 resources per selling long-term securities from the perspective of the individual core bank, holding aggregate liquidity demands unchanged.
However, the two variants have sharply different implications regarding the last item in the list above.
- With uncertainty aversion, a larger market share of troubled institutions dilutes the set of expert investors faster, leading more quickly to steep period-2 opportunity costs for providing period-1 liquidity, and thereby setting the stage for a systemic bank run.
- By contrast, with adverse selection, a larger pool of distressed institutions leads to less free-riding by unaffected core banks, thereby lowering the opportunity costs for providing liquidity.
I therefore argue that the 2008 financial crisis should be analysed and policy conclusions drawn using the tools of uncertainty aversion. For example, with uncertainty aversion, a government purchase of assets above market price may be a good deal for the taxpayers under uncertainty aversion but not under adverse selection. Generally, a number of current policy and regulatory proposals may be good to evaluate from that perspective.
One caveat, though. The whole analysis has presupposed that the markets indeed underpriced the stock of securities. My analysis has nothing to say whether that perspective is right or not. This is for other researchers to decide. An interesting investigation can be found in Huizinga and Laeven (2009).
Brunnermeier, Markus (2008), “Deciphering the 2007-2008 liquidity and credit crunch,” draft, Princeton University.
Bryant, J., (1980), “A Model of Reserves, Bank Runs and Deposit Insurance,” Journal of Banking and Finance 4, 335-344.
Diamond, Douglas W., and Philip H. Dybvig. 1983. “Bank Runs, Deposit Insurance, and Liquidity.” Journal of Political Economy 91 (5): 40119.
Gorton, Gary (2009), “Slapped in the Face by the Invisible Hand: Banking and the Panic of 2007”, draft, Yale University.
Huizinga, Harry and Luc Laeven, 2009, “Accounting discretion of banks during a financial crisis”, IMF working paper 09/207.
Uhlig, Harald (forthcoming) “A model of a systemic bank run” (forthcoming in the Journal of Monetary Economics).