Financial Fragility

Financial Fragility

Finance is important and necessary in advanced economies. The finance economy and the so-called “real economy” are intertwined. Finance promotes efficiency and growth, but it can also be a source of instability. It is difficult to explain financial instability in the representative-agent macro model: for example, the rational representative agent does not run on his own bank.

There are two separate assumptions behind the rational-expectations hypothesis (REH): First, individuals are not less intelligent than governments or economic modelers. Second, individuals coordinate their expectations around the solution of some constrained planning problem. One is willing to accept the first assumption as a good working hypothesis. The second assumption is more difficult to swallow, particularly for dynamic, multi-agent evolving economies. The sunspot equilibrium (SSE) concept allows for coordination of expectations in economies in which outcomes are not necessarily efficient, or in which information about sunspot realizations is noisy (or asymmetric across individuals). SSE is an equilibrium concept with roots in REH macro and in game theory, but it can, in some instances, turn REH on its head.

One literature that models financial fragility is the bank-runs work introduced by John Bryant (1980) and made operational by Douglas Diamond and Phil Dybvig (1983).

Jim Peck and I have contributed two papers to the Diamond-Dybvig banking literature.

In Peck and Shell (2003), we show that even if the powerful tool of partial-suspension-of-convertibility is feasible, the so-called “optimal banking contract” allows for run equilibria in the post-deposit game. This pure-run outcome is not an equilibrium to the pre-deposit game; no one would deposit in the bank if she believed that a bank run is sure to occur. There is, however, a tradeoff between efficiency and stability, which can be parameterized by the propensity to run. If the probability of a sunspot-driven run is sufficiently small, then it is optimal to tolerate the runs. In this way, Jim and I have put “runs back in the bank-runs literatures”.

In Peck and Shell (2010), the banking model is extended to capture two properties of the payments-transactions functions of checking account and debit cards: (1) If the check does not clear at par, the urgent consumption opportunity is lost or delayed. (2) To capture the long life ahead of many consumers, proxy utility is assigned to end-period bank balances. There are two assets that the bank can hold: A lower-return, liquid asset and a higher-return, illiquid asset. Two banking regimes are analyzed. In the first, banks are restricted to hold only the liquid asset. This could be thought of as the Glass-Steagall bank. In the second regime, banks are allowed to hold both assets. Surprisingly, the unrestricted bank is always immune to panic-driven runs, while the restriced (or Glass-Steagall) bank always faces a run equilibrium. The unrestricted bank can run out of cash in the early period, while the restricted bank runs out of cash only during a run on the bank. These results are at first blush surprising or even paradoxical. Some intuition is in order. The unrestricted bank is immune to bank runs because its greater asset position and higher-return portfolio ensure that end-of-period bank balances are sufficiently large to ensure incentive compatibility. The unrestricted bank can, however, run out of cash if aggregate transactions demand is high, but this will not jeopardize bank stability. The restricted (or Glass-Steagall) bank holds only lower return liquid investments. Individuals hold the higher return, illiquid investments outside the bank. Because the restricted bank has a smaller asset position and its portfolio has a lower return, it will not be able to ensure incentive compatibility. Because all of its assets are liquid, it does not run out of cash except during panic-based run. The unrestricted bank is thus pro-growth, immune to runs, and yields higher welfare than the Glass-Steagall bank. The Glass-Steagall bank over-invests in liquidity and is always subject to runs. As a consequence of its over-investment in the liquid asset, it only runs out of cash in a panic-induced bank run.