Notes
259
believe the equilibrium is riskless, the manager has the right incentives and does not take the money and run. The Modigliani-Miller theorem will hold locally within regions. Still, it is clear that when we go from case 1 to case 2, an expected amount pð1 aÞ y of the bank’s assets are destroyed, so the structure of liabilities does a¤ect the value of the firm. 2. The existence of a charter value is a substitute for K. It would decrease the value of K required for every type of equilibrium. Notes 1. The precise definition of a bank panic varies from one author to another. Kemmerer himself enumerates six major bank panics and fifteen minor ones during the period 1890–1908. Benston and Kaufman (1986), using another definition, found bank panics on three occasions: 1874, 1893, and 1908. Gorton (1985) also found panics in 1884, 1890, and 1896. 2. Miron uses this indicator to evaluate the real (as opposed to financial) e¤ects of bank panics. However, the inverse causality cannot be dismissed; it could be argued that decreases in GNP tend to shrink the value of banks’ assets, thus triggering bank panics. 3. Of course, bank runs can develop into bank panics; this is the contagion phenomenon. 4. For simplicity, we do not discount the utility of consumption at date 2. 5. This is true, for instance, if R ! Ru 0 ðRÞ is decreasing, which corresponds to assuming that the elasticity of substitution between periods is smaller than 1. 6. There is also a mixed-strategy equilibrium that is not considered here. 7. See Kareken (1986) and Mussa (1986). 8. By the law of large numbers, the realized proportion equals the theoretical frequency. This changes for aggregate liquidity risk (see section 7.6). 9. Engineer (1989) has shown that suspension of convertibility may fail to prevent a bank run if the Diamond-Dybvig (1983) model is extended to a framework with four dates and three types of agents. 10. The situation is more complex if the return on banks’ assets is uncertain, and if moral hazard can occur (see, for instance, Freeman 1988). 11. This is the key di¤erence with respect to market equilibrium. In a market equilibrium agents are free to choose the level of investment I . Here this level is set so as to maximize expected utility. 12. This is only true insofar as the uniformed lender cannot make the entrepreneur and the financial intermediation compete. This is an important assumption in Diamond and Rajan (2001) that is embodied in the timing of o¤ers and countero¤ers. 13. The alternative assumption, VL > aVH , is easier to deal with and allows for equity financing, but the cost of equity financing does not appear. In this case, if V takes the value VH , the banker cannot renegotiate its payment to the equity holders without triggering a bank run. Thus there is no cost of using equity, and the maximum amount EðV Þ can be raised from the two types of claim holders: depositors and equity holders. 14. Temzelides (1997) studies a repeated version of the Diamond-Dybvig model and models equilibrium selection (between the e‰cient and the panic equilibria) by an evolutionary process. He shows that the probability of panic decreases with the size of banks, and he studies the possibility of contagion e¤ects. 15. As reported in Benston et al. (1986), this ‘‘gambling for resurrection’’ behavior is frequently observed when a bank faces a crisis. Therefore, although it is unattractive from a theoretical viewpoint because the manager contract is not the optimal one, this assumption is consistent with casual empiricism. 16. See chapter 2.