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Individual Bank Runs and Systemic Risk
The fact that deposits are demandable is therefore a key characteristic that would be desirable even if all consumers were of equal type ðp1 ¼ 1Þ. Thus in the Chari and Jaggannathan model we have a disciplining role for demandable debt, a point subsequently developed and emphasized by Calomiris and Kahn (1991), Qi (1998), and Diamond and Rajan (2001). Three other contributions extend the Diamond-Dybvig framework to a context of random returns on the bank’s assets. They do not focus directly on bank runs but rather on the risk sharing provided by demand deposit contracts in this framework. Jacklin and Bhattacharya (1988) address the question of the relative performance of equity versus demand deposit in banks’ financing, in a context where some type 2 agents are informed on the bank’s future return. In an equity economy, equilibrium prices are fully revealing; in a demand deposit equilibrium, with suspension of convertibility, there is rationing on type 1 deposits, so these deposits are shared between type 1 and informed type 2 agents. Comparison of the relative performances for specific values of the model’s parameters shows that for a lower dispersion of returns, demand deposits perform better, whereas for a large dispersion, equity financing is preferred. Still, the demand deposit contract can be improved if it is required to remain incentive-compatible after type 2 agents become informed (Alonso 1991). Gorton and Pennacchi (1990) also consider that some of the type 2 agents are informed,16 but the agents’ behavior is not competitive, so the prices of an equity economy are not fully revealing. Informed traders benefit from trading in the equity market. Demand deposit contracts emerge then because they are riskless, so their value cannot be a¤ected by informed trading. Gorton and Pennacchi establish that in equilibrium uninformed traders invest in deposits and informed traders invest in equity of the financial intermediary, so there is no other market for equity. In that way, the authors elaborate on Jacklin’s (1987) contention that equity could perform as well as demand deposit contracts. Allen and Gale (1998) consider the e‰ciency properties of bank runs in the case where the long-run technology yields a random return. They argue that if liquidation of the long-run technology is impossible ðl ¼ 0Þ, then bank runs can be best information constrained e‰cient, thus allowing for optimal risk sharing between early and late withdrawing depositors. This is the case because, when returns on the long-run technology happen to be low, patient consumers will have an incentive to run the bank. By so doing, the remaining patient consumers withdrawing at time t ¼ 2 will have a larger consumption, and this will go on until the equality C1 ¼ C2 is reached and the incentives to run the bank disappear. Thus, as Allen and Gale argue, the problem is not bank runs per se but rather the cost of liquidating the long-run technology. When the cost of liquidation is taken into account, runs are not limited to a fraction of patient customers, and the best cannot be reached any longer.