Re-examining the case for government deposit insurance: reply.

• Author: Dowd, Kevin
• Position: Response to an article by Denise Hazlett in this issue. 1090

In a recent article in this journal, Kevin Dowd [2] presents a modified version of Diamond and Dybvig's [1] banking model. Dowd claims that for some parameters of his model, a bank capital holder can earn a profit by guaranteeing the optimal Diamond-Dybvig deposit withdrawals. According to Dowd, the capitalist willingly puts up his own resources as a guarantee on deposits, because of the profits he will earn from doing so. These profits, according to Dowd, make government-provided deposit insurance unnecessary. This comment shows that no such profits exist. By definition, the optimal Diamond-Dybvig deposit withdrawals require that all of the returns from deposited resources be paid out to depositors. There is no surplus for the bank capital holder to claim as profits.

Dowd's mistake came from forgetting that those Diamond-Dybvig depositors who ask for an early withdrawal receive a payout that is greater than the return provided by the underlying technology. The Diamond-Dybvig bank thus shares with early withdrawers some of the high return from long-term investment in the technology. Depositors insure themselves against the risk of being an impatient consumer by joining the Diamond-Dybvig bank, with its promise of a higher-than-autarkic return to those withdrawing early, and a lower-than-autarkic return for those withdrawing later. Let [r.sub.1] and [r.sub.2] be the optimal Diamond-Dybvig deposit payouts to the early and late withdrawers, respectively.(1) The underlying technology provides an early return of 1 or a later return of R on a unit deposited in it. The depositors are of measure one, so that if the fraction t of depositors asks for the early withdrawal, then (1 - t[r.sub.1]) is left in the technology to grow at the rate R. Dowd claims that the resources left in the bank, after all deposit payouts have been made and assuming that each depositor asks for the withdrawal intended for his type, would be KR + [t + (1 - t)R] - [t[r.sub.1] + (1 - t)[r.sub.2]], where K is the capital holder's contribution of resources, the first expression in brackets is supposedly the value of deposits invested in the technology, and the second term in brackets is the value of the bank's liabilities. In his expression for the value of deposits invested in the technology, Dowd has (1 - t) resources left in the technology to grow at rate R, rather than the smaller amount (1 - t[r.sub.1]) that are truly left in. Apparently he is forgetting that the bank...