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Work on this paper was done while I was a visiting scholar from Vanderbilt University. I am thankful to Michael Dooley and Kevin Salyer for helpful comments.
A study published in the Federal Reserve Bulletin (March 1987, pp. 190-1) reported that more than 88 percent of the U.S. currency stock circulating outside banks was “missing”; that is, it could not be accounted for by purposes related to measured domestic activity. According to the same study, there exists anecdotal evidence suggesting that the amount of U.S. cash held abroad may be large, but no quantitative information is available.
Dellas (1989) presents an explicit theoretical analysis of reserve choice in a Barro-Gordon type of economic environment where trade facilitation and portfolio considerations are the primary motives for holding reserves.
The partial currency switch in favor of the German and Japanese currencies that started in the 1970s seems to have been a result of concerns about excessive seigniorage payments on the U.S. dollar.
One can interpret this model as a principal-agent problem. The principal (the reserve user) can exert only indirect control over the actions of the agent (the reserve issuer) and he does so through the design of the payoff schedule. The payoff schedule is a self-enforcing implicit contract whose main characteristic is the threat of terminating the relationship (i.e., switching reserve currency).
There are reasons that make holding of positive real balances desirable for the reserve user. First, real balances enter the utility function and hence provide direct utility services. Second, money in this paper is the only store of value, so it enables people to choose a smoother consumption profile. For these reasons the reserve user will have an incentive to implement this scheme. It is also beneficial to the reserve issuer because, by construction, it guarantees the maximum possible inflation revenue.
Note that this definition of inflation is positively correlated, but differs from the conventional definition (Pt+1 - Pt)/Pt; and that it approaches an upper board of unity on the conventionally defined measures becomes infinite. Obstfeld (1988) has employed the same definition.
mt depends also on income Xt’ so n is a function of Xt. However, to focus on the game theoretic aspects of the model we have found useful for simplification purposes to assume that Xt = X, t = 0, 1, 2, … for the remaining of the paper. See footnote 1 on page 14 for the more general case.
If Xt ~ N (X, σ2) t = 0, 1, 2, … the time consistent solution is πt (n, Xt): π(nt, Xt)·m(nt, Xt) = nt (Xt) · Now suppose that in period t we have a high realization of Xt, say Xh > X so that m(n, Xh) > m(n, Xh). The gain from choosing πt = 1 is m(nt, Xh) > m(n, X), while the expected loss due to the switch is [1/(1-δ)] Et π (n, X)·m(n, X). Then the condition for π(nt, Xt) to be finite is to choose n so that π(n) > (1-δ)·e where e = m(n, max Xt)/m(n, X), e > 1 and max Xt is the highest possible realization of Xt.