Optimal Monetarist Arithmetic or How to Inflate If You Must

In their celebrated 1981 paper ”Some Unpleasant Monetarist Arithmetic,” Sargent and Wallace show that when a central bank is required to transfer resources to the fiscal authority, it faces a trade-off: if it chooses to keep inflation low in the short run, then it must be willing to accept higher inflation in the long run. In this paper I characterize the optimal interest rate (and inflation) policy by a central bank faced with a version of the Sargent-Wallace scenario. I explore this question in a setting in which a certain amount has to be transferred for an uncertain period of time. I find that uncertainty makes the optimal policy to deviate from a Barro-like martingale behavior of taxes or a Lucas-Stokey type of solution where the tax (or distortion) inherits the properties of the stochastic process for transfers. The optimal nominal interest rate (and inflation) is such that the central bank chooses to issue debt (e.g., reverse repos) instead of raising the required amount of seigniorage. Initially inflation is lower than what would be required to raise enough resources to pay for the transfer plus the interest on existing debt. The intuition for this result is that the monetary authority is taking advantage of an option: if the transfer period is short, then (relatively) low inflation today can spread the losses over time. Over time, as the debt increases, more revenue has to be raised. Interest rates increase. The time path of inflation depends on whether the monetary authority can “inflate away” part of the debt. If this default is costly, the end of the transfer period is associated with permanently lower inflation. If a sudden increase in the price level (default) is an option (and if it chooses to be exercised), the end of the transfer period is associated with high (and brief) inflation and then stabilization.