Long-term debt and optimal policy in the fiscal theory of the price level

摘要

The fiscal theory says that the price level is determined by the ratio of nominal debt to the present value of real primary surpluses. I analyze long-term debt and optimal policy in the fiscal theory. I find that the maturity structure of the debt matters. For example, it determines whether news of future deficits implies current inflation or future inflation. When long-term debt is present, the government can trade current inflation for future inflation by debt operations; this tradeoff is not present if the government rolls over short-term debt. The maturity structure of outstanding debt acts as a "budget constraint" determining which periods' price levels the government can affect by debt variation alone. In addition, debt policy-the expected pattern of future state-contingent debt sales, repurchases and redemptions-matters crucially for the effects of a debt operation. I solve for optimal debt policies to minimize the variance of inflation. I find cases in which long-term debt helps to stabilize inflation. I also find that the optimal policy produces time series that are similar to U.S. surplus and debt time series. To understand the data, I must assume that debt policy offsets the inflationary impact of cyclical surplus shocks, rather than causing price level disturbances by policy-induced shocks. Shifting the objective from price level variance to inflation variance, the optimal policy produces much less volatile inflation at the cost of a unit root in the price level; this is consistent with the stabilization of U.S. inflation after the gold standard was abandoned.