Dynamic Seigniorage Theory: An Exploration

This paper shows that the optimal extraction of seigniorage implies a strong tendency for inflation to fall over time toward its socially optimal level. The point is made using a multi-period model in which (i) the government can finance deficits through bond issue or money creation, (ii) private-sector expectations are rational, and (iii) the government sets the inflation rate each period in a discretionary manner. One way to view the model is as a synthesis of the "tax-smoothing" theory of government deficits, which predicts that the inflation tax follows approximately a martingale, and of models of discretionary policy making, which predict (absent reputation effects) that inflation is likely to exceed its socially optimal level. Both predictions are modified when the two approaches to explaining inflation are merged. Reputation effects play no role in the analysis.