INTEREST-RATE RULES: Framework for Analysis

We begin by reviewing the structure of the estimated sticky-price model developed in Rotemberg and Woodford (1997). This also allows us to derive the utility-based measure of deadweight loss due to price-level instability that is the basis for our subsequent discussion of optimal policy.

A Small, Structural Model of the U.S. Economy

We suppose that there is a continuum of households indexed by г where i runs between 0 and 1. Each of these households produces a single good while it consumes the composite good. The utility of household i at t is given by

where Rt is the gross return on a riskless nominal one-period asset in wrhich the household invests at t. We assume the existence of complete insurance markets, so that all households consume the same amount at any time, and have the same marginal utility of income. Then equations (1.5) and (1.6) also hold when we drop the i superscripts, and interpret them as equations relating aggregate consumption Ct to the marginal utility of income Xt of the representative household.

However, because of the conditional expectations in (1.5), these two equations still do not imply the standard Euler equation relating aggregate consumption spending in two consecutive periods to the real rate of return between those two periods. Finally, substituting into (1.5) the equilibrium requirement that Ct = Yt – Gu where Gt represents exogenous variation in government purchases of the composite good, we obtain an equilibrium relation between the index of aggregate demand Yt and variations in the marginal utility of income, which provides the crucial link in our model between interest rate variations and aggregate demand.