Inflation Stabilization and Welfare: The Case of a Distorted Steady State

We consider the appropriate objective for monetary stabilization policy in a canonical “new Keynesian†model with staggered pricing of the kind proposed by Calvo (1983), but with a complete DSGE structure of the kind presented by Yun (1996) or Woodford (2003). It is shown that under certain conditions, a quadratic approximation to the expected utility of the representative household can be expressed as a discounted sum of a weighted average of the square of the inflation rate and the square of a particular measure of the “output gap. We also show that minimization of this quadratic loss function, subject to the linear constraints implied by a log-linearization of the model structural equations, allows optimal policy to be characterized to first order in the amplitude of exogenous disturbances. Our analysis thus provides foundations for the kind of linear-quadratic analysis of optimal monetary policy undertaken in studies such as Clarida et al. (1999). Both the relative weights on the two objectives and the proper definition of the output target with respect to which the output gap is measured depend on model parameters, in a way that we characterize analytically. We also consider the second-order conditions for welfare maximization and the conditions under which welfare cannot be increased (at least locally) by arbitrary randomization of policy. We characterize optimal policy, derive targeting rules that implement optimal policy, and show how the welfare consequences of simple (sub-optimal) policy rules can be evaluated. A quadratic welfare measure of a similar sort is derived by Rotemberg and Woodford (1997) and Woodford (2002) under the special assumption that an output or employment subsidy exists that offsets the distortion due to the market power of monopolistically competitive firms, so that the steady-state equilibrium level of output is efficient (in the case of stable prices). Here we generalize those results to the case of an arbitrary level of distorting taxes, so that the steady-state level of output may be inefficient (due to taxes as well as market power). While the quadratic loss function, and hence the form of an optimal targeting rule for policy, continues to have the same general form, the size of the steady-state distortions has important consequences both for the relative weights on the alternative stabilization objectives and for the way in which various disturbances should affect the target level of output. These findings have important consequences, in turn, for the degree to which optimal policy involves inflation stabilization in the face of real disturbances.