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

This paper considers the appropriate stabilization objectives for monetary policy in a microfounded model with staggered price-setting. Rotemberg and Woodford (1997) and Woodford (2002) have shown that under certain conditions, a local approximation to the expected utility of the representative household in a model of this kind is related inversely to the expected discounted value of a conventional quadratic loss function, in which each period’s loss is a weighted average of squared deviations of inflation and an output gap measure from their optimal values (zero). However, those derivations rely on an assumption of the existence of an output or employment subsidy that offsets the distortion due to the market power of monopolistically-competitive price-setters, so that the steady state under a zero-inflation policy involves an efficient level of output. Here we show how to dispense with this unappealing assumption, so that a valid linear-quadratic approximation to the optimal policy problem is possible even when the steady state is distorted to an arbitrary extent (allowing for tax distortions as well as market power), and when, as a consequence, it is necessary to take account of the effects of stabilization policy on the average level of output. We again obtain a welfare-theoretic loss function that involves both inflation and an appropriately defined output gap, though the degree of distortion of the steady state affects both the weights on the two stabilization objectives and the definition of the welfare-relevant output gap. In the light of these results, we reconsider the conditions under which complete price stability is optimal, and find that they are more restrictive in the case of a distorted steady state. We also consider the conditions under which pure randomization of monetary policy can be welfare-improving, and find that this is possible in the case of a sufficiently distorted steady state, though the parameter values required are probably not empirically realistic. ∗We would like to thank Jordi Gali, Bob King, Andrew Scott, and Alex Wolman for comments, and the National Science Foundation for research support through a grant to the NBER. According to a common conception of the goals of monetary stabilization policy, it is appropriate for the monetary authority to aim to stabilize both some measure of inflation and some measure of real activity relative to potential. This is often represented by supposing that the authority should seek to minimize the expected discounted value of a quadratic loss function, in which each period’s loss consists of a weighted average of the square of the inflation rate and the square of the “output gap.” It is furthermore typically argued that the two stabilization goals are not fully compatible with one another, owing to the occurrence of “cost-push shocks,” which prevent a zero output gap from being consistent with zero inflation. The problem of finding an optimal tradeoff between the two goals is then non-trivial. This familiar framework raises a number of questions, however. Most obvious is the question of how to define the “output gap” that policy should seek to stabilize. Should this be understood to mean output relative to some smooth trend, or should the target output level vary in response to real disturbances of various sorts? A closely related question is the definition of the “cost-push shocks”: how should these be identified in practice, and how often do disturbances of this kind actually occur? And even supposing that we know how to identify the output gap and the cost-push disturbances, what relative weight should be placed on output-gap stabilization as opposed to inflation stabilization? Here we propose to answer such questions on welfare-theoretic grounds. The ultimate aim of monetary policy, in our view, should be the maximization of the expected utility of households. We show, however (following a method introduced by Rotemberg and Woodford, 1997, and further expounded in Woodford, 2002; 2003, chap. 6), that it is possible to derive a quadratic approximation to the expected utility of the representative household that takes the form of a discounted quadratic loss function of the kind assumed in the traditional literature on monetary policy evaluation. In the case that the exogenous disturbances are sufficiently small in amplitude, the best policy (in terms of expected utility) will also be the one that minimizes the discounted quadratic loss function. We thus obtain precise answers to the question of what terms should appear in a quadratic loss function, and with which relative weights, that depend on the specification of one’s model of the monetary transmission mechanism. See, e.g., Clarida et al. (1999) and Walsh (2003, chaps. 8, 11) for a number of analyses in this vein. For examples of the way in which alternative model specifications lead to alternative welfaretheoretic loss functions, see Woodford (2003, chap. 6) and Giannoni and Woodford (2003).