## Inflation Stabalization and Welfare: The Case of a Distorted Steady State, Issue 10838"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"--National Bureau of Economic Research web site. |

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aggregate aggregate-supply relation assumed Benigno and Woodford coefficients commitments consider consistent with 1.19 constraint convex convex function cost-push term defined distorted steady equal to zero evolution exogenous disturbances expected utility expression first-order conditions fluctuations Furthermore government purchases Hence implies impulse response inflation and output inflation rate inflation stabilization initial condition involves Khan Lagrange multiplier level of output linear terms linear-quadratic loss minimum maximize Michael Woodford monetary policy NBER nominal interest rate obtain optimal policy optimal response optimization problem paths consistent period perturbed processes Pierpaolo policy problem policy rule possible precommitted process xt processes ip Proposition purely quadratic quadratic approximation quadratic form quadratic loss function Ramsey policy Ramsey problem representative household Rotemberg and Woodford satisfy 3.2 second-order approximation second-order conditions solution solve state-contingent steady-state values Sticky Price stochastic processes structural equations substitute sunspot technology shock timeless perspective variables welfare-relevant output gap welfare-theoretic