Survey_Woodford_1999

Abstract

The model is similar, if not identical, to the small forward-looking models used in a number of recent analyses of monetary policy rules, including Kerr and King (1996), Woodford (1996), Bernanke and Woodford (1997), McCallum and Nelson (1997, 1998), Clarida et al. (1999), and Kiley (1998). As is explained in Woodford (1996), the model's equations can be derived as log-linear approximations to the equilibrium conditions of a simple intertemporal general equilibrium model with sticky prices. While the model is quite simple, it incorporates forward-looking private sector behavior in three respects, each of which is surely of considerable importance in reality, and would therefore also be present in some roughly similar form in any realistic model. It also shares many features with the econometric model of Rotemberg and Woodford (1997, 1998), and so analysis of this model can provide insight into the source of some of the numerical results obtained there. Formally, our problem is to choose stochastic processes xt , and rt | specifying each of these variables as a function of a random state It that includes not only the complete history of the exogenous disturbances (rnt , rnt1,:::,rn0 ), but also all public information at date t about the future evolution of the natural rate30| in order to minimize the criteriondened by (2.8) and (2.9), sub ject to the constraint that the processes satisfy equilibrium conditions (2.6) and (2.7) at all dates t 0: We imagine that a policymaker can choose the entire future (state-contingent) evolutions of these variables, once and for all, at date zero. Thus we wish to consider optimal policy under commitment on the part of the policymaker { even though we have not yet specied the type of explicit commitment, as to the way in which policy will be conducted, that is involved. Note that the assumed possibility of commitment matters, in the case of an optimization problem of this kind. For, because of the forward-looking terms in our structural equations (2.6) and (2.7), the value of the periodloss Lt that can be achieved at a given time depends upon what the private sector expects about the subsequent evolution of the endogenous variables.