سیاست های پولی بهینه استوار در میکرو مدل تاسیس شده جدید کینزی

We consider optimal monetary stabilization policy in a New Keynesian model with explicit microfoundations, when the central bank recognizes that private-sector expectations need not be precisely model-consistent, and wishes to choose a policy that will be as good as possible in the case of any beliefs close enough to model-consistency. We show how to characterize robustly optimal policy without restricting consideration a priori to a particular parametric family of candidate policy rules. We show that robustly optimal policy can be implemented through commitment to a target criterion involving only the paths of inflation and a suitably defined output gap, but that a concern for robustness requires greater resistance to surprise increases in inflation than would be considered optimal if one could count on the private sector to have “rational expectations

A central issue in macroeconomic policy analysis is the need to take account of the likely changes in people's expectations about the future that should result from the adoption of one policy or another. The most common approach to confronting this issue in analyses of macroeconomic policy over the past 30–40 years has been to hypothesize “rational” (or model-consistent) expectations on the part of all economic agents. For any contemplated policy, this involves determining the outcome (the predicted state-contingent evolution of the economy) that would represent a rational expectations equilibrium (REE) according to one's model and the policy under consideration. One then compares the outcomes under the different REE associated with the different policies, in order to decide which policy is preferable. While this is certainly a hypothesis of appealing simplicity and generality, it is also a very strong and restrictive hypothesis. There are important reasons to doubt the reliability of policy evaluation exercises that are based – or at least that are solely based – on models that assume that whatever policy may be adopted, everyone in the economy will necessarily and immediately understand the consequences of the policy commitment in exactly the same way as the policy analyst does. Even if one is willing to suppose that people are thoroughly rational and possess extraordinary abilities at calculation, it is hardly obvious that they must forecast the economy's evolution in the same way as an economist's own model forecasts it; for even if the economist's model is completely correct, there will be many other possible models of the economy's probabilistic evolution that are (i) internally consistent, and (ii) not plainly contradicted by observations of the economy's evolution in the past. This is especially true given the relatively short sample of past observations that will be available in practice. The assumption of model consistent expectations is an even more heroic one in the case that a change in policy is contemplated, relative to the pattern of conduct of policy with which people had experience in the past. Indeed, it is likely that there exist many internally consistent economic models that are consistent with the probabilistic evolution of the economy in the past, which make rather different predictions regarding the effects of a change in policy, while it is hard or even impossible to identify from past data which of these models is actually correct. Hence one should be cautious about drawing strong conclusions about the character of desirable policies solely on the basis of an analysis that maintains the assumption of model consistent expectations. Here we explore a different approach, under which the policy analyst should not pretend to be able to model the precise way in which people will form expectations, if a particular policy is adopted. Instead, under our recommended approach, the policy analyst recognizes that the public's beliefs might be anything in a certain set of possible beliefs, satisfying the requirements of (i) internal consistency, and (ii) not being too grossly inconsistent with what actually happens in equilibrium, when people act on the basis of those beliefs. These requirements reduce to the familiar assumption of model-consistent (“rational”) expectations if the words “not too grossly inconsistent” are replaced by “completely consistent.” 1 The weakening of the standard requirement of model-consistent expectations is motivated by the recognition that it makes sense to expect people's beliefs to take account of patterns in their environment that are clear enough to be obvious after even a modest period of observation, while there is much less reason to expect them to have rejected an alternative hypothesis that is not easily distinguishable from the true model after only a series of observations of modest length. Under this approach, the economic analyst's model will associate with each contemplated policy not a unique prediction about what people in the economy will expect under that policy, but rather a range of possible forecasts; and there will correspondingly be a range of possible predictions for economic outcomes under the policy, rather than a unique prediction. In essence, it is proposed that one's economic model be used to place bounds on what can occur under a given policy, rather than expecting a point prediction. In the spirit of the literatures on “ambiguity aversion” and on “robust control”, 2 and following Woodford (2010), we then suppose that the economic analyst chooses a policy that ensures as high as possible a value of one's objective under any of the set of possible outcomes associated with that policy. 3 Under a particular precise definition of what it means for expectations to be sufficiently close to model-consistency, this criterion again allows a unique policy to be recommended. It will, however, differ in general from the one that would be selected if one were confident that people's expectations would have to be fully consistent with the predictions of one's model. The present paper illustrates the consequences of this alternative approach to policy selection in the context of a New Keynesian model of the tradeoff between inflation and output stabilization that is based on explicit choice-theoretic foundations. As in Woodford (2010), we adopt a particular interpretation of the requirement of “near-rational expectations” by supposing that the policy analyst assumes that people's beliefs will be absolutely continuous with respect to the measure implied by her own model4 and that their beliefs will not be too different from the prediction of her model, where the distance is measured by a relative entropy criterion. A policy can then be said to be “robustly optimal” if it guarantees as high as possible a value of the policymaker's objective, under any of the subjective beliefs consistent with the above criterion. This non-parametric way of specifying the range of beliefs that are “close enough” to the policy analyst's own beliefs is based on the approach to bounding possible model mis-specifications in the robust policy analysis of Hansen and Sargent (2005).5 It has the advantage, in our view, of allowing us to be fairly agnostic about the nature of the possible alternative beliefs that may be entertained by the public. In addition, it retains a high degree of theoretical parsimony: it simply defines a one-parameter family of robustly optimal policies, indexed by a parameter that can be taken to measure the policy analyst's degree of concern for robustness to possible departures from model-consistent expectations. Using a model with explicit choice-theoretic foundations, the present paper re-examines the policy conclusions reached in Woodford (2010) who incorporates robustness concerns by modifying the linear quadratic approximation to the optimal policy problem that emerges from an analysis of the New Keynesian model under rational expectations.6 Such a re-examination is of interest because it is not obvious that the proposed modification of these equations can similarly be justified as a local approximation when expectations are allowed to deviate from model-consistent ones.7 Here we derive exact, nonlinear equations that characterize a robustly optimal policy commitment in the context of our microfounded model, before log-linearizing those equations to provide a local linear approximation to the solution to those equations; this is intended to guarantee that the linear approximations that are eventually relied upon to obtain our final, practical characterizations are invoked in an internally consistent manner. The present analysis also generalizes the approach in Woodford (2010) who optimizes policy over only a family of linear policy rules of a particular restrictive form. While this restriction is known not to matter in the case of an analysis of optimal policy in the log-linear approximate model under rational expectations,8 it is not obvious that there may not be advantages to alternative types of rules when one allows for departures for rational expectations. For this reason, we consider here robustly optimal policy choice from among a much more flexibly specified class of policies, including policies that allow for an explicit response to measures or indicators of private-sector expectations. While this has no advantage under an RE analysis, since no such discrepancy can ever exist in an REE, one might expect it to be desirable for policy to respond to observed departures of public expectations from those that the central bank regards as correct. Yet, to the extent that our criterion for robustness is simply one of ensuring that the highest possible lower bound for welfare across alternative “near-rational” beliefs is achieved, we find that there is no benefit from expanding the set of candidate policy commitments to include ones that are explicitly dependent on private-sector expectations.9 But it is an important advance of the current analysis that this can be shown rather than simply being assumed. Our findings confirm a key conclusion of Woodford (2010): a concern for robustness requires greater resistance to surprise increases in inflation than would be considered optimal if one could count on the private sector to have rational expectations.10 While we discuss a variety of policy commitments that can each equally be characterized as “robustly optimal” – as they ensure the same lower bound for expected utility across possible “near-rational” belief distortions – all of them involve dynamics of inflation in response to shocks, under the worst-case private-sector beliefs, with smaller surprise movements in inflation.11 A particularly convenient representation of a policy commitment is in terms of a target criterion—a linear relationship between the paths of inflation and the output gap that the central bank is committed to maintain regardless of the evolution of shocks. We show that the robustly optimal target criterion requires larger output-gap deviations to justify allowing a given size of inflation surprise than the criterion (derived in Benigno and Woodford, 2005) that would be optimal under rational expectations. 12 In Section 2, we explain our general approach to the characterization of robustly optimal policy. In addition to introducing our proposed definition of “near-rational expectations,” this section explains in general terms how it is possible for us to characterize robustly optimal policy without having to restrict the analysis to a parametric family of candidate policy rules, as is done in Woodford (2010). Section 3 then sets out the structure of the microfounded New Keynesian model, showing how the model's exact structural relations are modified by the allowance for distorted private-sector expectations. Section 4 begins the analysis of robustly optimal policy in the New Keynesian model by characterizing an evolution of the economy that represents an upper bound on what can possibly be achieved. Section 5 provides an approximate analysis of the upper-bound dynamics by log-linearizing the exact conditions established in Section 4; Section 6 then shows that (at least up to the linear approximation introduced in Section 5) the upper-bound dynamics are attainable by a variety of policies, and hence solve the robust policy problem stated earlier. Section 7 then briefly considers a stronger form of robustness, and Section 8 concludes.

We have shown how it is possible to analyze optimal monetary stabilization policy, taking into account the possibility that private-sector expectations may not be precisely model-consistent. Moreover, we have shown how to characterize robustly optimal policy without restricting consideration a priori to a particular parametric family of candidate policy rules. Among the policy commitments that we have shown achieves the highest possible lower bound for welfare, for any private-sector beliefs that are not too different from the policymaker's beliefs, is a commitment to a particular target criterion, that maintains a linear relationship between the paths of inflation and of a suitably defined output gap. This optimal target criterion is similar to the one derived by Benigno and Woodford (2005) and Giannoni and Woodford (2010) for the case of rational expectations, except that it no longer refers solely to variations in inflation, regardless of the extent to which these may be anticipated in advance. The additional inflation-surprise term in the modified target criterion implies that a concern for robustness requires greater resistance to surprise increases in inflation than would be considered optimal if one could count on the private sector to have rational expectations. Among the implications of this change in the target criterion is the fact that an optimal policy commitment no longer implies complete stationarity of the long-run price level. However, we do not feel that this result does much to weaken the case for the desirability of a (suitably flexible) price-level target. By comparison with the type of forward-looking inflation targets actually adopted by inflation-targeting central banks – under which temporary departures of the inflation rate from its long-run target are allowed to persist for a time and are certainly never reversed – a price-level target, which would require temporary departures from the price-level target path to eventually be reversed, would still be closer to the policy recommended by our analysis, in which complete reversal should always occur. Our specific conclusions depend, of course, on a specific conception of which kinds of departures from model-consistent expectations should be regarded as most plausible. We have proposed a non-parametric specification of the possible belief distortions that is intended to be fairly flexible, but we are well aware that in some ways our specification remains fairly restrictive. In particular, our assumption that the only belief distortions that are contemplated in the robust policy analysis are ones that are absolutely continuous with respect to the policy analyst's own probability measure – a restriction that is necessary in order for our relative entropy measure of the “size” of belief distortions to be defined – is hardly an innocuous one. We are concerned that this assumption may have an important effect on our results. It implies that a determination on the part of the central bank to ensure that a certain relation among variables will hold in all states of the world is sufficient to ensure that the private sector cannot doubt that it will hold in all states of the world; and such an assumption may well still exaggerate the extent to which central bank policy commitments can shape private-sector expectations, even if not to the extent that an assumption of fully model-consistent expectations would. This may lead us to exaggerate the value of a policy commitment to inflation stabilization. An extension of our analysis to allow for alternative definitions of “near-rational expectations” would accordingly be of great value in further clarifying the nature of a robust approach to the conduct of monetary policy.