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650
We derive the Bayes estimator of vectors of structural VAR impulse responses under a range of alternative loss functions. We also derive joint credible regions for vectors of impulse responses as the lowest posterior risk region under the same loss functions. We show that conventional impulse response estimators such as the posterior median response function or the posterior mean response function are not in general the Bayes estimator of the impulse response vector obtained by stacking the impulse responses of interest. We show that such pointwise estimators may imply response function shapes that are incompatible with any possible parameterization of the underlying model. Moreover, conventional pointwise quantile error bands are not a valid measure of the estimation uncertainty about the impulse response vector because they ignore the mutual dependence of the responses. In practice, they tend to understate substantially the estimation uncertainty about the impulse response vector.
660
Several recent studies have expressed concern that the Haar prior typically imposed in estimating sign-identi.ed VAR models may be unintentionally informative about the implied prior for the structural impulse responses. This question is indeed important, but we show that the tools that have been used in the literature to illustrate this potential problem are invalid. Speci.cally, we show that it does not make sense from a Bayesian point of view to characterize the impulse response prior based on the distribution of the impulse responses conditional on the maximum likelihood estimator of the reduced-form parameters, since the the prior does not, in general, depend on the data. We illustrate that this approach tends to produce highly misleading estimates of the impulse response priors. We formally derive the correct impulse response prior distribution and show that there is no evidence that typical sign-identi.ed VAR models estimated using conventional priors tend to imply unintentionally informative priors for the impulse response vector or that the corre- sponding posterior is dominated by the prior. Our evidence suggests that concerns about the Haar prior for the rotation matrix have been greatly overstated and that alternative estimation methods are not required in typical applications. Finally, we demonstrate that the alternative Bayesian approach to estimating sign-identi.ed VAR models proposed by Baumeister and Hamilton (2015) su¤ers from exactly the same conceptual shortcoming as the conventional approach. We illustrate that this alternative approach may imply highly economically implausible impulse response priors.
2011, 13
This paper outlines important lessons for monetary policy. In particular, the role of inflation targeting, which was much acclaimed prior to the financial crisis and since then has not lost much of its endorsement, is critically reviewed. Ignoring the relation between monetary policy and asset prices, as is the case in this monetary policy approach, can lead to financial instability. In contrast, giving, inter alia, monetary factors a role in central banks’ policy decisions, as is done in the ECB’s encompassing approach, helps prevent these potentially harmful side effects and thus allows for fostering financial stability. Finally, this paper makes a case against increasing the central banks’ inflation target. JEL Classification: E44, E52, E58 Keywords: Inflation Targeting, Asset Prices, Financial Stability, ECB
2009, 24
2013, 02
2012, 20
In this paper, we provide some reflections on the development of monetary theory and monetary policy over the last 150 years. Rather than presenting an encompassing overview, which would be overambitious, we simply concentrate on a few selected aspects that we view as milestones in the development of this subject. We also try to illustrate some of the interactions with the political and financial system, academic discussion and the views and actions of central banks.