Working Paper: CEPR ID: DP15545
Authors: Atsushi Inoue; Lutz Kilian
Abstract: Several recent studies have expressed concern that the Haar prior typically imposed in estimating sign-identified 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. Specifically, 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-identified VAR models estimated using conventional priorstend to imply unintentionally informative priors for the impulse response vector or that the corresponding 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-identified VAR models proposed by Baumeister and Hamilton (2015) suffers from exactly the same conceptual shortcoming as the conventional approach. We illustrate that this alternative approach may imply highly economically implausible impulse response priors.
Keywords: prior; posterior; impulse response; loss function; joint inference; absolute loss
JEL Codes: C22; C32; C52; E31; Q43
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Haar prior (C29) | unintentionally informative priors for impulse response vector (C51) |
| conventional priors (C11) | posterior dominated by prior (C69) |
| Haar prior concerns (Y80) | overstated (Y60) |
| alternative Bayesian approach (C11) | same conceptual shortcomings (C60) |
| posterior distribution of impulse responses (C32) | driven by data (Y10) |
| prior for impulse responses (C69) | largely uninformative (Y50) |
| posterior estimates (C51) | robust to changes in prior specification (C51) |