The role of the prior in estimating VAR models with sign restrictions

Arbeitspapier

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 priors tend 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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: CFS Working Paper Series ; No. 660

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models ; Model Evaluation, Validation, and Selection ; Price Level; Inflation; Deflation ; Energy and the Macroeconomy
• Thema: Prior ; posterior ; impulse response ; loss function ; joint inference ; absolute loss ; median

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Inoue, Atsushi ; Kilian, Lutz
• Ereignis: Veröffentlichung
• (wer): Goethe University Frankfurt, Center for Financial Studies (CFS)
• (wo): Frankfurt a. M.
• (wann): 2021

Weitere Informationen

• Handle: http://hdl.handle.net/10419/246872
• Letzte Aktualisierung: 10.03.2025, 11:45 MEZ