Inference for Impulse Responses under Model Uncertainty

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In many macroeconomic applications, impulse responses and their (bootstrap) confidence intervals are constructed by estimating a VAR model in levels - thus ignoring uncertainty regarding the true (unknown) cointegration rank. While it is well known that using a wrong cointegration rank leads to invalid (bootstrap) inference, we demonstrate that even if the rank is consistently estimated, ignoring uncertainty regarding the true rank can make inference highly unreliable for sample sizes encountered in macroeconomic applications. We investigate the effects of rank uncertainty in a simulation study, comparing several methods designed for handling model uncertainty. We propose a new method - Weighted Inference by Model Plausibility (WIMP) - that takes rank uncertainty into account in a fully data-driven way and outperforms all other methods considered in the simulation study. The WIMP method is shown to deliver intervals that are robust to rank uncertainty, yet allow for meaningful inference, approaching fixed rank intervals when evidence for a particular rank is strong. We study the potential ramifications of rank uncertainty on applied macroeconomic analysis by re-assessing the effects of fiscal policy shocks based on a variety of identification schemes that have been considered in the literature. We demonstrate how sensitive the results are to the treatment of the cointegration rank, and show how formally accounting for rank uncertainty can affect the conclusions.
Original languageEnglish
Publication statusPublished - 27 Sept 2017

Publication series

JEL classifications

  • c15 - Statistical Simulation Methods: General
  • c32 - "Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models"
  • c52 - Model Evaluation, Validation, and Selection
  • e62 - Fiscal Policy


  • Impulse response analysis
  • cointegration
  • model uncertainty
  • bootstrap inference
  • fiscal policy shocks

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