March 8th, 2016 by Stephan Smeekes
Inference for Impulse Responses under Model Uncertainty
Lenard Lieb and Stephan Smeekes
In many macroeconomic applications, impulse responses and their frequentist confidence intervals are constructed by estimating a VAR model in levels – thus ignoring uncertainty regarding the true (unknown) cointegration rank. In this paper we investigate the consequences of ignoring this uncertainty. We adapt several proposed methods for handling model uncertainty to perform inference in cointegrated VAR models and highlight their shortcomings in the present setting. Therefore, we propose a new method – Weighted Inference by Model Plausibility (WIMP) – that takes rank uncertainty into account in a fully data-driven way. In a simulation study the WIMP method outperforms all other methods considered, delivering intervals that are robust to rank uncertainty, yet not overly conservative. We also 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. 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.