Robust Inference in Models Identified via Heteroskedasticity

Simultaneous equations models identified via heteroskedasticity may be subject to weak identification concerns due to proportional changes in variance across series. Considering data from Nakamura & Steinsson (2017), I calibrate simulations to show the relevance of these concerns in practice. I propose conditions under which robust inference methods for a subset of the parameter vector are valid. In simulation, these methods avoid dramatic size-distortions present in strong-identification methods. While there is power loss relative to standard inference, they are less conservative than the previous alternative of projection methods. I propose two tests for weak identification. I offer a method for robust inference on IRFs for SVARs identified via heteroskedasticity. An empirical application to Nakamura & Steinsson (2017) shows that weak identification is a problem with daily policy shocks, but not higher-frequency shocks. This confirms the authors’ suspicions, and shows the value of focusing empirical work on carefully constructed shock series. JEL Classification: C12, C32, E43 ∗I would like to thank Jim Stock, Isaiah Andrews, Adam McCloskey, Jose Montiel Olea, Emi Nakamura, Mikkel Plagborg-Möller, and Jòn Steinsson for their helpful feedback.