Asymptotically Valid Bootstrap Inference for Proxy SVARs

Proxy structural vector autoregressions identify structural shocks in vector autoregressions with external variables that are correlated with the structural shocks of interest but uncorrelated with all other structural shocks. We provide asymptotic theory for this identification approach under mild α-mixing conditions that cover a large class of uncorrelated, but possibly dependent innovation processes. We prove consistency of a residual-based moving block bootstrap (MBB) for inference on statistics such as impulse response functions and forecast error variance decompositions. The MBB serves as the basis for constructing confidence intervals when the proxy variables are strongly correlated with the structural shocks of interest. For the case of one proxy variable used to identify one structural shock, we show that the MBB can be used to construct confidence sets for normalized impulse responses that are valid regardless of proxy strength based on the inversion of the Anderson and Rubin statistic suggested by Montiel Olea, Stock, and Watson.