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, including conditional heteroskedasticity. We prove consistency of a residual-based moving block bootstrap for inference on statistics such as impulse response functions and forecast error variance decompositions. Wild bootstraps are proven to be generally invalid for these statistics and their coverage rates can be badly and persistently mis-sized.