Bootstrapping structural VARs: Avoiding a potential bias in confidence intervals for impulse response functions

Constructing bootstrap confidence intervals for impulse response functions (IRFs) from structural vector autoregression (SVAR) models has become standard practice in empirical macroeconomic research. The accuracy of such confidence intervals can deteriorate severely, however, if the bootstrap IRFs are biased. We document an apparently common source of bias in the estimation of the VAR error covariance matrix which can be easily reduced by a scale adjustment. This bias is generally unrecognized because it only affects the bootstrap estimates of the error variance, not the original OLS estimates. Nevertheless, as we illustrate here, analytically, with sampling experiments, and in an example from the literature, the bootstrap error variance bias can have significant distorting effects on bootstrap IRF confidence intervals. We also show that scale-adjusted bootstrap confidence intervals can be expected to exhibit improved coverage accuracy.