Inference for Structural Impulse Responses in Svar-Garch Models

Abstract

Conditional heteroskedasticity can be exploited to identify the structural vector autoregressions (SVAR) but the implications for inference on structural impulse responses have not been investigated in detail yet. We consider the conditionally heteroskedastic SVAR-GARCH model and propose a bootstrap-based inference procedure on structural impulse responses. We compare the finite-sample properties of our bootstrap method with those of two competing bootstrap methods via extensive Monte Carlo simulations. We also present a three-step estimation procedure of the parameters of the SVAR-GARCH model that promises numerical stability even in scenarios with small sample sizes and/or large dimensions.

Bootstrapping impulse responses of structural vector autoregressive models identified through GARCH

“…For univariate GARCH processes the asymptotic validity of the GARCH residualbased bootstrap was established by Jeong (2017) who shows that it can lead to higher order improvements and is asymptotically superior to a block bootstrap for inference regarding the GARCH parameters. Bruder (2018) considers a slightly different version of this bootstrap which generates u * t =BΛ * 1/2 t|t−1 e * t in step (3), where Λ * t|t−1 = diag(σ * 2 1,t|t−1 , . .…”

“…RBB'. Bruder (2018) also studies a modified version of his RBB which turned out to have similar small sample properties and is therefore not considered in the following.…”

“…Therefore we do not consider it in the following. Bruder (2018) considers an alternative estimation method for the GARCH parameters and the structural parameters originally due to Boswijk and van der Weide (2011) which has computational advantages over our full ML procedure. We have not considered that estimator because refinements of the estimator of the GARCH parameters do not seem to be essential for improving inference for impulse responses, as we will see when we discuss our simulation results.…”

“…For smaller sample sizes (T = 200) WB is still often clearly superior, however. Bruder (2018) does not consider the WB procedure. Therefore we do not know whether his RBB method is competitive to WB more generally.…”

“…Assuming that the conditional heteroskedasticity is of GARCH type, yet another possibility is to use a GARCH residual-based bootstrap (see Hidalgo and Zaffaroni (2007), Jeong (2017) and Bruder (2018)). Some previous studies on bootstrap methods for conditionally heteroskedastic SVAR models focus on possible improvements for inference if identified structural shocks and impulse responses are considered.…”