Identification of Structural VAR Models via Independent Component Analysis: A Performance Evaluation Study

Abstract

Independent Component Analysis (ICA) is a statistical method that linearly transforms a random vector. Under the assumption that the observed data are mixtures of non-Gaussian and independent processes, ICA is able to recover the underlying components, but with a scale and order indeterminacy. Its application to structural vector autoregressive (SVAR) models allows the researcher to recover the impact of independent structural shocks on the observed series from estimated residuals. We analyze different ICA estimators, recently proposed within the field of SVAR analysis, and compare their performance in recovering structural coefficients. Moreover, we assess the size distortions of the estimators in hypothesis testing. We conduct our analysis by focusing on non-Gaussian distributional scenarios that get gradually close to the Gaussian case. The latter is the case where ICA methods fail to recover the independent components. Although the ICA estimators that we analyze show similar pattern of performance, two of them — the fastICA algorithm and the pseudo-maximum likelihood estimator — tend to perform relatively better in terms of variability, stability across sub- and super-Gaussian settings, and size distortion. We finally present an empirical illustration using US data to identify the effects of government spending and tax cuts on economic activity, thus providing an example where ICA techniques can be used for hypothesis testing.