Abstract
We propose simple specification tests for independent component analysis and structural vector autoregressions with non-Gaussian shocks that check the normality of a single shock and the potential cross-sectional dependence among several of them. Our tests compare the integer (product) moments of the shocks in the sample with their population counterparts. Importantly, we explicitly consider the sampling variability resulting from using shocks computed with consistent parameter estimators. We study the finite sample size of our tests in several simulation exercises and discuss some bootstrap procedures. We also show that our tests have non-negligible power against a variety of empirically plausible alternatives.
Highlights
The literature on structural vector autoregressions (Svar) is vast
We propose simple specification tests for independent component analysis and structural vector autoregressions with non-Gaussian shocks that check the normality of a single shock and the potential cross-sectional dependence among several of them
We explicitly consider the sampling variability resulting from using shocks computed with consistent parameter estimators
Summary
The literature on structural vector autoregressions (Svar) is vast. Popular identification schemes include short- and long-run homogenous restrictions [see, e.g. Sims (1980), Blanchard and Quah (1989)], sign restrictions [see, e.g. Faust (1998), Uhlig (2005)], time-varying heteroskedasticity (Sentana and Fiorentini 2001) or external instruments [see, e.g. Mertens and Ravn (2012), Stock and Watson (2018) or Dolado et al (2020)]. Assumption 1: Identification (1) the N shocks in (1) are cross-sectionally independent, (2) at least N − 1 of them follow a non-Gaussian distribution, and (3) C is invertible. The best known counterexample is a multivariate Gaussian model for ε∗, in which we can identify V ( y) = C C but not C without additional structural restrictions despite the fact that the elements of ε∗ are cross-sectionally independent. A less well-known counterexample would be a non-Gaussian spherical distribution for ε∗, such as the standardised multivariate Student t In this case, the lack of identifiability of C is due to the fact that ε∗ and ε∗∗ share their mean vector (0) and covariance matrix (I), and the same nonlinear dependence structure
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