Discrete mixtures of normals pseudo maximum likelihood estimators of structural vector autoregressions

Likelihood inference in structural vector autoregressions with independent non-Gaussian shocks leads to parametric identification and efficient estimation at the risk of inconsistencies under distributional misspecification. We prove that autoregressive coefficients (scaled) impact multipliers remain consistent, but drifts shocks’ standard deviations are generally inconsistent. Nevertheless, we show consistency when log-likelihood uses a discrete scale mixture normals symmetric case, or an unrestricted finite more generally, compare efficiency these estimators other consistent two-step proposals, including our own. Finally, empirical application looks dynamic linkages between three popular volatility indices.