Discrete mixtures of normals pseuda 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 and (scaled) impact multipliers remain consistent, but the drifts and shocks' standard deviations are generally inconsistent. Nevertheless, we show consistency when the non-Gaussian log-likelihood uses a discrete scale mixture of normals in the symmetric case, or an unrestricted finite mixture more generally, and compare the efficiency of these estimators to other consistent two-step proposals, including our own. Finally, our empirical application looks at dynamic linkages between three popular volatility indices.