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