DP15411 Discrete Mixtures of Normals Pseudo Maximum Likelihood Estimators of Structural Vector Autoregressions

Author(s): Gabriele Fiorentini, Enrique Sentana
Publication Date: October 2020
Keyword(s): consistency, Finite normal mixtures, Pseudo maximum likelihood estimators, Structural models, Volatility indices
JEL(s): C32, C46, C51, C58
Programme Areas: Financial Economics
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=15411

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.