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

39 Pages Posted: 3 Nov 2020

See all articles by Gabriele Fiorentini

Gabriele Fiorentini

Universita di Firenze - Dipartimento di Statistica

Enrique Sentana

Centro de Estudios Monetarios y Financieros (CEMFI); Financial Markets Group; Centre for Economic Policy Research (CEPR)

Date Written: October 2020

Abstract

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.

Keywords: consistency, Finite normal mixtures, Pseudo maximum likelihood estimators, Structural models, Volatility indices

JEL Classification: C32, C46, C51, C58

Suggested Citation

Fiorentini, Gabriele and Sentana, Enrique, Discrete Mixtures of Normals Pseudo Maximum Likelihood Estimators of Structural Vector Autoregressions (October 2020). CEPR Discussion Paper No. DP15411, Available at SSRN: https://ssrn.com/abstract=3723635

Gabriele Fiorentini (Contact Author)

Universita di Firenze - Dipartimento di Statistica ( email )

Viale Morgagni, 59
50134 Firenze
Italy
+39 055 4237 274 (Phone)
+39 055 4223 560 (Fax)

Enrique Sentana

Centro de Estudios Monetarios y Financieros (CEMFI) ( email )

Casado del Alisal 5
28014 Madrid
Spain
+34 91 429 0551 (Phone)
+34 91 429 1056 (Fax)

HOME PAGE: http://www.cemfi.es/~sentana/

Financial Markets Group

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London School of Economics & Political Science (LSE)
London WC2A 2AE
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+44 20 7955 7002 (Phone)
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Centre for Economic Policy Research (CEPR)

London
United Kingdom

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