Bayesian Inference for Structural Vector Autoregressions Identified by Markov-Switching Heteroskedasticity

39 Pages Posted: 19 Dec 2017

See all articles by Helmut Lütkepohl

Helmut Lütkepohl

Free University of Berlin (FUB)

Tomasz Wozniak

University of Melbourne - Department of Economics

Date Written: November 29, 2017

Abstract

In order to identify structural shocks that affect economic variables, restrictions need to be imposed on the parameters of structural vector autoregressive (SVAR) models. Economic theory is the primary source of such restrictions. However, only over-identifying restrictions can be tested with statistical methods which limits the statistical validation of many just-identified SVAR models. In this study, Bayesian inference is developed for SVAR models in which the structural parameters are identified via Markov-switching heteroskedasticity. In such a model, restrictions that are just-identifying in the homoskedastic case, become over-identifying and can be tested. A set of parametric restrictions is derived under which the structural matrix is globally identified and a Savage-Dickey density ratio is used to assess the validity of the identification conditions. For that purpose, a new probability distribution is defined that generalizes the beta, F, and compound gamma distributions. As an empirical example, monetary models are compared using heteroskedasticity as an additional device for identification. The empirical results support models with money in the interest rate reaction function.

Keywords: Identification through Heteroskedasticity, Markov-Switching Models, Savage-Dickey Density Ratio, Monetary Policy Shocks, Divisia Money

JEL Classification: C11, C12, C32, E32

Suggested Citation

Lütkepohl, Helmut and Wozniak, Tomasz, Bayesian Inference for Structural Vector Autoregressions Identified by Markov-Switching Heteroskedasticity (November 29, 2017). DIW Berlin Discussion Paper No. 1707, Available at SSRN: https://ssrn.com/abstract=3090264 or http://dx.doi.org/10.2139/ssrn.3090264

Helmut Lütkepohl (Contact Author)

Free University of Berlin (FUB)

Otto Suhr Institut for Political Science\
Ihnestrasse 21
Berlin
Germany

Tomasz Wozniak

University of Melbourne - Department of Economics ( email )

Melbourne, 3010
Australia

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