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

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractIn 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.

Testing identification via heteroskedasticity in structural vector autoregressive models

“…However, so far the asymptotic distributions of these tests have not been derived formally and it is unlikely that the assumed χ 2 distributions provide precise approximations to the true asymptotic distributions of the test statistics. Alternatively, some authors have proposed Bayesian methods for assessing identification in this context (e.g., Woźniak and Droumaguet (2015) and Lütkepohl and Woźniak (2017)).…”