Structural Vector Autoregressions With Markov Switching

In structural vector autoregressive (SVAR) analysis a Markov regime switching (MS) property can be exploited to identify shocks if the reduced form error covariance matrix varies across regimes. Unfortunately, these shocks may not have a meaningful structural economic interpretation. It is discussed how statistical and conventional identifying information can be combined. The discussion is based on a VAR model for the US containing oil prices, output, consumer prices and a shortterm interest rate. The system has been used for studying the causes of the early millennium economic slowdown based on traditional identication with zero and long-run restrictions and using sign restrictions. We find that previously drawn conclusions are questionable in our framework.

"This paper develops a new and easily implementable necessary and sufficient condition for the exact identification of a Markov-switching structural vector autoregression (SVAR) model. The theorem applies to models with both linear and some nonlinear restrictions on the structural parameters. We also derive efficient MCMC algorithms to implement sign and long-run restrictions in Markov-switching SVARs. Using our methods, four well-known identification schemes are used to study whether monetary policy has changed in the euro area since the introduction of the European Monetary Union. We find that models restricted to only time-varying shock variances dominate the other models. We find a persistent post-1993 regime that is associated with low volatility of shocks to output, prices, and interest rates. Finally, the output effects of monetary policy shocks are small and uncertain across regimes and models. These results are robust to the four identification schemes studied in this paper."--Federal Reserve Bank of Atlanta web site.

This paper develops a new and easily implementable necessary and sufficient condition for the exact identification of a Markov-switching structural vector autoregression (SVAR) model. The theorem applies to models with both linear and some nonlinear restrictions on the structural parameters. We also derive efficient MCMC algorithms to implement sign and long-run restrictions in Markov-switching SVARs. Using our methods, four well-known identification schemes are used to study whether monetary policy has changed in the euro area since the introduction of the European Monetary Union. We find that models restricted to only time-varying shock variances dominate the other models. We find a persistent post-1993 regime that is associated with low volatility of shocks to output, prices, and interest rates. Finally, the output effects of monetary policy shocks are small and uncertain across regimes and models. These results are robust to the four identification schemes studied in this paper.

This book contributes to re cent developments on the statistical analysis of multiple time series in the presence of regime shifts. Markov-switching models have become popular for modelling non-linearities and regime shifts, mainly, in univariate eco nomic time series. This study is intended to provide a systematic and operational ap proach to the econometric modelling of dynamic systems subject to shifts in regime, based on the Markov-switching vector autoregressive model. The study presents a comprehensive analysis of the theoretical properties of Markov-switching vector autoregressive processes and the related statistical methods. The statistical concepts are illustrated with applications to empirical business cyde research. This monograph is a revised version of my dissertation which has been accepted by the Economics Department of the Humboldt-University of Berlin in 1996. It con sists mainly of unpublished material which has been presented during the last years at conferences and in seminars. The major parts of this study were written while I was supported by the Deutsche Forschungsgemeinschajt (DFG), Berliner Graduier tenkolleg Angewandte Mikroökonomik and Sondeiforschungsbereich 373 at the Free University and Humboldt-University of Berlin. Work was finally completed in the project The Econometrics of Macroeconomic Forecasting founded by the Economic and Social Research Council (ESRC) at the Institute of Economies and Statistics, University of Oxford. It is a pleasure to record my thanks to these institutions for their support of my research embodied in this study.

Structural vector autoregressions are of great importance in applied macroeconometric work. The main di culty associated with structural analysis is to identify unique shocks of interest. In a conventional approach this is done via zero or sign restrictions. Heteroskedasticity is proposed for use in identi cation. Under certain assumptions when volatility of shocks changes over time, unique shocks can be obtained. Then formal testing of the restrictions and impulse response analysis can be performed. In this thesis I show how identi cation via heteroskedasticity can be used in di erent contexts. In the rst chapter I analyze the dynamics of trade balances in response to macroeconomic shocks. I show that identifying restrictions, which are known in the literature, are rejected for two out of seven countries. Partially identi ed models fail to provide enough information to fully identify shocks. The second chapter, coauthored with my supervisor, demonstrates how one can bene t from identi cation via heteroskedasticity when sign restrictions are used. The approach is illustrated with a model of the crude oil market. It is shown that shocks identi ed via previously known sign restrictions are in line with the properties of the data. Use of tighter restrictions uncovers that the approach can be discriminative. The third chapter reconsiders the con icting results in the debate on the e ects of technology shocks on hours worked. Using six ways of identifying technology shocks, I nd that not all of them are supported by the data. There is no clear-cut evidence in favor of positive reaction of hours to technology shocks. However, it is plausible for real wage and disentangled investment-speci c and neutral technology shocks, even though conventional identi cation of the latter shocks is rejected.

This book discusses the econometric foundations of structural vector autoregressive modeling, as used in empirical macroeconomics, finance, and related fields.