This paper aims to provide a comprehensive overview of the estimation methodology for the time-varying parameter structural vector autoregression (TVP-VAR) with stochastic volatility, in both methodology and empirical applications. The TVP-VAR model, combined with stochastic volatility, enables us to capture possible changes in underlying structure of the economy in a ﬂexible and robust manner. In this respect, as shown in simulation exercises in the paper, the incorporation of stochastic volatility into the TVP estimation signiﬁcantly improves estimation performance. The Markov chain Monte Carlo method is employed for the estimation of the TVP-VAR models with stochastic volatility. As an example of empirical application, the TVP-VAR model with stochastic volatility is estimated using the Japanese data with signiﬁcant structural changes in the dynamic relationship between the macroeconomic variables.
Keywords: Bayesian inference; Markov chain Monte Carlo; Monetary policy; State space model; Structural vector autoregression; Stochastic volatility; Time-varying parameter
Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.