Time-Varying Vector Autoregressions: Efficient Estimation, Random Inertia and Random Mean

Time-varying VAR models have become increasingly popular and are now widely used for policy analysis and forecast purposes. They constitute fundamental tools for the anticipation and analysis of economic crises, which represent rapid shifts in dynamic responses and shock volatility. Yet, despite their flexibility, time-varying VARs remain subject to a number of limitations. On the theoretical side, the conventional random walk assumption used for the dynamic parameters appears excessively restrictive. It also conceals the potential heterogeneities existing between the dynamic processes of different variables. On the application side, the standard two-pass procedure building on the Kalman filter proves excessively complicated and suffers from low efficiency. Based on these considerations, this paper contributes to the literature in four directions: i) it introduces a general time-varying VAR model which relaxes the standard random walk assumption and defines the dynamic parameters as general auto-regressive processes with variable- specific mean values and autoregressive coefficients. ii) it develops an estimation procedure for the model which is simple, transparent and efficient. The procedure requires no sophisticated Kalman filtering methods and reduces to a standard Gibbs sampling algorithm. iii) as an extension, it develops efficient procedures to estimate endogenously the mean values and autoregressive coefficients associated with each variable-specific autoregressive process. iv) through a case study of the Great Recession for four major economies (Canada, the Euro Area, Japan and the United States), it establishes that forecast accuracy can be significantly improved by using the proposed general time-varying model and its extensions in place of the traditional random walk specification.