Abstract
Time-varying parameter VARs with stochastic volatility are routinely used for structural analysis and forecasting in settings involving a few macroeconomic variables. Applying these models to high-dimensional datasets has proved to be challenging due to intensive computations and over-parameterization concerns. We develop an efficient Bayesian sparsification method for a class of models we call hybrid TVP-VARs - VARs with time-varying parameters in some equations but constant coefficients in others. Specifically, for each equation, the new method automatically decides (i) whether the VAR coefficients are constant or time-varying, and (ii) whether the error variance is constant or has a stochastic volatility specification. Using US datasets of various dimensions, we find evidence that the VAR coefficients and error variances in some, but not all, equations are time varying. These large hybrid TVP-VARs also forecast better than standard benchmarks.
Highlights
Time-varying parameter vector autoregressions (TVP-VARs) developed by Cogley and Sargent (2001, 2005) and Primiceri (2005) have become the workhorse models in empirical macroeconomics
For density forecasts, the results are similar: the median percentage gains in average of log predictive likelihoods (ALPL) for 1- and 4-quarter-ahead forecasts are, respectively, 0.8% and 3.1%. These results suggest that allowing for time variation in VAR coefficients—with appropriate shrinkage and sparsification—can further enhance the forecast performance of a VAR with stochastic volatility
Using US data, we found evidence that while VAR coefficients and error covariances in some equations are time varying, the data prefers constant coefficients in others
Summary
Time-varying parameter vector autoregressions (TVP-VARs) developed by Cogley and Sargent (2001, 2005) and Primiceri (2005) have become the workhorse models in empirical macroeconomics. The proposed approach is flexible—it includes many state-of-the-art models routinely used in applied work as special cases—it induces parsimony to ameliorate over-parameterization concerns This data-driven hybrid TVP-VAR can be interpreted as a Bayesian model average of 22n hybrid TVP-VARs with different forms of time variation, where the weights are determined by the posterior model probabilities p(γ | y). The dimension of the model is large and there are thousands of latent state processes—time-varying coefficients and stochastic volatilities—to simulate To overcome this challenge, in addition to using the equationby-equation estimation approach described earlier, we adopt the precision sampler of Chan and Jeliazkov (2009) to draw both the time-invariant and time-varying VAR coefficients, as well as the stochastic volatilities.
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