Large Hybrid Time-Varying Parameter VARs

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.