Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum

This 2015 Review of Economic Studies corrigendum by Marco Del Negro and Giorgio Primiceri identifies and fixes a flaw in the Gibbs-sampling algorithm that Primiceri (2005) used to estimate time-varying-parameter structural VARs (TVP-VARs) with stochastic volatility via the Kim-Shephard-Chib (KSC) mixture-of-normals approximation. The original three-block sampler draws the log-volatility history from an approximate density conditional on the coefficients and the KSC mixture-component indicators, then draws the indicators from another approximate density, and finally draws the coefficients from the correct likelihood conditional on the volatilities but not on the mixture indicators; the authors show this last step is invalid because the mixture indicators affect the coefficients’ conditional posterior, so the algorithm would not sample from the correct posterior even if the KSC approximation were made arbitrarily accurate. The fix, Algorithm 2, simply reorders the existing computational steps into two blocks – volatilities in one block, and coefficients followed immediately by the mixture indicators in the other – which the authors note is equivalent to swapping steps (d) and (e) in the original paper’s Appendix A.5 and is therefore trivial to implement in existing code; Algorithm 3 additionally replaces the volatility draw with a Metropolis-Hastings step (using the KSC density as a proposal) to remove the residual approximation error entirely. Geweke (2004) joint-distribution tests confirm Algorithm 3 is fully correct, Algorithm 2 is a close approximation to it, and Algorithm 1 is a poor approximation; separately, re-estimating the original Primiceri (2005) empirical exercise, the authors find Algorithm 2’s results are indistinguishable from Algorithm 3’s (the KSC approximation error is negligible in practice), while Algorithm 1’s results differ from both, albeit qualitatively similar; the main empirical consequence is that some of the estimated time-varying objects come out smoother under the corrected algorithms, with the paper’s qualitative conclusions described as similar to, but not identical to, the original results.

Marco Del Negro | Macro Paper Warehouse

Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum