Time Varying Structural Vector Autoregressions and Monetary Policy

This 2005 Review of Economic Studies paper by Giorgio Primiceri develops a Bayesian time-varying-parameter structural VAR (TVP-SVAR) with stochastic volatility — allowing not just the VAR coefficients but also the matrix of contemporaneous (“simultaneous”) relations among variables, and the shock standard deviations, to drift over time as random walks — and applies it to U.S. inflation (GDP deflator growth), unemployment, and the three-month Treasury bill rate over a 1953:I-2001:III sample (the first ten years, 1953:I-1962:IV, are used only to calibrate priors) to ask whether the poor macroeconomic performance of the 1970s and early 1980s reflects changes in the systematic component of monetary policy (drifting Taylor-rule-type coefficients), changes in the size of non-systematic policy shocks, or changes in non-policy shocks. Using a two-lag recursive VAR that identifies monetary-policy shocks by ordering the interest rate last (the identifying assumption that policy affects inflation and unemployment only with at least one lag), and a four-block Gibbs sampler (a Carter-Kohn/Fruhwirth-Schnatter state-space draw for the VAR coefficients, an equation-by-equation Kalman-filter draw for the simultaneous relations, a Kim-Shephard-Chib seven-component normal-mixture approximation for the stochastic volatilities, and inverse-Wishart draws for the innovation-covariance hyperparameters, selected via a reversible-jump MCMC comparison across 18 candidate models), Primiceri finds that the standard deviation of monetary-policy shocks was “substantially higher” during 1979-83 (the Volcker disinflation) and, on average, higher in the pre-Volcker than the post-Volcker period, while the impulse responses of inflation and unemployment to a given-size policy shock are not statistically distinguishable across the Burns (1975:I), Volcker (1981:III), and Greenspan (1996:I) periods. Using smoothed (full-sample) rather than filtered (real-time) parameter estimates, the paper finds the long-run (60-quarter) interest-rate response to a permanent one-percentage-point increase in inflation exceeded one — satisfying the Taylor principle — throughout the entire sample, including the Burns years, contradicting earlier filtered-estimate findings (e.g. Judd and Rudebusch 1998; Clarida, Galí and Gertler 2000; Cogley and Sargent 2001) of an inflation-accommodating regime before Volcker, which Primiceri attributes to small-sample bias toward stationarity in filtered estimates. A counterfactual exercise that replays history from 1970:I using systematic-policy coefficients (and, separately, policy-shock standard deviations) drawn from the 1991-1992 posterior — “planting Greenspan into the 1970s” — produces inflation and unemployment paths close to the historically observed ones, leading the paper to conclude that differences in systematic monetary policy across the Burns, Volcker, and Greenspan regimes “were not large enough to have any relevant effect,” and that the volatility of non-policy shocks better explains the poor performance of the 1970s and early 1980s. The paper’s model is restricted to a small three-variable system, and its headline Taylor-principle finding rests specifically on smoothed rather than real-time estimates. A subsequent corrigendum (Del Negro and Primiceri 2015) later identified and corrected a flaw in the paper’s original Gibbs-sampling algorithm for the volatility block, finding the substantive conclusions largely robust to the fix.

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.

Giorgio E. Primiceri | Macro Paper Warehouse

Time Varying Structural Vector Autoregressions and Monetary Policy

Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum