Time Varying Structural Vector Autoregressions and Monetary Policy

The paper asks whether the poor U.S. macroeconomic performance of the 1970s and early 1980s — high inflation and unemployment — reflects changes in the systematic component of monetary policy (time-varying Taylor-rule coefficients), changes in the size of non-systematic policy shocks, or changes in non-policy exogenous shocks. To answer this it develops a Bayesian time-varying structural VAR (TVP-SVAR) that allows the VAR coefficients, the matrix of contemporaneous relations among variables, and the shock variances all to evolve over time, applied to quarterly U.S. inflation, unemployment, and the three-month Treasury bill rate, 1953:I-2001:III (Introduction, pp. 821-823).

The model’s defining feature is that the matrix A_t of contemporaneous (“simultaneous”) relations among the VAR’s variables is allowed to vary over time, not just the reduced-form coefficients B_t and shock variances — a feature the paper argues is essential for a genuinely time-varying structural model, since holding A_t fixed “would imply time-invariant contemporaneous effects, which is clearly undesirable if the objective is modelling time variation in a simultaneous equation model” (Section 2, p. 824). In the model, y_t = c_t + B_{1,t}y_{t-1} + … + B_{k,t}y_{t-k} + u_t, with u_t’s time-varying covariance Ω_t factored as A_tΩ_tA_t’ = Σ_tΣ_t’; B_t, the off-diagonal elements of A_t, and log σ_t (the diagonal of Σ_t) all follow random walks (Eqs. 1-2, 5-7). This is the key extension over Cogley and Sargent (2005), whose trivariate TVP-VAR allows B_t and the reduced-form covariance to vary but restricts the simultaneous relations to be constant; that restriction is what let Cogley-Sargent read a passive-to-activist shift directly off B_t; Primiceri’s model instead separately tracks a drifting A_t and log σ_t (Related papers section; wiki summary).

The model is estimated with a four-block Gibbs sampler run for 10,000 iterations (first 2,000 discarded): (a) a Carter-Kohn/Fruhwirth-Schnatter state-space draw for the VAR coefficients B^T, (b) an equation-by-equation Kalman-filter draw for the simultaneous-relation parameters A^T, (c) a Kim-Shephard-Chib (1998) seven-component log-normal mixture approximation for the stochastic volatilities Σ^T, and (d) inverse-Wishart draws for the innovation-covariance hyperparameters (Q for coefficient drift, W for log-volatility drift, S for simultaneous-relation drift). Priors are calibrated by OLS on the first ten years of data (1953:I-1962:IV); the benchmark tightness parameters (k_Q=0.01, k_S=0.1, k_W=0.01) are selected via a reversible-jump MCMC comparison across 18 candidate models and receive posterior probability “essentially 1” (Sections 3.1-3.2, 4.4.1, pp. 826-828, 842-843). Monetary-policy shocks are identified recursively by ordering the interest rate last, on the assumption that “monetary policy actions affect inflation and unemployment with at least one period of lag” — described as “not an ordering issue… but an identification condition” and as “completely standard” in the literature (citing Leeper et al. 1996; Rotemberg and Woodford 1997; Bernanke and Mihov 1998; Christiano et al. 1999). The ordering of inflation before unemployment, by contrast, is an arbitrary normalization that does not affect results (Section 4.2, pp. 831-832).

The standard deviation of monetary-policy shocks shows “substantially higher variance” during 1979-83, the Volcker-era disinflation, and is on average higher in the pre-Volcker period than after it; but the impulse responses of inflation and unemployment to a policy shock of given size are not statistically distinguishable across the Burns (1975:I), Volcker (1981:III), and Greenspan (1996:I) periods (Section 4.2, Figures 1-3, p. 833). The paper summarizes: “there is no evidence of nonlinearities in the responses of the economy to non-systematic policy.” A small price-puzzle response present in the Burns/Volcker periods “almost disappears in the Greenspan period” but the difference is not statistically significant, and “the stability of the response of unemployment to policy shocks is remarkable” (p. 833). The residual volatility patterns also suggest that simple inflation/unemployment-based Taylor-type rules “are very good approximations” of policy in the last 15 years of the sample, while in the 1960s-70s the Fed was likely responding to other variables as well (p. 833).

Using smoothed (full-sample) estimates, the long-run (60-quarter) interest-rate response to a permanent one-percentage-point increase in inflation exceeds 1 throughout the entire sample, including the Burns period of the 1970s — satisfying the Taylor principle at all times (Section 4.3, Figure 4d, pp. 836-837). This directly contradicts Judd and Rudebusch (1998), Clarida, Galí and Gertler (2000), and Cogley and Sargent (2001), all of whom find an inflation response below 1 before the 1980s using filtered (real-time) estimates. Primiceri attributes the discrepancy to the fact that filtered estimates, which use only the information available up to each point in the sample, “suffer from small-sample bias toward stationarity” in the 1960s-70s, whereas his smoothed estimates use the full sample’s information (pp. 836-837). The contemporaneous (simultaneous) interest-rate response to inflation shows an upward trend over the sample — “a trend toward a more aggressive behaviour, despite remarkable oscillations” — and the long-run response trends up too, though with wide uncertainty bands at long horizons; the paper notes “neither the simultaneous reactions nor the long run ones seem to exhibit an absorbing state, but rather a frequent alternation among states” (p. 838). The contemporaneous response to unemployment is “almost the same as the long run one, suggesting that the Fed reacts to unemployment much faster than to inflation,” and the inflation and unemployment responses are “quite highly correlated” over time (p. 837).

Replaying history from 1970:I using systematic-policy-rule coefficients drawn from the 1991-1992 posterior produces counterfactual inflation and unemployment paths that “do not differ much” from the actual historical paths, and the same holds when only the policy-shock standard deviations (rather than the rule coefficients) are counterfactually replaced (Section 4.3, Figure 8, p. 841). The paper concludes that “the differences in the conduct of systematic interest rate policies under Burns, Volcker and Greenspan were not large enough to have any relevant effect on the dynamics of inflation and unemployment” (p. 841).

The paper’s central interpretation is that the high inflation and unemployment of the 1970s and early 1980s are better explained by unusually high volatility of non-policy shocks than by any failure of the systematic monetary-policy rule: “the peaks in inflation and unemployment of the 1970’s and early 1980’s seem to be better explained by the high volatility of the shocks that characterized those periods” (p. 841). This rejects the conventional “too-accommodative policy” narrative that filtered estimates in the prior literature had suggested. The paper notes that Blanchard and Simon (2001), Stock and Watson (2002), Hanson (2003), and Sims and Zha (2004) reach similar conclusions (p. 841).

The results are reported as robust across several checks: much flatter priors (variances 10-20 times larger) “give exactly the same results”; relaxing the block-diagonal restriction on the simultaneous-relations innovation covariance S gives results “very similar to the main ones,” with cross-equation correlations estimated as “basically zero”; and different orderings of the non-policy variables (inflation vs. unemployment) give “very similar” results because of the arbitrary-normalization argument (Section 4.4, pp. 842-843, and Section 3.1, p. 827). Estimated AR coefficients for the log-volatility processes (0.95-1.0) and for the simultaneous-relations processes (0.5-0.9) are not exactly 1, but results using these estimated persistence values are “not relevantly different from” the random-walk benchmark, which the paper interprets as suggesting the model also captures temporary parameter shifts reasonably well (Section 4.4.2).

The paper explicitly notes several limitations: it uses only a small three-variable system (inflation, unemployment, the T-bill rate), trading off a richer variable set against the tighter priors needed to keep a larger time-varying model well-behaved; its headline Taylor-principle finding depends specifically on smoothed rather than filtered estimates, so real-time policy monitoring would face the small-sample bias problem it identifies in earlier filtered-estimate studies; the counterfactual assumes private-sector behavior is policy-invariant (a Lucas-critique concern the paper argues is mitigated because the regime changes it considers were not large enough to constitute “a different, previously unknown regime”); and the coefficients are modeled as random walks, which can imply large cumulative drift over a long sample even though a robustness check (Q8) suggests this is not distorting the results (Section 4, p. 830; Caveats, pp. 830, 839-840). Separately — and importantly for interpreting the paper today — Primiceri (2005)’s original MCMC algorithm for time-varying volatility was later found to be flawed: the original Gibbs sampler drew the VAR coefficients B^T without correctly conditioning on the Kim-Shephard-Chib mixture indicators, creating an incorrect block structure in the sampler. Del Negro and Primiceri (2015) published a corrigendum in the same journal with a corrected algorithm (switching the order of two steps in the sampler), and found that the paper’s substantive qualitative conclusions were largely robust to the fix, though the corrected estimates are described as smoother than the originals.