Drifts and volatilities: monetary policies and outcomes in the post WWII US

The paper asks whether the behavior of post-WWII U.S. inflation and unemployment reflects changes in the systematic conduct of monetary policy (drifting VAR coefficients) or changes in the volatility of the shocks hitting the economy (drifting innovation variances), and it does so by extending Cogley and Sargent’s (2001) time-varying-parameter VAR (TVP-VAR) to include stochastic volatility. The extension directly answers Sims (2001) and Stock (2001), who argued that CS2001’s evidence of drifting VAR coefficients could be an artifact of failing to model heteroskedasticity in the shocks – if the “true” model has constant coefficients but volatile, changing shock variances, misspecified constant-variance estimation could spuriously generate the appearance of coefficient drift.

The model is a trivariate Bayesian TVP-VAR with two lags for CPI inflation, the unemployment rate, and the 3-month Treasury bill rate, estimated on quarterly U.S. data from 1948:Q1-2000:Q4 (the first ten years, 1948:Q1-1958:Q4, are used only to initialize priors; estimation results are reported for 1959:Q1-2000:Q4). The VAR coefficient vector theta_t follows a driftless random walk (theta_t = theta_{t-1} + v_t), with an added stability condition that rejects explosive draws so that the implied VAR always has roots inside the unit circle. The innovation covariance is factored as R_t = B^{-1} H_t B^{-1’}, where B is a lower-triangular matrix with unit diagonal (a Cholesky-type contemporaneous structure) and H_t is a diagonal matrix of time-varying variances that each evolve as independent log-random walks. Critically, the paper does not interpret the orthogonalized innovations from this Cholesky factorization as identified structural monetary policy shocks; it is explicitly a reduced-form exercise, so all its findings describe reduced-form dynamics rather than causal responses to identified shocks. Estimation uses a Metropolis-within-Gibbs MCMC sampler over five blocks (coefficients, their innovation-variance matrix Q, the volatility innovation variances, the B parameters, and the stochastic volatilities themselves), run for 100,000 replications with 50,000 discarded as burn-in and every tenth remaining draw retained, for 5,000 posterior draws.

Yes: the posterior for Q, the innovation-variance matrix governing how much theta_t can move each period, is shifted well to the right of its prior, with even the smallest posterior value about three times the trace of the prior mean Q-bar, so the paper concludes there is “strong evidence for drift in Q against the prior, much stronger than the prior.” Because this result holds after stochastic volatility has been added to absorb time-varying shock variance, the authors argue the coefficient drift documented in Cogley-Sargent (2001) is not simply an artifact of omitted heteroskedasticity, directly rebutting Sims (2001) and Stock (2001).

The drift is low-dimensional and structured rather than diffuse: a principal-component analysis of the smoothed coefficient path theta_{t|T} shows the first two principal components account for 83% of total variation, and the first principal component alone loads heavily on inflation dynamics. This suggests that although the coefficient vector has many elements, most of the time variation the model detects is driven by a small number of underlying factors, with the inflation-related dynamics doing much of the work.

The estimated time-varying innovation variances (H_t) show large spikes for the interest-rate and inflation equations around 1979-1981, followed by a substantial decline; the unemployment innovation standard deviation falls by roughly 40% from peak to trough in the early 1980s and by about 60% overall relative to the late 1950s. These magnitudes are approximate readings from the paper’s Figures 5-6 rather than tabulated point estimates. The decline in shock volatility is treated as a separate, coexisting empirical regularity alongside the coefficient drift – the paper does not claim one causes the other, only that both are present in the data.

Core inflation – the TVP-VAR’s implied long-run mean of the inflation process – rises from roughly 1.5% in the early 1960s to about 8% in the late 1970s, then falls to 2.5-3.5% in the 1980s-1990s, closely tracking the estimated natural rate of unemployment (correlation 0.748). Inflation persistence, measured by the normalized spectrum of inflation at zero frequency (the spectrum divided by the innovation variance, capturing autocorrelation rather than raw autocovariance), “sweeps gradually upward in the latter half of the 1960s and remains high throughout the 1970s,” then “falls sharply after 1980”; the paper characterizes inflation as “approximately white noise in the early 1960s and not far from white noise in the mid-1990s.” Two-sigma error bands put persistence roughly between 2 and 10 at its 1970s peak, comparable to a univariate AR(1) coefficient of 0.85-0.97. Core inflation and persistence are strongly positively correlated (0.92) – both rose together in the 1960s-1970s and fell together during the Volcker disinflation. The authors flag this positive correlation as “problematic for the escape route models of Sargent (1999) and Cho et al. (2002), which predict that inflation persistence should grow along the transition from high to low inflation,” since their estimates show the opposite pattern, and they do not themselves propose a structural resolution beyond citing alternative central-bank-learning models (Cogley-Sargent 2003; Primiceri 2003b) as consistent with the positive correlation.

Using a time-varying forward-looking Taylor rule (with the activism parameter A_t = beta_1/(1-beta_3), where A_t >= 1 means the nominal rate rises more than one-for-one with expected inflation), the estimated probability that policy was activist rose from 0.208 in 1975 (passive) to 0.919 in 1985 and 0.941 in 1995 (both strongly activist), with the probability that activism increased from 1975 to 1985 estimated at 0.923 and from 1975 to 1995 at 0.943. The activism parameter A_t is inversely correlated with both core inflation (-0.79) and the normalized spectrum at zero (-0.72), which the authors say is “suggesting that changes in policy activism may have contributed to the rise and fall of inflation as well as to changes in its persistence” – language kept hedged rather than causal, consistent with the paper’s reduced-form status. They conclude this “corroborate[s] the conclusion of Clarida et al. that monetary policy was passive in the 1970s and activist for much of the Volcker-Greenspan era,” and report the pattern is qualitatively similar under a shorter-horizon forward-looking rule and under a conventional Taylor rule with interest-rate smoothing. The authors also caution that “uncertainty about A is greatest when inflation is weakly persistent,” so the activism estimates are least reliable at the beginning and end of the sample, where instruments have little relevance.

Mostly no, but the authors argue this reflects low test power rather than absence of drift: the Andrews sup-LM and Nyblom-Hansen tests fail to reject time-invariance of theta_t at the 10% level for essentially every equation and for the full VAR system, with Monte Carlo power against the estimated drift process of only 0.076-0.252 in these tests. The Andrews sup-Wald test does reject for the inflation equation (at 1%) and for the VAR system (at 5%), consistent with its higher simulated power (0.296-0.711). Policy-rule stability tests and first-principal-component stability tests show a similar pattern of low power and mostly-failed rejections. The paper’s stated conclusion is that “most of our tests fail to reject time invariance of theta, but most also have low power to detect the patterns of drift we describe… a failure to reject should not be construed as an embarrassment to time-varying parameter models,” noting that the Andrews-style tests are designed to detect a single structural break at an unknown date rather than the continual drift the TVP-VAR describes.

The central limitation is that the paper is explicitly reduced-form: it imposes no structural identifying restrictions beyond a Cholesky ordering, so none of its findings should be read as causal responses to identified monetary policy shocks – they describe how the joint reduced-form dynamics of inflation, unemployment, and the interest rate have drifted, not what would happen if policy were counterfactually changed. The activism parameter is only weakly identified when inflation is weakly persistent, widening error bands at the sample’s beginning and end. The classical stability tests used as a robustness check are individually low-powered against continual drift by design (they target single breaks), which the authors treat as a caveat on how to interpret non-rejections rather than as evidence against their model. The trivariate system is small and could omit variables (forward-looking information, commodity prices) that affect the Fed’s reaction function, though the authors do not flag this themselves. Finally, the positive correlation between core inflation and inflation persistence is left as an open puzzle for escape-route learning models rather than resolved within the paper.