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

This 2005 Review of Economic Dynamics paper by Timothy Cogley and Thomas J. Sargent extends their earlier Cogley-Sargent (2001) time-varying-parameter VAR (TVP-VAR) of postwar U.S. inflation, unemployment, and the 3-month Treasury bill rate by adding stochastic volatility to the innovation covariance matrix, directly responding to Sims (2001) and Stock (2001)’s criticism that CS2001’s finding of drifting VAR coefficients could be an artifact of omitted heteroskedasticity. Using quarterly U.S. data from 1948:Q1-2000:Q4 (the first ten years used only to initialize priors, with estimation reported for 1959:Q1-2000:Q4), the authors estimate a trivariate reduced-form VAR – no structural shocks are identified – in which the coefficient vector theta_t follows a driftless random walk truncated to stationary draws and the innovation covariance R_t = B^{-1} H_t B^{-1’} has diagonal elements H_t that themselves evolve as independent log-random walks, all estimated via a Metropolis-within-Gibbs MCMC sampler (100,000 draws, 50,000 burn-in, every 10th draw retained). They find the drift in theta_t survives the addition of stochastic volatility: the posterior for the innovation-variance matrix Q governing the coefficient process is shifted well to the right of the prior, with even its smallest posterior value about three times the trace of the prior mean, and this drift is low-dimensional, with the first two principal components of the smoothed coefficient path accounting for 83% of its variation and the first component loading heavily on inflation dynamics. Separately, the paper documents a “Great Moderation” decline in shock volatility, with the unemployment innovation standard deviation falling by roughly 40% from peak to trough in the early 1980s and about 60% overall since the late 1950s (approximate readings from the paper’s figures). 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 before falling to 2.5-3.5% in the 1980s-1990s, tracking the estimated natural rate of unemployment closely (correlation 0.748); inflation persistence, measured by the normalized spectrum of inflation at zero frequency, sweeps upward through the late 1960s and stays high through the 1970s – with two-sigma error bands placing it roughly between 2 and 10 at its peak, comparable to a univariate AR(1) coefficient of 0.85-0.97 – then falls sharply after 1980, with inflation “approximately white noise” in the early 1960s and again in the mid-1990s; core inflation and persistence are strongly positively correlated (0.92), a pattern the authors describe as “problematic” for escape-route learning models that predict persistence should rise, not fall, along the transition from high to low inflation. Using a time-varying forward-looking Taylor rule, they estimate that the probability policy was “activist” (a coefficient on expected inflation of at least one) rose from 0.208 in 1975 to 0.919 in 1985 and 0.941 in 1995, with activism inversely correlated with both core inflation (-0.79) and persistence (-0.72) – corroborating Clarida, Gali and Gertler’s (2000) conclusion that policy was passive in the 1970s and activist for most of the Volcker-Greenspan era. Finally, classical stability tests (Andrews sup-LM, Nyblom-Hansen, and Andrews sup-Wald) mostly fail to reject time-invariance of theta_t at conventional significance levels, but Monte Carlo simulations show these tests have low power (as low as 0.076-0.252 in several specifications) against the kind of continual drift the model describes, so the authors argue that failure to reject should not be read as evidence against drift.

Trend Inflation, Indexation, and Inflation Persistence in the New Keynesian Phillips Curve

This 2008 American Economic Review paper by Timothy Cogley and Argia Sbordone asks whether the substantial persistence long observed in U.S. inflation reflects a genuine structural feature of price-setting – specifically the backward-looking price indexation built into the New Keynesian Phillips Curve (NKPC) in models like Christiano-Eichenbaum-Evans (2005) and Smets-Wouters (2007) – or is instead an artifact of estimating the NKPC around a constant or de-meaned inflation trend when trend inflation has in fact drifted with monetary policy; the authors argue for the latter, that “accounting for trend-inflation drift allows a purely forward-looking model to fit the data well” (Introduction, p. 2101). They answer this in two stages using quarterly U.S. data over 1960:I-2003:IV (with a 1954:I-1959:IV training sample): first, a Bayesian time-varying-parameter VAR(2) with stochastic volatility (following Cogley and Sargent 2005a), estimated over output growth, real marginal cost (labor share), GDP-deflator inflation, and the nominal rate, is used to extract trend inflation as the long-horizon limit of the VAR’s time-varying conditional mean of inflation; second, the free structural parameters of a Calvo pricing model extended to allow nonzero trend inflation – the Calvo stickiness parameter alpha, the indexation parameter rho, and the elasticity of substitution theta – are estimated by minimum distance, matching the TVP-VAR’s reduced-form forecasting coefficients to the cross-equation restrictions the NKPC implies at each date. The central finding is that once the model conditions on the drifting trend, the backward-indexation parameter is estimated at essentially zero (median rho = 0, 90% CI (0, 0.15), with about 78 percent of posterior draws exactly at the zero lower bound), while median Calvo stickiness is alpha = 0.588 (90% CI 0.44-0.70), implying an average price duration of about 3.9 months (90% CI 2.5-5.8 months), and, with theta = 9.8 (90% CI 7.4-12.1), a steady-state markup near 11 percent. The paper documents that the autocorrelation of raw inflation (0.834 over 1960-2003; 0.843 over 1960-83; 0.784 over 1984-2003) is close to that of the trend-based inflation gap before 1984 (0.801) but diverges sharply after the Volcker disinflation, when the gap’s autocorrelation falls to just 0.305 versus 0.784 for raw inflation – evidence that most of the apparent persistence, especially during the Great Moderation, resides in the trend rather than in gap dynamics a purely forward-looking model must explain. Trend inflation itself is estimated to have risen from about 2.3 percent in the early 1960s to roughly 4.75 percent in the 1970s before falling to about 1.65 percent by 2003:IV, and the resulting model’s cross-equation restrictions are not rejected – VAR-based and NKPC-restricted inflation forecasts correlate at 0.978, and the model fits well through both the Great Inflation and the Great Moderation. The NKPC’s coefficients vary substantially with the level of trend inflation (the marginal-cost coefficient falls as trend inflation rises; the coefficient on expected future inflation rises modestly above one), which the authors identify as the mechanism that generates a spurious appearance of backward-looking indexation when a model is instead estimated around a constant trend. The authors report the zero-indexation finding as robust across four alternative specifications (Appendix C) and broadly consistent with Bils-Klenow (2004) micro price-duration evidence, but they also flag, citing Beyer and Farmer (2007), that identification of forward- versus backward-looking NKPC components in this class of model rests on auxiliary assumptions not fully pinned down by the data, that their duration estimate lies below Nakamura-Steinsson’s (2007) roughly 8-month estimate, and that the sample ends in 2003:IV and so does not speak to the zero lower bound or the post-2008 environment.

Timothy Cogley | Macro Paper Warehouse

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

Trend Inflation, Indexation, and Inflation Persistence in the New Keynesian Phillips Curve