Primiceri (2005) Time Varying Structural Vector Autoregressions and Monetary Policy

Summary

This is the foundational paper for the time-varying-parameter structural VAR with stochastic volatility (TVP-SVAR). Primiceri models U.S. monetary policy and private-sector behavior as a structural VAR in which both the coefficients and the entire variance-covariance matrix of the innovations drift over time — the coefficients capturing changes in the systematic behavior of policy and the private sector, and the time-varying covariance capturing both changing simultaneous relations and heteroskedastic shocks. He introduces a simple triangular law of motion for the covariance matrix and an efficient Gibbs-sampling MCMC algorithm for estimation. Empirically he finds that both systematic and non-systematic monetary policy changed over the last forty years (policy became somewhat more aggressive against inflation under Greenspan), but that these changes had a negligible effect on the rest of the economy: the high inflation and unemployment of the 1970s are better explained by the larger volatility of exogenous non-policy shocks ("bad luck") than by policy ("bad policy"). (Published in the Review of Economic Studies 72(3): 821–852; working paper 2004.)

Key Claims

• Both coefficients and covariance drift. Earlier models allowed only one: Cogley–Sargent (2001, 2003) drift the reduced-form coefficients with time-varying variances but hold the simultaneous relations fixed; Uhlig (1997) allows multivariate stochastic volatility but constant VAR coefficients. Primiceri lets the VAR coefficients, the contemporaneous (simultaneous) relations, and the shock volatilities all vary — essential for separating changes in the size of shocks from changes in transmission.
• Triangular decomposition of the covariance. The reduced-form innovation covariance $\Omega_t$ is factored as $A_t\,\Omega_t\,A_t' = \Sigma_t\Sigma_t'$, i.e. $\Omega_t = A_t^{-1}\Sigma_t\Sigma_t'(A_t^{-1})'$, where $A_t$ is a lower-triangular matrix of time-varying simultaneous-relation coefficients and $\Sigma_t$ is diagonal with the time-varying standard deviations (stochastic volatilities). This separates the two sources of covariance change and gives a recursive structural identification.
• Laws of motion. The VAR coefficients $B_t$ and the free elements of $A_t$ follow random walks; the log standard deviations $\log\sigma_{it}$ follow geometric random walks (stochastic volatility). Random walks are used to limit the number of parameters and let the data determine the amount of drift, at the cost of admitting the possibility of nonstationary/explosive paths (bounded in estimation).
• Efficient MCMC. A Gibbs sampler draws the time-varying states with the Carter–Kohn (1994) forward-filter/backward-sampling simulation smoother; the stochastic-volatility block uses the Kim–Shephard–Chib (1998) mixture-of-normals approximation to the log-$\chi^2$ measurement error. This made full-blown TVP-SVAR estimation computationally feasible.
• Empirical finding 1 — policy did change. Both the systematic (rule) and non-systematic (shock) components of monetary policy varied over 1960s–2000s; non-systematic policy was relatively more important early in the sample (a Taylor rule fits the 1960s–70s poorly), and interest-rate responses to inflation/unemployment were somewhat stronger in the Greenspan era.
• Empirical finding 2 — but it didn't matter much. A counterfactual exercise indicates the changes in systematic policy did not play an important role in the high-inflation/high-unemployment episodes; the higher volatility of exogenous non-policy shocks accounts for a larger fraction of those outbursts — evidence on the "good luck vs. good policy" debate leaning toward luck.

Concepts Introduced or Extended

• Time-Varying Parameter VAR
• Stochastic Volatility
• Monetary Policy Shocks
• Great Moderation

Entities Mentioned

• Giorgio E. Primiceri

Quotes

"The sources of time variation are both the coefficients and the variance covariance matrix of the innovations."

"The role played by exogenous non-policy shocks seems more important than interest rate policy in explaining the high inflation and unemployment episodes in recent US economic history."

My Take

This paper is the workhorse template for modern time-varying macroeconometrics: the $A_t$/$\Sigma_t$ triangular factorization plus random-walk drift plus Carter–Kohn + Kim–Shephard–Chib sampling is exactly the recipe that hundreds of later TVP-VAR papers reuse. Its methodological insistence that you must let the covariance matrix vary — otherwise you conflate shrinking shocks with changed transmission — is the analytical core, and it is what lets the paper adjudicate the "good luck vs. good policy" question that Great Moderation research turns on. It sits opposite the Markov-switching approach (discrete regimes vs. smooth random-walk drift) as the two dominant ways to model instability, and its "bad luck" verdict is the natural counterpoint to the Clarida–Galí–Gertler "bad policy" reading of the same era. The main caveats are the usual ones for these models: random-walk states can wander, identification of the drift is delicate, and the recursive $A_t$ ordering is a genuine identifying assumption. Note: the MCMC algorithm as published has a step-ordering error; Del Negro–Primiceri (2015) provide the corrigendum (each Gibbs step is unchanged, but the order must be fixed for the sampler to target the correct posterior).