Sims (1993) A Nine-Variable Probabilistic Macroeconomic Forecasting Model

Summary

This NBER chapter (in Stock & Watson's Business Cycles, Indicators and Forecasting) documents the evolution of the Minneapolis-Fed Bayesian VAR (BVAR) forecasting model from Litterman's original six-variable version into the nine-variable "probabilistic" model Sims maintained. It is a full probability model — it produces predictive distributions, not just point forecasts — and departs from earlier BVARs (Litterman 1986; Doan–Litterman–Sims 1984) in three important ways: it allows time-varying (conditional) variances, non-normal disturbances (modeled as mixtures of two normals), and more time-varying autoregressive coefficients. By its own likelihood the richer model fits much better and delivers drastically better price-level forecasts both in and out of sample, while its advantages for real variables are smaller and uncertain. (In Business Cycles, Indicators and Forecasting, University of Chicago Press, pp. 179–212.)

Key Claims

• Lineage of the model. Litterman's BVAR (c. 1980) began with six variables — the Treasury-bill rate, M1, the GNP deflator, real GNP, real business fixed investment, and unemployment — and forecast aggregate macro variables remarkably well versus commercial models (McNees 1986), except for the price level. Litterman added three variables — the trade-weighted dollar, the S&P 500, and a commodity price index — to fix inflation forecasts; Sims took the model over in 1986 and revised it in 1987.
• A probability model, not a point-forecast rule. The model specifies a full likelihood, so it yields probability distributions for future variables (hence "probabilistic"), a departure from treating the BVAR as a mechanical shrinkage forecaster.
• Innovation 1 — conditional heteroskedasticity. The disturbance variances vary over time (time-varying variances), letting the model adapt to changing volatility rather than assuming a constant error covariance.
• Innovation 2 — non-normal (mixture) disturbances. The disturbances are modeled as mixtures of two normal random variables, accommodating fat tails / occasional large shocks and the non-normality of forecast errors that earlier BVARs ignored.
• Innovation 3 — time-varying coefficients. Extending the Doan–Litterman–Sims (1984) time-varying-parameters framework, the model implies much more time variation in the autoregressive coefficients than the earlier simpler models — needed to track shifts in trend inflation and productivity-growth rates.
• Performance. By its own likelihood the richer specification fits far better than the earlier models; price-level forecasts improve dramatically in and out of sample. For other (real) variables the gains over the simple six-variable Litterman model are smaller and uncertain — the added complexity mainly buys better inflation forecasts.
• Diagnostic motivation. The revisions were driven by observed pathologies of the simpler models — long runs of same-signed forecast errors for inflation (and later real GNP) — symptomatic of a model extrapolating trends at a fixed long-run average rate.

Concepts Introduced or Extended

• Bayesian VAR
• Minnesota Prior
• Time-Varying Parameter VAR
• Stochastic Volatility

Entities Mentioned

• Christopher Sims

Quotes

"It accounts for nonnormality of forecast errors and allows for time-varying variances as well as time-varying autoregressive coefficients. According to its own likelihood function, it fits much better than the simpler earlier models."

"Both within sample and out of sample it produces drastically better forecasts of the price level than the simpler models. For other variables, its advantages over the simpler models are smaller and uncertain."

My Take

This chapter is the missing link between Litterman's shrinkage-based Minnesota-prior BVAR and the modern TVP-VAR-with-stochastic-volatility program that Primiceri (2005) would formalize a decade later: Sims already has all three ingredients — drifting coefficients, time-varying variances, and non-Gaussian (mixture) shocks — assembled inside a full probability model, fit by likelihood. Its candid verdict is also worth remembering: the elaborate specification bought a big improvement for inflation and only ambiguous gains for real variables, an early instance of the recurring finding that the payoff to volatility/parameter drift in macro VARs is concentrated where the trends actually shift. For this wiki it is the applied, forecasting-oriented counterpart to BVAR theory and a direct precursor of Sims–Zha and the Great-Moderation-era literature on changing macro volatility.