Summary
A policy-accessible Atlanta Fed article presenting the Sims-Zha Bayesian vector autoregression (BVAR) in operation, occasioned by the March 1997 federal funds rate hike. Zha specifies a 6-variable monthly model (Box 1 gives the structural form y(t)A(L)=ε(t), heavily drawn from Sims-Zha 1998), motivates Bayesian priors through three ordinary least squares (OLS) failure modes, and evaluates the model's out-of-sample inflation forecasts over the 1980s and 1990s against Blue Chip consensus. The latter half demonstrates probability distributions and error bands — both univariate and joint — as the key output for forward-looking policy analysis.
Key Claims
- Three OLS failure modes for out-of-sample forecasting: (1) overfitting — Chart A shows M1 predicted with near-perfect accuracy in-sample from 1959 initial conditions, an "incredible outcome"; (2) erratic large coefficients from low degrees of freedom on distant lags; (3) explosiveness at long horizons. Bayesian priors resolve all three.
- Reference-nature Bayesian priors: following the likelihood principle, the priors favor unit roots and cointegration without imposing them exactly — widely-held, uncontroversial beliefs rather than strong structural assumptions.
- Six-variable monthly model (Box 2): Consumer Price Index (CPI; CPI-U series, Bureau of Economic Analysis [BEA]), commodity prices (IMF world index), federal funds rate (monthly average), real GDP (BEA, monthly interpolation via Leeper-Sims-Zha 1996 procedure), M2 (Bureau of Labor Statistics [BLS]), unemployment (civilian rate, ages 16+, BLS). Data: 1959:1–1997:9; 13-month lag length.
- Two sources of forecast uncertainty: (1) uncertainty about model parameters; (2) uncertainty from unpredictable exogenous shocks. Error bands account for both explicitly.
- 1980s forecasting (Chart 3): model tracks the Volcker disinflation at least as well as Blue Chip across most sub-periods without judgmental adjustments; model dynamically updates by systematically incorporating new data on output, rates, and unemployment.
- 1990s forecasting (Chart 4): Blue Chip over-predicted inflation every year since 1991 due to Phillips-curve heuristics applied to declining unemployment; model's multivariate dynamics captured the sustained disinflation more accurately.
- Regime-shift test (Chart 5): dropping pre-1983 data considerably worsens out-of-sample forecasting in several panels (especially D, E, F). Interpretation: the Fed's behavior during 1979–82 is complex — not a simple rule change — and discarding the data by a priori reasoning loses valuable information.
- 2/3 probability error bands (Charts 6–7): 1981 actual inflation inside band; 1982 actual inflation outside (genuine tail event acknowledged as low-probability). Blue Chip 1995 GDP growth forecast (+3.2%) lies far outside the model's error band and near the tail of the distribution (Chart 9).
- Joint error region (Chart 10): bivariate 2/3 probability ellipse for 1998 GDP growth × inflation, evaluated against 55 Wall Street Journal survey forecasters (Jan 2, 1998). At least one-fifth of firms fell outside the model's region; none produced forecasts that fall within the top half (high GDP growth, low inflation quadrant) implied by the model.
Concepts Introduced or Extended
- Error Bands — empirical demonstration of 2/3 univariate bands and joint bivariate error regions; error bands capture both parameter and shock uncertainty
- Sims-Zha Prior — canonical 6-variable monthly application with 13 lags; three OLS failure modes motivating the prior; regime-shift robustness test
- Vector Autoregression — regime-shift evidence; Blue Chip comparison; policy projection framework
Entities Mentioned
Quotes
"The dynamic multivariate model provides a useful tool for gauging future uncertainty and an empirically consistent way to update forecasts."
"Chart A displays actual values and in-sample forecasts of the stock of M1 from January 1960 to March 1996... one could, in 1959, predict with almost perfect accuracy the level of M1 stock in 1996—an incredible outcome."
"All models at best only approximate the actual economy. No model can forecast economic conditions with perfect accuracy. Thus, policymakers must use point forecasts cautiously and carefully."
My Take
This is an applied showcase, not a methodological paper — the technical details are deferred almost entirely to Sims-Zha (1998). Its value lies in demonstrating what the framework produces in practice: the regime-shift robustness check is particularly compelling (dropping Volcker-period data hurts forecasting), and Chart 10's joint error region is an underused tool in applied VAR work. The comparison with Blue Chip forecasts is frank about the model's failures (1982 inflation outside the band) while making a convincing empirical case for multivariate dynamics over simple heuristics.