Adolfson et al. (2005) Modern Forecasting Models in Action: Improving Macroeconomic Analyses at Central Banks

Summary

This paper demonstrates how Bayesian vector autoregression (BVAR) and small open economy dynamic stochastic general equilibrium (DSGE) models can be used in real-time central bank policy analysis, using Swedish data from 1999Q1–2005Q4. It benchmarks Riksbank official (judgmental) forecasts against model-based forecasts of consumer price index (CPI) inflation and the short-term interest rate, finding that formal models match or beat official forecasts at most horizons and that Bayesian forecast combination always outperforms individual methods. It further shows how structural analysis — historical decompositions and conditional forecasts — exposes the limits of atheoretical VARs for policy use and demonstrates the advantage of structurally identified DSGE models.

Key Claims

• The 7-variable BVAR (foreign and domestic gross domestic product [GDP] growth, CPI inflation, interest rate; real exchange rate) using Villani's (2005) steady-state Gibbs sampler with the Litterman prior on dynamic coefficients matches official Riksbank CPI forecasts within one year and beats them at 2–8 quarters ahead.
• The 15-variable small open economy DSGE (Adolfson et al. 2005b) — extending Christiano-Eichenbaum-Evans (2005) to an open economy with incomplete pass-through — beats official inflation forecasts at 5–8 quarters ahead. Both models beat naive no-change benchmarks at all horizons.
• Bayesian forecast combination (Winkler 1981) with an Inverted-Wishart prior on the forecast error covariance matrix achieves the lowest root mean squared error (RMSE) at all horizons for both CPI inflation and interest rates.
• Subjective sector-expert forecasting adds value at short horizons during unusual observable shocks: the 2001 mad-cow food price shock and 2003 electricity price shock were correctly identified as transitory by experts but over-extrapolated by the BVAR.
• BVAR impulse responses to a monetary policy shock are not statistically significant (wide 68% and 95% bands) — making the BVAR unsuitable for policy conditioning. DSGE responses are significant: a 0.35 percentage point (pp) rate increase produces a maximum $-0.15$ pp CPI effect after ~1.5 years.
• Historical decomposition for 2003–2004 Swedish low inflation: BVAR attributes it mainly to "foreign" shocks; DSGE confirms this and further identifies domestic technology shocks in 2004–2005. Markup shocks are negligible, contradicting a "competition" narrative.
• Conditioning both models on the same forward rate path (2004Q4 exercise) reveals very different inflation implications: DSGE predicts ~2% inflation two years ahead; BVAR predicts only ~1.1%.

Concepts Introduced or Extended

• Forecast Combination — Winkler (1981) Bayesian method; IW prior on forecast error covariance; weights $w_t' = u'\tilde\Sigma_t^{-1}/(u'\tilde\Sigma_t^{-1}u)$
• Historical Decomposition — Decomposing VAR and DSGE forecast errors into contributions from identified shock groups
• Steady State VAR — Applied to 7-variable open-economy BVAR; steady-state prior on inflation set to Riksbank's 2% target; Villani (2005) Gibbs sampler used for posterior
• Vector Autoregression — BVAR with Litterman prior and steady-state prior; Cholesky identification with foreign variables ordered first
• Impulse Response Function — BVAR vs. DSGE comparison for monetary policy shocks; BVAR error bands too wide for policy use

Entities Mentioned

• Malin Adolfson
• Jesper Lindé
• Mattias Villani
• Anders Vredin
• Christopher Sims — Sims (2002) review of central bank model use
• Tao Zha — Waggoner-Zha (1999) conditional forecast methodology cited

Quotes

"BVAR models summarize regularities in the data that forecasters should pay attention to. At the same time, judgments from sector experts based on their detailed knowledge about the economy can be extremely useful, in particular when unusual shocks have hit the economy."

"A model with good statistical properties but with little economic theory (i.e., a VAR) may be a good forecasting tool but is probably too overparameterized to give precise answers about the monetary transmission mechanism."

"When the economists work with some common models they believe in, it is easier to avoid being trapped in inefficient 'battles of anecdotes'."

My Take

The paper's central lesson is that BVAR and DSGE serve different purposes even within the same institution: BVAR for short-to-medium forecasting, DSGE for credible policy conditioning. The Winkler combination is particularly valuable — it is Bayesian, handles correlated errors between model-based and judgment-based forecasts, and requires only a short error history with prior stabilization. The BVAR used is Villani's steady-state form (WP 181/2005), not the standard Litterman Minnesota prior; the 2% inflation prior on the steady state is likely what drives medium-horizon forecast quality. The paper should be read alongside Villani (2008) for the full methodological exposition of the steady-state Gibbs sampler.