Macroeconomic Forecasting for the G7 countries under Uncertainty Shocks

TL;DR

The paper tackles macro forecasting for the G7 under pervasive uncertainty by introducing SZBVARx, a Sims–Zha Bayesian VAR with four exogenous uncertainty drivers (EPU, GPR, USEMV, USMPU). It blends wavelet coherence (time-frequency transmission) with nonlinear local projections (state-dependent impulse responses) and Bayesian predictive distributions to deliver robust, regime-aware forecasts. Empirical results show SZBVARx outperforms 14 benchmarks across 12- and 24-month horizons, with statistically significant improvements confirmed by MCB, DM, and GW tests, and credible intervals that provide reliable uncertainty quantification. The framework offers policy-relevant, regime-conditioned projections and scenario analysis tools, supporting risk management and forward guidance in uncertain environments, while remaining interpretable and computationally tractable for policymakers. Potential extensions include incorporating alternative uncertainty measures, composite regime indicators, and real-time nowcasting adjustments, with applicability to other economies beyond the G7.

Abstract

Accurate macroeconomic forecasting has become harder amid geopolitical disruptions, policy reversals, and volatile financial markets. Conventional vector autoregressions (VARs) overfit in high dimensional settings, while threshold VARs struggle with time varying interdependencies and complex parameter structures. We address these limitations by extending the Sims Zha Bayesian VAR with exogenous variables (SZBVARx) to incorporate domain-informed shrinkage and four newspaper based uncertainty shocks such as economic policy uncertainty, geopolitical risk, US equity market volatility, and US monetary policy uncertainty. The framework improves structural interpretability, mitigates dimensionality, and imposes empirically guided regularization. Using G7 data, we study spillovers from uncertainty shocks to five core variables (unemployment, real broad effective exchange rates, short term rates, oil prices, and CPI inflation), combining wavelet coherence (time frequency dynamics) with nonlinear local projections (state dependent impulse responses). Out-of-sample results at 12 and 24 month horizons show that SZBVARx outperforms 14 benchmarks, including classical VARs and leading machine learning models, as confirmed by Murphy difference diagrams, multivariate Diebold Mariano tests, and Giacomini White predictability tests. Credible Bayesian prediction intervals deliver robust uncertainty quantification for scenario analysis and risk management. The proposed SZBVARx offers G7 policymakers a transparent, well calibrated tool for modern macroeconomic forecasting under pervasive uncertainty.

Figures (35)

• Figure 1: Scale-wise FDR-corrected wavelet coherence spectra for Canada (Jan, 1995 – Mar, 2022), displaying Unemployment Rate, REER, SIR, Oil Price (WTI), and CPI Inflation against EPU, GPR, USEMV, and USMPU. Each subplot visualizes the time-frequency coherence between a macroeconomic variable (y-axis: Scale; x-axis: Frequency) and an uncertainty index, with warm colors (red/yellow) indicating intervals of high, statistically significant co-movement after FDR correction. The direction of phase arrows indicates lead-lag relationships: rightward arrows mean the series move in phase; leftward, in anti-phase; upward arrows signify the uncertainty index leads; downward, that it lags. Shaded regions inside the cone of influence reflect reliable coherence, while grid consistency enables robust cross-variable and cross-period comparison. The level of significance ($\alpha$) for the FDR adjustment is set at 10%.
• Figure 2: Impulse response functions (nonlinear local projections) of Unemployment Rate, REER, SIR, Oil Price (WTI), and CPI Inflation to EPU, GPR, USEMV, and USMPU shocks for Canada (high-rate regime). Each row shows responses of a macro variable; each column, a distinct uncertainty shock. Solid blue lines depict IRFs with 95% confidence bands (grey). The x-axis is horizon (months), the y-axis the response magnitude. Compare responses by reading across rows (by variable) or down columns (by shock); zero response is marked by the dotted line.
• Figure 3: IImpulse response functions (nonlinear local projections) of Unemployment Rate, REER, SIR, Oil Price (WTI), and CPI Inflation to EPU, GPR, USEMV, and USMPU shocks for Canada (low-rate regime). Each row shows responses of a macro variable; each column, a distinct uncertainty shock. Solid orange lines depict IRFs with 95% confidence bands (grey). The x-axis is horizon (months), the y-axis the response magnitude. Compare responses by reading across rows (by variable) or down columns (by shock); zero response is marked by the dotted line.
• Figure 4: Multiple comparisons with the best (MCB) plots for G7 economies across 12-month (semi-long-term) ahead and 24-month (long-term) ahead forecasting horizons, ranking algorithms by RMSE metric. Key indicators: Unemployment Rate, REER, SIR, Oil Price (WTI), and CPI Inflation. Labels (e.g., SZBVARx–2.71) denote model identifiers and their mean ranks, where lower values indicate superior out-of-sample predictive accuracy.
• Figure 5: Murphy diagram difference plots comparing SZBVARx forecasting performance against VARx and CatBoostx baselines across 12-month and 24-month-ahead forecast horizons for Canada. Panels in the first and second columns correspond to the 12-month horizon, while panels in the third and fourth columns display the results for the 24-month horizon. The analysis covers five key macroeconomic indicators: Unemployment Rate, REER, SIR, Oil Price (WTI), and CPI Inflation. Each subplot displays extremal score differences with 90% HAC-based confidence bands (gray shaded areas) across threshold parameter values. Negative differences indicate superior SZBVARx performance, while the magnitude reflects the strength of the performance advantage at each decision threshold.