Predictive Synthesis under Sporadic Participation: Evidence from Inflation Density Surveys

TL;DR

This paper tackles the challenge that irregular forecaster participation creates artificial shifts in density forecasts. It introduces a turnover-aware Bayesian predictive synthesis (BPS) that assigns a latent predictive state to every forecaster and updates the aggregated distribution coherently using only observed forecasts, avoiding renormalization and ad hoc imputations. The approach derives explicit entry and exit operators within a Gaussian BPS framework to preserve a fixed latent-state dimension and ensure smooth, interpretable dynamics in forecaster influence. Applied to the ECB SPF inflation densities, the method delivers substantially better density calibration and notably stronger gains during periods of high turnover, with point forecasts improving mainly in volatile regimes. The unemployment-rate extension confirms the method’s robustness and suggests broad applicability to other sporadic panels, offering policy-relevant improvements in real-time uncertainty assessment.

Abstract

Central banks rely on density forecasts from professional surveys to assess inflation risks and communicate uncertainty. A central challenge in using these surveys is irregular participation: forecasters enter and exit, skip rounds, and reappear after long gaps. In the European Central Bank's Survey of Professional Forecasters, turnover and missingness vary substantially over time, causing the set of submitted predictions to change from quarter to quarter. Standard aggregation rules -- such as equal-weight pooling, renormalization after dropping missing forecasters, or ad hoc imputation -- can generate artificial jumps in combined predictions driven by panel composition rather than economic information, complicating real-time interpretation and obscuring forecaster performance. We develop coherent Bayesian updating rules for forecast combination under sporadic participation that maintain a well-defined latent predictive state for each forecaster even when their forecast is unobserved. Rather than relying on renormalization or imputation, the combined predictive distribution is updated through the implied conditional structure of the panel. This approach isolates genuine performance differences from mechanical participation effects and yields interpretable dynamics in forecaster influence. In the ECB survey, it improves predictive accuracy relative to equal-weight benchmarks and delivers smoother and better-calibrated inflation density forecasts, particularly during periods of high turnover.

Figures (9)

• Figure 1: Participation of expert forecasters over time. Left panel: participation of the full panel. Right panel: participation of the subset panel used for analysis. Light gray indicates inactivity and red denotes active contributions.
• Figure 2: Descriptive characteristics of the central-bank forecasting panel.
• Figure 3: Correlation matrix of experts' forecast errors.
• Figure 4: One-year-ahead predictive accuracy of the proposed coherent Bayesian method compared with equal weights. Panel (a) tracks the evolution of RMSE in levels, and panel (b) reports the cumulative LPDR relative to the equal-weight benchmark.
• Figure 5: Evolution of posterior coefficients under different correlation and prior specifications. The coherent BPS model yields smooth, interpretable paths even in the presence of frequent entry and exit.