Predictive Synthesis under Sporadic Participation: Evidence from Inflation Density Surveys

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.

💡 Research Summary

The paper tackles a practical problem faced by central banks and other institutions that rely on professional forecasters’ surveys to obtain full predictive density forecasts of inflation. In the European Central Bank’s Survey of Professional Forecasters (SPF), participation is highly irregular: forecasters frequently enter, exit, skip rounds, and may be absent for long periods. Conventional aggregation methods—equal‑weight pooling, renormalisation after dropping missing forecasters, or simple imputation such as last‑observation‑carried‑forward—treat the set of contributors as fixed. When the active set changes, these methods unintentionally alter the conditioning set of the combined density, producing artificial jumps in the mean, variance, and tail probabilities that are unrelated to underlying economic information. Such artifacts can mislead policymakers about inflation risk and hinder proper evaluation of forecaster performance.

To address this, the authors extend the Bayesian Predictive Synthesis (BPS) framework by introducing “coherence‑based entry and exit operators.” Each forecaster j is assigned a latent predictive state θ_{j,t} that evolves over time. When a forecaster’s density is observed, the joint posterior π(θ_t | F_t) is updated via Bayes’ rule, where F_t denotes the set of densities actually reported at time t. If a forecaster is missing, the model retains their latent state and updates it conditionally on the observed subset, without inserting synthetic data. The entry operator injects a new forecaster’s prior into the existing joint prior, while the exit operator marginalises out a departing forecaster, preserving total probability mass. This construction guarantees that the combined predictive distribution p(y_t | F_t)=∫ g(y_t | θ_t) π(θ_t | F_t) dθ_t is always coherent with the information that is truly available.

The authors implement the method on nearly 25 years of quarterly ECB SPF density forecasts for year‑ahead euro‑area inflation. They focus on a “core panel” of 16 forecasters (robustness checks use 20) that exhibits substantial turnover and long gaps. The proposed approach is benchmarked against (i) equal‑weight pooling, (ii) weighted pooling based on inverse MSE, (iii) simple imputation plus equal‑weight, and (iv) a standard BPS model that assumes a fixed panel. Evaluation metrics include mean absolute error (MAE), log‑score, calibration via probability integral transform (PIT) histograms, and the stability of predictive variance and tail probabilities.

Results show that the coherence‑based BPS improves MAE by roughly 6 % and log‑score by about 8 % relative to equal‑weight pooling. The gains are especially pronounced during periods of heightened macroeconomic stress—2008‑09 financial crisis, the COVID‑19 pandemic, and the 2022‑23 energy shock—where the method markedly reduces spurious volatility in forecast dispersion and tail risk. PIT histograms indicate near‑uniformity, confirming superior calibration. Importantly, the combined density’s mean and variance no longer exhibit abrupt jumps at entry or exit dates, allowing policymakers to interpret changes in dispersion as genuine shifts in inflation uncertainty rather than artefacts of panel composition.

The paper contributes three main insights: (1) it formalises the problem of density forecast combination under irregular participation and demonstrates empirically that ad‑hoc fixes can materially distort uncertainty measures; (2) it develops a theoretically grounded, computationally simple coherence‑based adjustment within dynamic BPS that respects the conditional structure of the observed panel; (3) it provides an extensive empirical validation showing that the method yields more accurate and economically interpretable forecasts. The authors argue that the approach is readily extensible to other macro variables (e.g., unemployment) and to private‑sector consensus platforms, and they suggest future work on multivariate extensions and on modelling participation dynamics explicitly.

In sum, by preserving a latent predictive state for each forecaster and updating the joint distribution only with the actually observed densities, the proposed Bayesian predictive synthesis offers a robust solution to the long‑standing issue of sporadic participation in professional survey panels, delivering smoother, better‑calibrated inflation density forecasts that are more useful for real‑time monetary‑policy analysis.