Entropic tilting of forecasts ... Note

Entropic tilting of forecasts to SPF histograms: analytics & applications

We develop a direct approach to incorporating survey density forecasts into model-based predictive distributions. Histogram forecasts from the U.S. Survey of Professional Forecasters (SPF) carry rich nonparametric information about expected outcomes, but existing methods rely on moment-based approximations that discard part of it. We instead tilt entropically to the histogram probabilities themselves, matching them exactly. After reformulating the single-histogram problem, we derive a new analytic characterization of the multiple-histogram case, solved by Iterative Proportional Fitting and applicable to simulated densities from essentially any model. Applying the method to real-time forecasts from a Bayesian VAR with time-varying volatility, we find that tilting to SPF histograms substantially improves accuracy relative to the model’s baseline forecasts, especially during the Great Recession and the COVID-19 pandemic. The gains extend beyond the variables the SPF targets, improving forecasts for other variables in the system as well.