Entropic tilting of forecasts to SPF histograms: analytics & applications

Elmar Mertens and Todd E. Clark

No 3284, Working Paper Series from European Central Bank

Abstract: 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. JEL Classification: C11, C53, E37

Keywords: Bayesian vector autoregression; iterative proportional fitting; predictive densities; relative entropy; survey expectations (search for similar items in EconPapers)
Date: 2026-09
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Persistent link: https://EconPapers.repec.org/RePEc:ecb:ecbwps:20263284

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