with Todd E. Clark (Johns Hopkins University, Federal Reserve Bank of Cleveland)

• paper: pdf

• slides: pdf

Abstract: This paper develops a new, direct approach to entropic tilting of model-based predictive distributions to match histogram forecasts provided in the U.S. Survey of Professional Forecasters (SPF). We focus on tilting to histogram probabilities directly, rather than to moments of fitted distributions. We reformulate the single-histogram tilting problem and derive a novel analytic characterization for the multiple-histogram case, with iterative solutions via Iterative Proportional Fitting. Application to quarterly real-time forecasts of major macroeconomic aggregates from a Bayesian vector autoregression with time-varying volatility shows that tilting to SPF histograms significantly improves on the model's baseline forecasts, particularly during periods around the Great Recession and the COVID-19 pandemic. Crucially, entropic tilting not only improves accuracy for those model variables for which histogram targets are available but also for other model variables for which SPF targets are not available. 

Accepted for presentation at the Real-Time Economics Conference at Bundesbank in 2025

De Polis, Melosi and Petrella: "The Taming of the Skew: Asymmetric Inflation Risk and Monetary Policy" (@ESCBcluster1, 2026)

• • My discussion slides: pdf

  • their  paper: pdf

  • discussed at the ESCB cluster 1 workshop, Banque de France, Mar 26-27, 2026

with Andrea Carriero (Queen Mary University of London, U Bologna), Todd Clark (Federal Reserve Bank of Cleveland), Massimiliano Marcellino (Bocconi, IGIER and CEPR)

• Quantiative Economics 2025, Vol 16 (3): 759-822

• slides: pdf updated version of our presentation at NBER SI 2023)

• earlier Bundesbank DP at IDEAS, earlier Cleveland Fed WP version: https://doi.org/10.26509/frbc-wp-202109

• replication code (github) and https://doi.org/10.5281/zenodo.14814807 

Abstract: Vector autoregressions (VARs) are popular for forecasting, but ill-suited to handle occasionally binding constraints, like the effective lower bound on nominal interest rates. We examine reduced-form ``shadow-rate VARs'' that model interest rates as censored observations of a latent shadow-rate process and develop an efficient Bayesian estimation algorithm that accommodates large models.  When compared to a standard VAR, our better-performing shadow-rate VARs generate superior predictions for interest rates and broadly similar predictions for macroeconomic variables.  We obtain this result for shadow-rate VARs in which the federal funds rate is the only interest rate and in models including additional interest rates. Our shadow-rate VARs also deliver notable gains in forecast accuracy relative to a VAR that omits shorter-term interest rate data in order to avoid modeling the lower bound.

Earlier versions of this paper were also earlier circulated under the title “Shadow-Rate VARs.”

with Todd E. Clark (FRB Cleveland), and Gergely Ganics (Banco de España)

• https://doi.org/10.1162/rest_a_01565 

• latest draft: pdf and online appendix: pdf

• Slides: pdf (updated version of our presentation at NBER SI 2022)

• replication code: https://github.com/elmarmertens/ClarkGanicsMertensSPFfancharts and REStat Dataverse

Abstract: We develop models that take point forecasts from the Survey of Professional Forecasters (SPF) as inputs and produce estimates of survey-consistent term structures of expectations and uncertainty at arbitrary forecast horizons. Our models combine fixed-horizon and fixed-event forecasts, accommodating time-varying horizons and availability of survey data, as well as potential inefficiencies in survey forecasts. The estimated term structures of SPF-consistent expectations are comparable in quality to the published, widely used short-horizon forecasts. Our estimates of time-varying forecast uncertainty reflect historical variations in realized errors of SPF point forecasts, and generate fan charts with reliable coverage rates.

Parts of this paper were earlier circulated under the title “Constructing the Term Structure of Uncertainty from the Ragged Edge of SPF Forecasts.”