Mixture Models for Predictive Densities

Abstract

Understanding inflation expectations is central to monetary policy analysis, particularly in emerging economies, where uncertainty and structural change can amplify forecasting challenges. Surveys of professional forecasters increasingly rely on histogram-based density forecasts to capture not only point predictions but also the full distribution of expected inflation. Aggregating these density forecasts provides a richer characterization of the shape, dispersion, and uncertainty embedded in expert expectations. This study analyzes quarterly inflation expectations reported by Colombian professional forecasters from January 2016 to October 2023. We construct measures of disagreement and uncertainty at both the individual and aggregate levels, documenting their evolution through periods of macroeconomic stability, policy shifts, and the inflationary surge following the covid-19 pandemic. We synthesize individual predictive densities using the Bayesian predictive synthesis (BPS) framework with time-varying mixture weights that adapt to changes in relative forecast performance over time.