High-Dimensional Macroeconomic Forecasting Using Message Passing Algorithms

• Published in: Journal of business & economic statistics Vol. 39; no. 2; pp. 493 - 504
• Main Author: Korobilis, Dimitris
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 20.03.2021; Taylor & Francis Ltd
• Subjects: Bayesian shrinkage; Belief propagation; Factor graph; High-dimensional inference; Time-varying parameter model
• ISSN: 0735-0015; 1537-2707
• DOI: 10.1080/07350015.2019.1677472

This article proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility, and exogenous predictors, as an equivalent high-dimensional static regression problem with thousands of covariates. Inference in this specification proceeds using Bayesian hierarchical priors that shrink the high-dimensional vector of coefficients either toward zero or time-invariance. Second, it introduces the frameworks of factor graphs and message passing as a means of designing efficient Bayesian estimation algorithms. In particular, a generalized approximate message passing algorithm is derived that has low algorithmic complexity and is trivially parallelizable. The result is a comprehensive methodology that can be used to estimate time-varying parameter regressions with arbitrarily large number of exogenous predictors. In a forecasting exercise for U.S. price inflation this methodology is shown to work very well. Supplementary materials for this article are available online.