High-dimensional macroeconomic forecasting using message passing algorithms

arXiv 23 Apr 2020 · Statistics — Methodology · 13 citations (OpenAlex)

arXiv:2004.11485 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper 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 towards 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 (GAMP) 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.

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	Citing paper	Intensity	Mentions	Sections
1	Bayesian Approaches to Shrinkage and Sparse Estimation large A guide for applied econometricians large	0.737	3	2
2	Approximate Bayesian inference and forecasting in huge-dimensional multi-country VARs	0.644	2	2
3	Bayesian dynamic variable selection in high dimensions	0.405	1	1
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5	Real-time Inflation Forecasting Using Non-linear Dimension Reduction Techniques	0.405	1	1
6	General Bayesian time-varying parameter VARs for predicting government bond yields	0.405	1	1
7	The Time-Varying Multivariate Autoregressive Index Model	0.405	1	1
8	Bayesian Modeling of TVP-VARs Using Regression Trees	0.405	1	1
9	Exploring Monetary Policy Shocks with Large-Scale Bayesian VARs\@thefnmark\@footnotetext I would like to thank Martin Bruns, Luca Gambetti, Domenico Giannone, Michele Lenza, Nicolò Maffei-Faccioli, Mirela Miescu, Ivan Petrella, Giorgio Primiceri, Barbara Rossi and Lorenza Rossi for their valuable comments and suggestions. I also thank participants at the University of Lancaster's Workshop on Empirical and Theoretical Macroeconomics, the University of East Anglia “2nd Time Series Workshop”, the Collegio Carlo Alberto conference on “The Economics of Risk: Econometric Tools and Policy Implications”, and seminar participants at Universities of Manchester and Paris Dauphine for their insightful feedback. Any remaining errors are solely my responsibility. Correspondence: Professor of Econometrics, Adam Smith Business School, University of Glasgow, 2 Discovery Place, Glasgow, G11 6EY, United Kingdom	0.405	1	1