High-Dimensional Macroeconomic Forecasting Using Message Passing Algorithms
89 Pages Posted: 15 Nov 2018 Last revised: 18 Sep 2019
Date Written: June 21, 2019
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.
Keywords: High-Dimensional Inference, Factor Graph, Belief Propagation, Bayesian Shrinkage, Time-Varying Parameter Model
JEL Classification: C11, C22, C52, C55, C61
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