High-dimensional macroeconomic forecasting using message passing algorithms
This provides a scalable solution for economists and policymakers dealing with large datasets and structural changes, though it is incremental in applying existing message passing techniques to econometrics.
The paper tackles the problem of forecasting high-dimensional macroeconomic data with time-varying parameters by proposing a Bayesian method that transforms the model into a static regression and uses message passing algorithms for efficient estimation, achieving strong performance in forecasting U.S. price inflation.
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.