Revisiting useful approaches to data-rich macroeconomic forecasting

This paper revisits a number of data-rich prediction methods that are widely used in macroeconomic forecasting, such as factor models and Bayesian shrinkage regression, and compares these methods with a lesser known alternative: partial least squares regression. In this method, linear, orthogonal combinations of a large number of predictor variables are constructed such that the linear combinations maximize the covariance between the target variable and each of the common components constructed from the predictor variables. We provide a theorem that shows that when the data comply with a factor structure, principal components and partial least squares regressions provide asymptotically similar results. We also argue that forecast combinations can be interpreted as a restricted form of partial least squares regression. Monte Carlo experiments confirm our theoretical results that partial least squares regression performs at least as well as principal components regression and rivals Bayesian regression when the data have a factor structure. These experiments also indicate that when there is no factor structure in the data, partial least square regression outperforms both principal components and Bayesian regressions. Finally, we apply partial least squares, principal components, and Bayesian regressions on a large panel of monthly U.S. macroeconomic and financial data to forecast CPI inflation, core CPI inflation, industrial production, unemployment, and the federal funds rate across different subperiods. The results indicate that partial least squares regression usually has the best out-of-sample performance when compared with the two other data-rich prediction methods.