In-sample Inference and Forecasting in Misspecified Factor Models

This paper considers in-sample prediction and out-of-sample forecasting in regressions with many exogenous predictors. We consider four dimension reduction devices: principal compo- nents, Ridge, Landweber Fridman, and Partial Least Squares. We derive rates of convergence for two representative models: an ill-posed model and an approximate factor model. The theory is developed for a large cross-section and a large time-series. As all these methods depend on a tuning parameter to be selected, we also propose data-driven selection methods based on cross- validation and establish their optimality. Monte Carlo simulations and an empirical application to forecasting ináation and output growth in the U.S. show that data-reduction methods out- perform conventional methods in several relevant settings, and might e§ectively guard against instabilities in predictorsíforecasting ability.