Sparse Macro Factors

Abstract

We use machine-learning techniques to estimate sparse principal components (PCs) for 120 monthly macroeconomic variables from the FRED-MD database. Each sparse PC is a sparse linear combination of the underlying macroeconomic variables, allowing for their economic interpretation. Innovations to the sparse PCs constitute a set of sparse macro factors. Robust tests indicate that sparse macro factors corresponding to yields and housing earn statistically and economically significant risk premia. A three-factor model comprised of the market factor and mimicking portfolio returns for the yields and housing factors performs well compared to leading multifactor models in explaining numerous anomalies.

Keywords: Sparse principal component analysis, FRED-MD, Risk premia, Factor-mimicking portfolio, Three-pass regression, Multifactor models

JEL Classification: C38, C55, C58, E44, G12