“Quantile Factor Models”

Inspired by the generalization of linear regression to quantile regression (QR) models, this paper proposes a new generation of factor structures, labelled Quantile Factor Models (QFM), which extends conventional factor extraction models to a QR framework for high-dimensional panel data. In contrast to standard approximate factor models (AFM) which only retrieve mean-shifting factors, the estimation analysis of QFM developed in the paper allows to identify and estimate hidden common features that may shift characteristics (moments or quantiles) other than the means of the joint distribution of the variables in big panel data sets. In particular, the number of factors and its loadings are allowed to vary across the distribution of each unit in the panel.

Since the relevance of these features has been recently highlighted in the empirical finance, macro, and micro literatures, QFM provide solid econometric foundations of these findings . The proposed estimation approach of QFM allows to consistently estimate the number of factors at each quantile as well as draw inference on the estimated quantile-dependent objects in the factor structure whose average rates of convergence and asymptotic distributions are derived. As an empirical illustration of the usefulness of QFM, we provide evidence showing that extra quantile factors can significantly improve the density forecasting of inflation and GDP growth using a large panel of U.S. macro variables. Other applications (finance, climate, etc.) can be found in the working paper version.

The paper, “Quantile Factor Models” published in the March 2021 issue of Econometrica, concludes by mentioning some lines of research that QFM has opened: Dynamic QFM, QF Augmented Regressions, New approach for causality in high-dimensional panel data, etc.