Quantile Factor Models

TL;DR

Quantile Factor Models extend traditional factor analysis by capturing distribution-shifting factors across different quantiles, with a novel estimation method and applications demonstrating their practical relevance.

Contribution

The paper introduces Quantile Factor Analysis, a new estimation approach for quantile-dependent factors, along with model selection criteria and theoretical properties, applicable even with heavy-tailed errors.

Findings

QFM can recover unobserved distribution-shifting factors.

QFA remains valid with heavy-tailed error distributions.

Empirical applications show quantile-shifting factors are relevant in practice.

Abstract

Quantile Factor Models (QFM) represent a new class of factor models for high-dimensional panel data. Unlike Approximate Factor Models (AFM), where only location-shifting factors can be extracted, QFM also allow to recover unobserved factors shifting other relevant parts of the distributions of observed variables. A quantile regression approach, labeled Quantile Factor Analysis (QFA), is proposed to consistently estimate all the quantile-dependent factors and loadings. Their asymptotic distribution is then derived using a kernel-smoothed version of the QFA estimators. Two consistent model selection criteria, based on information criteria and rank minimization, are developed to determine the number of factors at each quantile. Moreover, in contrast to the conditions required for the use of Principal Components Analysis in AFM, QFA estimation remains valid even when the idiosyncratic errors have heavy-tailed distributions. Three empirical applications (regarding macroeconomic, climate and finance panel data) provide evidence that extra factors shifting the quantiles other than the means could be relevant in practice.