Quantile Factor Models

Quantile FactorModels (QFM) represent a new class of factor models for high-dimensional panel data. Unlike Approximate Factor Models (AFM), where only mean-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 climate, financial and macroeconomic panel data) provide evidence that extra factors shifting quantiles other than the means could be relevant in practice.Financial support from the National Natural Science Foundation of China (Grant No.71703089), The Open Society Foundation, The Oxford Martin School, the Spanish Ministerio de Economía y Competitividad (grants ECO2016-78652 andMaria de Maeztu MDM 2014-0431), Bank of Spain (ER grant program), and MadEco-CM (grant S205/HUM-3444) is gratefully acknowledged