  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.
