Quantile Factor Models

Abstract

Quantile factor models (QFM) represent a new class of factor models for high‐dimensional panel data. Unlike approximate factor models (AFM), which only extract mean factors, QFM also allow unobserved factors to shift other relevant parts of the distributions of observables. We propose a quantile regression approach, labeled Quantile Factor Analysis (QFA), to consistently estimate all the quantile‐dependent factors and loadings. Their asymptotic distributions are established 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. QFA estimation remains valid even when the idiosyncratic errors exhibit heavy‐tailed distributions. An empirical application illustrates the usefulness of QFA by highlighting the role of extra factors in the forecasts of U.S. GDP growth and inflation rates using a large set of predictors.

Quantile Regression with Generated Regressors

“…In particular, Xiao and Koenker (2009) develop QR with GR in the context of GARCH models. Chen et al (2015) propose a quantile factor model. Lee (2007) applied a control function approach to generate instruments and resolve the endogeneity, and Ma and Koenker (2006) develop QR for recursive structural equation models.…”

Common Correlated Effects Estimation of Heterogeneous Dynamic Panel Quantile Regression Models

“…Assumption 1 is similar to Assumption A3 in Ando and Bai (2017) and Assumption 4.iii in Chen, Dolado and Gonzalo (2017). The assumption is slightly weaker than other assumptions in the literature since it can allow for forms of serial dependence, as explicitly stated later in Assumptions 9 and 11.…”

“…Slope heterogeneity in quantile regression is investigated in . In related work, Ando and Bai (2017) and Chen, Dolado and Gonzalo (2017) investigate quantile factor models. With the exception of and Arellano and Bonhomme (2016), the literature has focused on estimating static models.…”

Factorisable Multitask Quantile Regression

“…However, in a situation with multivariate responses having the same predictors, equation-by-equation quantile regression fails to capture the latent common structure. Factor models have been used for quantile regression with multivariate responses (Ando and Tsay, 2011;Chen, Dolado, and Gonzalo, 2019), but these models do not include the exogenous predictors and the factors are invariant to the quantile level.…”