Estimation of characteristics-based quantile factor models

This paper studies the estimation of characteristics-based quantile factor models where the factor loadings are unknown functions of observed individual characteristics, and the idiosyncratic error terms are subject to conditional quantile restrictions. We propose a three-stage estimation procedure that is easy to implement and has nice properties. The convergence rates, the limiting distributions of the estimated factors and loading functions, plus a consistent selection criterion for the number of factors at each quantile are derived under general conditions. Our proposed estimators are shown to work satisfactorily when: (i) the idiosyncratic errors have heavy tails, (ii) the time dimension of the panel dataset is not large, and (iii) the number of factors differs from the number of characteristics. Further, a consistent estimation method based on quantile factor analysis and sieve regression is proposed when the factor loadings depend on additional unobserved characteristics. Monte Carlo simulations and an empirical application aimed at estimating the loading functions of the daily returns of a large panel of S&P 500 index securities help illustrate these properties.