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Title: Quantile factor models Authors:  Jesus Gonzalo - University Carlos III de Madrid (Spain) [presenting]
Juan jose Dolado - European Institute Florence and UC3M (Spain)
Liang Chen - Shanghai University of Finance and Economics (China)
Abstract: A novel concept is introduced: Quantile Factor Models (QFM), where a few unobserved common factors may affect all parts of the distributions of many observed variables in a panel data set of dimension $NxT$ . When the factors affecting the quantiles also affect the means of the observed variables, a simple two-step procedure is proposed to estimate the common factors and the quantile factor loadings. Conditions on $N$ and $T$ ensuring uniform consistency and weak convergence of the entire quantile factor loadings processes differ from standard conditions in factor-augmented regressions with smooth object functions. Based on these results, we show how to make inference on the quantile factor loadings in a location-scale shift factor model. When factors affecting the quantiles differ from those affecting the means of the observed variables, we propose an iterative procedure to estimate both factors and factor loadings at a given quantile. Simulation results confirm a satisfactory performance of our estimators in small to moderate sample sizes. In particular, it is shown that the iterative procedure can consistently estimate common factors that cannot be captured by PC estimators. Empirical applications of our methods to stocks and mutual fund returns are considered.