Seminario Semiparametric Panel Data Models with Observable and Latent Factors

Abstract

We extend static linear factor models within a semiparametric framework by allowing both latent and observable factors to explain the endogenous variable through some loadings that are modeled as unknown individual functions of a vector of covariates. These covariates are exogenous, time-varying, and differ across individuals. By explicitly combining observable and latent factors alongside explanatory variables, our model provides a more flexible representation than traditional factor models. We establish the consistency of the estimated loading functions and the latent factors under “large N and large T” asymptotics. The practical relevance of the proposed methodology is assessed through Monte Carlo simulations and an empirical application to stock returns.