Finite mixtures of linear quantile regressions with concomitant variables: a simple solution to endogeneity in longitudinal data models

Longitudinal data often give the chance to control for time-constant heterogeneity, which is added to the model formulation via individual-specific effects. Adopting a random effect specification, issues of endogeneity may arise. We discuss quantile regression models for longitudinal data and propose a concomitant variable framework to address endogeneity. Specifically, we assume that mixing proportions are unknown and depend on time-constant covariates, as well as on time-constant levels of time-varying covariates. A multinomial logit specification is considered to model the relation between such proportions and the (potentially) endogenous covariates. This provides a simple, efficient, and general solution to the aforementioned problem. The performance of the proposed model is examined using a simulation study. The results are promising and warrant additional discussion.