A comparative study on estimation methods to deal with the endogeneity in linear random-intercept models with an extension

In this paper, we investigate estimation methods to deal with situations where random intercepts are associated to time-varying covariates in the context of linear mixed models. First, a review of previous ways to deal with this so-called endogeneity issue is presented, then a new method based on shared random effects is proposed. Simulation studies and an empirical example are utilized to assess the performance of our proposed method. It is shown that our new approach is more efficient than most competitors and is robust to the misspecification of the random-effects distributions.