Endogeneity issues in mixed models

The paper explores the issue of endogeneity in mixed models, focusing on the case where the random effects are correlated with a level 1 covariate in a simple linear random intercept model. This type of endogeneity arises from a wrong equality restriction on the between-cluster and within-cluster slopes. We show that estimation of the between-cluster slope is affected by measurement error and we propose a correction to obtain consistent estimates. Then we compare some estimators proposed in the literature. A small simulation illustrates the main findings.