Unobserved heterogeneity or measurement errors? Testing for correlated effects with measurement errors

This paper addresses the problem of endogenous regressors due to the presence of unobserved heterogeneity, when this is correlated with the regressors, and caused by regressors' measurement errors. A simple two-stage testing procedure is proposed for the identification of the underlying cause of correlation between regressors and the error term. The statistical performance of the resulting sequential test is assessed using simulated data.