I am a econometrics newbie. I would like to ask a question. In the standard Hausman Taylor model, we need to specify exogeneous/endogenous variables for estimation.
However, suppose we have missing data. For example , female data are more likely to be missing and only the most capable one are in the dataset. Lets assume some wild theory that females may take on motherhood duties and only the most capable females remain in the workforce and have higher wage. As a result, female in the dataset with missing data may be correlated with skills which is in the unobservable causing endogeneity problem.
Theoretically, female has no relationship with skills and are truly exogenous. But can a variable become endogenous due to data missing systematically ? And this needs to be corrected in the Hausman Taylor specification (e.g., make FEM an endogeneous variable) if the dataset suffers this problem ?
Thanks ! thanks !