Testing the endogeneity hypothesis from Gauss Markov Theorem in OLS regression

[Antonio Carlos Dias]

Dear Stata Community,


I needed help in elaborating code for obtainning an endogeneity test for each of my 8 explanatory variables on wether they are endogenous or exogenous with respect to the error term.
I believe there are two ways of checking this, to which I would ask for help to elaborate code on. Either obtainning the expected value of the residuals conditional on a explanatory variable or having a test that checks wether the explanatory variable at hand is endogenous or exogenous with respect to the error term or residuals.

Thank you in advance.

[Jared Greathouse]

In the strictest sense of the term, the expected value of the error being 0 (the exogeneity assumption) is exactly that: an assumption. You cannot test for it. You can certainly show that two variables are highly correlated, and you can certainly make arguments from theory/stats about why two variables may be endogenous, but as far as I know it isn't possible, outside of synthetic studies and simulations, to literally test or verify this assumption, it is only something you can argue for and gesture to using basic tests.