Endogenous variables that aren't endogenous

[Margaret Dalziel]

If you (or reviewers) suspect a variable is endogenous, and you find a valid instrument and tests show that the variable was not endogenous, then do you just report the OLS or should you also report the IV results?

[FernandoRios]

I would say, show OLS, reporting the test showing it was exogenous. I would also include either as an appendix, or for the reviewer only information.
As a reviewer, I would appreciate you took the time to verify my concern, but i also understand that OLS (if X are exogenous) is better than IV.

[Joro Kolev]

Finding a valid instrument is always very difficult. If you have found a good instrument, you can report both IV and OLS. One thing is whether the two sets of estimates--IV and OLS--are statistically different, another thing is whether they are different in economically important way.

Note also that tests cannot "show that the variable was not endogenous." You fail to reject the null that the variable is exogenous. This is the same as failing to reject that a parameter is 0--it does not mean that the parameter is 0, it means that you cannot reject the null that it is 0.