In this note I investigate which alternatives are detected by over-identifying restrictions tests, when we test the null hypothesis that all excluded instruments are exogenous. A reformulated null hypothesis will result in a consistent test.
De Blander, R. (2008). Which Null Hypothesis Do Overidentification Restrictions Actually Test? Economics Bulletin, 3(76), 1-9. https://hdl.handle.net/2078.5/149369 (Original work published 2008)