Consistent Instrumental Variable Estimation with Endogenous Instruments

The purpose of this paper is to help dispel the common textbook misperception that consistent instrumental variable estimation requires exogenous instruments. A necessary and sufficient condition is presented that implies Stock and Watson's (2010, App. 12.6) conditional mean independence condition, as well as the textbook condition that instruments and controls be exogenous. The condition herein, when compared to the conditional mean independence condition, allows more cases of consistent estimation with endogenous instruments. Simulations are provided