Should I use 2SLS estimator if the suspected endogenous variable is exogenous?

[Matthew Williams]

Hi all,

I have a question regarding choosing between OLS and 2SLS estimators. Specifically, in my field (perhaps other fields as well), it is well known that maternal education is potentially endogenous to child health. However, in my case, results from standard tests (I used the test provided in ivreg2 (SSC) command and I also re-test by using the control function as suggested by Prof. Wooldridge) showed that maternal education could be treated as exogenous. Normally, for a standard presentation, one would want to report both OLS and IV estimates and discuss differences between the two. But, I am wondering what would happen to IV estimates if the suspected endogenous variable is exogenous?

Thank you.

[Sebastian Kripfganz]

The 2SLS estimator is still consistent if the endogenous variable is exogenous. It is just inefficient.

[Jackson Monroe]

2SLS is consistent but has very hairy finite sample properties. Unless you have infinite data (if so please share) I'd hesitate to treat 2SLS as merely inefficient OLS.

[Matthew Williams]

The 2SLS estimator is still consistent if the endogenous variable is exogenous. It is just inefficient.

2SLS is consistent but has very hairy finite sample properties. Unless you have infinite data (if so please share) I'd hesitate to treat 2SLS as merely inefficient OLS.

Thank you both. However, may I ask one follow-up question, what does "inefficient" mean in this case? Thanks.

[Maxence Morlet]

Efficiency = precise estimation of your parameter of interest (generally coefficient or standard error). Translated into English in this context, an efficient estimator would be one with a relatively narrow confidence interval.