I'm working on a a bivariate logistic regression. But I have an endogeneity problem and I want solve it through 2sls with 2 instrumental variables.

My thought was to regress (OLS) in first stage and later a bilogit in second stage. Is this a suitable analysis? Is it a "forbidden regression"? What would be the best option that helps to solve it?

  • 2
    $\begingroup$ If your only question is about (the existence of R) code, it is off topic here. If you have a statistical question about 2sls when 1 stage is a binary variable, please edit to clarify. $\endgroup$ Aug 11, 2017 at 15:36
  • $\begingroup$ I see what you mean. Ok. On other hand, to carry out a 2sls with ols in 1st stage and logit in 2nd is a "forbbiden regression", isn't it? thanks for you answer, gung. $\endgroup$
    – SMD
    Aug 11, 2017 at 15:49
  • $\begingroup$ If you have a statistical question about 2sls when 1 stage is a binary variable, please edit your question to focus on that. Otherwise, this will end up being closed. $\endgroup$ Aug 11, 2017 at 16:00
  • $\begingroup$ I've edited question, gung $\endgroup$
    – SMD
    Aug 11, 2017 at 16:17
  • $\begingroup$ This question is now on topic here. I'm voting to leave open. $\endgroup$ Aug 11, 2017 at 17:14

1 Answer 1


Short answer : No, you can't. That is indeed forbidden regression what you're trying to do.

Possible solutions : some brief discussion, google the keywords to learn more.

  1. Use LPM(linear probability model) - just use regular 2SLS with your data. sounds crazy, but a lot of people do this in economics literature. Make sure that you get the standard errors right.
  2. MLE - specify the distribution of your first stage equation, jointly with the second stage binary outcome equation. (i.e. use probit model with bi-variate normal errors)
  3. Control function approach - basically add the residuals from the first stage equation to covariates in the second stage.

for details, see Blundell & Powell(2004) or Rivers & Vuong(1988).

  • $\begingroup$ If I could, I would rate your answer as useful. Thank you so much $\endgroup$
    – SMD
    Nov 17, 2017 at 20:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.