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I have a binary endogenous variable (retirement) with a binary instrumental variable and the final outcome variable is also binary. I run ivreg2 in Stata. I know that ivreg2 might not be optimal to use for a binary endogenous variable. Anyway my question is that when I run a regression, ivreg2 gives me a second-stage coefficient larger than 1. How can I interpret it? Can I interpret it as the effect of retirement?

My concern is that since the retirement is the predicted value from the first stage, I'm not sure how to interpret it.

Any ideas?

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Try using biprobit, with margins to get the marginal effects. This might help you avoid all the LPM nonsense with marginal effects that don't make sense:

webuse school
biprobit (private = i.vote) (vote = loginc logptax years)
margins, dydx(vote) predict(pmarg1) force

These estimates imply that voting for increasing property taxes makes someone 18 percentage points more likely to send their children to private school.

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  • $\begingroup$ To add to this response: Be aware that there are 2 flavors of -biprobit- in Stata. The one you want is the Seemingly Unrelated Bivariate Probit Regression, given by Dimitriy above, and shows the 2 equations with the endogenous variable appearing as a predictor in one and as an outcome in the other equation. The other flavor of -biprobit- ("Bivariate Probit Regression") will not give you what you need. $\endgroup$ Mar 30 '16 at 5:38

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