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I am trying to implement heckprobit for my dataset. The one issue I am running into is that the stata does not give estimates of the effect of the endogenous binary regressor on the dependent variable in the probit equation. For example, in the example of heckprobit in stata manual, vote (yes or no) is a binary endogenous regressor and is used in the selection equation. However, How do I find the effect of vote on private education (second binary outcomes). Any help is appreciated. Thanks.

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In a bivariate probit model with selection (i.e. heckprob), the first-stage probit model predicts the likelihood of selecting into the sample. Simply put, by running this correction, you are indicating that the outcome variable (i.e. children attending private school) is only observed for when the endogenous regressor (i.e. voting for increase in property taxes) is equal to 1. By definition, if the endogenous regressor is included in the second stage of the correction, no variation in the outcome variable would be observed for when the endogenous regressor = 0, and therefore a coefficient will not be estimated for it.

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  • $\begingroup$ Thanks for the answer. That makes sense. But what if the outcome variable is also observed even when the endogenous regressor is 0. In that case, is there a way to estimate predicted probabilities from the selection equation and use them in the second stage? Heckman 2 stage model does that but the second stage in that model is OLS. Is there a variation for the probit model? $\endgroup$
    – Stan
    Nov 28 '20 at 19:12
  • $\begingroup$ You will have to manually run the selection probit model and calculate the Inverse Mills Ratio, which will then be used as the predictor in the treatment equation. Code to do so: predict probitxb, xb gen val_pdf = normalden(probitxb) gen val_cdf = normal(probitxb) gen lambda = pdf/cdf $\endgroup$
    – Anavir
    Nov 28 '20 at 20:19
  • $\begingroup$ Thanks. But is this approach still valid when the second stage model is Probit as opposed to OLS? Is there any source that confirms that? $\endgroup$
    – Stan
    Nov 28 '20 at 20:26
  • $\begingroup$ Not to my knowledge, but something could be there. You could still run the binary dependent variable in the second stage with OLS while noting the limitations of linear probability models. $\endgroup$
    – Anavir
    Nov 29 '20 at 3:47

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