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  • IV 2sls in case of binary endogenous variable

    Hello all.

    I am working with a regression where I have a binary endogenous variable. I have two models:

    ​​​1. Y1= ax1+ bx2+u1 , here y1 is a continuous outcome, X1 binary endogenous variable, X2 set of controls, u1 is error term.

    2. Y2= cx1+ dx2+u2 , here y2 is a binary outcome, X1 binary endogenous variable, X2 set of controls, u2 is error term.

    I have an instrument z for X1. I will estimate these two models separately.

    My concern: ivregress 2sls y1 X2 (X1=z) , this command as far as I know carries out the 2sls procedure when both x1 and y1 are continuous. Which is not my case.

    For 1, my first stage regression will be probit and 2nd stage ols, What will be appropriate command in this case?
    Does this work?

    probit X1 X2 z
    Predict phat
    Ivregress 2sls y1 X2 ( X1=phat)


    For 2, first and 2nd stage regression both will be probit, what is appropriate command to carry these out in Stata?
    I have no clue about this one. Any help is appreciated.

    ​​​​​​
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