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st: 2SLS with Probit in the first-stage regression
I’d like to do a 2SLS estimation where the first-stage
regression is Probit.
For example, the model is
y = a + b1X1 + b2X2 + u
where X1 is an endogenous binary variable.
I’d like to instrument X1 with Z1 and Z2 where the
first-stage regression is a Probit
X1 = a + b1Z1 + b2Z2 + b3X2 + e
I tried to use ivreg but it seems the first-stage
regression ivreg does is OLS rather than Probit.
Although I can do the first-stage Probit regression
manually and then use the predicted X1 in the
second-stage regression, I don’t think it is accurate
since the OLS standard errors of the second-stage
regression will be incorrect in such a case.
Does Stata has a procedure that does 2SLS with Probit
in the first-stage?
Any suggestions would be greatly appreciated!
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