I assumed you would need to do an IV probit in this scenario, but it was not used in this AER paper - Children and Their Parents' Labor Supply (Angrist and Evans, 1998).
The first stage is estimated using OLS:
- more than 2 kids(1 or 0) = IV(1 or 0) + error
The second stage is:
- labor force participation (1 or 0) = more than two kids (1 or 0) + error
These are all estimated using regular 2SLS, which involves OLS, and I thought that would not be appropriate?
The second stage uses different dependent variables which are usually continuous, but the first stage is always OLS with a dependent variable dummy. Why is this something that is okay for the first stage of a 2SLS?