In a model with binary endogenous w with IVs z,
y = a + b*w + x*g + u
E(u|x,z) = 0
what are the relative merits of usual 2SLS, with a linear first stage for w, versus using a probit for w and then using probit fitted values as IVs in the second stage?
#metricstotheface
y = a + b*w + x*g + u
E(u|x,z) = 0
what are the relative merits of usual 2SLS, with a linear first stage for w, versus using a probit for w and then using probit fitted values as IVs in the second stage?
#metricstotheface
Both are consistent under standard identification assumptions. Using a probit first stage could be more efficient. Those are the optimal IVs if (1) Var(u|x,z) is constant and (2) P(w = 1|x,z) = probit. It's consistent without either assumption, just like 2SLS.
As shown by my former student Ruonan Xu, the probit first stage can help with a weak IV problem:
xuruonan.weebly.com/uploads/1/2/7/…
The fitted probit fitted values should be IVs, not regressors. And robust standard errors should be used, as always.
xuruonan.weebly.com/uploads/1/2/7/…
The fitted probit fitted values should be IVs, not regressors. And robust standard errors should be used, as always.
If the slope on w is heterogeneous, 2SLS and IV with probit fitted values identify different "weighted treatment effects." I'd try to be less vague but I'd soon be out of my depth.
• • •
Missing some Tweet in this thread? You can try to
force a refresh
