Hello, I'm in interested in examining the effect of an endogenous dummy variable, D, that on the dependent variable Y. i.e., D has a potential self-selected issue.
If I run:
Yi =αi +βDi+Xλ +ei
β is apparently biased and inconsistent so what I'd like to do is run a two-stage probit model, where in the first stage I use a criterion function:
D*i=Zσ +ei (1)
where Z a vector of exogenous variables that include at least one instrument variable.
Then I plugged the fitted value of D and the inverse mill ratio variable into the structural model:
Yi =αi +β'Dhati +Xλ +τ INVERSEMILL + ei (2)
if τ is significant, there is self-selection issue, then I report coefficient for β'
if τ is not significant, there is no self-selection issue, then using OLS and report coefficient for β is fine.
However, I've been told that this 2SLS with a binary endogenous variable is called Forbidden regression and yields biased and inconsistent estimates of β'. is this model wrong? or what's the solution to an endogenous binary variable.
Thank you very much.
If I run:
Yi =αi +βDi+Xλ +ei
β is apparently biased and inconsistent so what I'd like to do is run a two-stage probit model, where in the first stage I use a criterion function:
D*i=Zσ +ei (1)
where Z a vector of exogenous variables that include at least one instrument variable.
Then I plugged the fitted value of D and the inverse mill ratio variable into the structural model:
Yi =αi +β'Dhati +Xλ +τ INVERSEMILL + ei (2)
if τ is significant, there is self-selection issue, then I report coefficient for β'
if τ is not significant, there is no self-selection issue, then using OLS and report coefficient for β is fine.
However, I've been told that this 2SLS with a binary endogenous variable is called Forbidden regression and yields biased and inconsistent estimates of β'. is this model wrong? or what's the solution to an endogenous binary variable.
Thank you very much.
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