Hello econometricians,
I am working on a project, which involves:
- structural equation: y = beta0 + beta1*x1 + beta2*z2 + beta3*z3 + u
All values of y are greater or equal to 0.
There is some possible correlation between x1 and u (endogeneity).
- reduced-form equation: x1 = alpha0 + alpha1*z4 + alpha2*z5 + v
x1 is a binary variable
In order to account for endogeneity in x1 and the nonnegative nature of y, I attempt to use control function method, which involves:
- estimating reduced-form equation of x1 by using probit, then take the residuals value and call it vhat.
- steps to predict residuals vhat: (1) calculate fitted values using command "predict yhat" (2) generate vhat using command "gen vhat=y-yhat."
- estimating the structural equation of y using tobit, this equation involves vhat, x1, z2 and z3 as regressors.
However, I've been getting results that are very weird looking (2SLS generates completely different results compared to the control function using probit and tobit, extremely wide confidence interval and large standard errors). I also run into the problem of vhat=y-yhat=0, this makes me unable to proceed to tobit properly.
I wonder if my methods are incorrect. I've been lurking here for a while and come across the concept of "forbidden regression." Does the method I am using fall under the problem of forbidden regression?
Any clarifications would be much appreciated. Thank you.
I am working on a project, which involves:
- structural equation: y = beta0 + beta1*x1 + beta2*z2 + beta3*z3 + u
All values of y are greater or equal to 0.
There is some possible correlation between x1 and u (endogeneity).
- reduced-form equation: x1 = alpha0 + alpha1*z4 + alpha2*z5 + v
x1 is a binary variable
In order to account for endogeneity in x1 and the nonnegative nature of y, I attempt to use control function method, which involves:
- estimating reduced-form equation of x1 by using probit, then take the residuals value and call it vhat.
- steps to predict residuals vhat: (1) calculate fitted values using command "predict yhat" (2) generate vhat using command "gen vhat=y-yhat."
- estimating the structural equation of y using tobit, this equation involves vhat, x1, z2 and z3 as regressors.
However, I've been getting results that are very weird looking (2SLS generates completely different results compared to the control function using probit and tobit, extremely wide confidence interval and large standard errors). I also run into the problem of vhat=y-yhat=0, this makes me unable to proceed to tobit properly.
I wonder if my methods are incorrect. I've been lurking here for a while and come across the concept of "forbidden regression." Does the method I am using fall under the problem of forbidden regression?
Any clarifications would be much appreciated. Thank you.
