Hello,
I want to examine the effect of a state program (dummy variable D) on the unemployment rate (Y) . My observation unit is city i.
for OLS, I'd run :
Yi =αi +βDi+Xλ +ei
However, this program is generally located in cities that tend to have a lower unemployment rate. so D is not random and we have a selection bias problem.
Now I can, of course, do the traditional IV approach by finding an instrument of D.
However, I've been told that I could also address this selection bias with Heckman selection model or control function approach.
So first,
(1) do a probit model first to predict the likelihood the city i is being selected to have the program D.
D*i=Zσ +ei (1)
(2) do an OLS with selectivity variable included in the second stage
Yi =αi +β'D +Xλ +τ Selectivity + ei (2)
and my questions are that
(1) is this approach called Heckman correction approach or control function approach?
(3) I know Heckman approach tends to require variables for D=0 are unobservable(Censoring?) . But in my case, variables for D=0 are observable. Can I still use this approach?
(4) Lastly, is the Selectivity variable different than Inverse mill ratio? or is the Selectivity variable just another name for Generalized Residual from a control function approach.
(5) if τ is significantly different from zero, does that mean I have the evidence of endogeneity and I have to report β' which is consistent and unbiased?
Thank you very much.
Alex
I want to examine the effect of a state program (dummy variable D) on the unemployment rate (Y) . My observation unit is city i.
for OLS, I'd run :
Yi =αi +βDi+Xλ +ei
However, this program is generally located in cities that tend to have a lower unemployment rate. so D is not random and we have a selection bias problem.
Now I can, of course, do the traditional IV approach by finding an instrument of D.
However, I've been told that I could also address this selection bias with Heckman selection model or control function approach.
So first,
(1) do a probit model first to predict the likelihood the city i is being selected to have the program D.
D*i=Zσ +ei (1)
(2) do an OLS with selectivity variable included in the second stage
Yi =αi +β'D +Xλ +τ Selectivity + ei (2)
and my questions are that
(1) is this approach called Heckman correction approach or control function approach?
(3) I know Heckman approach tends to require variables for D=0 are unobservable(Censoring?) . But in my case, variables for D=0 are observable. Can I still use this approach?
(4) Lastly, is the Selectivity variable different than Inverse mill ratio? or is the Selectivity variable just another name for Generalized Residual from a control function approach.
(5) if τ is significantly different from zero, does that mean I have the evidence of endogeneity and I have to report β' which is consistent and unbiased?
Thank you very much.
Alex
Comment