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st: LR-Test Tobit vs. Heckman two step

Subject   st: LR-Test Tobit vs. Heckman two step
Date   Wed, 13 Feb 2008 17:06:14 +0100

 Dear Statalist Members

I am currently doing research on comparing 3 types of models: Tobit Model, Heckman two step model, and Craggs Two Part model. I have to compare this 3 types of models as it is my research design my prof gave me. I think Heckman does not fit very well, but in the literature it has been used simultanously with the tobit model so there is no way to get around this problem.

My Problem: 
Following Amemiya(Tobit Models a Survey, 1984), the Tobit Model is a special case of the Heckman Model. If in the Heckman Model the same set of explanatory variables is used for selection and for the outcome estimation,then, the Heckman Model should reduce to the Tobit Model. So the two models are nested and a likelihood ratio test could be used to compare the two models.

I am not shure if this is the case. If Heckman is estimated with the same set of explanatory variables, than the model suffers from identification. What does this exactly mean for the results estimated?
As I understand Heckman was designed to model sample selection problems, contrary to this, my tobit model is a corner solution model. so the zeros are "true" zeroes, but the heckman should treat them as "not true zeroes but not observed" so the estimates for the heckman model should be higher than those of the tobit model in my opinion.

In my opinion to have tobit as a nested heckmanmodel the same set of explanatory variables is needed AND inverse Mills ratio should be zero as there is no selction problem then.

Is my argument ok? I would appreciate any help with this problem, as every textbook tells different stories. In my opinion Heckman and tobit are not nested the way Amemiya proposed it.  

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