Tobit vs Heckman Two Stage Model

[Apoorva Jain]

Dear All,

Greetings!

Recently I was going through a research article wherein the dependent variable is R&D expenditure. This is a censored variable since there was R&D investment for some firms while they were not there for the other firms. Hence the authors handled such a situation using Heckman Two-Stage Model. 

I believe such a scenario can be handled by tobit regression also. I was trying to understand the difference between the two models, however, a clear distinction could not be understood.

It would be really great if someone could share the actual difference between them.

Also, some sources say that the coefficients obtain from tobit regression are more efficient than obtained through Heckman (Gujarati, 2004). Thus, which one is better to use.

I have also attached the article for reference.

Thanks & Regards

Apoorva Jain 

[Miklesh Yadav]

Apoorva,

Yes, this situation can be handled by Tobit regression also. Let me clarify about James Heckman's two steps procedure.

James Heckman's two steps procedure is an alternative to Maximum Likelihood (ML). It is famous in terms of two steps where in step 1, probability of happening (For example: Probability of a consumer owning a house) is calculated on the basis of probit model. Further in step 2, model is estimated adding inverse mills ratio which again calculated from the probit estimate (Inverse mills ratio is of the probability density function to the cumulative distribution function). 

Heckman procedure gives consistent estimates of the parameters but not efficient like ML estimates. Hence, coefficients obtained from tobit regression are more efficient than obtained through Heckman (Gujarati, 2004) because Tobit used ML estimates.  

Now, talking about difference, Tobit model uses ML method for estimation whereas Heckman's uses two different steps (as mentioned above) based on probit model. In majority of the software, ML is used for it.

Note: you can also refer Heckman's paper entitled " Sample Selection Bias as a specification Error", Econometrica , vol 47, pp. 153-161. 

Thanks and Regards

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[Apoorva Jain]

Okay, Thanks alot sir.

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