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I have a tobit model the looks like Y = cons + B*(X) + error. This model is estimated twice on two different samples. I want to be able to test if, say, B is different across the two models (the sample A model vs the sample B model).

I have done this before for logit models using two approaches that yielded the same results. My issue is that these two approaches are not matching when using the tobit model.

Approach 1:

I stack the two samples. If SA is a dummy that is 1 when sample A and SB is a dummy that is one when Sample B then I estimate:

Y = SA + SB + B1*(SA*X) + B2*(SB*X) + error

then I test B1==B2 and done.

Approach 2: Here I use something called seemingly unrelated models. I am using stata, and the procedure involves the following:

estimate Y = cons + B*X + error for sample A

estimates store ...

estimate Y = cons + B*X + error for sample B

estimates store ...

combine the estimates using:

suest sample_A_model sample_B_model

then test the coefficients.

Approaches 1 and 2 show different results. Note that if I set up the regressions so that no values are censored, the results are identical. The problem arises when there are censored values. Any thoughts? Thanks in advance!

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  • $\begingroup$ How do you combine the estimates for the SUR model if they are different samples? $\endgroup$
    – Andy W
    Commented Aug 20, 2011 at 12:59
  • $\begingroup$ Can you reproduce this with auto.dta? $\endgroup$
    – StasK
    Commented Aug 20, 2011 at 17:15
  • $\begingroup$ @AndyW - I would do it as it is outlined in approach 2. In approach 1, this is done by a procedure in STATA, which I think works directly with the matrices. $\endgroup$
    – Bruno
    Commented Aug 20, 2011 at 22:17
  • $\begingroup$ @StasK I can generate data and run the different models. I will go ahead and post the code (here) within the next 3 hours. $\endgroup$
    – Bruno
    Commented Aug 20, 2011 at 22:19

1 Answer 1

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Your approach 1 constrains variances of the error terms to be the same, while your suest approach 2 does not. This may not matter much with linear regression, but it does with censored and other limited dependent variable models.

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  • $\begingroup$ Would robust standard errors solve this (the ones that handle heteroscedastic errors)? I tried and it did not help. I am randomly trying things, and I will let you know if I get lucky. $\endgroup$
    – Bruno
    Commented Aug 20, 2011 at 22:23
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    $\begingroup$ No, robust standard errors are a part of a different story. The tobit model is known to be so sensitive to the underlying assumptions (you would probably find the discussion in Wooldridge's black book, amazon.com/Econometric-Analysis-Cross-Section-Panel/dp/…) that once you admit something is wrong with it (and that's what you imply when using the robust standard errors), you can just as well forget the whole model. $\endgroup$
    – StasK
    Commented Aug 22, 2011 at 18:50

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