Difference between truncreg and tobit on a truncated data set

[Xu Zhang]

Dear All,

I have a question about the difference between tobit and truncreg. The data set includes a censored dependent variable, say wage. I assume the underlying model is a tobit model. But due to some contamination issues, I do not want to use the censored observations in the regression, but just use the uncensored observations (i.e. wage > 0). If I drop the censored observations (wage == 0), I assume that I made the censored data set to a truncated data set. Thus, I tried the following two lines.

tobit wage age education if wage > 0,ll(0)
truncreg wage age education if wage > 0, ll(0)

I expected the results should be the same from the two lines. But it turns out that the estimated results differ a little bit. Could anyone explain why there exist a difference between the two?

Thank you,
Xu

[Joao Santos Silva]

Dear Xu,

Running Tobit just with positive observations is the same as doing OLS on the positives; clearly this does not account for the truncation. If you check the likelihood functions of the models you are estimating, this should be clear.

All the best,

Joao

[Xu Zhang]

Oh, I see. Thank you, Joao. This is very helpful.