Tobit Regression

[Abdulsalam Alquhaif]

In my research, the dependent variable is limited so I apply Tobit regression. What is the right assumptions for Tobit Regression?

[Abdulsalam Alquhaif]

Is there any different in terms of assumptions between OLS and Tobit regression?

[Carlo Lazzaro]

Abdusalam:
see -help tobit- and related entry in Stata .pdf manual.

[Phil Bromiley]

You should also look up tobit in any descent econometrics text. Generally, it is good to check the Stata documentation and an econometrics text (or even two) says before posting an econometrics question. By the way, the subject index is very helpful - it appears within the index "book" in documentation.

[Joao Santos Silva]

Dear Abdulsalam,

In addition to the excellent advice provided by Phil and Carlo, note that having a limited dependent variable does not imply that you should use Tobit. Also, going more directly to your question, the validity of the Tobit depends on very strong assumptions such as normality and homoskedasticity; OLS is robust to violations of these, Tobit is not.

Best wishes,

Joao

[Weiwen Ng]

Is there any different in terms of assumptions between OLS and Tobit regression?

I'll chime in. I've been doing some reading on the Tobit model myself, as I was introduced to it by my methods professor, who is an econometrician. I'm not in economics or econometrics myself, but I am in health services research.

The key assumption of the Tobit model is that there's a latent (unobserved) continuous variable that meets the assumptions of OLS, but the latent variable has been censored at a certain upper and/or lower bound. Ideal cases are income in a survey, where they top-coded the income for privacy (e.g. actual income recorded up to $100,000, but incomes above that are all coded as $100,000). In my case, we know that some survey instruments have ceiling or floor effects, they can't measure above that ceiling or below that floor, and it's reasonable to think that the constructs they are trying to measure (e.g. health-related quality of life or patient satisfaction) may continue above or below the threshold, and that they might continue linearly above and below the threshold. Alternatively, you could be trying to measure some biological parameter where the test instrument has some limit of detection.

One of the key restrictions of the Tobit model is that the same processes have to govern whether or not the variable gets censored, or its level if observed. That would be true in my case; the limits of detection/floor or ceiling effects are arguably exogenous. But for many processes of interest to economics, that might not be the case. You would need to consider if something like a hurdle model fits your theory better. For example, maybe individuals are deciding whether or not to purchase something at all, and if they decide yes, then some other process governs how much they decide to spend.

I've seen at least two sources say that the Tobit model is even more vulnerable to heteroskedasticity than OLS:
http://www.stat.columbia.edu/~madiga...isticTobit.pdf
http://www.statalist.org/forums/foru...roskedasticity