When to use Tobit regression?

[Mathilde SB]

Hallo,

I have been recommended to use a Tobit regression because my independent variable is very right-skewed (mostly because of social desirability bias), but not censored. I'm not sure whether the recommendation is correct, because (as I understand it) Tobit regression is only to be used when data is censored? I have never used Tobit regression before, does someone know if it would be suitable to use it in this situation?

Thanks,
Mathilde

[Joao Santos Silva]

Dear Mathilde SB,

If your data is non-negative, consider using Poisson regression with robust standard errors (PPML). But maybe you can tell us more about your data and about the purpose of the model?

Best wishes,

Joao

[Mathilde SB]

Thanks for the answer.

Specifically I am looking at the effect of personal discrimination, but the variable constructed for the purpose is very right-screwed because people haven't been reporting their experiences. The purpose of the model was to investigate if the effect between my X (personal discrimination) and Y is robust, even though my X is highly screwed (and might not reflect reality completely). Is there something that I can do, to make my results more robust?

[Jeff Wooldridge]

A Tobit model is applied to Y when it is nonnegative but takes on the value zero with nontrivial frequency. The nature of your X variables is mostly irrelevant. What is your Y variable? As per the FAQ, you'll get much better answers if you show a sample of data. Then we'd know something about Y. If Y is nonnegative then you should take Joao's suggestion and use Poisson regression.

[Mathilde SB]

Thanks, my Y is measuring political trust (an index) and it is not nonnegative.
This is the distribution on my Y, political trust.


My professor recommended the tobit regression because he believed it would make a more robust regression, when my X is highly right-skewed - as you can see in the distribution of the histogram (personal discrimination).

[Joseph Coveney]

Y is measuring political trust (an index) and it is not nonnegative.

Why do you say that? Output from -tabulate- indicates that it is indeed nonnegative.

Try the recommended Poisson regression method and see whether the model's predictions are reasonable. If so, then take it back to your professor. If not, then report back here, showing what you got.

[Jeff Wooldridge]

Mathilde: You might have misunderstood your professor. Again, no model for Y puts restrictions on the nature of the X -- whether it's linear, exponential, Tobit, and so on. Of course, one wants to try different possibilities -- such as putting in a dummy variable for X = 0 and then using log(X) for X > 0 if X is nonnegative but with zero outcomes. Your outcome is actually fractional, and so Poisson regression isn't the best choice because it uses an unbounded mean function (exponential). I would use fractional logit or fractional probit. You could use two-limit Tobit but that's actually harder to interpret. I'm guessing your professor noticed the outcomes at zero and one and suggested two-limit Tobit.

For fractional logit, where xk is discrete:

fracreg logit y x1 x2 ... i.xk vce(robust)
margins, dydx(x1 x2 ... xk)

You will have to decide how to transform the xj variables.

[Joao Santos Silva]

Dear Mathilde SB,

Your dependent variables is bounded between 0 and 1, so I would recommend a fractional logit model. Jeff Wooldridge is the expert on that, so he may want to add to this.

I think that the problem you have is that your main explanatory variable may be measured with error, due to under-reporting. It is not easy to deal with that in this context, but the Tobit will not help you for sure. Depending on the purpose of what you are doing, you may simply acknowledge that in the text.

Best wishes,

Joao