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  • xttobit - assumptions of normality and homoscedasticity

    Dear forum users,
    I am trying to run a tobit model with data censored at zero. I have panel data of n places over n years. My dependent variable is right skewed, with slightly less than 20 percent of the DV values equal to 0. My original code was: xttobit depvar indepvars i.year, ll(0)

    I’ve read through many threads and as I currently understand it, by doing -xtset place year-, Stata understands the panel nature of the dataset, and therefore I don’t need to add -i.place-, but because Stata doesn’t take into consideration effects of time with xtset, I added –i.year-. Does this make sense?

    I am also hoping to find ways to test the tobit assumptions of homoscedasticity and normality of error distribution. It seems like making residual plots after xttobit wasn't as straightforward as I imagined (anyone know how to easily do this?), so I did that with R, and the plot suggested a violation of normality of error terms. I decided to try and do –ln(depvar)- to transform the dependent variable, and after doing that, the residuals does look better. I am slightly confused here, however, because tobit is often used with censored data with lots of zeros and is precisely designed for the kind of data we have. Does it make sense to do transform the dependent variable with tobit? Because this makes a straightforward interpretation of the results difficult, I'd like to know if there are other options than DV transformation.

    As for heteroscedasticity, I was unable to find straightforward ways to test/correct this after running xttobit. As I understand it, one way to sort of address this is to have robust SEs instead of standard SEs, but xttobit does not allow the robust option. Is there any other way? I’ve read that we can informally compare tobit and probit models to see whether tobit is appropriate – and I saw examples of doing this with –tobit- and –probit- Stata commands (comparing signs/directions of both models), but I should be comparing –xttobit- and –xtprobit- in my case, correct? In that case, the xtprobit model doesn’t seem to run, and I end up with never-ending “not concave” iterations.

    I’ve found one book chapter using tobit model, and the authors tested the assumptions by 1) adding quadratic/cubic regressors and conducting a Wald test, and 2) estimating heteroscedastic models and running LR test. I would love to learn more about how to actually do this, if anyone could kindly point me to resources/codes.

    Best regards,

  • #2
    I am facing the same confusion.. Can you please suggest if we need to add i.year following the xtreg command??

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