Tobit or OLS?

[Masanori Matsuura]

when a variable is an index, it's from zero to one, and around one-third of observations is zero, should I use the Tobit model or still use OLS?

[John Mullahy]

If your goal is to estimate the conditional mean of the index then you might consider fractional regression. See

help fracreg

for details.

[Masanori Matsuura]

John Mullahy Thank you for your prompt reply.
The fractional regression is an interesting option but the index is not from binomial variables and I don't aim to estimate the conditional mean. The distribution of the index looks like below. And this is panel data.

It's a diversification index (Herfindahl-Hirschman index) and a dependent variable. Do you have any ideas about the specification of the regression model? I don't think the variable is not truncated and censored. there is just a corner at zero for specific households?
So, maybe OLS?

[John Mullahy]

OLS is certainly a possibility. But in using OLS you are implicitly estimating the conditional mean (which is also what -fracreg- is doing). Moreover -fracreg- does not depend on the index deriving from underlying binomial variates. Its only key assumptions are that 0≤y≤1 and that 0<E[y|x]<1.

If your aim is not to estimate the conditional mean but rather some other features of the conditional distribution f(y|x) then you would likely have to assume and estimate a specific probability model.

[Masanori Matsuura]

John Mullahy Thank you so much for the useful suggestion.
I will reconsider fractional regression if I understand the fractional regression with panel data!
Thanks again.