Fractional regression for panel data - Independent variable ratio of ratio

[consuelo moraga]

Dear Statalists,

I'm working with fractional regression in Stata 14 with a couple of regressions using Gini index as independent variable in one case. For the second regression my independent variable is more complex, since is the ratio of a ratio, meaning I'm comparing the ratio between cultivated land and total land (I call this Z) used by large farmers and small farmers, therefore y= Z(large farmers)/Z (small farmers). The minimum value I obtain is 0.00024 and the maximum is 1.9603. As you may notice I cannot use fracreg in stata since I need an independent variable which goes from 0 to 1. Could you help me find another option for my data?

Thanks guys!!!

[Clyde Schechter]

It really depends on the distributional properties of y conditional on your predictors. You might do perfectly fine with ordinary least squares linear regression. Or perhaps a generalized linear model using any of the combinations of links and families suitable for use with a continuous dependent variable. If there is no theory to guide you on a model, you can just try fitting them and then choosing what seems to work best for your data. Also consider linear regression with some transform of y as the dependent variable. There are so many possibilities, and nothing you have said about the nature of your dependent variable really narrows them down.

[consuelo moraga]

Dear Clyde, Thank you very much for your response. I tryed with the OLS and my next option was GLM. I was concerned about having a ratio as a dependent variable, since I used fracreg for Gini. It is always good to have feedback on this forum! Best regards from Chile !!

[Jimmy Yang]

Fractional model is at best to deal with the boundary issue of dependent variable. If the distribution will have a lot of data points on boundary, you can mitigate the effect by using glm.
Your y=Z(large farmers)/Z (small farmers) have no chance to have a value zero, but have a chance to approaching infinity. My reasoning is that cultivated land can not be zero but can approach zero. So you need to use a transformed distribution of dependent variable with this kind of theoretical property in my opinion.
Further more the categorical variable (whether it is large farmer or not) shall be determined by model, since it is obvious that it is endogenous.