Fractional outcomes are common. You might be modeling participation rates in a 401(k) pension plan, the pass rate on standardized tests, expenditure shares, or the like.
Fractional response models are a flexible and intuitive way to model outcomes that lie between 0 and 1. They do not have the problem of linear models that will yield predictions outside 0 and 1 or the problem of log-odds models that are undefined at 0 and 1. Fractional response models can be fit using the existing fracreg command.
What if you are concerned that one or more of your model covariates are endogenous? With the new ivfprobit command, you can fit a model for a fractional dependent variable and account for endogeneity in one or more of the covariates.