Fractional response models with endogeneous explanatory variables and heterogeneity

In this talk, I will discuss ways of using Stata to fit fractional response models when explanatory variables are not exogenous. Two questions are of primary concern: First, how does one account for endogenous explanatory variables, both continuous and discrete, when the response variable is fractional and may take values at the corners? Second, how can we incorporate unobserved heterogeneity in panel-data fractional models when the panel might be unbalanced? I will draw on Papke and Wooldridge (2008, Journal of Econometrics 145: 121–133) and two unpublished papers of mine, "Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables" and "Correlated random effects models with unbalanced panels". One practically important conclusion is that by expanding the scope of existing Stata commands to allow fractional responses—in particular, the ivprobit, biprobit, hetprob, and (user-written) gllamm commands—flexible fractional response models can easily be fit.