Is neglected heterogeneity really an issue in binary and fractional regression models? A simulation exercise for logit, probit and loglog models

Theoretical and simulation analysis is performed to examine whether unobserved heterogeneity independent of the included regressors is really an issue in logit, probit and loglog models with both binary and fractional data. It is found that unobserved heterogeneity has the following effects. First, it produces an attenuation bias in the estimation of regression coefficients. Second, although it is innocuous for logit estimation of average sample partial effects, it may generate biased estimation of those effects in the probit and loglog models. Third, it has much more deleterious effects on the estimation of population partial effects. Fourth, it is only for logit models that it does not substantially affect the prediction of outcomes. Fifth, it is innocuous for the size of Wald tests for the significance of observed regressors but, in small samples, it substantially reduces their power.