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

In this paper we examine theoretically and by simulation whether or not unobserved heterogeneity independent of the included regressors is really an issue in logit, probit and loglog models with both binary and fractional data. We found that unobserved heterogeneity: (i) produces an attenuation bias in the estimation of regression coefficients; (ii) is innocuous for logit estimation of average sample partial effects, while in the probit and loglog cases there may be important biases in the estimation of those quantities; (iii) has much more destructive effects over the estimation of population partial effects; (iv) only for logit models does not affect substantially the prediction of outcomes; and (v) is innocuous for the size and consistency of Wald tests for the significance of observed regressors but, in small samples, reduces their power substantially.