Robustness of Logit analysis: Unobserved heterogeneity and mis-specified disturbances

In probit and logit models, the beta coefficients vary inversely with the variance of the disturbances. The omission of a relevant orthogonal regressor leads to increased unobserved heterogeneity, and this depresses the beta coefficients of the remaining regressors towards zero. For the probit model, Wooldridge (Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, MA, 2002) has shown that this bias does not carry over to the effect of these regressors on the outcome. We find by simulations that this also holds for the logit model, even when omitting a variable leads to severe mis-specification of the disturbance. More simulations show that logit analysis is quite insensitive to pure mis-specification of the disturbance as such.