  Data separation is a well-studied phenomenon that can cause problems in the
estimation and inference from binary response models. Complete or
quasi-complete separation occurs when there is a combination of regressors in
the model whose value can perfectly predict one or both outcomes. In such
cases, and such cases only, the maximum likelihood estimates and the
corresponding standard errors are infinite. It is less widely known that the
same can happen in further microeconometric models. One of the few works in the
area is Santos Silva and Tenreyro (2010) who note that the finiteness of the
maximum likelihood estimates in Poisson regression depends on the data
configuration and propose a strategy to detect and overcome the consequences of
data separation. However, their approach can lead to notable bias on the
parameter estimates when the regressors are correlated. We illustrate how
bias-reducing adjustments to the maximum likelihood score equations can
overcome the consequences of separation in Poisson and Tobit regression models.
