Bias Reduction as a Remedy to the Consequences of Infinite Estimates in Poisson and Tobit Regression

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.