With panel data important issues can be resolved that can not be addressed with cross sectional data. A major drawback is that panel data su er from more severe missing data problems. Adding a sample consisting of new units randomly drawn from the original population as replacements for units who have dropped out of the panel, a so called refreshment sample, can be helpful in mitigating the e ects of attrition, both by allowing for estimation of richer models and by making estimation of conventional models more precise. In this paper we develop a family of models that incorporate refreshment samples, and we demonstrate in an application to a Dutch data set on travel behaviour that such models can lead to substantially di erent results than models that assume that the missing data process is ignorable or conventional econometric models for panel data with attrition.