Durations in panel data subject to attrition: a note on estimation in the case of a stock sample

In the empirical analysis of unemployment durations or job durations, it is generally assumed that the stochastic processes underlying labour market behaviour and the behaviour concerning participation in a panel survey are independent. As a consequence, spells that are incomplete due to attrition can be treated as spells that are subjected to independent right censoring. However, if the assumption of independence is violated, i.e. if for example the probability of dropping out of the panel is related to the rate at which a job is found, then attrition may have to be modelled and estimated jointly with the unemployment duration distribution to avoid biased estimates of the rate at which individuals become employed. A way to model the joint dependence is by means of stochastically related unobserved determinants. We discuss some properties of these kinds of models and state conditions needed to estimate such models in the case of stock sampled duration data.