A note on stock sampling and maximum duration

An issue hardly ever mentioned in the analysis of labour market transitions is that for some individuals labour market transitions occur at a very low rate. Therefore, these individuals might stay on disability benefits or in domestic care till they reach the retirement age of 65. This implies that the duration on disability and of non-participating women has a upper bound of the time till retirement. Despite the growing availability of panel data on labour market transitions many household surveys are still based on stock based sampling. In this paper estimation of a duration model in which a positive fraction of individuals reaches a maximum duration is derived for stock sampled data. A mixed proportional hazard model with a piecewise constant baseline hazard leads to a relatively simple closed-form expression in the log likelihood. Discrete unobserved heterogeneity is assumed. Non-constant entry rates into the labour market state are allowed for by assuming a yearly fluctuating rate.