The type of studies considered in this talk are common in labor economics and medicine. An illustrating example is the Stanford heart transplant program where survival times of potential heart transplant recipients are recorded after their acceptance into the program. The choice of heart recipients is not randomized, and, therefore, background characteristics affecting both treatment assignment and survival time must be controlled for when evaluating the effect of heart transplantation. One of the peculiarities of this type of studies is that individuals may change treatment status during the follow-up time, being first controls (not transplanted) and later treated (transplanted). In this talk it is shown how a treatment effect can be estimated non-parametrically in this type of studies. Survival functions are estimated on a treated and a control group which are made comparable through matching on observed covariates. To justify the estimator and the related inference, we build on the potential outcome framework of J. Neyman and D. Rubin. An application, where the interest lies in the estimation of the effect of an employment subsidy program on unemployment duration, will also be presented in some detail.
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