Practical causal analysis for the treatment timing effect on doubly censored duration: effect of fertility on work span

We present a practical causal framework to estimate the effects of a treatment and its timing on a doubly censored response. We then apply the methodology to find the effect of fertility on work duration where, not just fertility itself, but the timing of fertility should matter greatly. Since fertility and its decision of timing are chosen by the individual, it is likely to be endogenous. We use a populationwide data set over mothers with two children to address the endogeneity issue by using the first two children's same-sex instrument in a ‘control function’ setting. We find that having a third child reduces the average labour market work duration, and that the magnitude of the effect increases monotonically with the waiting time between the second and third children. Moreover, the negative effect varies substantially over education and second-birth age, being stronger for mothers with higher education and lower second-birth age.