Optimally Combining Censored and Uncensored Datasets

We develop a simple semiparametric framework for combining censored and uncensored samples so that the resulting estimators are consistent, asymptotically normal, and use all information optimally. No nonparametric smoothing is required to implement our estimators. To illustrate our results in an empirical setting, we show how to estimate the effect of changes in compulsory schooling laws on age at first marriage, a variable that is censored for younger individuals. We find positive effects of the laws on age at first marriage but the effects are much smaller than would be inferred if one ignored the censoring problem. Results from a small simulation experiment suggest that the estimator proposed in this paper can work very well in finite samples.