Length-bias Correction in Transformation Models with Supplementary Data

In this article, I propose an inferential procedure of monotone transformation models with random truncation points, which may not be observable. This class includes length-biased samples that are common in duration analysis. The proposed estimator can be applied to more general situations than existing estimators, since it imposes restrictions on neither the transformation function nor the error terms. Furthermore, it does not require observed truncation points either. It is sufficient for point identification to know the cdf of the truncation variable, which can be estimated from supplementary data that are easily found in applications. The estimator converges to a normal distribution at the rate of and Monte Carlo simulations confirm its robustness to error distributions in finite samples. For an empirical illustration, I estimate the effect of unemployment insurance benefits on unemployment duration, using length-biased microdata and supplementary macrodata.