  In this paper, we consider the problem of estimating the causal effect of an
endogenous variable $Z$ on a survival time $T$ that can be subject to different
types of dependent censoring. Firstly, we extend the current literature by
simultaneously allowing for both independent ($A$) and dependent ($C$)
censoring. Moreover, we have different parametric transformations for $T$ and
$C$ that result in a more additive structure with approximately normal and
homoscedastic error terms. The model is shown to be identified and a two-step
estimation method is specified. It is shown that this estimator results in
consistent and asymptotically normal estimates. Secondly, a goodness-of-fit
test is developed to check the model's validity. To estimate the distribution
of the statistic, a parametric bootstrap approach is used. Lastly, we show how
the model naturally extends to a competing risks setting. Simulations are used
to evaluate the finite-sample performance of the proposed methods and
approaches. Moreover, we investigate two data applications regarding the effect
of job training programs on unemployment duration and the effect of periodic
screenings on breast cancer mortality rates.
