  This paper considers the problem of inferring the causal effect of a variable
$Z$ on a dependently censored survival time $T$. We allow for unobserved
confounding variables, such that the error term of the regression model for $T$
is correlated with the confounded variable $Z$. Moreover, $T$ is subject to
dependent censoring. This means that $T$ is right censored by a censoring time
$C$, which is dependent on $T$ (even after conditioning out the effects of the
measured covariates). A control function approach, relying on an instrumental
variable, is leveraged to tackle the confounding issue. Further, it is assumed
that $T$ and $C$ follow a joint regression model with bivariate Gaussian error
terms and an unspecified covariance matrix such that the dependent censoring
can be handled in a flexible manner. Conditions under which the model is
identifiable are given, a two-step estimation procedure is proposed, and it is
shown that the resulting estimator is consistent and asymptotically normal.
Simulations are used to confirm the validity and finite-sample performance of
the estimation procedure. Finally, the proposed method is used to estimate the
causal effect of job training programs on unemployment duration.
