In this paper we consider the problem of inferring the causal effect of the variable $Z$ on the dependently censored survival times $T$. Consider unobserved confounding variables such that the error terms in the regression model for $T$ are correlated with the confounding variables $Z$. In addition, $T$ is subject to dependent censoring. This means that $T$ is correctly censored by the $T$ dependent censoring time $C$ (even after adjusting for the effects of the measured covariates). Leverage the instrumental variable-dependent control function approach to tackle the confounding problem. In addition, $T$ and $C$ are assumed to follow a joint regression model with bivariate Gaussian error terms and an unspecified covariance matrix for flexible handling of dependent censoring. Given the conditions under which the models are discriminative, a two-step estimation procedure is proposed and the resulting estimators are shown to be consistent and asymptotically normal. Simulations are used to check the effectiveness and finite-sample performance of the estimation procedure. Finally, we use the proposed method to estimate the causal effect of vocational training programs on duration of unemployment.
