This paper analyzes the effect of a discrete treatment Z on a duration T . The treatment is not randomly assigned. The confounding issue is treated using a discrete instrumental variable explaining the treatment and independent of the error term of the model. Our framework is nonparametric and allows for random right censoring. This specification generates a nonlinear inverse problem and the average treatment effect is derived from its solution. We provide local and global identification properties that rely on a nonlinear system of equations. We propose an estimation procedure to solve this system and derive rates of convergence and conditions under which the estimator is asymptotically normal. When censoring makes identification fail, we develop partial identification results. Our estimators exhibit good finite sample properties in simulations. We also apply our methodology to the Illinois Reemployment Bonus Experiment.

This paper considers a nuclear norm penalized estimator for panel data models with interactive effects. The low-rank interactive effects can be an approximate model and the rank of the best approximation unknown and grow with sample size. The estimator is solution of a well-structured convex optimization problem and can be solved in polynomial-time. We derive rates of convergence, study the low-rank properties of the estimator, estimation of the rank and of annihilator matrices when the number of time periods grows with the sample size. We propose and analyze a two-stage estimator and prove its asymptotic normality. We can also use the baseline estimator as an initialization for any sequential algorithm. None of the procedures require knowledge of the variance of the errors.The authors acknowledge financial support from the grant ERC POEMH 337665. They are grateful to Thierry Magnac for helpful discussions.

This paper considers the problem of inference in a linear regression model with outliers where the number of outliers can grow with sample size but their proportion goes to 0. We apply the square-root lasso estimator penalizing the ℓ 1 -norm of a random vector which is non-zero for outliers. We derive rates of convergence and asymptotic normality. Our estimator has the same asymptotic variance as the OLS estimator in the standard linear model. This enables to build tests and confidence sets in the usual and simple manner. The proposed procedure is also computationally advantageous as it amounts to solving a convex optimization program. Overall, the suggested approach constitutes a practical robust alternative to the ordinary least squares estimator.

This paper discusses endogenous treatment models with duration outcomes, competing risks and random right censoring. The endogeneity issue is solved using a discrete instrumental variable. We show that the competing risks model generates a nonparametric quantile instrumental regression problem. The cause-specific cumulative incidence, the cause-specific hazard and the subdistribution hazard can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for which exact identification is possible and give partial identification results for other quantiles. We outline an estimation procedure and discuss its properties. The finite sample performance of the estimator is evaluated through simulations. We apply the proposed method to the Health Insurance Plan of Greater New York experiment.

This paper considers identification and estimation of the time Z until a subject is treated on a duration T . The treatment is not randomly assigned, T is randomly right censored by a random variable C, and the time to treatment Z is right censored by min(T, C). The endogeneity issue is treated using an instrumental variable explaining Z and independent of the error term of the model. We study identification in a fully nonparametric framework. We show that our specification generates a system of integral equations, of which the regression function of interest is a solution. We provide identification conditions that rely on this identification equation. We assume that the regression function follows a parametric model for estimation purposes. We propose an estimation procedure and give conditions under which the estimator is asymptotically normal. The estimators exhibit good finite sample properties in simulations. Our methodology is applied to find evidence supporting the efficacy of a therapy for burnout.