Nonparametric Instrumental Regression With Right Censored Duration Outcomes

Abstract

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.

Nonparametric estimation of accelerated failure-time models with unobservable confounders and random censoring

“…For instance, when T represents unemployment spells and a randomly assigned interview determines censoring, Assumption 2.2 implies that the longest duration of a spell is finite and that interviews can be conducted late enough to guarantee that at least some of the individuals with the longest spell are interviewed after they found employment. If Assumption 2.2 does not hold, one can only hope to identify ϕ for those t which are in the interior of the support of C [6]. Assumption 2.2 is violated, in particular, when censoring is fixed (see Remark 1 below).…”

“…Frandsen [35] discusses nonparametric identification and estimation of a model with a binary endogenous treatment variable and a binary instrument, independent of the error term [see also 70]. More recently, Beyhum et al [6] analyze a nonparametric duration model with endogenous treatment. They provide identification and estimation based on an instrumental variable assumption when the outcome is randomly censored on the right.…”

Two-stage least squares with a randomly right censored outcome

“…Bijwaard and Ridder (2005), Tchetgen et al (2015), Li et al (2015), Chan (2016) and Chernozhukov et al (2015) estimate causal effects in semiparametric frameworks, which do not correspond to the linear model of our paper. Frandsen (2015), Richardson et al (2017), Blanco et al (2019), Beyhum et al (2021), Sant'Anna (2016), Sant'Anna (2020, and Centorrino and Florens (2021) provide nonparametric estimation results. The last three papers of the latter list are especially close to the present work.…”

Instrumental variable estimation of dynamic treatment effects on a duration outcome

“…Frandsen (2015), Sant'Anna (2016), Richardson et al (2017), Blanco et al (2020) provide nonparametric estimation results for the average treatment effects on the compliers (see Angrist et al (1996)) with binary treatment and instrument. Moreover, Beyhum et al (2021) nonparametrically estimate the average treatment effect over the whole population when both the treatment and the instrument are categorical. Also, Centorrino and Florens (2021) study nonparametric estimation when the treatment is continuous.…”