Bounds on Average and Quantile Treatment Effects on Duration Outcomes Under Censoring, Selection, and Noncompliance

Abstract

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Instrumental variable estimation of dynamic treatment effects on a duration outcome

“…In this context, Tchetgen et al (2015), Li et al (2015), Chan (2016) and Chernozhukov et al (2015) estimate causal effects in a semiparametric framework. 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.…”

Nonparametric Instrumental Regression With Right Censored Duration Outcomes

“…Some papers focus on the case where both the treatment and the instrumental variable are binary. Frandsen (2015), Sant'Anna (2016), Blanco et al (2019) make a monotonicity assumption stating that there are no defiers (see Angrist et al (1996)). This condition has been criticized in the literature because it restricts the treatment allocation mechanism (see De Chaisemartin (2017)).…”

“…Unlike ours, these articles are interested in local average treatment effects on the population of compliers which they are able to estimate thanks to this monotonicity assumption (see Wüthrich (2020)). It should be noted that Blanco et al (2019) does not focus on the treatment effects of the full population of compliers but only on the ones that experience the spell of interest (e.g. employment).…”

“…In contrast with the monotonicity assumption, the rank invariance assumption is a condition on potential outcomes but does not restrict treatment allocation. When there is one-sided noncompliance, like in our empirical application, the compliers correspond to the treated and therefore Frandsen (2015), Sant'Anna (2016) and Blanco et al (2019) target the average treatment effect on the treated, while we identify the average treatment effect of the complete population. Another difference between our paper and Frandsen (2015) and Sant'Anna ( 2016) is that the latter papers estimate the counterfactual cumulative distribution functions before inverting them to obtain estimates of the quantile treatment effects.…”

“…We discuss how to extend our methodology to allow for additional regressors in the conclusion but do not provide theoretical results. Blanco et al (2019) consider the same binary setting but allows for selection and endogenous censoring. Using principal stratification, it develops bounds on the quantile treatment effects.…”