Instrumental Variable Estimation of Dynamic Treatment Effects on a Duration Outcome

Jad Beyhum, Samuele Centorrino, Jean-Pierre Florens and Ingrid Van Keilegom

Journal of Business & Economic Statistics, 2024, vol. 42, issue 2, 732-742

Abstract: This article considers identification and estimation of the causal effect of the time Z until a subject is treated on a duration T. The time-to-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 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 an integral equation, 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 evaluate the effect of the timing of a therapy for burnout.

Date: 2024
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Working Paper: Instrumental variable estimation of dynamic treatment effects on a duration outcome (2022)
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DOI: 10.1080/07350015.2023.2231053

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