Nonlinear and nonseparable structural functions in regression discontinuity designs with a continuous treatment

Haitian Xie

Journal of Econometrics, 2024, vol. 242, issue 1

Abstract: Many empirical examples of regression discontinuity (RD) designs concern a continuous treatment variable, but the theoretical aspects of such models are less studied. This study examines the identification and estimation of the structural function in fuzzy RD designs with a continuous treatment variable. The structural function fully describes the causal impact of the treatment on the outcome. We show that the nonlinear and nonseparable structural function can be nonparametrically identified at the RD cutoff under shape restrictions, including monotonicity and smoothness conditions. Based on the nonparametric identification equation, we propose a three-step semiparametric estimation procedure and establish the asymptotic normality of the estimator. The semiparametric estimator achieves the same convergence rate as in the case of a binary treatment variable. As an application of the method, we estimate the causal effect of sleep time on health status by using the discontinuity in natural light timing at time zone boundaries.

Keywords: Causal inference; Continuous treatment; Dual monotonicity; Nonparametric identification; Semiparametric estimation; Asymptotic normality (search for similar items in EconPapers)
JEL-codes: C14 C21 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:242:y:2024:i:1:s0304407624001301

DOI: 10.1016/j.jeconom.2024.105784

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