Nonparametric Estimation of Local Treatment Effects with Continuous Instruments

JungHo Lee, Zhenghao Zeng, Alexander W. Levis, Edward Kennedy, Luke Keele

Abstract:

Instrumental variable methods are widely used to address unmeasured confounding, yet much
of the existing literature has focused on the binary instrument setting. Extensions to continuous
instruments often impose strong parametric assumptions for identification and estimation, which
can be difficult to justify and may limit their applicability in complex real-world settings. In
this work, we develop theory and methods for nonparametric estimation of treatment effects
with a continuous instrumental variable. We introduce an estimand that, under a monotonicity
assumption, quantifies the treatment effect among the maximal complier class, generalizing the
local average treatment effect framework to continuous instruments. Considering this estimand
and the local instrumental variable curve, we draw connections to the dose-response function and
its derivative, and propose doubly robust estimation methods. We establish convergence rates and
conditions for asymptotic normality, providing valuable insights into the role of nuisance function
estimation when the instrument is continuous. Additionally, we present practical procedures for
bandwidth selection and variance estimation. Through extensive simulations, we demonstrate
the advantages of the proposed nonparametric estimators. Finally, we apply our methods to data
where excess travel time is an instrument for patients’ likelihood of receiving care at specialized
health care facilities. We use this instrument to estimate the effect of delivering at low-quality
neonatal intensive care units (NICUs) on infant mortality.