Nonparametric Estimation of the Continuous Treatment Effect with Measurement Error

TL;DR

This paper develops a nonparametric method to estimate the average dose-response function for continuous treatments contaminated with measurement error, using deconvolution kernels and empirical likelihood, with theoretical and practical validation.

Contribution

It introduces a novel nonparametric estimator for the ADRF under measurement error, incorporating a new extrapolation procedure for smoothing parameter selection.

Findings

Estimator has desirable asymptotic properties.

Method performs well in simulations.

Application demonstrates practical utility.

Abstract

We identify the average dose-response function (ADRF) for a continuously valued error-contaminated treatment by a weighted conditional expectation. We then estimate the weights nonparametrically by maximising a local generalised empirical likelihood subject to an expanding set of conditional moment equations incorporated into the deconvolution kernels. Thereafter, we construct a deconvolution kernel estimator of ADRF. We derive the asymptotic bias and variance of our ADRF estimator and provide its asymptotic linear expansion, which helps conduct statistical inference. To select our smoothing parameters, we adopt the simulation-extrapolation method and propose a new extrapolation procedure to stabilise the computation. Monte Carlo simulations and a real data study illustrate our method's practical performance.