MTE with Misspecification

TL;DR

This paper examines how non-responders to an instrument affect the estimation of the Marginal Treatment Effect (MTE) and proposes a re-weighting method to restore identification when the propensity score covers the entire interval.

Contribution

It introduces a method to identify the MTE curve despite non-responders by using re-weighting when the propensity score is fully supported.

Findings

Non-responders bias the MTE curve and its functionals.

Re-weighting can restore MTE identification under full support of the propensity score.

The approach extends MTE analysis to settings with partial instrument response.

Abstract

This paper studies the implication of a fraction of the population not responding to the instrument when selecting into treatment. We show that, in general, the presence of non-responders biases the Marginal Treatment Effect (MTE) curve and many of its functionals. Yet, we show that, when the propensity score is fully supported on the unit interval, it is still possible to restore identification of the MTE curve and its functionals with an appropriate re-weighting.