LATE With Missing or Mismeasured Treatment

Abstract

We provide a new estimator, MR-LATE, that consistently estimates local average treatment effects when treatment is missing for some observations, not at random. If instead treatment is mismeasured for some observations, MR-LATE usually has less bias than the standard LATE estimator. We discuss potential applications where an endogenous binary treatment may be unobserved or mismeasured. We apply MR-LATE to study the impact of women's control over household resources on health outcomes in Indian families. This application illustrates the use of MR-LATE when treatment is estimated rather than observed. In these situations, treatment mismeasurement may arise from model misspecification and estimation errors.

Identifying Program Benefits When Participation is Misreported

“…Assumption 3.3-(i) is similar to the non-differential misclassification assumption of, e.g., Lewbel (2007), Hu (2008) and Battistin and Sianesi (2011), and is weaker than Assumption 2-(ii) of Calvi, Lewbel, and Tommasi (2021). It says that, for compliers C k , given the actual treatment status D, the proxies T a and T b contain no extra information about the mean of the outcome.…”

“…First, we provide sufficient conditions under which the point identification the effect of the treatment can be achieved. Importantly, we generalize the MR-LATE approach for binary instrument and binary treatment proposed by Calvi, Lewbel, and Tommasi (2021) to incorporate discrete instrument(s) and discrete treatment. Second, we establish the asymptotic properties of the proposed estimator to infer the parameter of interest.…”

“…Theorem 3.1 generalizes the MR-LATE method of Calvi, Lewbel, and Tommasi (2021) to cases with discrete and multiple-discrete instrument(s). It shows that each LATE is a linear combination of ( a k , b k ) of the same complier group, and the IV estimand ↵ I V is a linear combination of ( a , b ).…”

“…Then, we review the key idea of the MR-LATE approach introduced by Calvi, Lewbel, and Tommasi (2021), and applied in Tommasi (2019), which addresses the problem of treatment misclassification in this simple setting. This is a natural starting point because later we generalize the approach to other settings and develop a novel inferential procedure.…”

“…Recent scholarship addresses the problem of non-differential misclassification of binary treatment variables. Calvi, Lewbel, and Tommasi (2021) propose a novel instrumental variables (IV) approach to identify the average causal effect on compliers. Their estimator, the mismeasured robust local average treatment effect (MR-LATE), requires two binary proxies for the same treatment, which can be constructed using estimated treatments, different sources of treatment status, or multiple or repeated treatment measures.…”