When Should We (Not) Interpret Linear IV Estimands as LATE?

Abstract

In this paper I revisit the interpretation of the linear instrumental variables (IV) estimand as a weighted average of conditional local average treatment effects (LATEs). I focus on a practically relevant situation in which additional covariates are required for identification while the reduced-form and first-stage regressions implicitly restrict the effects of the instrument to be homogeneous, and are thus possibly misspecified. I show that the weights on some conditional LATEs are negative and the IV estimand is no longer interpretable as a causal effect under conditional monotonicity, i.e. when there are compliers but no defiers at some covariate values and defiers but no compliers elsewhere. Even if monotonicity holds unconditionally, the IV estimand is not interpretable as the unconditional LATE parameter unless the groups with different values of the instrument are roughly equal sized.

Global Representation of the Conditional LATE Model: A Separability Result*

“…Then under the local monotonicity condition (1), it is possible that for some x, there are compliers but no defier; while for other x, there are defiers but no complier. This notion of local monotonicity can be found, for example, in Kolesár (2013) and Słoczyński (2020). However, it is important to have uniformity in the direction of monotonicity in order to obtain the separability result in the global representation.…”

Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey

“…In this survey, we have focused on estimators relying on parallel trends assumptions, but this question is also relevant for other estimators. See for instance Słoczyński (2020) and Blandhol et al (2022) for instrumental variables estimators with covariates. More closely related to our set-up, the impact of heterogeneous treatment effects in the "group fixed-effects" model of Bonhomme and Manresa (2015) remains to be studied.…”

Labor Market Effects of Short-Cycle Higher Education Programs: Lessons from Colombia

“…12 Recent work underlines the role of covariates in the interpretation of TSLS estimates as LATEs. Słoczyński (2021) and Blandhol et al (2022) show that only under flexible specifications and strong monotonicity assumptions can one interpret TSLS estimates as convex combinations of conditional (on covariates) LATEs. While we recognize this caveat, the approach in this paper entails the appropriate TSLS specification under multiple instruments.…”