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

TL;DR

This paper examines when linear IV estimands can be validly interpreted as LATEs, highlighting issues with negative weights and misspecification, and proposing an interacted specification to address these problems.

Contribution

It reveals conditions under which IV estimates are not interpretable as LATEs and advocates for using interacted specifications to improve causal inference.

Findings

Negative weights on some LATEs can occur, invalidating causal interpretation.

Interacted specifications mitigate misspecification and negative weighting issues.

Application shows different estimates depending on specification, affecting policy conclusions.

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 situation in which additional covariates are required for identification while the reduced-form and first-stage regressions may be misspecified due to an implicit homogeneity restriction on the effects of the instrument. I show that the weights on some conditional LATEs are negative and the IV estimand is no longer interpretable as a causal effect under a weaker version of monotonicity, i.e. when there are compliers but no defiers at some covariate values and defiers but no compliers elsewhere. The problem of negative weights disappears in the interacted specification of Angrist and Imbens (1995), which avoids misspecification and seems to be underused in applied work. I illustrate my findings in an application to the causal effects of pretrial detention on case outcomes. In this setting, I reject the stronger version of monotonicity, demonstrate that the interacted instruments are sufficiently strong for consistent estimation using the jackknife methodology, and present several estimates that are economically and statistically different, depending on whether the interacted instruments are used.