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