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 but the reduced-form and first-stage regressions are possibly misspecified as a result of neglected heterogeneity in the effects of the instrument . If we also allow for conditional monotonicity, i. e. the existence of compliers but no defiers at some covariate values and the existence of defiers but no compliers elsewhere, then the weights on some conditional LATEs are negative and the IV estimand is no longer interpretable as a causal effect . Even if monotonicity holds unconditionally, the IV estimand is not interpretable as the unconditional LATE parameter unless the groups that are encouraged and not encouraged to get treated are roughly equal sized.
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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are possibly misspecified as a result of neglected heterogeneity in
implicitly restrict
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. If we also allow for conditional monotonicity, i. e. the existence of compliers but no defiers at some covariate values and the existence of defiers but no compliers elsewhere, then the
to be homogeneous, and are thus possibly misspecified. I show that the
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under conditional monotonicity, i.e. when there are compliers but no defiers at some covariate values and defiers but no compliers elsewhere.
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that are encouraged and not encouraged to get treated
with different values of the instrument