Before revision:  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 .
After revision:  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 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 .