In this brief note I propose a condition called “conditional average monotonicity” that extends the average monotonicity condition from Frandsen et al. (2023) to a setting in which the instrument is only exogenous conditional on covariates. I lean on a proof from Blandhol et al. (2022) to show that, along with exogeneity and “rich covariates,” conditional average monotonicity is sufficient and necessary for the two-stage least squares estimand to be weakly causal in a setting with heterogeneous, nonlinear treatment effects.
Citation
Megan T. Stevenson, Average monotonicity in a setting with covariates (2023).