Description:

Phillip Heiler (Aarhus): (Generalized) LATE:  Identification and Inference under Weak and Non-Monotonic Treatment Choice

Abstract: Instrumental-variables (IV) analyses with heterogeneous treatment effects are routinely interpreted through a local ATE lens under the strong assumption of monotonic treatment choice. This paper studies identification and inference for the ATE among units whose treatment status responds to the instrument (switchers) when treatment choice is only weakly monotonic or fully non-monotonic. We first establish a sharp impossibility result: absent weak monotonicity, no generally untestable restriction on latent compliance types can point-identify the switcher ATE. Under weak monotonicity, the switcher ATE is a re-ordered IV estimand that can be estimated semiparametrically efficiently. By contrast, textbook IV, saturated IV, or fully nonparametric IV specifications target distinct weighted averages of switcher effects when treatment effects and first stages are heterogeneous. Moving beyond weak monotonicity, we develop a sharp partial identification approach for the switcher average treatment effect without restricting effect heterogeneity. Our approach combines observed first-stage information with agnostic bounds on the prevalence of switchers and exploits mixture restrictions implied by the IV design. The resulting bounds admit a clear economic interpretation and can be further tightened in terms of restrictions on the variance of the structural treatment choice probability effects, i.e. unobserved interaction effects.