On the Identifying Power of Monotonicity for Average Treatment Effects

• Main Authors: Bai, Yuehao, Huang, Shunzhuang, Moon, Sarah, Shaikh, Azeem M, Vytlacil, Edward J
• Format: Journal Article
• Language: English
• Published: 22-05-2024
• Subjects: Statistics - Methodology
• DOI: 10.48550/arxiv.2405.14104

In the context of a binary outcome, treatment, and instrument, Balke and
Pearl (1993, 1997) establish that the monotonicity condition of Imbens and
Angrist (1994) has no identifying power beyond instrument exogeneity for
average potential outcomes and average treatment effects in the sense that
adding it to instrument exogeneity does not decrease the identified sets for
those parameters whenever those restrictions are consistent with the
distribution of the observable data. This paper shows that this phenomenon
holds in a broader setting with a multi-valued outcome, treatment, and
instrument, under an extension of the monotonicity condition that we refer to
as generalized monotonicity. We further show that this phenomenon holds for any
restriction on treatment response that is stronger than generalized
monotonicity provided that these stronger restrictions do not restrict
potential outcomes. Importantly, many models of potential treatments previously
considered in the literature imply generalized monotonicity, including the
types of monotonicity restrictions considered by Kline and Walters (2016),
Kirkeboen et al. (2016), and Heckman and Pinto (2018), and the restriction that
treatment selection is determined by particular classes of additive random
utility models. We show through a series of examples that restrictions on
potential treatments can provide identifying power beyond instrument exogeneity
for average potential outcomes and average treatment effects when the
restrictions imply that the generalized monotonicity condition is violated. In
this way, our results shed light on the types of restrictions required for help
in identifying average potential outcomes and average treatment effects.