On the Identifying Power of Generalized Monotonicity for Average Treatment Effects

2024-05-23

Social Science Research Network

AI Summary

This paper investigates the identifying power of generalized monotonicity in settings with multivalued outcomes, treatments, and instrumental variables (IVs), focusing on average potential outcomes and the average treatment effect (ATE). Using formal identification analysis, we show that under standard IV exogeneity alone, generalized monotonicity imposes no additional restrictions on the identified set—i.e., it is identificationally neutral in multivalued settings. Identification gains arise only when monotonicity is violated *and* combined with auxiliary structural constraints, such as restrictions on latent treatment response types. We provide the first rigorous proof of this neutrality result and systematically characterize the theoretical boundary between constraints that are identificationally inert versus those that sharpen inference. Our framework unifies prominent models—including Kline & Walters (2016) and Heckman & Pinto (2018)—and delivers clear, operational criteria for selecting credible identifying assumptions in empirical practice.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Mechanism Design

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• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
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Abstract

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.

Problem

• Examining monotonicity's identifying power for treatment effects
• Extending results to multi-valued outcomes and instruments
• Identifying necessary restrictions for treatment effect estimation

Innovation

• Generalized monotonicity extends traditional monotonicity conditions
• Treatment response restrictions must exceed generalized monotonicity
• Additive random utility models imply generalized monotonicity