Yuehao Bai, Shunzhuang Huang, Sarah Moon, Azeem M. Shaikh, Edward J. Vytlacil
arXiv 23 May 2024 · Econometrics
arXiv:2405.14104 · PDF · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Imbens, Guido W and Angrist, Joshua D (1994) Identification and estimation of local average treatment effects | 1.000 | 12 | 5 | 100% |
| 2 | Balke, Alexander and Pearl, Judea Nonparametric bounds on causal effects from partial compliance data | 0.909 | 8 | 4 | 75% |
| 3 | Balke, Alexander and Pearl, Judea (1997) Bounds on treatment effects from studies with imperfect compliance | 0.874 | 9 | 4 | 67% |
| 4 | Heckman, James J and Pinto, Rodrigo (2018) Unordered monotonicity | 0.843 | 4 | 4 | 75% |
| 5 | Kirkeboen, Lars J. and Leuven, Edwin and Mogstad, Magne (2016) Field of Study, Earnings, and Self-Selection | 0.843 | 4 | 4 | 75% |
| 6 | Kline, Patrick and Walters, Christopher R (2016) Evaluating public programs with close substitutes: The case of Head Start | 0.843 | 5 | 4 | 60% |
| 7 | Richardson, Thomas S and Robins, James M (2013) Single world intervention graphs (SWIGs): A unification of the counterfactual and graphical approaches to causality | 0.737 | 3 | 2 | 100% |
| 8 | Lee, Sokbae and Salanié, Bernard (2023) Treatment Effects with Targeting Instruments | 0.675 | 13 | 5 | 31% |
| 9 | Angrist, Joshua D and Imbens, Guido W and Rubin, Donald B (1996) Identification of causal effects using instrumental variables | 0.644 | 2 | 2 | 100% |
| 10 | Frangakis, Constantine E and Rubin, Donald B (2002) Principal stratification in causal inference | 0.511 | 2 | 2 | 50% |
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