Yuehao Bai, Shunzhuang Huang, Sarah Moon, Andres Santos, Azeem M. Shaikh, Edward J. Vytlacil
arXiv 7 Nov 2024 · Econometrics
arXiv:2411.05220 · PDF · DOI · OpenAlex · Extracted main text
We propose a general approach for inference for a broad class of treatment effect parameters in a setting of a discrete valued treatment and instrument with a general outcome variable. The class of parameters considered are those that can be expressed as the expectation of a function of the response type conditional on a generalized principal stratum. Here, the response type refers to the vector of potential outcomes and potential treatments, and a generalized principal stratum is a set of possible values for the response type. In addition to instrument exogeneity, the main substantive restriction imposed rules out certain values for the response types in the sense that they are assumed to occur with probability zero. It is shown through a series of examples that this framework includes a wide variety of parameters and assumptions that have been considered in the previous literature. A key result in our analysis is a characterization of the identified set for such parameters under these assumptions in terms of existence of a non-negative solution to linear systems of equations with a special structure. We propose methods for inference exploiting this special structure and recent results in Fang et al. (2023).
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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 | Heckman, James J and Pinto, Rodrigo (2018) Unordered monotonicity | 1.000 | 11 | 4 | 100% |
| 2 | Machado, Cecilia and Shaikh, Azeem M and Vytlacil, Edward J (2019) Instrumental variables and the sign of the average treatment effect self | 0.928 | 5 | 4 | 80% |
| 3 | Cheng, Jing and Small, Dylan S (2006) Bounds on causal effects in three-arm trials with non-compliance | 0.894 | 7 | 3 | 71% |
| 4 | Kline, Patrick and Walters, Christopher R (2016) Evaluating public programs with close substitutes: The case of Head Start | 0.874 | 5 | 2 | 100% |
| 5 | Manski, Charles F (1997) Monotone treatment response | 0.874 | 5 | 2 | 100% |
| 6 | Imbens, Guido W and Angrist, Joshua D (1994) Identification and estimation of local average treatment effects | 0.811 | 4 | 2 | 100% |
| 7 | Fang, Zheng and Santos, Andres and Shaikh, Azeem M and Torgovitsky,… (2023) Inference for Large-Scale Linear Systems With Known Coefficients self | 0.766 | 20 | 5 | 45% |
| 8 | Bai, Yuehao and Huang, Shunzhuang and Moon, Sarah and Shaikh, Azeem… (2024) On the Identifying Power of Generalized Monotonicity for Average Treatment Effects self | 0.737 | 3 | 2 | 100% |
| 9 | Kirkeboen, Lars J. and Leuven, Edwin and Mogstad, Magne (2016) Field of Study, Earnings, and Self-Selection | 0.737 | 3 | 2 | 100% |
| 10 | Bai, Yuehao and Huang, Shunzhuang and Tabord-Meehan, Max (2025) Sharp Testable Implications of Encouragement Designs self | 0.644 | 2 | 2 | 100% |
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