Yuehao Bai, Shunzhuang Huang, Max Tabord-Meehan
arXiv 14 Nov 2024 · Econometrics
arXiv:2411.09808 · PDF · DOI · OpenAlex · Extracted main text
This paper studies a potential outcome model with a continuous or discrete outcome, a discrete multi-valued treatment, and a discrete multi-valued instrument. We derive sharp, closed-form testable implications for a class of restrictions on potential treatments where each value of the instrument encourages towards at most one unique treatment choice; such restrictions serve as the key identifying assumption in several prominent recent empirical papers. Borrowing the terminology used in randomized experiments, we call such a setting an encouragement design. The testable implications are inequalities in terms of the conditional distributions of choices and the outcome given the instrument. Through a novel constructive argument, we show these inequalities are sharp in the sense that any distribution of the observed data that satisfies these inequalities is compatible with this class of restrictions on potential treatments. Based on these inequalities, we propose tests of the restrictions. In an empirical application, we show some of these restrictions are violated and pinpoint the substitution pattern that leads to the violation.
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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 | Fang, Zheng and Santos, Andres and Shaikh, Azeem M. and Torgovitsky,… (2023) Inference for Large-Scale Linear Systems With Known Coefficients | 1.000 | 13 | 3 | 100% |
| 2 | Kitagawa, Toru (2015) A Test for Instrument Validity | 1.000 | 7 | 5 | 100% |
| 3 | Kirkeboen, Lars J and Leuven, Edwin and Mogstad, Magne (2016) Field of study, earnings, and self-selection | 1.000 | 7 | 4 | 100% |
| 4 | Kline, Patrick and Walters, Christopher R (2016) Evaluating public programs with close substitutes: The case of Head Start | 0.974 | 13 | 4 | 92% |
| 5 | Behaghel, Luc and Crépon, Bruno and Gurgand, Marc (2014) Private and Public Provision of Counseling to Job Seekers: Evidence from a Large Controlled Experiment | 0.969 | 11 | 6 | 91% |
| 6 | Behaghel, Luc and Crépon, Bruno and Gurgand, Marc (2013) Robustness of the encouragement design in a two-treatment randomized control trial | 0.941 | 12 | 6 | 83% |
| 7 | Mourifié, Ismael and Wan, Yuanyuan (2017) Testing Local Average Treatment Effect Assumptions | 0.920 | 9 | 5 | 78% |
| 8 | Chernozhukov, Victor and Lee, Sokbae and Rosen, Adam M (2013) Intersection Bounds: Estimation and Inference | 0.909 | 8 | 4 | 75% |
| 9 | Balke, Alexander and Pearl, Judea (1997) Bounds on Treatment Effects from Studies with Imperfect Compliance | 0.737 | 3 | 2 | 100% |
| 10 | Balke, Alexander A and Pearl, Judea (1997) Probabilistic Counterfactuals: Semantics, Computation, and Applications | 0.737 | 3 | 2 | 100% |
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