Neil Christy, Amanda Ellen Kowalski
arXiv 20 Dec 2024 · Econometrics
arXiv:2412.16352 · PDF · DOI · OpenAlex · Extracted main text
Leveraging structure from the randomization process, a design-based model of an experiment with a binary intervention and outcome can reveal evidence beyond the average effect without additional data. Our proposed statistical decision rule yields a design-based maximum likelihood estimate (MLE) of the joint distribution of potential outcomes in intervention and control, specified by the numbers of always takers, compliers, defiers, and never takers in the sample. With a visualization, we explain why the likelihood varies with the number of defiers within the Frechet bounds determined by the estimated marginal distributions. We illustrate how the MLE varies with all possible data in samples of 50 and 200: when the estimated average effect is positive, the MLE includes defiers if takeup is below half in control and above half in intervention, unless takeup is zero in control or full in intervention. Under optimality conditions, for increasing sample sizes in which exhaustive grid search is possible, our rule's performance increases relative to a rule that places equal probability on all numbers of defiers within the estimated Frechet bounds. We offer insights into effect heterogeneity in two published experiments with positive, statistically significant average effects on takeup of desired health behaviors and plausible defiers. Our 95% smallest credible sets for defiers include zero and the estimated upper Frechet bound, demonstrating that evidence is weak. Yet, our rule yields no defiers in one experiment. In the other, our rule yields the estimated upper Frechet bound on defiers -- a count representing over 18% of the sample.
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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 | Guido W. Imbens and Joshua D. Angrist (1994) Identification and Estimation of Local Average Treatment Effects | 0.928 | 5 | 4 | 80% |
| 2 | Li, Ang and Pearl, Judea (2019) Unit selection based on counterfactual logic | 0.928 | 4 | 4 | 100% |
| 3 | Angrist, Joshua D and Imbens, Guido W and Rubin, Donald B (1996) Identification of causal effects using instrumental variables | 0.928 | 4 | 3 | 100% |
| 4 | Copas, J. B (1973) Randomization models for the matched and unmatched 2 x 2 tables | 0.843 | 5 | 3 | 60% |
| 5 | Jaynes, Edwin T (1957) Information theory and statistical mechanics | 0.737 | 3 | 3 | 67% |
| 6 | Jaynes, Edwin T (1957) Information theory and statistical mechanics. II | 0.737 | 3 | 3 | 67% |
| 7 | Jaynes, Edwin T (1968) Prior probabilities | 0.737 | 3 | 3 | 67% |
| 8 | Imbens, Guido W and Manski, Charles F (2004) Confidence intervals for partially identified parameters | 0.737 | 3 | 2 | 100% |
| 9 | Ferguson, Thomas S (1967) Mathematical Statistics: A Decision Theoretic Approach | 0.644 | 4 | 2 | 50% |
| 10 | Tappin, David and Bauld, Linda and Purves, David and Boyd, Kathleen… (2015) Financial incentives for smoking cessation in pregnancy: randomised controlled trial | 0.644 | 4 | 1 | 100% |
Showing the top 10 of 119 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Testing Monotonicity in a Finite Population | 0.811 | 4 | 2 |
| 2 | Toggling the Defiers to Relax Monotonicity: The Difference-in-Instrumental-Variables Estimand | 0.405 | 1 | 1 |