Ting Ye, Luke Keele, Raiden Hasegawa, Dylan S. Small
arXiv 3 Jun 2020 · Statistics — Methodology · publishedJournal of the American Statistical Association (2023) · 15 citations (OpenAlex)
arXiv:2006.02423 · PDF · DOI · OpenAlex · Extracted main text
The method of difference-in-differences (DID) is widely used to study the causal effect of policy interventions in observational studies. DID employs a before and after comparison of the treated and control units to remove bias due to time-invariant unmeasured confounders under the parallel trends assumption. Estimates from DID, however, will be biased if the outcomes for the treated and control units evolve differently in the absence of treatment, namely if the parallel trends assumption is violated. We propose a general identification strategy that leverages two groups of control units whose outcomes relative to the treated units exhibit a negative correlation, and achieves partial identification of the average treatment effect for the treated. The identified set is of a union bounds form that involves the minimum and maximum operators, which makes the canonical bootstrap generally inconsistent and naive methods overly conservative. By utilizing the directional inconsistency of the bootstrap distribution, we develop a novel bootstrap method to construct uniformly valid confidence intervals for the identified set and parameter of interest when the identified set is of a union bounds form, and we establish the method's theoretical properties. We develop a simple falsification test and sensitivity analysis. We apply the proposed strategy for bracketing to study whether minimum wage laws affect employment levels.
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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 | Manski, C. F. and Pepper, J. V (2018) How do right-to-carry laws affect crime rates? coping with ambiguity using bounded-variation assumptions | 0.843 | 3 | 3 | 100% |
| 2 | Berger, R. L. and Hsu, J. C (1996) Bioequivalence trials, intersection-union tests and equivalence confidence sets | 0.843 | 3 | 3 | 100% |
| 3 | Hasegawa, R. B., Webster, D. W., and Small, D. S (2019) Bracketing in the comparative interrupted time-series design to address concerns about history interacting with group: Evaluatin… self | 0.811 | 15 | 4 | 53% |
| 4 | Chernozhukov, V., Lee, S., and Rosen, A. M (2013) Intersection bounds: estimation and inference | 0.811 | 4 | 2 | 100% |
| 5 | Athey, S. and Imbens, G. W (2006) Indentification and inference in nonlinear difference-in-difference models | 0.737 | 3 | 3 | 67% |
| 6 | Donald, S. G. and Lang, K (2007) Inference with differences-in-differences and other panel data | 0.737 | 3 | 2 | 100% |
| 7 | Romano, J. P. and Shaikh, A. M (2012) On the uniform asymptotic validity of subsampling and the bootstrap | 0.644 | 4 | 2 | 50% |
| 8 | Derenoncourt, E. and Montialoux, C (2021) Minimum wages and racial inequality | 0.644 | 4 | 1 | 100% |
| 9 | Angrist, J. D. and Pischke, J.-S (2009) Mostly Harmless Econometrics | 0.644 | 2 | 2 | 100% |
| 10 | Bertrand, M., Duflo, E., and Mullainathan, S (2004) How much should we trust differences-in-differences estimates? | 0.644 | 2 | 2 | 100% |
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