arXiv 28 Sep 2020 · Statistics — Applications · 3 citations (OpenAlex)
arXiv:2009.13404 · PDF · DOI · OpenAlex · Extracted main text
The difference-in-differences (DID) design is widely used in observational studies to estimate the causal effect of a treatment when repeated observations over time are available. Yet, almost all existing methods assume linearity in the potential outcome (parallel trends assumption) and target the additive effect. In social science research, however, many outcomes of interest are measured on an ordinal scale. This makes the linearity assumption inappropriate because the difference between two ordinal potential outcomes is not well defined. In this paper, I propose a method to draw causal inferences for ordinal outcomes under the DID design. Unlike existing methods, the proposed method utilizes the latent variable framework to handle the non-numeric nature of the outcome, enabling identification and estimation of causal effects based on the assumption on the quantile of the latent continuous variable. The paper also proposes an equivalence-based test to assess the plausibility of the key identification assumption when additional pre-treatment periods are available. The proposed method is applied to a study estimating the causal effect of mass shootings on the public's support for gun control. I find little evidence for a uniform shift toward pro-gun control policies as found in the previous study, but find that the effect is concentrated on left-leaning respondents who experienced the shooting for the first time in more than a decade.
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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 | Athey \ Imbens (2006) Identification and inference in nonlinear difference-in-differences models | 0.874 | 6 | 2 | 100% |
| 2 | Hartman \ Newman (2019) Accounting for Pre-Treatment Exposure in Panel Data: Re-Estimating the Effect of Mass Public Shootings | 0.843 | 4 | 3 | 75% |
| 3 | Angrist \ Pischke (2008) Mostly harmless econometrics: An empiricist's companion | 0.843 | 3 | 3 | 100% |
| 4 | Newman \ Hartman (2019) Mass shootings and public support for gun control | 0.737 | 10 | 5 | 40% |
| 5 | Barney \ Schaffner (2019) Reexamining the Effect of Mass Shootings on Public Support for Gun Control | 0.675 | 13 | 5 | 31% |
| 6 | Lu, Ding \ Dasgupta (2018) Treatment effects on ordinal outcomes: Causal estimands and sharp bounds | 0.659 | 7 | 4 | 29% |
| 7 | Sofer, Richardson, Colicino, Schwartz \ Tchetgen (2016) On negative outcome control of unobserved confounding as a generalization of difference-in-differences | 0.644 | 2 | 2 | 100% |
| 8 | Volfovsky, Airoldi \ Rubin (2015) Causal inference for ordinal outcomes | 0.511 | 2 | 2 | 50% |
| 9 | Abadie (2005) Semiparametric difference-in-differences estimators | 0.511 | 2 | 1 | 100% |
| 10 | Kuriwaki (2018) Cumulative CCES Common Content (2006-2018) | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 34 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Quantile and Distribution Treatment Effects on the Treated with Possibly Non-Continuous Outcomes | 0.811 | 4 | 2 |
| 2 | Causal Inference for Qualitative Outcomes | 0.511 | 2 | 1 |