arXiv 12 Nov 2022 · Econometrics
arXiv:2211.06710 · PDF · DOI · OpenAlex · Extracted main text
The difference-in-differences (DID) method identifies the average treatment effects on the treated (ATT) under mainly the so-called parallel trends (PT) assumption. The most common and widely used approach to justify the PT assumption is the pre-treatment period examination. If a null hypothesis of the same trend in the outcome means for both treatment and control groups in the pre-treatment periods is rejected, researchers believe less in PT and the DID results. This paper develops a robust generalized DID method that utilizes all the information available not only from the pre-treatment periods but also from multiple data sources. Our approach interprets PT in a different way using a notion of selection bias, which enables us to generalize the standard DID estimand by defining an information set that may contain multiple pre-treatment periods or other baseline covariates. Our main assumption states that the selection bias in the post-treatment period lies within the convex hull of all selection biases in the pre-treatment periods. We provide a sufficient condition for this assumption to hold. Based on the baseline information set we construct, we provide an identified set for the ATT that always contains the true ATT under our identifying assumption, and also the standard DID estimand. We extend our proposed approach to multiple treatment periods DID settings. We propose a flexible and easy way to implement the method. Finally, we illustrate our methodology through some numerical and empirical examples.
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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 | Callaway, B. and Pedro H.C. Sant’Anna (2021) Difference-in-Differences with multiple time periods | 1.000 | 9 | 3 | 100% |
| 2 | Kresch, Evan Plous (2020) The buck stops where? federalism, uncertainty, and investment in the brazilian water and sanitation sector | 0.984 | 21 | 3 | 95% |
| 3 | Cawley, John, David Frisvold, David Jones, and Chelsea Lensing (2021) The Pass‐Through of a Tax on Sugar‐Sweetened Beverages in Boulder, Colorado | 0.956 | 8 | 3 | 88% |
| 4 | Cai, Jing (2016) The Impact of Insurance Provision on Household Production and Financial Decisions | 0.946 | 13 | 3 | 85% |
| 5 | Rambachan, A. and J. Roth (2022) A More Credible Approach to Parallel Trends | 0.909 | 24 | 3 | 75% |
| 6 | Manski, Charles F. and John V. Pepper (2018) How Do Right-to-Carry Laws Affect Crime Rates? Coping with Ambiguity Using Bounded-Variation Assumptions | 0.874 | 9 | 2 | 100% |
| 7 | Ashenfelter, Orley (1978) Estimating the Effect of Training Programs on Earnings | 0.874 | 6 | 2 | 100% |
| 8 | Wooldridge, J. M (2021) Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators | 0.737 | 3 | 2 | 100% |
| 9 | Ashenfelter, Orley and David Card (1985) Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs | 0.644 | 2 | 2 | 100% |
| 10 | Caetano, C., B. Callaway, S. Paye, and H. Sant'Anna Rodrigues (2022) Difference in Differences with Time-Varying Covariates | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 61 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Compositional Difference-in-Differences | 0.843 | 3 | 3 |
| 2 | Synthetic Parallel Trends | 0.737 | 3 | 2 |