A Bracketing Relationship between Difference-in-Differences and Lagged-Dependent-Variable Adjustment
By Peng Ding, Fan Li. Political Analysis, 2019
78 citations recorded by the source corpus.
Difference-in-differences is a widely used evaluation strategy that draws causal inference from observational panel data. Its causal identification relies on the assumption of parallel trends, which is scale-dependent and may be questionable in some applications. A common alternative is a regression model that adjusts for the lagged dependent variable, which rests on the assumption of ignorability conditional on past outcomes. In the context of linear models, Angrist and Pischke (2009) show that the difference-in-differences and lagged-dependent-variable regression estimates have a bracketing relationship. Namely, for a true positive effect, if ignorability is correct, then mistakenly assuming parallel trends will overestimate the effect; in contrast, if the parallel trends assumption is correct, then mistakenly assuming ignorability will underestimate the effect. We show that the same bracketing relationship holds in general nonparametric (model-free) settings. We also extend the result to semiparametric estimation based on inverse probability weighting. We provide three examples to illustrate the theoretical results with replication files in Ding and Li (2019).
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ca3f235479a5c050a8a1b73222ef4be4c5e4e358
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Statistics and Probability
- Jonathan Roth
- Pedro H. C. Sant’Anna
- Brantly Callaway
- X. d'Haultfoeuille
- C. Chaisemartin
- David F. Larcker
- A. Baker
- Charles C. Y. Wang
Citations in the corpus
- What’s trending in difference-in-differences? A synthesis of the recent econometrics literature (2022, unknown): “See Chabé-Ferret (2015), Angrist and Pischke (2009, Chapter 5.4), and Ding and Li (2019) for related discussion.”
- Efficient Estimation for Staggered Rollout Designs (2021, background): “…will often be biased as well, e.g. when treatment is randomly assigned conditional on lagged 15Future work might also consider an estimator that uses a high-dimensional X̂, but considers some form of regularization on the coefficient β̂. outcomes (Angrist and Pischke, 2009; Ding and Li, 2019).16 N”