# A bracketing relationship between difference-in-differences and lagged-dependent-variable adjustment

arXiv: https://arxiv.org/abs/1903.06286 · HTML: https://mlsanity.com/paper/1903.06286/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2019.

## Built on by (most cited first, 2 of 2)

- [Dynamic covariate balancing: estimating treatment effects over time with potential local projections](https://mlsanity.com/paper/2103.01280/) (2021)
- [Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumption](https://mlsanity.com/paper/2309.16409/) (2023)

## Abstract (arXiv)

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, citetAPbook 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 citetding2019bracketingData.