A Bracketing Relationship between Difference-in-Differences and Lagged-Dependent-Variable Adjustment

Journal Article (Journal Article)

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).

Full Text

Duke Authors

Cited Authors

  • Ding, P; Li, F

Published Date

  • October 1, 2019

Published In

Volume / Issue

  • 27 / 4

Start / End Page

  • 605 - 615

Electronic International Standard Serial Number (EISSN)

  • 1476-4989

International Standard Serial Number (ISSN)

  • 1047-1987

Digital Object Identifier (DOI)

  • 10.1017/pan.2019.25

Citation Source

  • Scopus