A Bracketing Relationship between Difference-in-Differences and Lagged-Dependent-Variable Adjustment. (11th July 2019)

• Record Type: Journal Article
• Authors: Ding, Peng; Li, Fan
• Is Part Of: Political analysis. Volume 27:Number 4(2019)
• Page Start: 605
• Page End: 615
• Publication Date: 2019-07-11
• Subjects: causal inference, -- ignorability, -- nonparametric, -- panel data, -- parallel trends; Political science -- Methodology -- Periodicals; Electronic journals; 320.011
• DOI: 10.1017/pan.2019.25
• Languages: English
• ISSNs: 1047-1987

Abstract

Abstract : 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 ).