A BRACKETING RELATIONSHIP BETWEEN DIFFERENCE-IN-DIFFERENCES AND LAGGED-DEPENDENT-VARIABLE ADJUSTMENT
FAN LI – DUKE UNIVERSITY
Difference-in-differences is one of the most widely-used causal inference methods for 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 this paper, we show a general nonparametric bracketing relationship between the difference-in-differences and lagged-dependent-variable regression estimates, under testable assumptions. 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. This provides a general strategy to construct bounds for the treatment effects. We provide three examples to illustrate the theoretical results.
This is a joint work with Peng Ding of UC Berkeley.