Difference-in-Differences vs Lagged-Outcome Regression

Difference-in-Differences (DiD) and Lagged-Outcome Regression are two methods for estimating causal effects from non-randomized, self-selected treatments. DiD assumes parallel trends between treated and control groups, while lagged-outcome regression assumes no unobserved confounding after conditioning on past outcomes. A simulation study demonstrates the specific failure modes for each approach. Lagged-outcome regression is biased by unobserved time-invariant confounders, whereas DiD is biased when users select into treatment because of a temporary dip in the outcome variable. The analysis concludes that the choice of method depends on the underlying data-generating process, as each is biased under different, common scenarios.