Difference in Differences, Ratio in Ratios, and Ratio in Odds Ratios for Limited Dependent Variables: A Review and More

Difference in differences (DD) is widely used to find policy/treatment effects with observational data, but applying DD to limited dependent variables (LDV's) Y has been problematic. This paper addresses how to apply DD and related approaches, such as "ratio in ratios"and "ratio in odds ratios", to LDV's under the unifying framework of 'generalized linear models with link functions'. We review and evaluate DD and the related approaches with simulation and empirical studies, and recommend 'Poisson Quasi-MLE' for non-negative (such as count or zero-censored) Y and (multinomial) logit MLE for binary, fractional or multinomial Y.