This review evaluates difference in differences and other methods for estimating policy effects on limited dependent variables, suggesting specific approaches.
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 .
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Lee et al. (2025) studied this question.
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