Difference in Differences and Ratio in Ratios for Limited Dependent Variables

TL;DR

This paper develops a unified framework for applying difference-in-differences and ratio-in-ratios methods to limited dependent variables using generalized linear models, supported by simulations and empirical analysis.

Contribution

It introduces a comprehensive approach to implement DD and related methods for various limited dependent variables within the GLM framework, recommending specific estimators.

Findings

Poisson Quasi-MLE is recommended for non-negative Y.

(Multinomial) logit MLE is suitable for binary, fractional, or multinomial Y.

Simulation and empirical results support the proposed methods.

Abstract

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" or "ratio in odds ratios") to binary, count, fractional, multinomial or zero-censored Y under the unifying framework of `generalized linear models with link functions'. We 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.