Evaluating the Impact of Regulatory Policies on Social Welfare in Difference-in-Difference Settings

TL;DR

This paper develops a new method to evaluate how regulatory policies affect social welfare by providing bounds on counterfactual outcomes, accommodating outcome discontinuities and unobserved factors, with application to minimum wage policies.

Contribution

It introduces a copula stability-based partial identification approach that handles outcome discontinuities and unobserved heterogeneity in difference-in-difference analyses.

Findings

Provides sharp bounds on counterfactual distributions for various outcome types

Bounds are invariant to monotonic transformations of outcomes

Application demonstrates the method's usefulness in minimum wage impact analysis

Abstract

Quantifying the impact of regulatory policies on social welfare generally requires the identification of counterfactual distributions. Many of these policies (e.g. minimum wages or minimum working time) generate mass points and/or discontinuities in the outcome distribution. Existing approaches in the difference-in-difference literature cannot accommodate these discontinuities while accounting for selection on unobservables and non-stationary outcome distributions. We provide a unifying partial identification result that can account for these features. Our main identifying assumption is the stability of the dependence (copula) between the distribution of the untreated potential outcome and group membership (treatment assignment) across time. Exploiting this copula stability assumption allows us to provide an identification result that is invariant to monotonic transformations. We provide sharp bounds on the counterfactual distribution of the treatment group suitable for any outcome, whether discrete, continuous, or mixed. Our bounds collapse to the point-identification result in Athey and Imbens (2006) for continuous outcomes with strictly increasing distribution functions. We illustrate our approach and the informativeness of our bounds by analyzing the impact of an increase in the legal minimum wage using data from a recent minimum wage study (Cengiz et al 2019).