Quantile treatment effects in difference in differences models with panel data

Copyright © 2019 The Authors. This paper considers identification and estimation of the Quantile Treatment Effect on the Treated (QTT) under a straightforward distributional extension of the most commonly invoked Mean Difference in Differences Assumption used for identifying the Average Treatment Effect on the Treated (ATT). Identification of the QTT is more complicated than the ATT though because it depends on the unknown dependence (or copula) between the change in untreated potential outcomes and the initial level of untreated potential outcomes for the treated group. To address this issue, we introduce a new Copula Stability Assumption that says that the missing dependence is constant over time. Under this assumption and when panel data is available, the missing dependence can be recovered, and the QTT is identified. We use our method to estimate the effect of increasing the minimum wage on quantiles of local labor markets\u27 unemployment rates and find significant heterogeneity

Evaluating Policies Early in a Pandemic: Bounding Policy Effects with Nonrandomly Missing Data

During the early stages of the Covid-19 pandemic, national and local governments introduced a large number of policies, particularly non-pharmaceutical interventions, to combat the spread of Covid-19. Understanding the effects that these policies had (both on Covid-19 cases and on other outcomes) is particularly challenging though because (i) Covid-19 testing was not widely available, (ii) the availability of tests varied across locations, and (iii) the tests that were available were generally targeted towards individuals meeting certain eligibility criteria. In this paper, we propose a new approach to evaluate the effect of policies early in the pandemic that accommodates limited and nonrandom testing. Our approach results in (generally informative) bounds on the effect of the policy on actual cases and in point identification of the effect of the policy on other outcomes. We apply our approach to study the effect of Tennessee's open-testing policy during the early stage of the pandemic. For this policy, we find suggestive evidence that the policy decreased the number of Covid-19 cases in the state relative to what they would have been if the policy had not been implemented.Comment: 36 pages, 8 figure

Difference-in-Differences for Policy Evaluation

Difference-in-differences is one of the most used identification strategies in empirical work in economics. This chapter reviews a number of important, recent developments related to difference-in-differences. First, this chapter reviews recent work pointing out limitations of two way fixed effects regressions (these are panel data regressions that have been the dominant approach to implementing difference-in-differences identification strategies) that arise in empirically relevant settings where there are more than two time periods, variation in treatment timing across units, and treatment effect heterogeneity. Second, this chapter reviews recently proposed alternative approaches that are able to circumvent these issues without being substantially more complicated to implement. Third, this chapter covers a number of extensions to these results, paying particular attention to (i) parallel trends assumptions that hold only after conditioning on observed covariates and (ii) strategies to partially identify causal effect parameters in difference-in-differences applications in cases where the parallel trends assumption may be violated.Comment: This version has been removed by arXiv administrators because the submitter did not have the authority to grant the license at the time of submissio