Quantile Treatment Effects in Difference in Differences Models with Panel Data

58 Pages Posted: 4 Aug 2017

See all articles by Brantly Callaway

Brantly Callaway

Temple University

Tong Li

Vanderbilt University

Date Written: August 3, 2017

Abstract

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 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. Second, we allow for identification to hold only after conditioning on covariates and provide very simple estimators based on propensity score re-weighting for this case. We use our method to estimate the effect of increasing the minimum wage on quantiles of local labor markets’ unemployment rates and find significant heterogeneity.

Keywords: Quantile Treatment Effect on the Treated, Difference in Differences, Copula, Panel Data, Propensity Score Re-Weighting

JEL Classification: C14, C20, C23

Suggested Citation

Callaway, Brantly and Li, Tong, Quantile Treatment Effects in Difference in Differences Models with Panel Data (August 3, 2017). Available at SSRN: https://ssrn.com/abstract=3013341 or http://dx.doi.org/10.2139/ssrn.3013341

Brantly Callaway (Contact Author)

Temple University ( email )

Philadelphia, PA 19122
United States

HOME PAGE: http://brantlycallaway.com

Tong Li

Vanderbilt University ( email )

2301 Vanderbilt Place
Nashville, TN 37240
United States

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