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Quantile Treatment Effects in Difference in Differences Models with Panel Data

Brantly Callaway () and Tong Li

No 1701, DETU Working Papers from Department of Economics, Temple University

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 (search for similar items in EconPapers)
JEL-codes: C14 C20 C23 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2017-08
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http://www.cla.temple.edu/RePEc/documents/DETU_17_01.pdf First version, 2017 (application/pdf)

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