Statistics Seminar: Tong Li (Vanderbilt University) -- Quantile Treatment Effects in Difference in Differences Models with Panel Data

Abstract 

This talk considers identification and estimation of the Quantile Treatment Effect on
the Treated (QTET) 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 QTET 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 QTET is identified.  Second, we provide identification results for the case when
the identifying assumptions hold conditional on covariates.  Under slightly stronger
versions of the conditional assumptions, we provide very simple estimators based on
propensity score re-weighting.  We compare the performance of our method to existing
methods for estimating QTETs using Lalonde (1986)’s job training dataset.  Using this
dataset, we find the performance of our method compares favorably to the performance of
existing methods.