SMU SOE Seminar Series (May 2, 2025): On Quantile Treatment Effects, Rank Similarity, and Variation of Instrumental Variables

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ABSTRACT

This paper proposes a general approach for the nonparametric identification and estimation of distributional treatment effects in the presence of nonseparable endogeneity. To motivate our approach, we begin by characterizing a commonly used identification assumption in the literature, namely, rank similarity (RS), in terms of the relationship between observed and counterfactual distributions of potential outcomes. This characterization highlights the stringency of the RS assumption and naturally leads to a weaker identifying condition that we propose. Building on this new condition, we derive bounds for the distributional treatment effects of interest using a linear programming (LP) approach. The proposed identification strategy also provides justification for leveraging richer exogenous variation in instrumental variables (e.g., multi-valued or multiple instruments), as such variation can help tighten these bounds. Finally, we establish the asymptotic properties of the estimated bounds obtained by solving the empirical LP problem.

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