An IV Model of Quantile Treatment Effects

Authors

  • Victor Chernozhukov,

    1. 1 Dept. Economics, Massachusetts Institute of Technology, E52-262F, 50 Memorial Drive, Cambridge, MA 02142, U.S.A.; vchern@mit.edu; www.mit.edu/~vchern
      and
      2Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, IL 60637, U.S.A.; chansen1@gsb.uchicago.edu.
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  • and 1 Christian Hansen 2

    1. 1 Dept. Economics, Massachusetts Institute of Technology, E52-262F, 50 Memorial Drive, Cambridge, MA 02142, U.S.A.; vchern@mit.edu; www.mit.edu/~vchern
      and
      2Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, IL 60637, U.S.A.; chansen1@gsb.uchicago.edu.
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    • We benefited from seminars at Cornell, Penn, University of Illinois at Urbana-Champaign (all in 2001), Harvard-MIT in 2002, and the EC2 2001 Conference on Causality and Exogeneity in Econometrics in Louvain-la-Neueve. Conversations with Takeshi Amemiya, Tom MaCurdy and especially Alberto Abadie motivated the line of research taken here. We thank Jerry Hausman and Whitney Newey for careful readings of the paper and for help with presentation. We also thank Josh Angrist, Moshe Buchinsky, Jin Hahn, James Heckman, Guido Imbens, Roger Koenker, Joanna Lahey, Igor Makarov, the coeditor, and anonymous referees for many valuable comments.


Abstract

The ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications. However, in observational studies, the variables of interest (e.g., education, prices) are often endogenous, making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes. In order to address this problem, we develop a model of quantile treatment effects (QTE) in the presence of endogeneity and obtain conditions for identification of the QTE without functional form assumptions. The principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states. This feature allows us to overcome the endogeneity problem and recover the true QTE through the use of instrumental variables. The proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors, where QTE can be interpreted as the structural quantile effects (SQE).

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