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.
An IV Model of Quantile Treatment Effects
Article first published online: 3 DEC 2004
Volume 73, Issue 1, pages 245–261, January 2005
How to Cite
Chernozhukov, V. and Hansen, C. (2005), An IV Model of Quantile Treatment Effects. Econometrica, 73: 245–261. doi: 10.1111/j.1468-0262.2005.00570.x
- Issue published online: 3 DEC 2004
- Article first published online: 3 DEC 2004
- Manuscript received January, 2002; final revision received March, 2004.
- quantile regression;
- simultaneous equations;
- instrumental regression;
- nonlinear model;
- monotone likelihood ratio;
- bounded completeness;
- partial identification
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).