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SHARP BOUNDS ON THE DISTRIBUTION OF TREATMENT EFFECTS AND THEIR STATISTICAL INFERENCE

Published online by Cambridge University Press:  07 October 2009

Yanqin Fan  and
Sang Soo Park
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Abstract

In this paper, we propose nonparametric estimators of sharp bounds on the distribution of treatment effects of a binary treatment and establish their asymptotic distributions. We note the possible failure of the standard bootstrap with the same sample size and apply the fewer-than-n bootstrap to making inferences on these bounds. The finite sample performances of the confidence intervals for the bounds based on normal critical values, the standard bootstrap, and the fewer-than-n bootstrap are investigated via a simulation study. Finally we establish sharp bounds on the treatment effect distribution when covariates are available.

Type
Brief Report
Information
Econometric Theory , Volume 26 , Issue 3 , June 2010 , pp. 931 - 951
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

We thank Jinyong Hahn and two anonymous referees for their valuable suggestions that greatly improved the paper. We thank Jianqing Fan, Joel Horowitz, Chuck Manski, Per Mykland, Bryan Shepherd, Elie Tamer, and seminar participants in the Department of Statistics at the University of Chicago and in the Department of Economics at Northwestern University, UNC at Chapel Hill, and Princeton University for helpful discussions. We also thank Jeff Smith and Jörg Stoye for providing useful references. Y. Fan acknowledges financial support from the National Science Foundation.

References

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