I thank Hidehiko Ichimura, Roger Koenker, Valérie Lechene, Charles Manski, Whitney Newey, Joao Santos Silva, Richard Spady, Elie Tamer, the referees, and seminar participants at Northwestern University, University of Chicago, the Harvard–MIT econometrics worshop and the 14th EC2 Meeting for comments. I am grateful to the Leverhulme Trust for financial support through grants to the Centre for Microdata Methods and Practice and to the project “Evidence, Inference and Enquiry.”
Nonparametric Identification under Discrete Variation
Version of Record online: 5 AUG 2005
Volume 73, Issue 5, pages 1525–1550, September 2005
How to Cite
Chesher, A. (2005), Nonparametric Identification under Discrete Variation. Econometrica, 73: 1525–1550. doi: 10.1111/j.1468-0262.2005.00628.x
- Issue online: 5 AUG 2005
- Version of Record online: 5 AUG 2005
- Manuscript received December, 2003; final revision received March, 2005.
- nonparametric models;
- discrete endogenous variables;
- partial identification;
- weak instruments;
- quantile regression;
- control function methods
This paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates. The function delivers values of a discrete or continuous outcome and instruments may be discrete valued. Application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions. The results are used to investigate the nonparametric identifying power of the quarter-of-birth instruments used in Angrist and Krueger's 1991 study of the returns to schooling.