Discrete endogenous variables in weakly separable models
Article first published online: 17 JUL 2012
© 2012 The Author(s). The Econometrics Journal © 2012 Royal Economic Society.
The Econometrics Journal
Volume 15, Issue 2, pages 288–303, June 2012
How to Cite
Jun, S. J., Pinkse, J. and Xu, H. (2012), Discrete endogenous variables in weakly separable models. The Econometrics Journal, 15: 288–303. doi: 10.1111/j.1368-423X.2012.00373.x
- Issue published online: 17 JUL 2012
- Article first published online: 17 JUL 2012
- Accepted manuscript online: 22 MAR 2012 12:00AM EST
- First version received: November 2010; final version accepted: March 2012
- Non-parametric identification;
- Weak separability
Summary This paper contains an extension of the identification method proposed in Jun et al. (2011), hereafter JPX, which is based on a generated collection of sets, that is a ‘Dynkin system’. We demonstrate the usefulness of this extension in the context of the model proposed by Vytlacil and Yildiz (2007), hereafter VY. VY formulate a fully non-parametric model featuring a nested weakly separable structure in which an endogenous regressor is binary-valued. The extension of the JPX approach considered here allows for non-binary-valued discrete endogenous regressors and requires weaker support conditions than VY in the binary case, which substantially broadens the range of potential applications of the VY model. In this paper we focus on the binary case for which we provide several alternative simpler sufficient conditions and outline an estimation strategy.