This research was partially completed while the second author was a fellow at the Center for Advanced Study in the Behavioral Sciences. The NSF provided partial financial support through Grants SES 0136789 (Imbens) and SES 0136869 (Newey). Versions were presented at seminars in March 2001 and December 2003. We are grateful for comments by S. Athey, L. Benkard, S. Berry, R. Blundell, G. Chamberlain, A. Chesher, J. Heckman, O. Linton, A. Nevo, A. Pakes, J. Powell, and participants at seminars at Stanford, University College London, Harvard, MIT, Northwestern, and Yale. We especially thank R. Blundell for providing the data and initial empirical results.
Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity
Version of Record online: 6 OCT 2009
© 2009 The Econometric Society
Volume 77, Issue 5, pages 1481–1512, September 2009
How to Cite
Imbens, G. W. and Newey, W. K. (2009), Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity. Econometrica, 77: 1481–1512. doi: 10.3982/ECTA7108
- Issue online: 6 OCT 2009
- Version of Record online: 6 OCT 2009
- Manuscript received April, 2007; final revision received January, 2009.
- Nonseparable models;
- control variables;
- quantile effects;
- average derivative;
- policy effect;
- nonparametric estimation;
- demand analysis
This paper uses control variables to identify and estimate models with nonseparable, multidimensional disturbances. Triangular simultaneous equations models are considered, with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance. Here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable. Also, for any control variable, identification results are given for quantile, average, and policy effects. Bounds are given when a common support assumption is not satisfied. Estimators of identified objects and bounds are provided, and a demand analysis empirical example is given.