We thank a co-editor and three referees for their insightful comments. Our research was supported by National Science Foundation Grant SBR-9512009, the Institute for Policy Research, Northwestern University, the Economic Growth Center and the Cowles Foundation, and Yale University (Altonji), JSPS Basic Research (B) Grant 18330040 (Ichimura), and National Science Foundation Grant SES-0720961 (Otsu).
Estimating Derivatives in Nonseparable Models With Limited Dependent Variables
Article first published online: 25 JUL 2012
© 2012 The Econometric Society
Volume 80, Issue 4, pages 1701–1719, July 2012
How to Cite
Altonji, J. G., Ichimura, H. and Otsu, T. (2012), Estimating Derivatives in Nonseparable Models With Limited Dependent Variables. Econometrica, 80: 1701–1719. doi: 10.3982/ECTA8004
- Issue published online: 25 JUL 2012
- Article first published online: 25 JUL 2012
- Manuscript received June, 2008; final revision received May, 2011.
- Nonseparable models;
- extreme quantiles;
- censored dependent variables;
- average derivatives
We present a simple way to estimate the effects of changes in a vector of observable variables X on a limited dependent variable Y when Y is a general nonseparable function of X and unobservables, and X is independent of the unobservables. We treat models in which Y is censored from above, below, or both. The basic idea is to first estimate the derivative of the conditional mean of Y given X at x with respect to x on the uncensored sample without correcting for the effect of x on the censored population. We then correct the derivative for the effects of the selection bias. We discuss nonparametric and semiparametric estimators for the derivative. We also discuss the cases of discrete regressors and of endogenous regressors in both cross section and panel data contexts.