Estimating Derivatives in Nonseparable Models with Limited Dependent Variables

21 Pages Posted: 13 May 2011

See all articles by Joseph G. Altonji

Joseph G. Altonji

Yale University - Economic Growth Center; National Bureau of Economic Research (NBER); Yale University - Cowles Foundation

Hidehiko Ichimura

Graduate School of Economics, University of Tokyo

Taisuke Otsu

Yale University - Cowles Foundation

Multiple version iconThere are 3 versions of this paper

Date Written: April 2011

Abstract

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.

Keywords: Censored regression, Nonseparable models, Endogenous regressors, Tobit, Extreme quantiles

JEL Classification: C1, C14, C23, C24

Suggested Citation

Altonji, Joseph G. and Ichimura, Hidehiko and Otsu, Taisuke, Estimating Derivatives in Nonseparable Models with Limited Dependent Variables (April 2011). Cowles Foundation Discussion Paper No. 1668R, Available at SSRN: https://ssrn.com/abstract=1830131 or http://dx.doi.org/10.2139/ssrn.1830131

Joseph G. Altonji

Yale University - Economic Growth Center ( email )

Box 208269
New Haven, CT 06520-8269
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Hidehiko Ichimura

Graduate School of Economics, University of Tokyo ( email )

7-3-1 Hongo Bunkyo-ku
Tokyo 113-0033
Japan

Taisuke Otsu (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
54
Abstract Views
1,500
rank
249,343
PlumX Metrics