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Estimating Derivatives in Nonseparable Models with Limited Dependent Variables

42 Pages Posted: 15 Jul 2008 Last revised: 20 Jul 2008

Joseph G. Altonji

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

Taisuke Otsu

Yale University - Cowles Foundation

Hidehiko Ichimura

Graduate School of Economics, University of Tokyo

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Date Written: July 15, 2008

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. We treat models in which Y is censored from above or below or potentially from 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 changes in x induced on the censored population. We then correct the derivative for the effects of the selection bias. We propose nonparametric and semiparametric estimators for the derivative. As extensions, we discuss the cases of discrete regressors, measurement error in dependent variables, and endogenous regressors in a cross section and panel data context.

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

JEL Classification: C1, C14, C23, C24

Suggested Citation

Altonji, Joseph G. and Otsu, Taisuke and Ichimura, Hidehiko, Estimating Derivatives in Nonseparable Models with Limited Dependent Variables (July 15, 2008). Cowles Foundation Discussion Paper No. 1668. Available at SSRN: https://ssrn.com/abstract=1160262

Joseph G. Altonji (Contact Author)

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

Taisuke Otsu

Yale University - Cowles Foundation ( email )

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

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