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Estimating derivatives in nonseparable models with limited dependent variables

Authors: Joseph Altonji , Hidehiko Ichimura and Taisuke Otsu
Date: 25 July 2012
Type: Journal article, Econometrica, Vol. 80, No. 4, pp. 1701--1719
DOI: 10.3982/ECTA8004


We present a simple way to estimate the effects of changes in a vector of observable variables Xon 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.

Previous version:
Joseph Altonji, Hidehiko Ichimura and Taisuke Otsu July 2008, Estimating derivatives in nonseparable models with limited dependent variables, cemmap Working Paper

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