Econometrica: Jul 2012, Volume 80, Issue 4

Estimating Derivatives in Nonseparable Models With Limited Dependent Variables
p. 1701-1719

Joseph G. Altonji, Hidehiko Ichimura, Taisuke Otsu

We present a simple way to estimate the effects of changes in a vector of observable variables on a limited dependent variable when is a general nonseparable function of and unobservables, and is independent of the unobservables. We treat models in which is censored from above, below, or both. The basic idea is to first estimate the derivative of the conditional mean of given at with respect to on the uncensored sample without correcting for the effect of 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.

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