CFDP 1668R

Estimating Derivatives in Nonseparable Models with Limited Dependent Variables


Publication Date: June 2008

Revision Date: May 2011

Pages: 20


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.


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

JEL Classification Codes:  C1, C14, C23, C24

See CFP: 1369