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Estimating Derivatives in Nonseparable Models with Limited Dependent Variables

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.

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1668R.

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Length: 20 pages
Date of creation: Jul 2008
Date of revision: May 2011
Publication status: Published in Econometrica (July 2012), 80(4): 1701-1719
Handle: RePEc:cwl:cwldpp:1668r
Note: CFP 1369.
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