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Estimating derivatives in nonseparable models with limited dependent variables

  • Joseph Altonji

    (Institute for Fiscal Studies)

  • Hidehiko Ichimura

    ()

    (Institute for Fiscal Studies and University of Tokyo)

  • Taisuke Otsu

    ()

    (Institute for Fiscal Studies and London School of Economics and Political Science)

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.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP20/08.

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Date of creation: Jul 2008
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Handle: RePEc:ifs:cemmap:20/08
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