Estimating Derivatives in Nonseparable Models With Limited Dependent Variables

Joseph G. Altonji, Hidehiko Ichimura, Taisuke Otsu

Research output: Contribution to journalComment/debatepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1701-1719
Number of pages19
Issue number4
StatePublished - Jul 2012


  • Average derivatives
  • Censored dependent variables
  • Extreme quantiles
  • Nonparametric
  • Nonseparable models
  • Semiparametric

ASJC Scopus subject areas

  • Economics and Econometrics


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