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Estimating Derivatives in Nonseparable Models with Limited Dependent Variables

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  • Joseph G. Altonji
  • Hidehiko Ichimura
  • Taisuke Otsu

Abstract

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 National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14161.

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Date of creation: Jul 2008
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Publication status: published as Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2012. "Estimating Derivatives in Nonseparable Models With Limited Dependent Variables," Econometrica, Econometric Society, vol. 80(4), pages 1701-1719, 07.
Handle: RePEc:nbr:nberwo:14161

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Citations

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Cited by:
  1. Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2008. "Estimating Derivatives in Nonseparable Models with Limited Dependent Variables," NBER Working Papers 14161, National Bureau of Economic Research, Inc.
  2. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, 09.
  3. Ana Fernandes, 2000. "Altruism with Endogenous Labor Supply," Econometric Society World Congress 2000 Contributed Papers 0844, Econometric Society.
  4. Ernesto Villanueva, 2002. "Parental altruism under imperfect information: Theory and evidence," Economics Working Papers 650, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Whitney Newey & Guido Imbens, 2004. "Identification and Estimation of Triangular Simultaneous Equations Models without Additivity," Econometric Society 2004 North American Summer Meetings 594, Econometric Society.
  6. Kazianga, H., 2006. "Motives for household private transfers in Burkina Faso," Journal of Development Economics, Elsevier, vol. 79(1), pages 73-117, February.
  7. Christian Ben Lakhdar & Grégoire Cauchie & Nicolas Gérard Vaillant & François-Charles Wolff, 2012. "The role of family incomes in cigarette smoking: Evidence from French students," Working Papers hal-00694336, HAL.
  8. Elin Halvorsen & Thor Olav Thoresen, 2008. "Parents' Desire to Make Equal Inter Vivos Transfers," CESifo Working Paper Series 2468, CESifo Group Munich.
  9. Joseph G. Altonji & Rosa L. Matzkin, 2001. "Panel Data Estimators for Nonseparable Models with Endogenous Regressors," NBER Technical Working Papers 0267, National Bureau of Economic Research, Inc.
  10. Rosa L. Matzkin & James Heckman & Lars Nesheim, 2002. "Nonparametric Estimation and Nonadditive Hedonic Models," Working Papers 51, Universidad de San Andres, Departamento de Economia, revised Jun 2002.
  11. Julie Zissimopoulos, 2001. "Resource Transfers to the Elderly: Do Adult Children Substitute Financial Transfers for Time Transfers?," Working Papers 01-05, RAND Corporation Publications Department.

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