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Estimating Derivatives in Nonseparable Models with Limited Dependent Variables

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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, 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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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1668-r.pdf
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Bibliographic Info

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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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Censored regression; Nonseparable models; Endogenous regressors; Tobit; Extreme quantiles;

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Citations

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Cited by:
  1. Ben Lakhdar, Christian & Cauchie, Grégoire & Vaillant, Nicolas Gérard & Wolff, François-Charles, 2012. "The role of family incomes in cigarette smoking: Evidence from French students," Social Science & Medicine, Elsevier, vol. 74(12), pages 1864-1873.
  2. 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.
  3. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, 09.
  4. Ernesto Villanueva, 2001. "Parental altruism under imperfect information: Theory and evidence," Economics Working Papers 566, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2002.
  5. Ana Fernandes, 2000. "Altruism with Endogenous Labor Supply," Econometric Society World Congress 2000 Contributed Papers 0844, Econometric Society.
  6. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, 09.
  7. 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.
  8. 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.
  9. Kazianga, H., 2006. "Motives for household private transfers in Burkina Faso," Journal of Development Economics, Elsevier, vol. 79(1), pages 73-117, February.
  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. Elin Halvorsen & Thor Olav Thoresen, 2008. "Parents' Desire to Make Equal Inter Vivos Transfers," CESifo Working Paper Series 2468, CESifo Group Munich.

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