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

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Cited by:
  1. Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2008. "Estimating Derivatives in Nonseparable Models with Limited Dependent Variables," Cowles Foundation Discussion Papers 1668R, Cowles Foundation for Research in Economics, Yale University, revised May 2011.
  2. Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
  3. Ana Fernandes, 2000. "Altruism with Endogenous Labor Supply," Econometric Society World Congress 2000 Contributed Papers 0844, Econometric Society.
  4. Ernesto Villanueva, 2003. "Parental altruism under imperfect information: theory and evidence," Working Papers 19, Barcelona Graduate School of Economics.
  5. Guido W. Imbens & Whitney K. Newey, 2002. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," NBER Technical Working Papers 0285, National Bureau of Economic Research, Inc.
  6. Harounan Kaziango, 2004. "Motives for Household Private Transfers in Burkina Faso," Working Papers, Economic Growth Center, Yale University 895, Economic Growth Center, Yale University.
  7. 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.
  8. 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.
  9. Julie Zissimopoulos, 2001. "Resource Transfers to the Elderly: Do Adult Children Substitute Financial Transfers for Time Transfers?," Working Papers, RAND Corporation Publications Department 01-05, RAND Corporation Publications Department.
  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.
  12. Taisuke Otsu & Luke Taylor, 2014. "Estimation of Nonseparable Models with Censored Dependent Variables and Endogenous Regressors," STICERD - Econometrics Paper Series /2014/575, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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