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Estimating derivatives in nonseparable models with limited dependent variables

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Author Info
Joseph Altonji
Hidehiko Ichimura () (Institute for Fiscal Studies and University of Tokyo)
Taisuke Otsu

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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. 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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  6. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November. [Downloadable!] (restricted)
  7. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, 07. [Downloadable!] (restricted)
  8. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 120-137 National Bureau of Economic Research, Inc. [Downloadable!]
  9. Arthur Lewbel & Oliver Linton, 2002. "Nonparametric Censored and Truncated Regression," Econometrica, Econometric Society, vol. 70(2), pages 765-779, March. [Downloadable!] (restricted)
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  10. Chaudhuri, Probal, 1991. "Global nonparametric estimation of conditional quantile functions and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 246-269, November. [Downloadable!] (restricted)
  11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
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  13. Barro, Robert J, 1974. "Are Government Bonds Net Wealth?," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1095-1117, Nov.-Dec.. [Downloadable!] (restricted)
  14. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July. [Downloadable!] (restricted)
  15. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November. [Downloadable!] (restricted)
  16. Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-85, May. [Downloadable!] (restricted)
  17. Kazianga, H., 2006. "Motives for household private transfers in Burkina Faso," Journal of Development Economics, Elsevier, vol. 79(1), pages 73-117, February. [Downloadable!] (restricted)
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  18. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
  19. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Blackwell Publishing, vol. 71, pages 655-679, 07. [Downloadable!] (restricted)
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  20. Altonji, Joseph G & Hayashi, Fumio & Kotlikoff, Laurence J, 1997. "Parental Altruism and Inter Vivos Transfers: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1121-66, December.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ana Fernandes, 2000. "Altruism with Endogenous Labor Supply," Econometric Society World Congress 2000 Contributed Papers 0844, Econometric Society. [Downloadable!]
    Other versions:
  2. Ernesto Villanueva, 2002. "Parental Altruism under Imperfect Information: Theory and Evidence," Economics Working Papers 650, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!] (restricted)
    Other versions:
  4. Harounan Kaziango, 2004. "Motives for Household Private Transfers in Burkina Faso," Working Papers 895, Economic Growth Center, Yale University. [Downloadable!]
    Other versions:
  5. 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. [Downloadable!] (restricted)
  6. 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. [Downloadable!]
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