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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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  • 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.
  • Handle: RePEc:cwl:cwldpp:1668r
    Note: CFP 1369.
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    Cited by:

    1. Cheolsung Park, 2014. "Why do children transfer to their parents? Evidence from South Korea," Review of Economics of the Household, Springer, vol. 12(3), pages 461-485, September.
    2. 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.
    3. 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, July.
    4. Fernandes, A., 2000. "Altruism with Endogenous Labor Supply," Papers 0002, Centro de Estudios Monetarios Y Financieros-.
    5. Ham, John C. & Song, Heonjae, 2014. "The determinants of bargaining power in an empirical model of transfers between adult children, parents, and in-laws for South Korea," Journal of Development Economics, Elsevier, vol. 109(C), pages 73-86.
    6. 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.
    7. 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, September.
    8. Kazianga, H., 2006. "Motives for household private transfers in Burkina Faso," Journal of Development Economics, Elsevier, vol. 79(1), pages 73-117, February.
    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. repec:cep:stiecm:/2014/575 is not listed on IDEAS
    11. Elin Halvorsen & Thor O. Thoresen, 2011. "Parents' Desire to Make Equal Inter Vivos Transfers," CESifo Economic Studies, CESifo, vol. 57(1), pages 121-155, March.
    12. La, Hai Anh & Xu, Ying, 2017. "Remittances, social security, and the crowding-out effect: Evidence from Vietnam," Journal of Asian Economics, Elsevier, vol. 49(C), pages 42-59.
    13. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    14. Taisuke Otsu & Luke Taylor, 2014. "Estimation of Nonseparable Models with Censored Dependent Variables and Endogenous Regressors," STICERD - Econometrics Paper Series 575, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    15. 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.
    16. Julie Zissimopoulos, 2001. "Resource Transfers to the Elderly: Do Adult Children Substitute Financial Transfers for Time Transfers?," Working Papers 01-05, RAND Corporation.
    17. Xiong, Qizhou, 2015. "Censored Fractional Response Model: Estimating Heterogeneous Relative Risk Aversion of European Households," IWH Discussion Papers 11/2015, Halle Institute for Economic Research (IWH).

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    Keywords

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

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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