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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. 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.

Suggested Citation

  • Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2008. "Estimating Derivatives in Nonseparable Models with Limited Dependent Variables," Cowles Foundation Discussion Papers 1668, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1668
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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 & Rosa L. Matzkin, 2001. "Panel Data Estimators for Nonseparable Models with Endogenous Regressors," NBER Technical Working Papers 0267, National Bureau of Economic Research, Inc.
    4. Elin Halvorsen & Thor O. Thoresen, 2011. "Parents' Desire to Make Equal Inter Vivos Transfers," CESifo Economic Studies, CESifo Group, vol. 57(1), pages 121-155, March.
    5. 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.
    6. Luke Taylor & Taisuke Otsu, 2019. "Estimation of nonseparable models with censored dependent variables and endogenous regressors," Econometric Reviews, Taylor & Francis Journals, vol. 38(1), pages 4-24, January.
    7. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    8. 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.
    9. 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.
    10. repec:cep:stiecm:/2014/575 is not listed on IDEAS
    11. Kazianga, H., 2006. "Motives for household private transfers in Burkina Faso," Journal of Development Economics, Elsevier, vol. 79(1), pages 73-117, February.
    12. Julie Zissimopoulos, 2001. "Resource Transfers to the Elderly: Do Adult Children Substitute Financial Transfers for Time Transfers?," Working Papers 01-05, RAND Corporation.
    13. 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.
    14. Fernandes, A., 2000. "Altruism with Endogenous Labor Supply," Papers 0002, Centro de Estudios Monetarios Y Financieros-.
    15. 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).
    16. 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.
    17. 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.
    18. Yuri Fonseca & Marcelo Medeiros & Gabriel Vasconcelos & Alvaro Veiga, 2018. "BooST: Boosting Smooth Trees for Partial Effect Estimation in Nonlinear Regressions," Papers 1808.03698, arXiv.org, revised Jul 2020.

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    More about this item

    Keywords

    Censored regression; Nonseparable models; Endogenous regressors; Tobit; Extreme quantiles;
    All these keywords.

    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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