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Nonparametric Two-Stage Estimation of Simultaneous Equations with Limited Endogenous Regressors


  • Lee, Myoung-Jae


Estimation of simultaneous equations with limited (or transformed) endogenous regressors has been difficult in the parametric literature for various reasons. In this paper, we propose a nonparametric two-stage method that is analogous to two-stage least-squares estimation. A simultaneous censored model is used to illustrate our approach, and then its generalization to other cases is developed. The technical highlight is in handling a nondifferentiable second-stage minimand with an infinite-dimensional first-stage nuisance parameter when the first-stage error is not orthogonal to the second.

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  • Lee, Myoung-Jae, 1996. "Nonparametric Two-Stage Estimation of Simultaneous Equations with Limited Endogenous Regressors," Econometric Theory, Cambridge University Press, vol. 12(02), pages 305-330, June.
  • Handle: RePEc:cup:etheor:v:12:y:1996:i:02:p:305-330_00

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    References listed on IDEAS

    1. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    2. Mikosch, T., 1991. "Functional limit theorems for random quadratic forms," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 81-98, February.
    3. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    4. Phillips, Peter C. B., 1977. "An approximation to the finite sample distribution of Zellner's seemingly unrelated regression estimator," Journal of Econometrics, Elsevier, vol. 6(2), pages 147-164, September.
    5. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August.
    6. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    7. Phillips, Peter C B, 1977. "A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators," Econometrica, Econometric Society, vol. 45(6), pages 1517-1534, September.
    8. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
    9. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    10. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
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    Cited by:

    1. Changhui Kang & Myoung-jae Lee, 2010. "Performance Of Various Estimators For Censored Response Models With Endogenous Regressors," Pacific Economic Review, Wiley Blackwell, vol. 15(4), pages 447-463, October.
    2. Chen, Songnian & Zhou, Yahong, 2010. "Semiparametric and nonparametric estimation of sample selection models under symmetry," Journal of Econometrics, Elsevier, vol. 157(1), pages 143-150, July.
    3. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    4. Angelov, Nikolay & Johansson, Per & Lee, Myoung-jae, 2017. "The effect of fertility timing on labor market work duration," Working Paper Series 2017:13, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    5. Puhani, Patrick A., 1997. "Foul or Fair? The Heckman Correction for Sample Selection and Its Critique. A Short Survey," ZEW Discussion Papers 97-07, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    6. Pao-Li Chang & Myoung-Jae Lee, 2006. "Protection for Sale Under Monopolistic Competition : An Empirical Investigation," Microeconomics Working Papers 22061, East Asian Bureau of Economic Research.
    7. Bertrand Melenberg & Arthur van Soest & Erwin Charlier, 2000. "An analysis of housing expenditure using semiparametric cross-section models," Empirical Economics, Springer, vol. 25(3), pages 437-462.
    8. Chen, Songnian, 2000. "Rank estimation of a location parameter in the binary choice model," Journal of Econometrics, Elsevier, vol. 98(2), pages 317-334, October.

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