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Estimating a Class of Triangular Simultaneous Equations Models Without Exclusion Restrictions

Author

Listed:
  • Klein, Roger

    (Rutgers University)

  • Vella, Francis

    (Georgetown University)

Abstract
This paper provides a control function estimator to adjust for endogeneity in the triangular simultaneous equations model where there are no available exclusion restrictions to generate suitable instruments. Our approach is to exploit the dependence of the errors on exogenous variables (e.g. heteroscedasticity) to adjust the conventional control function estimator. The form of the error dependence on the exogenous variables is subject to restrictions, but is not parametrically specified. In addition to providing the estimator and deriving its large-sample properties, we present simulation evidence which indicates the estimator works well.

Suggested Citation

  • Klein, Roger & Vella, Francis, 2006. "Estimating a Class of Triangular Simultaneous Equations Models Without Exclusion Restrictions," IZA Discussion Papers 2378, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp2378
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    References listed on IDEAS

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    1. Roger Klein & Francis Vella, 2009. "A semiparametric model for binary response and continuous outcomes under index heteroscedasticity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 735-762.
    2. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
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    5. Rummery, Sarah & Vella, Francis & Verbeek, Marno, 1999. "Estimating the returns to education for Australian youth via rank-order instrumental variables," Labour Economics, Elsevier, vol. 6(4), pages 491-507, November.
    6. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, May.
    7. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
    8. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
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    11. Klein, R.W., 1991. "Specification Tests for Binery Choice Models Based on Index Quantiles," Papers 71, Bell Communications - Economic Research Group.
    12. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
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    Cited by:

    1. Lewbel, Arthur, 2018. "Identification and estimation using heteroscedasticity without instruments: The binary endogenous regressor case," Economics Letters, Elsevier, vol. 165(C), pages 10-12.
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    4. Arthur Lewbel, 2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80.
    5. M. Shahe Emran & Forhad Shilpi, 2017. "Land Market Restrictions, Women's Labour Force Participation and Wages in a Rural Economy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 747-768, October.
    6. Nils Saniter, 2012. "Estimating Heterogeneous Returns to Education in Germany via Conditional Heteroskedasticity," SOEPpapers on Multidisciplinary Panel Data Research 458, DIW Berlin, The German Socio-Economic Panel (SOEP).
    7. Prono, Todd, 2015. "Market proxies as factors in linear asset pricing models: Still living with the roll critique," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 36-53.
    8. Simon Gilchrist & Egon Zakrajšek, 2013. "The Impact of the Federal Reserve's Large‐Scale Asset Purchase Programs on Corporate Credit Risk," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(s2), pages 29-57, December.
    9. Fortin, Bernard & Ragued, Safa, 2017. "Does temporary interruption in postsecondary education induce a wage penalty? Evidence from Canada," Economics of Education Review, Elsevier, vol. 58(C), pages 108-122.
    10. Milunovich George & Yang Minxian, 2013. "On Identifying Structural VAR Models via ARCH Effects," Journal of Time Series Econometrics, De Gruyter, vol. 5(2), pages 117-131, May.
    11. Lütkepohl, Helmut & Milunovich, George & Yang, Minxian, 2020. "Inference in partially identified heteroskedastic simultaneous equations models," Journal of Econometrics, Elsevier, vol. 218(2), pages 317-345.
    12. Ben-Moshe, Dan & D’Haultfœuille, Xavier & Lewbel, Arthur, 2017. "Identification of additive and polynomial models of mismeasured regressors without instruments," Journal of Econometrics, Elsevier, vol. 200(2), pages 207-222.
    13. Lídia Farré & Roger Klein & Francis Vella, 2013. "A parametric control function approach to estimating the returns to schooling in the absence of exclusion restrictions: an application to the NLSY," Empirical Economics, Springer, vol. 44(1), pages 111-133, February.
    14. Dungey, Mardi & Milunovich, George & Thorp, Susan & Yang, Minxian, 2015. "Endogenous crisis dating and contagion using smooth transition structural GARCH," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 71-79.
    15. Faqin Lin & Can Huang & Xiaobo He & Chao Zhang, 2013. "Do more highly educated entrepreneurs matter?," Asian-Pacific Economic Literature, The Crawford School, The Australian National University, vol. 27(2), pages 104-116, November.
    16. Faria, João Ricardo & Wang, Le & Wu, Zhongmin, 2012. "Debts on debts," The North American Journal of Economics and Finance, Elsevier, vol. 23(2), pages 203-219.
    17. Alex Klein & Guy Tchuente, 2017. "Spatial differencing for sample selection models," Studies in Economics 1701, School of Economics, University of Kent.
    18. Montes-Rojas, Gabriel & Galvao, Antonio F., 2014. "Bayesian endogeneity bias modeling," Economics Letters, Elsevier, vol. 122(1), pages 36-39.
    19. Aleksandr Grigoryan & Knar Khachatryan, 2018. "Remittances and Emigration Intentions: Evidence from Armenia," CERGE-EI Working Papers wp626, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    20. Nikolay Arefiev, 2014. "A Theory Of Data-Oriented Identification With A Svar Application," HSE Working papers WP BRP 79/EC/2014, National Research University Higher School of Economics.
    21. D’Haultfœuille, Xavier & Hoderlein, Stefan & Sasaki, Yuya, 2024. "Testing and relaxing the exclusion restriction in the control function approach," Journal of Econometrics, Elsevier, vol. 240(2).
    22. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    23. Lima, Ricardo Carvalho de Andrade & Silveira Neto, Raul da Mota, 2019. "Zoning ordinances and the housing market in developing countries: Evidence from Brazilian municipalities," Journal of Housing Economics, Elsevier, vol. 46(C).
    24. Wayne Yuan Gao & Rui Wang, 2023. "IV Regressions without Exclusion Restrictions," Papers 2304.00626, arXiv.org, revised Jul 2023.
    25. Christophe Bruneel-Zupanc, 2023. "Don't (fully) exclude me, it's not necessary! Identification with semi-IVs," Papers 2303.12667, arXiv.org, revised Jul 2023.

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    More about this item

    Keywords

    heteroskedasticity; control function; endogeneity;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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