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Estimating a Class of Triangular Simultaneous Equations Models Without Exclusion Restrictions


  • Klein, Roger

    () (Rutgers University)

  • Vella, Francis

    () (Georgetown University)


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 for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp2378

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    6. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    7. 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.
    8. Klein, R.W., 1991. "Specification Tests for Binery Choice Models Based on Index Quantiles," Papers 71, Bell Communications - Economic Research Group.
    9. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
    10. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    11. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    12. Powell, James L. & Stock, James H. & Stoker, Thomas M., 1986. "Semiparametric estimation of weighted average derivatives," Working papers 1793-86., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    13. 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.
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    Cited by:

    1. Alex Klein & Guy Tchuente, 2017. "Spatial differencing for sample selection models," Studies in Economics 1701, School of Economics, University of Kent.
    2. Montes-Rojas, Gabriel & Galvao, Antonio F., 2014. "Bayesian endogeneity bias modeling," Economics Letters, Elsevier, vol. 122(1), pages 36-39.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. repec:eee:ecoedu:v:58:y:2017:i:c:p:108-122 is not listed on IDEAS
    8. repec:eee:econom:v:200:y:2017:i:2:p:207-222 is not listed on IDEAS
    9. 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.
    10. 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.
    11. Faqin Lin & Can Huang & Xiaobo He & Chao Zhang, 2013. "Do more highly educated entrepreneurs matter?," Asian-Pacific Economic Literature, Asia Pacific School of Economics and Government, The Australian National University, vol. 27(2), pages 104-116, November.
    12. 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.
      • Joao Ricardo Faria & Le Wang & Zhongmin Wu, 2009. "Debts on debts," Working Papers 2009/7, Nottingham Trent University, Nottingham Business School, Economics Division.

    More about this item


    heteroskedasticity; control function; endogeneity;

    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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