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Estimating a class of triangular simultaneous equations models without exclusion restrictions

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  • Klein, Roger
  • Vella, Francis

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 154 (2010)
Issue (Month): 2 (February)
Pages: 154-164

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Handle: RePEc:eee:econom:v:154:y:2010:i:2:p:154-164

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Triangular semiparametric models Heteroscedasticity Identification;

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References

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  1. 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.
  2. 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, 05.
  3. 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.
  4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  5. Klein, Roger & Vella, Francis, 2006. "A Semiparametric Model for Binary Response and Continuous Outcomes Under Index Heteroscedasticity," IZA Discussion Papers 2383, Institute for the Study of Labor (IZA).
  6. 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.
  7. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
  8. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  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. 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.
  11. 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.
  12. 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.
  13. Klein, R.W., 1991. "Specification Tests for Binery Choice Models Based on Index Quantiles," Papers 71, Bell Communications - Economic Research Group.
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Cited by:
  1. Nils Saniter, 2012. "Estimating Heterogeneous Returns to Education in Germany via Conditional Heteroskedasticity," Discussion Papers of DIW Berlin 1213, DIW Berlin, German Institute for Economic Research.
  2. 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.
  3. Montes-Rojas, Gabriel & Galvao, Antonio F., 2014. "Bayesian endogeneity bias modeling," Economics Letters, Elsevier, vol. 122(1), pages 36-39.
  4. 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.

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