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CUE with many weak instruments and nearly singular design

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  • Caner, Mehmet
  • Yıldız, Neşe

Abstract

This paper analyzes many weak moment asymptotics under the possibility of similar moments. The possibility of highly related moments arises when there are many of them. Knight and Fu (2000) designate the issue of similar regressors as the “nearly singular” design in the least squares case. In the nearly singular design, the sample variance converges to a singular limit term. However, Knight and Fu (2000) assume that on the nullspace of the limit term, the difference between the sample variance and the singular matrix converges in probability to a positive definite matrix when multiplied by an appropriate rate. We consider specifically Continuous Updating Estimator (CUE) with many weak moments under nearly singular design. We show that the nearly singular design affects the form of the limit of the many weak moment asymptotics that is introduced by Newey and Windmeijer (2009a). However, the estimator is still consistent and the Wald test has the standard χ2 limit.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 170 (2012)
Issue (Month): 2 ()
Pages: 422-441

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Handle: RePEc:eee:econom:v:170:y:2012:i:2:p:422-441

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

Related research

Keywords: Singular matrix; Variance; Bias;

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References

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  1. Mehmet Caner, 2005. "Nearly Singular design in gmm and generalized empirical likelihood estimators," Working Papers 211, University of Pittsburgh, Department of Economics, revised Jan 2005.
  2. John Chao & Norman Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Departmental Working Papers 200421, Rutgers University, Department of Economics.
  3. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
  4. Chirok Han & Peter C.B. Phillips, 2005. "GMM with Many Moment Conditions," Cowles Foundation Discussion Papers 1515, Cowles Foundation for Research in Economics, Yale University.
  5. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01.
  6. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
  7. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  8. Donald W.K. Andrews, 1985. "Asymptotic Results for Generalized Wald Tests," Cowles Foundation Discussion Papers 761R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1986.
  9. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  10. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November.
  11. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
  12. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, December.
  13. Mehmet Caner, 2006. "A lasso type gmm estimator," Working Papers 210, University of Pittsburgh, Department of Economics, revised Jan 2006.
  14. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-95, November.
  15. Knight, Keith, 2008. "Shrinkage Estimation For Nearly Singular Designs," Econometric Theory, Cambridge University Press, vol. 24(02), pages 323-337, April.
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