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Testing Over-Identifying Restrictions without Consistent Estimation of the Asymptotic Covariance Matrix

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We extend the KVB approach of Kiefer, Vogelsang, and Bunzel (2000, Econometrica) and Kiefer and Vogelsang (2002b, Econometric Theory) to construct a class of robust tests for over-identifying restrictions in the context of GMM. The proposed test does not require consistent estimation of the asymptotic covariance matrix but relies on kernel-based normalizing matrices to eliminate the nuisance parameters in the limit. Moreover, the proposed test is valid for any consistent GMM estimator, in contrast with the conventional test that requires the optimal GMM estimator, and hence is easy to implement. Our simulations show that the proposed test is properly sized and may even be more powerful than the conventional test computed with an inappropriate user-chosen parameter.

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Paper provided by Institute of Economics, Academia Sinica, Taipei, Taiwan in its series IEAS Working Paper : academic research with number 06-A009.

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Length: 19 pages
Date of creation: Sep 2006
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Handle: RePEc:sin:wpaper:06-a009

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Keywords: generalized method of moments; kernel function; KVB approach; overidentifying restrictions; robust test;

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  1. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers 1832, Iowa State University, Department of Economics.
  2. Andrews, Donald W. K., 1987. "Asymptotic Results for Generalized Wald Tests," Econometric Theory, Cambridge University Press, vol. 3(03), pages 348-358, June.
  3. Nicholas M. Kiefer & Timothy J. Vogelsang, 2002. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using The Bartlett Kernel Without Truncation," Econometrica, Econometric Society, vol. 70(5), pages 2093-2095, September.
  4. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  5. Hall, Alastair R. & Inoue, Atsushi & Peixe, Fernanda P.M., 2003. "Covariance Matrix Estimation And The Limiting Behavior Of The Overidentifying Restrictions Test In The Presence Of Neglected Structural Instability," Econometric Theory, Cambridge University Press, vol. 19(06), pages 962-983, December.
  6. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
  7. Alastair R. Hall, 2000. "Covariance Matrix Estimation and the Power of the Overidentifying Restrictions Test," Econometrica, Econometric Society, vol. 68(6), pages 1517-1528, November.
  8. Phillips, Peter C.B. & Sun, Yixiao & Jin, Sainan, 2004. "Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation," University of California at San Diego, Economics Working Paper Series qt6mf9q2rt, Department of Economics, UC San Diego.
  9. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  10. Bunzel, Helle & Kiefer, Nicholas M. & Vogelsang, Timothy, 2001. "Simple Robust Testing of Hypothesis in Non-Linear Models," Staff General Research Papers 5214, Iowa State University, Department of Economics.
  11. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1350-1366, December.
  12. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
  13. Vogelsang, Timothy J., 2001. "Testing in GMM Models without Truncation," Working Papers 01-12, Cornell University, Center for Analytic Economics.
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