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Simultaneous selection and weighting of moments in GMM using a trapezoidal kernel

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  • Canay, Ivan A.

Abstract

This paper proposes a novel procedure to estimate linear models when the number of instruments is large. At the heart of such models is the need to balance the trade off between attaining asymptotic efficiency, which requires more instruments, and minimizing bias, which is adversely affected by the addition of instruments. Two questions are of central concern: (1) What is the optimal number of instruments to use? (2) Should the instruments receive different weights? This paper contains the following contributions toward resolving these issues. First, I propose a kernel weighted generalized method of moments (GMM) estimator that uses a trapezoidal kernel. This kernel turns out to be attractive to select and weight the number of moments. Second, I derive the higher order mean squared error of the kernel weighted GMM estimator and show that the trapezoidal kernel generates a lower asymptotic variance than regular kernels. Finally, Monte Carlo simulations show that in finite samples the kernel weighted GMM estimator performs on par with other estimators that choose optimal instruments and improves upon a GMM estimator that uses all instruments.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 156 (2010)
Issue (Month): 2 (June)
Pages: 284-303

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Handle: RePEc:eee:econom:v:156:y:2010:i:2:p:284-303

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

Related research

Keywords: Optimal instruments Flat-top kernels Empirical likelihood bootstrap GMM;

References

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  1. Peter C. B. Phillips & Chirok Han, 2004. "GMM with Many Moment Conditions," Econometric Society 2004 Far Eastern Meetings 525, Econometric Society.
  2. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  3. Kuersteiner, Guido M., 2001. "Optimal instrumental variables estimation for ARMA models," Journal of Econometrics, Elsevier, vol. 104(2), pages 359-405, September.
  4. Jinyong Hahn & Jerry Hausman, 1999. "A New Specification Test for the Validity of Instrumental Variables," Working papers 99-11, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Brown, Bryan W & Newey, Whitney K, 2002. "Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 507-17, October.
  6. Hausman & Newey & Woutersen & Chao & Swanson, 2009. "Instrumental Variable Estimation with Heteroskedasticity and Many Instruments," Economics Working Paper Archive 566, The Johns Hopkins University,Department of Economics.
  7. 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.
  8. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  9. Gary Chamberlain & Guido Imbens, 2004. "Random Effects Estimators with many Instrumental Variables," Econometrica, Econometric Society, vol. 72(1), pages 295-306, 01.
  10. Christian Hansen & Jerry Hausman & Whitney Newey, 2006. "Estimation with many instrumental variables," CeMMAP working papers CWP19/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, 06.
  12. Atsushi Inoue, 2006. "A bootstrap approach to moment selection," Econometrics Journal, Royal Economic Society, vol. 9(1), pages 48-75, 03.
  13. Morimune, Kimio, 1983. "Approximate Distributions of k-Class Estimators When the Degree of Overidentifiability Is Large Compared with the Sample Size," Econometrica, Econometric Society, vol. 51(3), pages 821-41, May.
  14. Politis, Dimitris N. & Romano, Joseph P., 1999. "Multivariate Density Estimation with General Flat-Top Kernels of Infinite Order," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 1-25, January.
  15. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2009. "Choosing instrumental variables in conditional moment restriction models," Journal of Econometrics, Elsevier, vol. 152(1), pages 28-36, September.
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Cited by:
  1. Kuersteiner, Guido M., 2012. "Kernel-weighted GMM estimators for linear time series models," Journal of Econometrics, Elsevier, vol. 170(2), pages 399-421.
  2. Martins, Luis F. & Gabriel, Vasco J., 2014. "Linear instrumental variables model averaging estimation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 709-724.

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