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Higher Order Properties of the Symmetricallr Normalized Instrumental Variable Estimator

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Rodrigo Alfaro

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Abstract

This paper provides the second order bias for the Symmetrically Normalized Instrumental Variable Estimator (SNIV), using Edgeworth expansions for both the estimator and the minimum eigenvalue. SNIV was proposed by Alonso-Borrego and Arellano (1999) as an alternative for the Limited Information Maximum Likelihood Estimator (LIML), based solely on simulations. The paper shows that second order biases of SNIV and 2SLS are similar meanwhile LIML is second order unbiased. Previous results can be obtained in a specific design: small number of strong instruments, where biases of 2SLS, SNIV, and LIML are zero.

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Paper provided by Central Bank of Chile in its series Working Papers Central Bank of Chile with number 500.

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Date of creation: Oct 2008
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Handle: RePEc:chb:bcchwp:500

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  1. Mariano, Roberto S, 1982. "Analytical Small-Sample Distribution Theory in Econometrics: The Simultaneous-Equations Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 503-33, October. [Downloadable!] (restricted)
  2. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  3. Alonso-Borrego, Cesar & Arellano, Manuel, 1999. "Symmetrically Normalized Instrumental-Variable Estimation Using Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 36-49, January.
  4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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  5. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  6. Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-94, September. [Downloadable!] (restricted)
  7. John Chao & Norman Swanson, 2003. "Alternative Approximations of the Bias and MSE of the IV Estimator Under Weak Identification With an Application to Bias Correction," Departmental Working Papers 200315, Rutgers University, Department of Economics. [Downloadable!]
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  8. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May. [Downloadable!] (restricted)
  9. Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February. [Downloadable!] (restricted)
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  10. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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