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Higher Order Properties of the Symmetricallr Normalized Instrumental Variable Estimator

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  • Rodrigo Alfaro

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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Bibliographic Info

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. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  2. Peter C.B. Phillips, 1982. "The Exact Distribution of LIML: I," Cowles Foundation Discussion Papers 658, Cowles Foundation for Research in Economics, Yale University.
  3. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  4. 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.
  5. 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.
  6. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  7. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  8. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, edition 1, number 9780198774488.
  9. Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-94, September.
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