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Tests for Over-identifying Restrictions in Partially Identified Linear Structural Equations

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  • Giovanni Forchini

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Abstract

Cragg and Donald (1996) have pointed out that the asymptotic size of tests for overidentifying restrictions can be much smaller than the asymptotic nominal size when the structural equation is partially identified. This may lead to misleading inference if the critical values are obtained from a chi-square distribution. To overcome this problem we derive the exact asymptotic distribution of the Byron test statistic. This allows the calculation of asymptotic critical values and p-values corrected for possible failure of identification.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2006/wp20-06.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 20/06.

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Length: 24 pages
Date of creation: Nov 2006
Date of revision:
Handle: RePEc:msh:ebswps:2006-20

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Keywords: Invariant Tests; Over-identifying restrictions; Partially identified structural equation;

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  1. In Choi & Peter C.B. Phillips, 1989. "Asymptotic and Finite Sample Distribution Theory for IV Estimators and Tests in Partially Identified Structural Equations," Cowles Foundation Discussion Papers 929, Cowles Foundation for Research in Economics, Yale University.
  2. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1988.
  3. Hillier, Grant H., 1985. "On the Joint and Marginal Densities of Instrumental Variable Estimators in a General Structural Equation," Econometric Theory, Cambridge University Press, vol. 1(01), pages 53-72, April.
  4. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April.
  5. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  8. Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-94, September.
  9. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
  10. Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448 Elsevier.
  11. Hillier, Grant, 2006. "Yet More On The Exact Properties Of Iv Estimators," Econometric Theory, Cambridge University Press, vol. 22(05), pages 913-931, October.
  12. Byron, R P, 1974. "Testing Structural Specification Using the Unrestricted Reduced Form," Econometrica, Econometric Society, vol. 42(5), pages 869-83, September.
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