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Ill-posed Problems and Instruments' Weakness

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  • Grant Hillier
  • Giovanni Forchini

Abstract

Potscher (Econometrica, 2002) has pointed out that several estimation problems in econometrics are ill-posed. This paper further studies the nature of ill-posed problems in parametric models. Our starting point is that both parameters and estimators may be seen as maps from the manifold of density functions to an m-dimensional Euclidean space, and we investigate the properties that these maps have to transmit perturbations. In the special case of structural equations models, we argue that this framework provides coherent measures of instruments' weakness

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 Australasian Meetings with number 357.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:ausm04:357

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Keywords: Ill-posed Problems; Weak Instruments; Parametric Models;

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  1. 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.
  2. Rolf Sundberg, 2003. "Conditional statistical inference and quantification of relevance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 299-315.
  3. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  4. Jinyong Hahn & Jerry Hausman, 2002. "A New Specification Test for the Validity of Instrumental Variables," Econometrica, Econometric Society, vol. 70(1), pages 163-189, January.
  5. Forchini, G. & Hillier, G.H., 1999. "Conditional inference for possibly unidentified structural equations," Discussion Paper Series In Economics And Econometrics 9906, Economics Division, School of Social Sciences, University of Southampton.
  6. Matteo Bottai, 2003. "Confidence regions when the Fisher information is zero," Biometrika, Biometrika Trust, vol. 90(1), pages 73-84, March.
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  8. D.S. Poskitt & C.L. Skeels, 2002. "Assessing Instrumental Variable Relevance:An Alternative Measure and Some Exact Finite Sample Theory," Department of Economics - Working Papers Series 862, The University of Melbourne.
  9. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  10. Dufour, J.M., 1995. "Some Impossibility Theorems in Econometrics with Applications to Instrumental Variables, Dynamic Models and Cointegration," Cahiers de recherche 9539, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  11. 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.
  12. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  13. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
  14. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-91, May.
  15. van Garderen, K.J., 1995. "Variance inflation in curved exponential models," Discussion Paper Series In Economics And Econometrics 9522, Economics Division, School of Social Sciences, University of Southampton.
  16. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
  17. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-74, November.
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