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Ill-posed Problems and Instruments' Weakness

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Author Info
Grant Hillier
Giovanni Forchini

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

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(05), pages 707-743, October. [Downloadable!]
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  2. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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  5. 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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  6. 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.
  7. Dufour, J.M., 1995. "Some Impossibility Theorems in Econometrics with Applications to Instrumental Variables, Dynamic Models and Cointegration," Cahiers de recherche 9539, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  8. Gary Chamberlain & Guido Imbens, 2004. "Random Effects Estimators with many Instrumental Variables," Econometrica, Econometric Society, vol. 72(1), pages 295-306, 01. [Downloadable!] (restricted)
  9. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-74, November. [Downloadable!] (restricted)
  10. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November. [Downloadable!] (restricted)
  11. 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. [Downloadable!]
  12. 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. [Downloadable!] (restricted)
  13. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-91, May. [Downloadable!] (restricted)
  14. Matteo Bottai, 2003. "Confidence regions when the Fisher information is zero," Biometrika, Oxford University Press for Biometrika Trust, vol. 90(1), pages 73-84, March.
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This page was last updated on 2009-12-2.

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