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Ill-posed Problems and Instruments' Weakness

  • Grant Hillier
  • Giovanni Forchini

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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  1. J. Dufour, 1995. "Some Impossibility Theorems in Econometrics with Applications to Instrumental Variables, Dynamic Models and Cointegration," SFB 373 Discussion Papers 1995,27, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. 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.
  3. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  4. 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.
  5. Jinyong Hahn & Jerry Hausman, 1999. "A New Specification Test for the Validity of Instrumental Variables," Working papers 99-11, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-91, May.
  7. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(05), pages 707-743, October.
  8. Choi, In & Phillips, Peter C. B., 1992. "Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 113-150.
  9. 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.
  10. Gary Chamberlain & Guido Imbens, 2004. "Random Effects Estimators with many Instrumental Variables," Econometrica, Econometric Society, vol. 72(1), pages 295-306, 01.
  11. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  12. 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.
  13. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
  14. 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.
  15. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-74, November.
  16. 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.
  17. 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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