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Local sensitivity and diagnostic tests

  • Jan R. Magnus
  • Andrey L. Vasnev

In this paper, we confront sensitivity analysis with diagnostic testing. Every model is misspecified (in the sense that no model coincides with the data-generating process), but a model is useful if the parameters of interest (the focus) are not sensitive to small perturbations in the underlying assumptions. The study of the effect of these violations on the focus is called sensitivity analysis. Diagnostic testing, on the other hand, attempts to find out whether a nuisance parameter is (statistically) "large" or "small". Both aspects are important, but traditional applied econometrics tends to use only diagnostics and forget about sensitivity analysis. We develop a theory of sensitivity in a maximum likelihood framework, give conditions under which the diagnostic and the sensitivity are asymptotically independent, and demonstrate with three core examples that this independence is the rule rather than the exception, thus underlying the importance of sensitivity analysis. Copyright Royal Economic Society 2007

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Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 10 (2007)
Issue (Month): 1 (03)
Pages: 166-192

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Handle: RePEc:ect:emjrnl:v:10:y:2007:i:1:p:166-192
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  1. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Karim M. Abadir & Jan R. Magnus, 2002. "Notation in econometrics: a proposal for a standard," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 76-90, June.
  3. Andrews, Donald W. K., 1998. "Hypothesis testing with a restricted parameter space," Journal of Econometrics, Elsevier, vol. 84(1), pages 155-199, May.
  4. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
  5. Geert Verbeke & Geert Molenberghs & Herbert Thijs & Emmanuel Lesaffre & Michael G. Kenward, 2001. "Sensitivity Analysis for Nonrandom Dropout: A Local Influence Approach," Biometrics, The International Biometric Society, vol. 57(1), pages 7-14, 03.
  6. Magnus, Jan R., 1978. "Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix," Journal of Econometrics, Elsevier, vol. 7(3), pages 281-312, April.
  7. Heijmans, R.D.H. & Magnus, J.R., 1986. "On the first-order efficiency and asymptotic normality of maximum likelihood estimators obtained from dependent observations," Other publications TiSEM b2fc9176-e950-4580-90e6-5, Tilburg University, School of Economics and Management.
  8. Banerjee, Anurag N. & Magnus, Jan R., 2000. "On the sensitivity of the usual t- and F-tests to covariance misspecification," Journal of Econometrics, Elsevier, vol. 95(1), pages 157-176, March.
  9. Banerjee, Anurag N. & Magnus, Jan R., 1999. "The sensitivity of OLS when the variance matrix is (partially) unknown," Journal of Econometrics, Elsevier, vol. 92(2), pages 295-323, October.
  10. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644, March.
  11. Shi, Lei & Wang, Xueren, 1999. "Local influence in ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 341-353, September.
  12. Magnus, J.R., 1978. "Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix," Other publications TiSEM 388c2c25-0925-4b56-834a-7, Tilburg University, School of Economics and Management.
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