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Local sensitivity and diagnostic tests

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  • Jan R. Magnus
  • Andrey L. Vasnev

Abstract

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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Bibliographic Info

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. Heijmans, R.D.H. & Magnus, J.R., 1986. "On the first-order efficiency and asymptotic normality of maximum likelihood estimators obtained from dependent observations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153217, Tilburg University.
  2. Edward E. Leamer, 1983. "Global Sensitivity Results for Generalized Least Squares Estimates," UCLA Economics Working Papers 296, UCLA Department of Economics.
  3. Kleijnen, J.P.C., 1997. "Sensitivity analysis and related analyses: A review of some statistical techniques," Open Access publications from Tilburg University urn:nbn:nl:ui:12-73904, Tilburg University.
  4. Abadir, K.M. & Magnus, J.R., 2001. "Notation in Econometrics: A Proposal for a Standard," Discussion Paper 2001-8, Tilburg University, Center for Economic Research.
  5. Heijmans, Risto D. H. & Magnus, Jan R., 1986. "Consistent maximum-likelihood estimation with dependent observations : The general (non-normal) case and the normal case," Journal of Econometrics, Elsevier, vol. 32(2), pages 253-285, July.
  6. Magnus, J.R., 1978. "Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153204, Tilburg University.
  7. 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.
  8. Shi, Lei & Wang, Xueren, 1999. "Local influence in ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 341-353, September.
  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. Donald W.K. Andrews, 1994. "Hypothesis Testing with a Restricted Parameter Space," Cowles Foundation Discussion Papers 1060R, Cowles Foundation for Research in Economics, Yale University.
  11. 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.
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Cited by:
  1. Vasnev, Andrey L., 2010. "Sensitivity of GLS estimators in random effects models," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1252-1262, May.
  2. Shuangzhe Liu & Tiefeng Ma & Wolfgang Polasek, 2012. "Spatial System Estimators for Panel Models: A Sensitivity and Simulation Study," Working Paper Series 75_12, The Rimini Centre for Economic Analysis.
  3. Zhang, Xinyu & Chen, Ti & Wan, Alan T.K. & Zou, Guohua, 2009. "Robustness of Stein-type estimators under a non-scalar error covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2376-2388, November.
  4. Eric Manes, 2009. "Pakistan's Investment Climate : Laying the Foundation for Growth, Volume 2. Annexes," World Bank Other Operational Studies 12411, The World Bank.
  5. Cibele Russo & Reiko Aoki & Gilberto Paula, 2012. "Assessment of variance components in nonlinear mixed-effects elliptical models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(3), pages 519-545, September.
  6. Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Cancho, Vicente G. & Cordeiro, Gauss M., 2010. "The log-exponentiated Weibull regression model for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1017-1035, April.
  7. Mayston, David, 2009. "The determinants of cumulative endogeneity bias in multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1120-1136, July.
  8. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Paula, Gilberto A., 2008. "Log-modified Weibull regression models with censored data: Sensitivity and residual analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4021-4039, April.

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