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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

Suggested Citation

  • Jan R. Magnus & Andrey L. Vasnev, 2007. "Local sensitivity and diagnostic tests," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 166-192, March.
    • Handle: RePEc:ect:emjrnl:v:10:y:2007:i:1:p:166-192
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    References listed on IDEAS

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    1. 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.
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    4. Shi, Lei & Wang, Xueren, 1999. "Local influence in ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 341-353, September.
    5. R.D.H. Heijmans & J.R. Magnus, 1986. "On The First–Order Efficiency And Asymptotic Normality Of Maximum Likelihood Estimators Obtained From Dependent Observations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 40(3), pages 169-188, September.
    6. 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.
    7. Kleijnen, J.P.C., 1997. "Sensitivity analysis and related analyses : A review of some statistical techniques," Other publications TiSEM 7969b135-47c5-4d76-9241-c, Tilburg University, School of Economics and Management.
    8. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    9. 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.
    10. 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, March.
    11. 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.
    12. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
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    Cited by:

    1. 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.
    2. Eric Manes, 2009. "Pakistan's Investment Climate : Laying the Foundation for Growth, Volume 2. Annexes," World Bank Publications - Reports 12411, The World Bank Group.
    3. Mayston, David, 2009. "The determinants of cumulative endogeneity bias in multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1120-1136, July.
    4. Magnus, Jan R. & Vasnev, Andrey L., 2015. "Interpretation and use of sensitivity in econometrics, illustrated with forecast combinations," International Journal of Forecasting, Elsevier, vol. 31(3), pages 769-781.
    5. Qin, Huaizhen & Wan, Alan T.K. & Zou, Guohua, 2009. "On the sensitivity of the one-sided t test to covariance misspecification," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1593-1609, September.
    6. Liu, Shuangzhe & Ma, Tiefeng & Polasek, Wolfgang, 2014. "Spatial system estimators for panel models: A sensitivity and simulation study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 78-102.
    7. Vasnev, Andrey L., 2010. "Sensitivity of GLS estimators in random effects models," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1252-1262, May.
    8. Giuseppe De Luca & Jan Magnus & Franco Peracchi, 2015. "On the Ambiguous Consequences of Omitting Variables," Tinbergen Institute Discussion Papers 15-061/III, Tinbergen Institute.
    9. 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.
    10. Giuseppe De Luca & Jan R. Magnus & Franco Peracchi, 2018. "Balanced Variable Addition In Linear Models," Journal of Economic Surveys, Wiley Blackwell, vol. 32(4), pages 1183-1200, September.
    11. 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.
    12. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    13. 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;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 519-545, September.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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