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When is it really justifiable to ignore explanatory variable endogeneity in a regression model?

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  • Jan F. Kiviet

    (Division of Economics, Nanyang Technological University, 14 Nanyang Drive, Singapore 637332.)

Abstract

A procedure that aims to pinpoint the sensitivity of ordinary least-squares based inferences regarding the degree of endogeneity of some regressors has been put forward in Ashley and Parmeter, Economics Letters, 137 (2015) 70-74. Here it is demonstrated that this procedure is based on an incorrect and systematically too optimistic asymptotic approximation to the variance of inconsistent least- squares. Therefore, and because the suggested sensitivity Öndings pertain to a random set of estimated endogeneity correlations, the claimed signiÖcance levels are misleading. For a very basic one coe¢ cient model it is demonstrated why much more sophisticated asymptotic expansions under a stricter set of assumptions are required. This enables to replace some of the áawed sensitivity analysis results for an empirical growth model by Öndings based on a proper limiting distribution for a feasible inconsistency corrected least-squares estimator, given an adopted Öxed range for the correlation between the endogenous regressor and the disturbance. Finally it is discussed how similar results could be achieved for models with several possibly endogenous regressors estimated by possibly endogenous instruments.

Suggested Citation

  • Jan F. Kiviet, 2016. "When is it really justifiable to ignore explanatory variable endogeneity in a regression model?," Economic Growth Centre Working Paper Series 1607, Nanyang Technological University, School of Social Sciences, Economic Growth Centre.
    • Handle: RePEc:nan:wpaper:1607
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    References listed on IDEAS

    as
    1. Ashley, Richard A. & Parmeter, Christopher F., 2015. "When is it justifiable to ignore explanatory variable endogeneity in a regression model?," Economics Letters, Elsevier, vol. 137(C), pages 70-74.
    2. Richard Ashley & Christopher Parmeter, 2015. "Sensitivity analysis for inference in 2SLS/GMM estimation with possibly flawed instruments," Empirical Economics, Springer, vol. 49(4), pages 1153-1171, December.
    3. Jan F. Kiviet, 2013. "Identification and inference in a simultaneous equation under alternative information sets and sampling schemes," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 24-59, February.
    4. Kiviet Jan F., 2017. "Discriminating between (in)valid External Instruments and (in)valid Exclusion Restrictions," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-9, January.
    5. Timothy G. Conley & Christian B. Hansen & Peter E. Rossi, 2012. "Plausibly Exogenous," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 260-272, February.
    6. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 407-437.
    7. Richard Ashley, 2009. "Assessing the credibility of instrumental variables inference with imperfect instruments via sensitivity analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(2), pages 325-337, March.
    8. Small, Dylan S., 2007. "Sensitivity Analysis for Instrumental Variables Regression With Overidentifying Restrictions," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1049-1058, September.
    9. Aart Kraay, 2012. "Instrumental variables regressions with uncertain exclusion restrictions: a Bayesian approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(1), pages 108-128, January.
    10. Richard A. Ashley & Christopher F. Parmeter, 2013. "Sensitivity Analysis For Inference In 2SLS Estimation With Possibly-Flawes Instruments," Working Papers e07-38, Virginia Polytechnic Institute and State University, Department of Economics.
    11. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
    12. Peter Ebbes & Michel Wedel & Ulf Böckenholt, 2009. "Frugal IV alternatives to identify the parameter for an endogenous regressor," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(3), pages 446-468, April.
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    Cited by:

    1. Briel, Stephanie & Osikominu, Aderonke & Pfeifer, Gregor & Reutter, Mirjam & Satlukal, Sascha, 2020. "Overconfidence and Gender Differences in Wage Expectations," IZA Discussion Papers 13517, Institute of Labor Economics (IZA).
    2. Kiviet, Jan F., 2020. "Testing the impossible: Identifying exclusion restrictions," Journal of Econometrics, Elsevier, vol. 218(2), pages 294-316.
    3. Richard Ashley & Christopher F. Parmeter, 2018. "A Correction/Update to “When Is It Justifiable to Ignore Variable Endogeneity In A Regression Model?â€," Working Papers 2018-01, University of Miami, Department of Economics.
    4. Kiviet, Jan, 2019. "Instrument-free inference under confined regressor endogeneity; derivations and applications," MPRA Paper 96839, University Library of Munich, Germany.
    5. Richard A. Ashley & Christopher F. Parmeter, 2020. "Sensitivity Analysis of an OLS Multiple Regression Inference with Respect to Possible Linear Endogeneity in the Explanatory Variables, for Both Modest and for Extremely Large Samples," Econometrics, MDPI, vol. 8(1), pages 1-24, March.
    6. Kiviet, Jan F., 2023. "Instrument-free inference under confined regressor endogeneity and mild regularity," Econometrics and Statistics, Elsevier, vol. 25(C), pages 1-22.

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    More about this item

    Keywords

    sensitivity analysis; simultaneity; asymptotic expansions; least-squares; growth regression;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • O5 - Economic Development, Innovation, Technological Change, and Growth - - Economywide Country Studies

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