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Instrument endogeneity and identification-robust tests: some analytical results

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  • Doko Tchatoka, Firmin Sabro
  • Dufour, Jean-Marie

Abstract

When some explanatory variables in a regression are correlated with the disturbance term, instrumental variable methods are typically employed to make reliable inferences. Furthermore, to avoid difficulties associated with weak instruments, identification robust methods are often proposed. However, it is hard to assess whether an instrumental variable is valid in practice because instrument validity is based on the questionable assumption that some of them are exogenous. In this paper, we focus on structural models and analyze the effects of instrument endogeneity on two identification-robust procedures, the Anderson-Rubin (1949, AR) and the Kleibergen (2002, K) tests, with or without weak instruments. Two main setups are considered: (1) the level of “instrument” endogeneity is fixed (does not depend on the sample size), and (2) the instruments are locally exogenous, i.e. the parameter which controls instrument endogeneity approaches zero as the sample size increases. In the first setup, we show that both test procedures are in general consistent against the presence of invalid instruments (hence asymptotically invalid for the hypothesis of interest), whether the instruments are “strong” or “weak”. We also describe cases where test consistency may not hold, but the asymptotic distribution is modified in a way that would lead to size distortions in large samples. These include, in particular, cases where the 2SLS estimator remains consistent, but the AR and K tests are asymptotically invalid. In the second setup, we find (non-degenerate) asymptotic non-central chi-square distributions in all cases, and describe cases where the non-centrality parameter is zero and the asymptotic distribution remains the same as in the case of valid instruments (despite the presence of invalid instruments). Overall, our results underscore the importance of checking for the presence of possibly invalid instruments when applying “identification-robust” tests.

Suggested Citation

  • Doko Tchatoka, Firmin Sabro & Dufour, Jean-Marie, 2008. "Instrument endogeneity and identification-robust tests: some analytical results," MPRA Paper 29613, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:29613
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    References listed on IDEAS

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    1. Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, July.
    2. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation for Research in Economics, Yale University.
    3. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    4. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-843, August.
    5. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    6. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    7. 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 518-529, October.
    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. Kadane, Joseph B & Anderson, T W, 1977. "A Comment on the Test of Overidentifying Restrictions," Econometrica, Econometric Society, vol. 45(4), pages 1027-1031, May.
    10. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    11. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 66(6), pages 1389-1404, November.
    12. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    13. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
    14. Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-298, May.
    15. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    16. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    17. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    18. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    19. Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
    20. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    21. 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.
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    Citations

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    Cited by:

    1. Therese F. Azeng & Thierry U. Yogo, 2015. "Youth Unemployment, Education and Political Instability: Evidence from Selected Developing Countries 1991-2009," HiCN Working Papers 200, Households in Conflict Network.
    2. Tchatoka, Firmin Doko, 2015. "Subset Hypotheses Testing And Instrument Exclusion In The Linear Iv Regression," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1192-1228, December.
    3. Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Uniform Inference after Pretesting for Exogeneity with Heteroskedastic Data," MPRA Paper 106408, University Library of Munich, Germany.
    4. Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Size-corrected Bootstrap Test after Pretesting for Exogeneity with Heteroskedastic or Clustered Data," MPRA Paper 110899, University Library of Munich, Germany.
    5. Doko Tchatoka, Firmin & Wang, Wenjie, 2020. "Uniform Inference after Pretesting for Exogeneity," MPRA Paper 99243, University Library of Munich, Germany.
    6. Caner, Mehmet, 2014. "Near exogeneity and weak identification in generalized empirical likelihood estimators: Many moment asymptotics," Journal of Econometrics, Elsevier, vol. 182(2), pages 247-268.
    7. Therese F. Azeng & Thierry Yogo Urbain, 2013. "Working Paper 171 - Youth Unemployment and Political Instability in Selected Developing Countries," Working Paper Series 467, African Development Bank.
    8. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2010. "On the precision of Calvo parameter estimates in structural NKPC models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1582-1595, September.
    9. Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
    10. Tae-Hwan Kim & Christophe Muller, 2017. "A Robust Test of Exogeneity Based on Quantile Regressions," AMSE Working Papers 1716, Aix-Marseille School of Economics, France.
    11. Armand Totouom & Vincent De Paul Mboutchouang & Hervé Kaffo Fotio, 2018. "The Effects of Education on Labour Force Participation in Cameroon: A Gender Perspective," African Development Review, African Development Bank, vol. 30(1), pages 45-55, March.
    12. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2013. "Identification-robust analysis of DSGE and structural macroeconomic models," Journal of Monetary Economics, Elsevier, vol. 60(3), pages 340-350.
    13. Kapetanios, George & Khalaf, Lynda & Marcellino, Massimiliano, 2015. "Factor based identification-robust inference in IV regressions," CEPR Discussion Papers 10390, C.E.P.R. Discussion Papers.
    14. Yogo, Urbain Thierry & Mallaye, Douzounet, 2012. "Social Network and Social Protection: Evidence from Cameroon," MPRA Paper 44935, University Library of Munich, Germany.
    15. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.

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    More about this item

    Keywords

    simultaneous equations; instrumental variables; locally weak instruments; invalid instruments; locally exogenous instruments.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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