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On the Behavior of Inconsistent Instrumental Variable Estimators

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Abstract

Results published recently by Hendry (1979) for the limiting distribution of inconsistent instrumental variable estimators in misspecified dynamic systems are incorrect. In particular, Hendry's derivations involve the use of an appropriate control variate and lead to an expression for the covariance matrix of the limiting distribution which, in general, omits many additional terms. Correct formulae are given in the present paper and the accuracy of the asymptotic distribution in finite samples is investigated in a simple case using the know exact small sample distribution. On the basis of our exact results, we argue for caution in the use of response surface regressions of the type recommended by Hendry in Monte Carlo experiments; and we emphasize the need for qualifying statements concerning the parameter environments in which the adequacy of these regressions has been substantiated.

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  • Esfandier Maasoumi & Peter C.B. Phillips, 1980. "On the Behavior of Inconsistent Instrumental Variable Estimators," Cowles Foundation Discussion Papers 568, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:568
    Note: CFP 554.
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    Cited by:

    1. Marmer, Vadim & Otsu, Taisuke, 2012. "Optimal comparison of misspecified moment restriction models under a chosen measure of fit," Journal of Econometrics, Elsevier, vol. 170(2), pages 538-550.
    2. Neil R. Ericsson, 1986. "Post-simulation Analysis of Monte Carlo Experiments: Interpreting Pesaran's (1974) Study of Non-nested Hypothesis Test Statistics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 691-707.
    3. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2018. "Asymptotic variance approximations for invariant estimators in uncertain asset-pricing models," Econometric Reviews, Taylor & Francis Journals, vol. 37(7), pages 695-718, August.
    4. Antoine, Bertille & Dovonon, Prosper, 2021. "Robust estimation with exponentially tilted Hellinger distance," Journal of Econometrics, Elsevier, vol. 224(2), pages 330-344.
    5. Hwang, Jungbin & Kang, Byunghoon & Lee, Seojeong, 2022. "A doubly corrected robust variance estimator for linear GMM," Journal of Econometrics, Elsevier, vol. 229(2), pages 276-298.
    6. Kirill S. Evdokimov & Michal Kolesár, 2018. "Inference in Instrumental Variable Regression Analysis with Heterogeneous Treatment Effects," Working Papers 2018-16, Princeton University. Economics Department..
    7. Yong Bao & Aman Ullah, 2021. "Analytical Finite Sample Econometrics: From A. L. Nagar to Now," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 17-37, December.
    8. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    9. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    10. Jan F. Kiviet & Jerzy Niemczyk, 2014. "On the Limiting and Empirical Distributions of IV Estimators When Some of the Instruments are Actually Endogenous," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 425-490, Emerald Group Publishing Limited.
    11. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976, Elsevier.
    12. Partha Deb & James F. Burgess, Jr., 2003. "A Quasi-experimental Comparison of Econometric Models for Health Care Expenditures," Economics Working Paper Archive at Hunter College 212, Hunter College Department of Economics.
    13. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
    14. Hnatkovska, Viktoria & Marmer, Vadim & Tang, Yao, 2012. "Comparison of misspecified calibrated models: The minimum distance approach," Journal of Econometrics, Elsevier, vol. 169(1), pages 131-138.
    15. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    16. Neil R. Ericsson, 1987. "Monte Carlo methodology and the finite sample properties of statistics for testing nested and non-nested hypotheses," International Finance Discussion Papers 317, Board of Governors of the Federal Reserve System (U.S.).
    17. Jondeau, Eric & Le Bihan, Hervé, 2008. "Examining bias in estimators of linear rational expectations models under misspecification," Journal of Econometrics, Elsevier, vol. 143(2), pages 375-395, April.
    18. Kiviet, Jan F. & Niemczyk, Jerzy, 2007. "The asymptotic and finite sample distributions of OLS and simple IV in simultaneous equations," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3296-3318, April.
    19. Gospodinov, Nikolay & Maasoumi, Esfandiar, 2021. "Generalized aggregation of misspecified models: With an application to asset pricing," Journal of Econometrics, Elsevier, vol. 222(1), pages 451-467.
    20. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.

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