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Testing for weak identification in possibly nonlinear models

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  • Inoue, Atsushi
  • Rossi, Barbara

Abstract

In this paper we propose a chi-square test for identification. Our proposed test statistic is based on the distance between two shrinkage extremum estimators. The two estimators converge in probability to the same limit when identification is strong, and their asymptotic distributions are different when identification is weak. The proposed test is consistent not only for the alternative hypothesis of no identification but also for the alternative of weak identification, which is confirmed by our Monte Carlo results. We apply the proposed technique to test whether the structural parameters of a representative Taylor-rule monetary policy reaction function are identified.

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  • Inoue, Atsushi & Rossi, Barbara, 2011. "Testing for weak identification in possibly nonlinear models," Journal of Econometrics, Elsevier, vol. 161(2), pages 246-261, April.
    • Handle: RePEc:eee:econom:v:161:y:2011:i:2:p:246-261
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    Cited by:

    1. Khalaf, Lynda & Lin, Zhenjiang, 2021. "Projection-based inference with particle swarm optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    2. Inoue, Atsushi & Kuo, Chun-Hung & Rossi, Barbara, 2020. "Identifying the sources of model misspecification," Journal of Monetary Economics, Elsevier, vol. 110(C), pages 1-18.
    3. Yuya Sasaki & Yulong Wang, 2020. "Testing Finite Moment Conditions for the Consistency and the Root-N Asymptotic Normality of the GMM and M Estimators," Papers 2006.02541, arXiv.org, revised Sep 2020.
    4. 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.
    5. Jean-Jacques Forneron, 2019. "Detecting Identification Failure in Moment Condition Models," Papers 1907.13093, arXiv.org, revised Oct 2023.
    6. Zisimos Koustas & Jean-François Lamarche, 2012. "Instrumental variable estimation of a nonlinear Taylor rule," Empirical Economics, Springer, vol. 42(1), pages 1-20, February.
    7. Xiaohong Chen & David Jacho-Chávez & Oliver Linton, 2012. "Averaging of moment condition estimators," CeMMAP working papers 26/12, Institute for Fiscal Studies.
    8. Giovanni Angelini & Giuseppe Cavaliere & Luca Fanelli, 2022. "Bootstrap inference and diagnostics in state space models: With applications to dynamic macro models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 3-22, January.
    9. Antoine, Bertille & Renault, Eric, 2020. "Testing identification strength," Journal of Econometrics, Elsevier, vol. 218(2), pages 271-293.
    10. Dimitris Hatzinikolaou & Agathi Tsoka, 2016. "Modeling and Estimating the Effects of Institutional Variables on a Pay-as-you-go Social Security System and on Household Saving," Public Finance Review, , vol. 44(5), pages 589-609, September.
    11. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    12. Morris, Stephen D., 2017. "DSGE pileups," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 56-86.
    13. Rachida Ouysse, 2014. "On the performance of block-bootstrap continuously updated GMM for a class of non-linear conditional moment models," Computational Statistics, Springer, vol. 29(1), pages 233-261, February.

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    Keywords

    GMM Shrinkage Weak identification;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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