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The Asymptotic Properties of GMM and Indirect Inference under Second-order Identification

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  • Prosper Dovonon
  • Alastair Hall

Abstract

This paper presents a limiting distribution theory for GMM and Indirect Inference estimators when local identification conditions fail at first-order but hold at second-order. These limit distributions are shown to be non-standard, but we show that they can be easily simulated, making it possible to perform inference about the parameters in this setting. We illustrate our results in the context of a dynamic panel data model in which the parameter of interest is identified locally at second order by non-linear moment restrictions but not at first order at a particular point in the parameter space. Our simulation results indicate that our theory leads to reliable inferences in moderate to large samples in the neighbourhood of this point of first-order identification failure. In contrast, inferences based on standard asymptotic theory (derived under the assumption of first-order local identification) are very misleading in the neighbourhood of the point of first-order local identification failure.

Suggested Citation

  • Prosper Dovonon & Alastair Hall, 2018. "The Asymptotic Properties of GMM and Indirect Inference under Second-order Identification," CIRANO Working Papers 2018s-37, CIRANO.
    • Handle: RePEc:cir:cirwor:2018s-37
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    File URL: https://cirano.qc.ca/files/publications/2018s-37.pdf
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    Cited by:

    1. Manuel A. Domínguez & Ignacio N. Lobato, 2020. "Specification testing with estimated variables," Econometric Reviews, Taylor & Francis Journals, vol. 39(5), pages 476-494, May.
    2. Hugo Kruiniger, 2023. "Large sample properties of GMM estimators under second-order identification," Papers 2307.13475, arXiv.org.
    3. Fève, Patrick & Beaudry, Paul & Collard, Fabrice & Guay, Alain & Portier, Franck, 2022. "Dynamic Identification in VARs," TSE Working Papers 22-1384, Toulouse School of Economics (TSE).
    4. Kruiniger, Hugo, 2018. "A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions," MPRA Paper 110375, University Library of Munich, Germany, revised 15 Aug 2021.
    5. Prosper Dovonon & Alastair Hall & Frank Kleibergen, 2018. "Inference in Second-Order Identified Models," CIRANO Working Papers 2018s-36, CIRANO.
    6. Alain Guay, 2020. "Identification of Structural Vector Autoregressions Through Higher Unconditional Moments," Working Papers 20-19, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management.
    7. Jean-Jacques Forneron, 2019. "Detecting Identification Failure in Moment Condition Models," Papers 1907.13093, arXiv.org, revised Oct 2023.
    8. Guay, Alain, 2021. "Identification of structural vector autoregressions through higher unconditional moments," Journal of Econometrics, Elsevier, vol. 225(1), pages 27-46.
    9. Sentana, Enrique, 2024. "Finite underidentification," Journal of Econometrics, Elsevier, vol. 240(1).
    10. Prosper Dovonon & Firmin Doko Tchatoka & Michael Aguessy, 2019. "Relevant moment selection under mixed identification strength," School of Economics and Public Policy Working Papers 2019-04, University of Adelaide, School of Economics and Public Policy.
    11. Dovonon, Prosper & Hall, Alastair R. & Kleibergen, Frank, 2020. "Inference in second-order identified models," Journal of Econometrics, Elsevier, vol. 218(2), pages 346-372.
    12. David T. Frazier & Eric Renault, 2019. "Indirect Inference: Which Moments to Match?," Econometrics, MDPI, vol. 7(1), pages 1-17, March.
    13. Bun, Maurice J.G. & Kleibergen, Frank, 2022. "Identification Robust Inference For Moments-Based Analysis Of Linear Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 38(4), pages 689-751, August.
    14. Forneron, Jean-Jacques, 2024. "Detecting identification failure in moment condition models," Journal of Econometrics, Elsevier, vol. 238(1).

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    Keywords

    Moment-based estimation; First-order identification failure; Minimum-chi squared estimation; Simulation-based estimation;
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