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On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators

Author

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  • Stelios Arvanitis
  • Antonis Demos

    (www.aueb.gr/users/demos)

Abstract

This paper deals with higher order asymptotic properties for three indirect inference estimators. We provide conditions that ensure the validity of locally uniform Edgeworth approximations. When these are of sufficiently high order they also form integrability conditions that validate locally uniform moment approximations. We derive the relevant 2nd order bias and MSE approximations for the three estimators as functions of the respective approximations for the auxiliary estimator. We allow the possibility of stochastic weighting in any of the steps of the estimation procedure. We confirm that in the special case of deterministic weighting and affinity of the binding function, one of them is second order unbiased. The other two estimators do not have this property under the same conditions. Moreover, in this case, the second order approximate MSEs imply the superiority of the first estimator. We generalize to multistep procedures that provide recursive indirect estimators which are locally uniformly unbiased at any given order. Furthermore, in a particular case, we manage to validate locally uniform Edgeworth expansions for one of the estimators without any differentiability requirements for the estimating equations.

Suggested Citation

  • Stelios Arvanitis & Antonis Demos, 2014. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," DEOS Working Papers 1406, Athens University of Economics and Business.
  • Handle: RePEc:aue:wpaper:1406
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    3. Liang Jiang & Xiaohu Wang & Jun Yu, 2014. "On Bias in the Estimation of Structural Break Points," Working Papers 22-2014, Singapore Management University, School of Economics.
    4. Jiang, Liang & Wang, Xiaohu & Yu, Jun, 2018. "New distribution theory for the estimation of structural break point in mean," Journal of Econometrics, Elsevier, vol. 205(1), pages 156-176.

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    More about this item

    Keywords

    Locally Uniform Edgeworth Expansions; Locally Uniform Moment Approximations; Bias Approximation; MSE Approximation; Binding Function; Recursive Indirect Estimators;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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