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Stochastic Expansions and Moment Approximations for Three Indirect Estimators

Author

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  • Antonis Demos

    () (www.aueb.gr/users/demos)

  • Stelios Arvanitis

    ()

Abstract

This paper deals with properties of three indirect estimators that are known to be (first order) asymptotically equivalent. Specifically, we examine a) the issue of validity of the formal Edgeworth expansion of an arbitrary order. b) Given a), we are concerned with valid moment approximations and employ them to characterize the second order bias structure of the estimators. Our motivation resides on the fact that one of the three is reported by the relevant literature to be second order unbiased. However, this result was derived without any establishment of validity. We provide this establishment, but we are also able to massively generalize the conditions under which this second order property remains true. In this way, we essentially prove their higher order inequivalence. We generalize indirect estimators by introducing recursive ones, emerging from multistep optimization procedures. We are able to establish higher order unbiaseness for estimators of this sort.

Suggested Citation

  • Antonis Demos & Stelios Arvanitis, 2010. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators," DEOS Working Papers 1004, Athens University of Economics and Business.
  • Handle: RePEc:aue:wpaper:1004
    as

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    File URL: http://wpa.deos.aueb.gr/docs/bias-ii-f.pdf
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    References listed on IDEAS

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    1. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    2. Andrews, Donald W.K., 2002. "EQUIVALENCE OF THE HIGHER ORDER ASYMPTOTIC EFFICIENCY OF k-STEP AND EXTREMUM STATISTICS," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1040-1085, October.
    3. Calzorali, Giorgio & Fiorentini, Gabriele & Sentana, Enrique, 2001. "Constrained indirect inference estimation," LSE Research Online Documents on Economics 25061, London School of Economics and Political Science, LSE Library.
    4. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    5. P. C. B. Phillips, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 183-224.
    6. Magdalinos, Michael A., 1992. "Stochastic Expansions and Asymptotic Approximations," Econometric Theory, Cambridge University Press, vol. 8(03), pages 343-367, September.
    7. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-448, May.
    8. Tripathi, Gautam, 2000. "Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(01), pages 139-142, February.
    9. Andersen, Torben G., 2000. "Simulation-Based Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(01), pages 131-138, February.
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    Citations

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    Cited by:

    1. repec:aue:wpaper:1214 is not listed on IDEAS
    2. Stelios Arvanitis & Antonis Demos, 2012. "Valid Locally Uniform Edgeworth Expansions Under Weak Dependence and Sequences of Smooth Transformations," DEOS Working Papers 1229, Athens University of Economics and Business, revised 24 Aug 2012.
    3. Stelios Arvanitis, 2014. "A simple example of an indirect estimator with discontinuous limit theory in the MA(1) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 536-557, November.
    4. Stelios Arvanitis & Antonis Demos, "undated". "A Class of Indirect Inference Estimators: Higher Order Asymptotics and Approximate Bias Correction (Revised)," DEOS Working Papers 1411, Athens University of Economics and Business, revised 23 Sep 2014.
    5. Antonis Demos & Stelios Arvanitis, 2010. "A New Class of Indirect Estimators and Bias Correction," DEOS Working Papers 1023, Athens University of Economics and Business.

    More about this item

    Keywords

    Asymptotic Approximation; Second Order Bias Structure; Binding Function; Local Canonical Representation; Convex Variational Distance; Recursive Indirect Estimators; Higher order Bias.;

    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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