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Stochastic Expansions and Moment Approximations for Three Indirect Estimators

  • Antonis Demos



  • Stelios Arvanitis


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.

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Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1004.

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Date of creation: 17 Mar 2010
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Handle: RePEc:aue:wpaper:1004
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  1. Tripathi, Gautam, 2000. "Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(01), pages 139-142, February.
  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. Giorgio Calzorali & Gabriele Fiorentini & Enrique Sentana, 2001. "Constrained indirect inference estimation," LSE Research Online Documents on Economics 25061, London School of Economics and Political Science, LSE Library.
  4. Andersen, Torben G., 2000. "Simulation-Based Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(01), pages 131-138, February.
  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. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-48, May.
  7. Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers 92.279, Toulouse - GREMAQ.
  8. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
  9. Magdalinos, Michael A., 1992. "Stochastic Expansions and Asymptotic Approximations," Econometric Theory, Cambridge University Press, vol. 8(03), pages 343-367, September.
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