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Optimal inference in dynamic models with conditional moment restrictions

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Author Info

  • Bent Jesper Christensen
  • Michael Sørensen

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

By an application of the theory of optimal estimating function, optimal in- struments for dynamic models with conditional moment restrictions are derived. The general efficiency bound is provided, along with estimators attaining the bound. It is demonstrated that the optimal estimators are always at least as ef- ficient as the traditional optimal generalized method of moments estimator, and usually more efficient. The form of our optimal instruments resembles that from Newey (1990), but involves conditioning on the history of the stochastic pro- cess. In the special case of i.i.d. observations, our optimal estimator reduces to Newey’s. Specification and hypothesis testing in our framework are introduced. We derive the theory of optimal instruments and the associated asymptotic dis- tribution theory for general cases including non-martingale estimating functions and general history dependence. Examples involving time-varying conditional volatility and stochastic volatility are offered.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-51.

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Length: 39
Date of creation: 11 Sep 2008
Date of revision:
Handle: RePEc:aah:create:2008-51

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: optimal estimating function; generalized method of moments; conditional moment restrictions; dynamic models; optimal instruments; martingale estimating function; specification test;

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References

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  1. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  3. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-96, May.
  4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  5. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
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Cited by:
  1. Michael Sørensen, 2008. "Efficient estimation for ergodic diffusions sampled at high frequency," CREATES Research Papers 2007-46, School of Economics and Management, University of Aarhus.
  2. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 35(3), pages 438-465.

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