Optimal inference in dynamic models with conditional moment restrictions

    Research output: Working paper/Preprint Working paperResearch


    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.
    Original languageEnglish
    Place of publicationAarhus
    PublisherInstitut for Økonomi, Aarhus Universitet
    Number of pages39
    Publication statusPublished - 2008


    • optimal estimating function, generalized method of moments, conditional moment restrictions, dynamic models, optimal instruments, martingale estimating function, specification test


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