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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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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