Optimal Inference in Dynamic Models with Conditional Moment Restrictions
CREATES Research Paper No. 2008-51
41 Pages Posted: 11 Sep 2008
Date Written: July 4, 2008
By an application of the theory of optimal estimating function, optimal instruments 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 efficient 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 process. 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 distribution theory for general cases including non-martingale estimating functions and general history dependence. Examples involving time-varying conditional volatility and stochastic volatility are offered.
Keywords: optimal estimating function, generalized method of moments, conditional moment restrictions, dynamic models, optimal instruments, martingale estimating function, specification test
JEL Classification: C12, C13, C22, C32
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