Optimal Inference in Dynamic Models with Conditional Moment Restrictions

CREATES Research Paper No. 2008-51

41 Pages Posted: 11 Sep 2008

See all articles by Bent Jesper Christensen

Bent Jesper Christensen

Aarhus University; Aarhus University; Aarhus University

Michael Sorensen

University of Copenhagen - Institute for Mathematical Sciences; University of Aarhus

Date Written: July 4, 2008

Abstract

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

Suggested Citation

Christensen, Bent Jesper and Sorensen, Michael, Optimal Inference in Dynamic Models with Conditional Moment Restrictions (July 4, 2008). CREATES Research Paper No. 2008-51. Available at SSRN: https://ssrn.com/abstract=1266586 or http://dx.doi.org/10.2139/ssrn.1266586

Bent Jesper Christensen (Contact Author)

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Michael Sorensen

University of Copenhagen - Institute for Mathematical Sciences ( email )

Universitetsparken 5
DK-2100 Copenhagen, DK - 2200
Denmark
+45 3532 0899 (Phone)
+45 3532 0772 (Fax)

University of Aarhus ( email )

DK-8000 Aarhus C
Denmark

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