Generalization of GMM to a continuum of moment conditions

Citation
M. Carrasco et Jp. Florens, Generalization of GMM to a continuum of moment conditions, ECONOMET TH, 16(6), 2000, pp. 797-834
Citations number
33
Categorie Soggetti
Economics
Journal title
ECONOMETRIC THEORY
ISSN journal
02664666 → ACNP
Volume
16
Issue
6
Year of publication
2000
Pages
797 - 834
Database
ISI
SICI code
0266-4666(200012)16:6<797:GOGTAC>2.0.ZU;2-O
Abstract
This paper proposes a version of the generalized method of moments procedur e that handles both the case where the number of moment conditions is finit e and the case where there is a continuum of moment conditions. Typically, the moment conditions are indexed by an index parameter that takes its valu es in an interval, The objective function to minimize is then the norm of t he moment conditions in a Hilbert space. The estimator is shown to be consi stent and asymptotically normal. The optimal estimator is obtained by minim izing the norm of the moment conditions in the reproducing kernel Hilbert s pace associated with the covariance, We show an easy way to calculate this estimator, Finally, we study properties of a specification test using overi dentifying restrictions. Results of this paper are useful in many instances where a continuum of moment conditions arises. Examples include efficient estimation of continuous time regression models, cross-sectional models tha t satisfy conditional moment restrictions, and scalar diffusion processes.