Efficiency bounds for moment condition models with mixed identification strength
Date
2024
Authors
Dovonon, P.
Atchadé, Y.F.
Doko Tchatoka, F.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Journal of Econometrics, 2024; 248:105723-1-105723-25
Statement of Responsibility
Prosper Dovonon, Yves F. Atchadé, Firmin Doko Tchatoka
Conference Name
Abstract
Moment condition models with mixed identification strength are models that are point identified but with estimating moment functions that are allowed to drift to 0 uniformly over the parameter space. Even though identification fails in the limit, depending on how slow the moment functions vanish, consistent estimation is possible. Existing estimators such as the generalized method of moment (GMM) estimator exhibit a pattern of nonstandard or even heterogeneous rate of convergence that materializes by some parameter directions being estimated at a slower rate than others. This paper derives asymptotic semiparametric efficiency bounds for regular estimators of parameters of these models. We show that GMM estimators are regular and that the so-called two-step GMM estimator – using the inverse of estimating function’s variance as weighting matrix – is semiparametrically efficient as it reaches the minimum variance attainable by regular estimators. This estimator is also asymptotically minimax efficient with respect to a large family of loss functions. Monte Carlo simulations are provided that confirm these results.
School/Discipline
Dissertation Note
Provenance
Description
Access Status
Rights
© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).