Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions

Ragusa, Giuseppe (2008) Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions. [Working Paper]. p. 45. Working Papers (No. 080906). (Submitted)

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This paper studies the Minimum Divergence (MD) class of estimators for econometric models specified through moment restrictions. We show that MD estimators can be obtained as solutions to a computationally tractable optimization problem. This problem is similar to the one solved by the Generalized Empirical Likelihood estimators of Newey and Smith (2004), but it is equivalent to it only for a subclass of divergences. The MD framework provides a coherent testing theory: tests for overidentification and parametric restrictions in this framework can be interpreted as semiparametric versions of Pearson-type goodness of fit tests. The higher order properties of MD estimators are also studied and it is shown that MD estimators that have the same higher order bias as the Empirical Likelihood (EL) estimator also share the same higher order Mean Square Error and are all higher order efficient. We identify members of the MD class that are not only higher order efficient, but, unlike the EL estimator, well behaved when the moment restrictions are misspecified.

Item Type: Report / Paper (Working Paper)
Research documents and activity classification: Working Papers > Non-Refereed Working Papers / of national relevance only
Divisions: Department of Business and Management
Uncontrolled Keywords: Minimum divergence; GMM; Generalized empirical likelihood; Higher order efficiency; Misspecified models.
MIUR Scientific Area: Area 13 - Economics and Statistics > SECS-P/05 Econometrics
Deposited by: Maria Teresa Nisticò
Date Deposited: 16 Dec 2010 17:48
Last Modified: 22 Apr 2015 00:13


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