EconPapers    
Economics at your fingertips  
 

On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions

Yuichi Kitamura (), Andres Santos and Azeem Shaikh ()
Additional contact information
Yuichi Kitamura: Cowles Foundation, Yale University, http://economics.yale.edu/people/yuichi-kitamura

No 1722, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: In this paper we make two contributions. First, we show by example that empirical likelihood and other commonly used tests for parametric moment restrictions, including the GMM-based J-test of Hansen (1982), are unable to control the rate at which the probability of a Type I error tends to zero. From this it follows that, for the optimality claim for empirical likelihood in Kitamura (2001) to hold, additional assumptions and qualifications need to be introduced. The example also reveals that empirical and parametric likelihood may have non-negligible differences for the types of properties we consider, even in models in which they are first-order asymptotically equivalent. Second, under stronger assumptions than those in Kitamura (2001), we establish the following optimality result: (i) empirical likelihood controls the rate at which the probability of a Type I error tends to zero and (ii) among all procedures for which the probability of a Type I error tends to zero at least as fast, empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for "most" alternatives. This result further implies that empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their Type I error probabilities.

Keywords: Empirical likelihood; Large deviations; Hoeffding optimality; Moment restrictions (search for similar items in EconPapers)
JEL-codes: C12 C14 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2009-08
Note: CFP 1378.
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4) Track citations by RSS feed

Published in Econometrica (March 2013), 81(2): 581-607

Downloads: (external link)
http://cowles.yale.edu/sites/default/files/files/pub/d17/d1722.pdf (application/pdf)

Related works:
Journal Article: On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions (2012) Downloads
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:1722

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Matthew Regan ().

 
Page updated 2019-10-15
Handle: RePEc:cwl:cwldpp:1722