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EFFICIENT METHOD OF MOMENTS IN MISSPECIFIED I.I.D. MODELS
The paper presents the asymptotic theory of the efficient method of moments when the model of interest is not correctly specified. The paper assumes a sequence of independent and identically distributed observations and a global misspecification. It is found that the limiting distribution of the est...
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Published in: | Econometric theory 2004-06, Vol.20 (3), p.513-534 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | The paper presents the asymptotic theory of the efficient method of
moments when the model of interest is not correctly specified. The
paper assumes a sequence of independent and identically distributed
observations and a global misspecification. It is found that the
limiting distribution of the estimator is still asymptotically normal,
but it suffers a strong impact in the covariance matrix. A consistent
estimator of this covariance matrix is provided. The large sample
distribution on the estimated moment function is also obtained. These
results are used to discuss the situation when the moment conditions
hold but the model is misspecified. It also is shown that the
overidentifying restrictions test has asymptotic power one whenever the
limit moment function is different from zero. It is also proved that
the bootstrap distributions converge almost surely to the previously
mentioned distributions and hence they could be used as an alternative
to draw inferences under misspecification. Interestingly, it is also
shown that bootstrap can be reliably applied even if the number of
bootstrap replications is very small.The
authors express their gratitude to Professor A.R. Gallant for his support
and for helpful discussions about this topic. They also thank Professor
Donald Andrews for his revision and for the suggestion to read the work by
Hall and Inoue (2003). They thank Hall and Inoue
for sending them their technical report. Finally the authors thank two
anonymous referees for their helpful comments, which led to a significant
improvement of the paper. The views expressed in this paper are our sole
responsibility. Víctor Aguirre-Torres acknowledges partial support
from the Asociación Mexicana de la Cultura A.C. Manuel A.
Domínguez acknowledges funding from CONACYT, research project
J38076-D, and partial support from Asociación Mexicana de la Cultura
A.C. |
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ISSN: | 0266-4666 1469-4360 |
DOI: | 10.1017/S0266466604203048 |