FIXED-SMOOTHING ASYMPTOTICS IN A TWO-STEP GENERALIZED METHOD OF MOMENTS FRAMEWORK

FIXED-SMOOTHING ASYMPTOTICS IN A TWO-STEP GENERALIZED METHOD OF MOMENTS FRAMEWORK

This paper develops the fixed-smoothing asymptotics in a two-step generalized method of moments (GMM) framework. Under this type of asymptotics, the weighting matrix in the second-step GMM criterion function converges weakly to a random matrix and the two-step GMM estimator is asymptotically mixed n...

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Bibliographic Details
Published in:Econometrica 2014-11, Vol.82 (6), p.2327-2370
Main Author: Sun, Yixiao
Format: Article
Language:eng
Subjects:
Approximation
Asymptotic methods
Autocorrelation
Consistent estimators
Covariance
Critical values
Distribution
Econometrics
Estimation methods
Estimation theory
Estimators
F distribution
fixed‐smoothing asymptotics
Generalized method of moments
heteroskedasticity and autocorrelation robustness
increasing‐smoothing asymptotics
Inference
Lagrange multiplier
noncentral F test
NOTES AND COMMENTS
Simulation
Statistical variance
Statistics
Studies
Term weighting
Test design
two‐step GMM estimation
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Summary:This paper develops the fixed-smoothing asymptotics in a two-step generalized method of moments (GMM) framework. Under this type of asymptotics, the weighting matrix in the second-step GMM criterion function converges weakly to a random matrix and the two-step GMM estimator is asymptotically mixed normal. Nevertheless, the Wald statistic, the GMM criterion function statistic, and the Lagrange multiplier statistic remain asymptotically pivotal. It is shown that critical values from the fixed-smoothing asymptotic distribution are high order correct under the conventional increasing-smoothing asymptotics. When an orthonormal series covariance estimator is used, the critical values can be approximated very well by the quantiles of a noncentral F distribution. A simulation study shows that statistical tests based on the new fixed-smoothing approximation are much more accurate in size than existing tests.
ISSN:0012-9682
1468-0262