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Consider GMM estimation of a regression model as shown at the beginning of Example 18.8. Let W1 be the optimal weighting matrix based on the moment equations. Let W2 be some other positive definite matrix. Compare the asymptotic covariance matrices of the two proposed estimators. Show conclusively that the asymptotic covariance matrix of the estimator based on W1 is not larger than that based on W2. |
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