Therefore,

(We have treated this as an approximation because we are not dealing formally with the higher order term in the Taylor series. We will make this explicit in the treatment of the GMM estimator below.) The argument needed to characterize the large sample behavior of the estimator, 6, are discussed in Appendix D. We have from Theorem D.18 (the Central Limit Theorem) that m„(60) has a limiting normal distribution with mean vector 0 and covariance matrix equal to Assuming that the functions in the moment equation are continuous and functionally independent, we can expect G„(60) to converge to a nonsingular matrix of constants, T(6 0). Under general conditions, the limiting distribution of the right hand side of (18-1) will be that of a linear function of a normally distributed vector. Jumping to the conclusion, we expect the asymptotic distribution of 6 to be normal with mean vector 60 and covariance matrix (1/n) x {-[r'(60)]--[r(60)]-*}. Thus, the asymptotic covariance matrix for the method of moments estimator may be estimated with

Example 18.5 (Continued)

-1 /k |
P/k2' |

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