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When EViews performs the pre-whitening in GMM estimation, what is the value of parameters used?

Depends on the setting you use, but in general terms, a VAR is applied to the weighted residuals, and the coefficients from the VAR are used to prewhiten.

The User's Guide has quite a long discussion.

Do you mean P453 of User guide II?
In Eq31.46, coefficients in matrix A is by VAR, that is no problem. My question is how to know m (sample moment)? Since sample moments are functions of GMM parameters, how to determine the value of GMM parameters to compute m for pre-whitening.

Appendix E.

Thanks, I've read Appendix E.
But which theta is used in computing V hat ?

theta?

the paragraph above Eq (E.1). V depend on K-vector parameters theta.

As outlined in Appendix E, no "values of theta" are really used in computing V hat.

Let me just add that in the context in which we are typically working, the V are the long-run covariances for the product of the instruments and the errors. In this case, the residuals depend on the vector of parameters in the mean equation. Estimation of the Vhat thus does depend on the coefficient estimates used in constructing the residuals. But beyond that, theta does not enter into the calculation once you have the estimate of the residuals.

Thanks for your explanation.
In the context of GMM, E(V)=0 is the moment condition. How to estimate V hat to be used in computing the auto-covariance matrix Gamma? which is the component of long-run cov matrix Omega.

hmm, P70, the Wighting matrix iteration gives the procedure, using the TSLS coef.
Solved