# GMM estimator: Two-step vs. Iterated estimator

I'm currently trying to understand the differences between the two-step efficient GMM estimator, and the Iterated GMM estimator. As I understand the T-S, is based on the First-step and depends on the initial weight matrix. The iterated process repeats the first and two step, until convergence - hence it will not depend on the initial weight matrix.

Since it doesn't depend on the initial weight matrix, is it then relevant to derive the optimal weight, $$W_T^{opt}=S_T^{-1}$$? Or could i just propose a random matrix like the HC or HAC - whereas it should find the same estimates.

When computing this with different weights, the estimates changes for (i.i.d, HC and HAC), using Bartlett Kernel weights! But I'm confused about the assumption, regarding the initial weight doesn't matter.