**Implementation**

One difficulty with implementing the outlined method is that we cannot take *W* = Ω−1 because, by the definition of matrix Ω, we need to know the value of *θ*_{0} in order to compute this matrix, and *θ*_{0} is precisely the quantity we don’t know and are trying to estimate in the first place.

Several approaches exist to deal with this issue, the first one being the most popular:

**Two-step feasible GMM**:*Step 1*: Take*W = I*(the identity matrix), and compute preliminary GMM estimate . This estimator is consistent for*θ*_{0}, although not efficient.*Step 2*: Take

**Iterated GMM**. Essentially the same procedure as 2-step GMM, except that the matrix is recalculated several times. That is, the estimate obtained in step 2 is used to calculate the weighting matrix for step 3, and so on. Such estimator, denoted, is equivalent to solving the following system of equations:**Continuously Updating GMM**(CUGMM, or CUE). Estimates simultaneously with estimating the weighting matrix*W*:

Another important issue in implementation of minimization procedure is that the function is supposed to search through (possibly high-dimensional) parameter space *Θ* and find the value of *θ* which minimizes the objective function. No generic recommendation for such procedure exists, it is a subject of its own field, numerical optimization.

Read more about this topic: Generalized Method Of Moments