There are many examples with highly correlated data; as a result, the determinant of the covariance matrix of moments becomes very small (e.g. in an example the determinant of the covariance matrix of moments is 3e-12). In other words, moments are linearly dependent; accordingly, the covariance matrix is not invertible, or is badly invertible, and if a method such as simulated method of moments is used, the estimation of unknown parameters becomes problematic.

[Recall: Beta=argmin(e W e'), where W is inverse of covariance matrix and e is the difference between simulated and empirical moments].

Let's say there are 40 moments out of which 35 are correlated (no more information about the data is available), and there are 10 unknown parameters to estimate. So eliminating some of the moments wouldn't be a feasible option.

Any help is appreciated.