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.
Hi Jalali,
You can choose HAC (Heteroskedasticity and Autocorrelation Consistent) option in your software...........
From spss select analyze menu then data reduction, press extraction, from analyze there are two selection press covariance matrix then press continue and ok
I would also opt for regularization, which basically implies you reduce the observed correlation by a common factor. An alternative solution is to set negative eigenvalues equal to zero. Other solutions I can think of could try to approximate the observed covariance matrix by some cholesky decompositions
I advise you to review your data, and to eliminate the autocorrelation if it's possible. Or you can use the option of autocorrelation and heteroscedasticity; because your data don't satisfy the hypothesis of convergence and efficiency
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