Continuous updating gmm
When the number of moment conditions is greater than the dimension of the parameter vector θ, the model is said to be over-identified.
Over-identification allows us to check whether the model's moment conditions match the data well or not.
By using the shorter notation, we need only specify the derivative with respect to the entire linear combination instead of each parameter individually.
There exist simpler necessary but not sufficient conditions, which may be used to detect non-identification problem: Asymptotic normality is a useful property, as it allows us to construct confidence bands for the estimator, and conduct different tests.
The GMM method then minimizes a certain norm of the sample averages of the moment conditions.
The GMM estimators are known to be consistent, asymptotically normal, and efficient in the class of all estimators that do not use any extra information aside from that contained in the moment conditions.
The asymptotic covariance matrix simplifies considerably in this case so that.
It also shows that the weighing matrix type was White, and this weighting matrix was used for the covariance matrix, with no degree of freedom adjustment.
Order Stata Stata’s gmm makes generalized method of moments estimation as simple as nonlinear least-squares estimation and nonlinear seemingly unrelated regression.