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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.
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.
Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the data's distribution function may not be known, and therefore maximum likelihood estimation is not applicable.
Here we fit a Poisson model of the number of doctor visits as a function of gender, income, and whether a person has a chronic disease or private health insurance.