This post was written jointly with Joerg Luedicke, Senior Social Scientist and Statistician, StataCorp.
The command gmm is used to estimate the parameters of a model using the generalized method of moments (GMM). GMM can be used to estimate the parameters of models that have more identification conditions than parameters, overidentified models. The specification of these models can be evaluated using Hansen’s J statistic (Hansen, 1982).
We use gmm to estimate the parameters of a Poisson model with an endogenous regressor. More instruments than regressors are available, so the model is overidentified. We then use estat overid to calculate Hansen’s J statistic and test the validity of the overidentification restrictions.
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