GMM regression vs OLS regression?
In: Mathematics
As its name would suggest, GMM is a generalized approach that includes OLS for a particular choice of how to do it.
The “method of moments” is a way of estimating some statistical parameters. For any choice of the parameters, an input dataset, and a statistical model, you can generate a dataset of the outcomes you would get if your model was true and you’ve chosen the right parameters. You can then summarize this data as a set of statistical moments (mean, variance, etc.) and compare the moments in the generated dataset to the moments in the *actual* outcome dataset. The goal is to choose the parameters that make this difference as small as possible.
OLS is choosing a statistical model that makes this all (relatively) easy. By assuming the outcome is just the sum of the inputs, weighted by your parameters, you can find the exact minimizing set of parameters using linear algebra. GMM lets you apply the same concept but for a more complicated model. Importantly, it also tells you how to do things like calculate the standard errors of your estimated parameters.
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