GMM regression vs OLS regression?

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GMM regression vs OLS regression?

In: Mathematics

2 Answers

Anonymous 0 Comments

OLS takes a bunch of points in N-dimensional space (1 dimension for each factor plus one for the result) and finds a line that gets as close to hitting those points as possible.

The results of OLS also give you some other information about your data (how distributed it is, how likely that the actual line is just flat, etc.)

But in order for those results (and even the line itself) to be correct we have to satisfy certain assumptions about the data. These are called the Gauss-Markov assumptions.

Those assumptions are pretty easy to make true when you’re running a double blind experiment. Unfortunately there are many types of research where double blind trials are unethical, impractical or both. These are basically the observational sciences, particularly social sciences (including economics).

To make up for this we’ve come up with a bunch of techniques for when any given G-M assumption isn’t met. GMM is one of those techniques.

Anonymous 0 Comments

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.