Thread by @pedrohcgs

Well, although I skipped last week, here I am with another interesting econometrics paper that I really enjoyed reading --- Chen and Santos (2018, ECMA), "Overidentification in Regular Models",

Link: onlinelibrary.wiley.com/doi/full/10.39…

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The main idea of the paper is simple and very powerful.

In (unconditional) GMM models, we know that some estimators are more efficient than others when you've # moment restrictions > parameters of interest. In this case, we can also test the validity of the moments (J-test)

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In many applications, however, our model is not based on unconditional moment restrictions, but on conditional moment restrictions . Furthermore, many times we are also interested in estimating functions (i.e., infinite dimensional parameters).

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Leading examples I can come up with (that is not in the paper) are when one wants to estimate treatment effects parameters using nonparametric outcome regressions and/or propensity scores.

This works under CIA, IV, MTE, and Diff-in-Diff!

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In such cases, one may wonder if the choice of estimation method has any impact on the (asymptotic) efficiency of the estimator, or if the underlying model at hands is actually testable.

Here we can't just count the # of moments because there are infinitely many of them!

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Chen and Santos provide a powerful machinery to answer such type of questions: as you can't simply count the # of moments, they provide an alternative characterization for "local overidentification" based on tangent sets. I know, this sounds a bit technical, but we can do it!
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They also show that many types of models we are familiar with such as the BLP, Selection Model, production functions, are locally overidentified, implying that the choice of estimation method can matter!

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The message I got from this paper is that, although identification is indeed very important for our work, the choice of estimation procedure can also matter!

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If you can estimate what you are after using a less "data hungry" estimation procedure, we should probably favor that!

Simply but powerful message.

Hope you enjoy reading the paper, too!

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