Monday, October 14, 2013

GMM and the structural vs. reduced form debate

stolen from Wikipedia
Among this year's economics Nobel laureates is Lars Hansen, who pioneered the generalized method of moments approach for estimating economic models. Tyler Cowen gives a nice summary of Hansen's contributions to economics and finance, and Alex Tabarrok attempts to explain GMM to the layman.

I think that one underappreciated aspect of GMM is that is illustrates how silly the structural vs. reduced form debate is. GMM allows us to estimate equations derived from structural models at low computational cost and with minimal assumptions. We don't have to assume that the entire structural model is "true;" we only have to assume that the functional form of the estimated equation is meaningful relative to the parameters being estimated.

Vocal opponents of structural approaches seem to think that estimating a structural model requires far more heroic assumptions than estimating the typical linear model used in reduced form work. GMM shows that this is not necessarily the case.

Ultimately the difference between reduced form work and a lot of structural estimation work boils down to functional form. Structural approaches choose the functional form of the estimated equation based on a derivation from a structural model. Reduced form approaches choose based on treatment effect concerns, and they typically choose from within the universe of linear or nearly linear functional forms. They both fit the equation to data by minimizing error. I fail to see how one approach is more realistic than the other. It's not immediately obvious that a linear model of anything is a more or less accurate representation of the real world than any other functional form; rather, it likely depends on the research question and the items being measured. It's nice to approach the discipline with a variety of tools so we can find the right tool for each job.

7 comments:

  1. http://www.jstor.org/stable/1912775 says stationary and non-ergodic. Can you provide a ref for "functional form"?

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  2. For one thing it looks like he's assuming the parameter space is flat and totally connected.

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  3. I'm not sure what you're asking. I'm speaking in very broad terms here--of course GMM has a host of technical assumptions behind it. OLS does as well (in fact, they're both special cases of the same generalized extremum estimator). I'm just suggesting that, relative to typical reduced form approaches, estimating a structural model doesn't mean adding a huge amount of unrealistic assumptions, particularly if our estimation method is something like GMM (as opposed to MLE).

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  4. can you give an example of a structural model WITHOUT many strong assumptions?

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  5. brero321--No. I can't give you an example of ANY model without many strong assumptions. See http://updatedpriors.blogspot.com/2013/08/a-comment-on-math-and-economics.html.

    How should we even decide which assumptions are "strong" vs. otherwise? It all depends on what we're trying to do with the model.

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  6. There is a fundamental difference between reduced and structural. It's hard to speak in general, and it depends on a case-by-case basis, but
    1) sometimes reduced form suffers from the lucas critique. structural does not to the extent that one believes the model of course
    2) some other times we don't exactly know what we are estimating in reduced form, if there is heterogeneity in the parameter of interest. Put it differently: whomever does reduced form assumes there is homogeneity even in cases where it can't be true (think about returns to schooling in a mincerian regression or IV equivalent).
    3) Reduced form doesn't let you perform meaningful welfare analysis and counterfactual. This is always true if (1) OR (2) hold, but sometimes also if they don't hold.

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    1. Nice points, thanks. I agree with all of that. I was making a broader point about the notion that every estimation activity requires assumptions about functional form, so RF people who criticize structural people for making a lot of assumptions are ignoring the fact that writing down a linear regression model is not an assumption-free activity. Assuming the whole world is linear requires a lot of faith.

      Your point #2 is very good, and related to this http://updatedpriors.blogspot.com/2013/03/i-dont-know-what-fiscal-multiplier-is.html

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