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Wednesday, March 7, 2012

Microfoundations: a bias-variance trade-off?

A recent flurry of blog posts from Noah SmithSimon Wren-Lewis, Paul Krugman, and others related to microfoundations and their relevance/usefulness for macro encouraged me to write my a post summarizing my own thoughts. Update: Paul Krugman has written another gem on the topic. Either I agree with him or he agrees with me...I can't decide which!

I think that choosing whether to use a macro model base solely on relationships between aggregate variables or a macro model with microfoundations basically boils down to balancing a kind of bias-variance trade-off.  As Paul Krugman notes, all microfoundations are biased representation of "true" individual behavior:
And when making such comparisons between economics and physical science, there’s yet another point: what we call “microfoundations” are not like physical laws. Heck, they’re not even true. Maximizing consumers are just a metaphor, possibly useful in making sense of behavior, but possibly not. The metaphors we use for microfoundations have no claim to be regarded as representing a higher order of truth than the ad hoc aggregate metaphors we use in IS-LM or whatever; in fact, we have much more supportive evidence for Keynesian macro than we do for standard micro.
Given that we don't know what the "true" microfoundations are (or that they even exist?), and given that all microfoundations (whether based on rational expectations and optimization, or insights from behavioral economics) are at best approximations of the "true" microfoundations, the inclusion of any microfoundations into our (already biased) macro models adds an additional source of approximation error to the model which should negatively impact the model's predictive ability.1

However, microfoundations also typically discipline a model by forcing it to satisfy optimality conditions or other behavioral constraints that should reduce the variance of the model's predictions.  Thus it could be the case that:
  1. introducing biased microfoundations into the model achieves a reduction in the variance of our model's predictions that more than compensates for the added bias, or
  2. introducing biased microfoundations does not achieve a reduction in the variance of our model's prediction that compensates for the added bias.
In case 1, the inclusion of biased microfoundations improves the overall predictive capability of our macro model; while is case 2 the microfoundations makes the model worse (at least in terms of predictive ability!).  I see no reason why case 1 should always turn out to be true...

It is in this sense that I disagree with Noah's argument that microfoundations probably lead to better models:
A better reason to use microfoundations, in my opinion, is that they probably lead to better models. "Better," of course, means "more useful for predicting the future." If our models predict future aggregate macro variables (GDP, etc.) based solely on the past values of those variables, we'll almost certainly be using less information than is available; if we figure out how economic actors are making their decisions, we will have a lot more information. More information = better model. And there are all kinds of ways to observe and model individual behavior - survey data, lab experiments, etc.
I am willing to concede that models predicting future macro variables based solely on historical data uses less "information," than say DSGE models with all the attendant restrictions on individual behavior, but I disagree that using more "information" necessarily implies that the model's predictions are superior.  If we knew the "true" microfoundations, then including them in the model would  unambiguously improve the model's prediction.  However, if our microfoundations are doomed to be at best an approximation of the "truth," then including them in our model will not automatically improve the model's predictive ability.  Reading Noah's post in its entirety makes me think that he is referring to models using "correct" microfoundations in the above quote.   

1 Although I suppose that it is possible for the bias introduced by including microfoundations to "offset" some of the preexisting bias in the macro model.

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