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Showing posts with label Lucas Critique. Show all posts
Showing posts with label Lucas Critique. Show all posts

Wednesday, March 7, 2012

Microfoundations: a bias-variance trade-off?

A recent flurry of blog posts from Noah Smith,  Simon 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.

Thursday, July 8, 2010

Ramblings on Micro-foundations, Part II...

Here I attach an interesting technical discussion of problems with microfoundations (or perhaps more appropraitely "Lucas-style" microfoundations).  Ever since I took my first graduate-level course in macroeconomics at the University of Edinburgh I have been interested in the issues raised by the Lucas-style microfoundations paradigm.  These issues are important as I believe they cut to the core of macroeconomics, and now that I have decided to pursue a PhD I will have some time (hopefully!) to explore these issues a bit more formally.

In my mind the following are closely linked (but as of yet I have only inklings of how the pieces fit together):

  1. Mantel-Sonnenschein-Debreu (MSD)'s "anything goes" theorm concerning the form of aggregate excess demand functions...
  2. Disequilibrium dynamics/issues with General Equilibrium
  3. The aggregation problem
  4. Issues with the Lucas Critique
  5. The economy as a complex adaptive system
There is already a well-defined (although perhaps not that well-known?) link between 1, 2 and a version of 3.  What Arrow et al. proved was that IF aggregate excess demand functions 'looked like' individual demand functions (i.e. satisfied the Weak Axiom of Revealed Preference (WARP)), THEN the dynamics of the economy would converge.  What the MSD theorem states is that given the assumptions made on individual behavior and the corresponding individual demand functions within the General Equilibrium (GE) (i.e., Arrow-Debreu) framework, the IF statement above does not hold in general (i.e. aggregate excess demand functions will not necessarily satisfy WARP).  The MSD theorem implies that tatonnement dynamics will not converge (in general).  The reason for this (i.e. that aggregate excess demand functions do not look like individual demand functions) is a version of the aggregation problem.

For me the issues related to 1, 2, and 3 outlined above reinforced my intuition that the economy is best described as a complex adaptive system.  In a complex system, by definition, efficient descriptions of the system depend on the level of aggregation and as such one would not expect that properties of microeconomic excess demand functions would necessarily hold true for an aggregate excess demand function.  Within the complex adaptive systems framework that emphasizes decentralized, local interactions between economic agents, aggregate excess demand is an emergent property. 

Approaches within the complex adaptive systems framework have also been more successful in proving convergence results using models that involve decentralized, local interactions.  The use of decentralized, local interactions in complex systems models contrasts sharply with tatonnement dynamics and the GE framework which are very centralized.  In my opinion the decentralized, local interaction approach is a more intuitive description of reality.