## 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.