A new paper, “On the Implications of Micro Price Data for Macro Models” (SSRN download here) finds a striking lack of correspondence between highly detailed micro level models and their mappings into macro level models.
The paper comes up with a few good suggestions to increase the accuracy of the mapping between levels of modeling, but the main findings are pretty negative. They find (pg. 3):
We provide two examples to show that there may be no simple mapping between the frequency of price changes in micro data and the speed of impulse responses of prices and quantities to shocks.
The key finding is that macro-level time series models built from micro data don’t much behave like the DSGE impulse-response models predict they should. It’s a poor approximation, especially when trying to measure a macro-property like the Phillips Curve (of New Keynesian vintage).
This is kind of depressing, because we should be able to go from microscales to macroscales if the modeling methodology is correct. Readers of this blog know I’m no fan of the DSGE approach, but, with some approximation, the model should work, if micro founded macro models are accurate descriptors of economic reality. If they are not, perhaps another methodology might provide more insight?
A new paper in this issue of the AER by LeBaron and Tesfatsion (link to final version) gives an example of an alternative modeling framework, the Agent Based Computational (ACE) framework. Say the authors (pg. 2)
ACE is a culture-dish approach to the study of economic worlds. Once initial conditions have been specified by the modeler, all subsequent world events are driven by agent interactions.
The idea here is to have macroeconomic fundamentals (the Phillips curve, Okun’s law, a country’s income distribution, what have you) emerge from the localised interaction of informationally constrained actors with their environment and with each other. Delli Gatti et al have a new book, Emergent Macroeconomics (download the full book here), devoted to this very topic, where an ACE based micro model evolves into a set of observed macroeconomic regularities.
The idea I’d like to talk about here is emergence of macrostates from microstates. A standard reductionist approach is to assume we have a (noisy) mapping from the individual micro level to the aggregate macro level. In a new book, Reinventing the Sacred, Stuart Kaufmann refutes this naive reductionist approach. Kaufmann’s metaphor is the human heart.
The heart is an evolved piece of biological hardware. It’s primary purpose is to pump blood about the body. It is true to say it is a clump of cells, and those cells are made from molecules, and those molecules from atoms, so the physicist’s description is true, but only partially true. While the heart is one collection of atoms arranged in a specific fashion, the physicist cannot describe the heart at the atomic level, nor can she identify or predict that arrangement of atoms purpose. Even assuming the physicist could describe the heart using the atom as the bottom level of description, she could not tell us which of the heart’s characteristics—its electrical impulse function, its pumping function, and the sound it emits while pumping—are the most important in securing the continuance of life.
So the physicist’s description of the aggregate ‘heart’ as the sum of the interactions of particles is correct, but only partially so (even though some macro properties can be deduced from micro relations in thermodynamics: see this paper for details). The heart is an emergent property of the evolutionary process, whose description at lower levels is incomplete. Descriptions of things, concepts built from these descriptions, and models designed to produce predictions about the movements of these concepts, all need to be couched at the right level for an appropriate analysis to take place.
All of which begs the question, what is the appropriate level of analysis for the economic system? Marx begins from commodities. Marshall from consumers. Modern mainstream theorists consider Homo Economicus and his behavioural cousins as the atoms of the economic system. Individuals group together into households. Firms are considered next, then regions, then countries. then supranational entities like the EU. All in all, economists span a wide range of analytical macrostates—from the mind of an individual and their preferences to the movements of pan governmental organisations. It’s a lot to deal with.
So, how do we classify macrostates? Two other really interesting pieces of work on the problem come from Statistical Mechanics and Philosophy.
Shalizi et al (download the paper) try to classify macrostates by the level of predictive ability a certain set of states has. Once a set of states has the ability to predict itself, Shalizi et al argue the predictor thus dervived is the optimal statistical predictor of observed values.
From philosophy, AJ Julius (download the paper) shows a basic structure argument where the most just state emerges from the collision of several unjust states.
Where do we go from here? In economics, using these views, there are as many potential macrostates as microstates. We have each individual, groups of them, coalitions of these groups, and so on, all modeled game theoretically or using the new tools of neuroeconomics.
Really, we’re looking for an ontologically appropriate analogy, as Douglas Hofstadter shows in chapter 9 of his I am a Strange Loop. What matters to just about every non-physicist adult person is not the atoms they are composed of, but the world at their level of description: what we perceive as every day reality. And generating an analogy (or mapping, or isomorphism or translation, whatever jargon applies to your field) appropriate for those individuals is not the same as the analogy you might apply to another level of abstraction. The stories at different levels don’t mesh.
Consider the micro founded macro model, which only works when we constrain each household to be godlike and identical before our description of the micro and macro economies coincide. Or try to move the other way: to go from macro phenomena like Okun’s law to micro phenomena like regional or sectoral unemployment and growth patterns. It is very hard to do this, because we don’t have the tools to dig back down, unless the analogies or stories or models, are rather strained as descriptions of the real world.
Let me ask you, dear reader, a question, email me if you’ve any thoughts on the subject.
What is the appropriate macrostate in neuroeconomics?
There’s definitely more on this topic, perhaps even a paper. We’ll see.
