Reflections from PI’s economics conference, May 1-4 2009

Lee Smolin summarizes his impressions:

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My most lasting impression is that there is a growing field of research, which is at a stage where it could advance rapidly. Good work has been done over the last several decades, which has given us a store of results, hypotheses, conjectured laws and principles, methods etc which provide a good foundation for continued work. But much remains to be done before there can be a claim that these results add up to an approach to economic theory and modeling that can take over from the neoclassical paradigm as the foundation of economic theory.

To say that there is a field of research is not the same as saying that there is a theory or approach that everyone agrees on. Quite the opposite, what we saw was several distinct strands of thought, each with their own methodology, some of which were meeting each other for the first time. There is no consensus about the right way to approach economics out of equilibrium, even among those who take this as their goal. Even within approaches that share a common methodology, such as agent based models, we saw at least three very different frameworks based on different philosophies as to how agents are modeled and what the aim is. What makes it possible to group these diverse projects within a single field is so far only that they share a common aim, which is to develop an approach to economics which is dynamical and capable of describing markets out of equilibrium. For this goal to succeed it is not necessary that these directions become part of an eventual successful theory. But at least some of us suspect that there are latent and possibly important relationships between some of the directions, such as agent based models, insights from biology and the gauge theoretic approach. If this is right then there is a great deal to be gained from cross talk and collaboration amongst these approaches.

What should this field, which aims to be go beyond the study of equilibrium economics, be called? The term econophysics is useful but not general enough as we are not all physicists. Leigh Tesfatsion uses the term “non-equilibrium dynamical model (NED).” One possibility would be to shorten this to dynamical economics, as dynamical implies that it can encompass both non-equilibriium and equilibrium.

Another alternative is nonequilibrium economics, but this recalls the confusion between physicists and economists notions of equilibrium, due to the suggestion that the economists notion of equilibrium may correspond to a physicists’ notion of non-equilibrium steady state. Dynamical brings to mind the neoclassical conception of equilibrium as analogous to a static balance of forces. It encompasses everything having to do with the dynamics of an economy, ie with evolution in time. This includes agent based models and the gauge theoretic approaches.

Leigh Tesfatsion’s definition of NED I believe applies:

“A model of an economic system is an NED model if and only if the model generates the motion of the economic state between at least two **distinct** time points without dependence on external coordination conditions ("skyhooks"), i.e., coordination conditions imposed outside of any structural conditions, institutional arrangements, and behaviors arising from within the modeled economy.”

The biggest question that I am left with from the conference is whether there can be unification or at least cross talk amongst different approaches that could be so characterized. A possible route to this would be a unifying idea. Here is a candidate for one: the notion of path dependence in economic dynamics. This comes from the ecological and complex systems approaches to economics, as cycles are central to those programs, through Morowitz’s 1968 cycle theorem. We saw evidence for the importance of cycles in Kelly John Rose’s presentation and there were hints of it in some of the discussions of agent based models.

Path dependence is also the central idea of the gauge theory, as discussed by Pia Malaney and Eric Weinstein. The key insight of the gauge theory approach is that evolution of a market in time is generically path dependent, as a consequence of embodying in the mathematics the decomposition of a history of a portfolio or inventory into components of substitution, during which value doesn’t change, and growth, during which it does. This is the definition of what mathematicians call a connection. The efficient market hypothesis characterizes equilibrium as equivalent to path independence, which is in turn related to no-arbitrage. Hence, the evolution out of and fluctuations around equilibrium are path dependent, hence they are measured by what mathematicians call curvatures of the gauge connection. That is, in a gauge system the observables are connected with cycles; what they measure is path dependence around closed curves. This way of looking at it suggest that gauge invariance is a deep notion that underlies the dynamics of economics out of equilibrium, but the proof must be in what results this leads to.

Could the notion of gauge invariance be helpful for agent-based approaches? This is a step towards investigating the power of the notion of path dependence. This has been the particular interest of our small PI effort, with Sam Vazquez, Simone Severini and others, and what we have found is that gauge invariance can be imposed on agent based models and it helps to constrain the freedom in the choice of dynamics and point to interesting observables for measuring departures from equilibrium. Big questions remain such as whether the gauge invariance should be fundamental, or should be emergent, say when price discovery happens.

Another way to seek to bring the approaches together is to articulate common goals. Here is an attempt to do that:

Main goals of this field.

1. Develop a new theory of economics which extends neoclassical economics by discovering principles and laws which govern the dynamics of economies and markets.


2. Build a suite of toy models to illustrate and test these principles. These will be primarily agent based models, but they will be supported and checked by various analytic approximations.


3. Build a family of increasingly more realistic models to be compared to real markets, against real data. This is the goal of the test-bed that Leigh talks about. Develop a common format and language for both the toy and more realistic models and make them modular and open source, so that different researchers and groups may contribute their own ideas and models within the overall project.


4. Develop a family of data sets which can be used to test models against, and make them available in a common format for download from a project web page. It would be good if this data set encompasses several if not many countries as well as as long a time span as is practicable. As Danny Goroff emphasized, the construction, formatting and maintanence of these data sets are major efforts in themselves. Another point, raised by Sabine Hossenfelder, is that it would be very good to develop visualization tools to help in working with the data sets.


5. After sufficient development of models and testing against data sets the goal is the construction of tools for policy makers which might then be used “in the basements of central banks.”


6. Finally, integrate these newer approaches to economics with neoclassical economics, as the former, to the extent that they succeed, represent a deepening of the latter and are built on it rather than in opposition to it.

These goals are interconnected and it is likely that major progress in any of them will go hand in hand with progress in the others. A great deal has been done with agent based models, and, as Doyne Farmer emphasized, some laws and hypotheses are known. But I don’t think it is the case that there is yet a principle based theory of the dynamics of economics on the same level of robustness and canonicalness of the neoclassical theory of economic equilibrium.

A final way to seek to connect approaches is through common questions, so this is my last list.

Some key issues going forward from the conference

Here are the issues we wrote down on the board during the last morning as well as some which have been mentioned or occurred to me since. I would invite others to contribute their own.

1. What is the important data to explain/match? Where can it be found, how easy is it to get? Does there need to be work to define data sets and make them available online in specified formats?


2. Can we specify the minimal elements a model must have to be considered an “in principle” model of a market or an economy.


3. Can we specify the minimal elements a model must have to have the possibility of modeling a real world modern economy?


4. Can we define a framework, test-bed, set of protocols etc to define a class of economic models to allow them to be interchanged and developed efficiently?


5. What are the observables of an economic model? Are there unobvious observables? Are all the things in models genuinely observable? Are there non-obvious observables such as those associated with cycles? Is it a problem that many economic models/theories have elements such as utilities that are not observable? The notion of gauge invariance strongly constrains the choice of observables in physics, will it play a similarly powerful role in picking out the observables of economics?


6. What is the role of unobservables in economic models, such as utilities? Can models be constructed without them? Or, is there a necessary place in the model to represent the large variability in how real people and corporations make decisions, which are not readable off the economic data? That is, is it possible that the utilities represent factors that are and will remain unknown to the theorist that do influence market decisions? The goal of an economic theory and models may then be to understand and model a system, within the constraint that a component of the causes for decisions are unobservable to the modeler, because they are in the heads of the people involved?


7. What are the goals of economic modeling? Given Taleb’s point that we cannot hope to predict unusual events that have strong influence on markets, are there still questions that can be answered and patterns that can be found and understood? Can we investigate questions such as how to construct more or less stable markets, or possible tradeoffs between rate of growth and stability, without being able to predict exactly how a market will evolve?


8. What is the role of cycles in economic models? How relevant is Morowitz’s cycle theorem? A common theme of diverse approaches to non-equilibrium economics is path dependence. This arises in cycles in models of complex economies, including Kelly John Rose’s model of the US economy, it is also the key point in the application of gauge fields to economics. Is the role of cycles and path dependence a key insight which provides the basis for a unification of these diverse approaches?


9. Would it be interesting and novel to develop agent based models of trade among many countries? What questions could such models investigate? Would it be good to see if a dynamical economics approach could confirm or correct the principle of comparative advantage?


10. The role of innovation, technological development etc, appear to offer opportunities and challenges for theories of economics. They are good challenges because innovation is at the same time central to economic growth and impossible to predict in detail.


11. To what extent is market regulation a computer science problem? Given that all the major markets are instantiated in software and run across computer networks, can we conceive of the goal of stable markets, regulated as well as designed to be self-stablizing, which contribute to economic growth without being parasitic on it, as a design problem in computer science. Could we make use of experience computer scientists have of designing stable, dynamic networks?


12. Can we give meaning to the slogan, “economics is the continuation of natural selection by other means”? One hypothesis is that when accounting is invented there comes into existence a new entity, called the economic agent, which the books refer to. Whether this is an individual, family or a firm, it has specific existence and properties by virtue of the fact that books are kept of its activities. Is it possible that this economic agent defined by accounting becomes a unit of selection?


13. Can we define a sufficient set of characteristics, which define human behavior in market situations to design agents which are realistic mimics of human agents?


14. On the other hand, are there questions about markets for which the answers involve appeal to a universality class of models, where all or most of the specification of properties of agents become irrelevant? To put this differently, can we distinguish the relevant from the irrelevant parameters in microscopic models of agent interactions?


15. There seem to be two very distinct ways in which biology and evolution enters the discussion of economics. One, as a better understood example of a complex, self-organized system, from which ideas and strategies for economics have been drawn. Second, as a source of knowledge about how real human beings behave within markets. There does not appear to me to be a strong relation between these two claims for the relevance of biology to economics. Is this a problem?


16. Several times in the discussion there appeared evidence that in the real markets, at least recently, the majority of traders occupy a small number of positions in the spaces of positions and strategies. This point was made by people with experience in the markets, as well as by Sasha Outkin and Mike Brown in their discussion of the NASDAQ model. This appears to contradict the efficient market hypothesis, which holds that the market embodies all the information available to it in prices because all possible positions are taken. It is only if positions are held on all sides that equilibrium, in the sense of a static balance of opposing forces, can obtain, in a high dimensional space of products and prices. It is also only if a large number of strategies have been covered that arbitrage can be eliminated. If this it is really the case that a very small number of positions dominate markets, is this characteristic of dangerously unstable or overleveraged markets, or a general characteristic of metastable equilibria which is not captured by the efficient market hypothesis?


17. What are the next steps for developing this research program and field?

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The talks of this conference have been recorded and can be found in the PIRSA Collection C09006.

Other reports on the conference: Barkley Rosser from EconoSpeak: Do We Need an "Economic Manhattan Project"?, Steve Hsu from Information Processing: Economics, ant farmers and free will theorems, and some photos here.

The Frankfurter Allgemeine Zeitung had an article "Die Vermessung der Krise" by Jordan Mejias who reported on the meeting. You can find an English translation on Edge here.

Related postings on this blog: The Trouble with Economics, Assumptions and Limitations, Science and the Economic Crisis, This is Your Economy on Drugs, When Capitalism Fails, and the Recession Playlist.