What is Econophysics and Complexity?
It seems that "What do you do?" or "What are you up to now?", in case we are acquainted with someone already, seem to be some of the first questions people ask each other after getting back in touch. Ever since I received the fabulous news that I would be welcome to do my PhD I have responded to these questions with "I will be starting my PhD at the Chair of Econophysics and Complex Systems in Paris". There is a mixture of reactions: those that know the chair and the subject matter nodded in approval, so did those that didn't know but thought it sounded impressive so they didn't ask. The majority however follow-up with: What is Econophysics? This is the question I hope to answer here.
By no means is this investigation an exhaustive exploration of the topic. Economics and physics have been interconnected since the notion of an equilibrium was introduced, and many papers have written on their interaction. My primary goal here is to introduce both Econophysics as I view it, the notion of a complex system, and some of the contributions of Econophysics.
A First Definition
If I was going to continue assuming my counterparts know about physics and economics, then I might be tempted to sum up the idea of Econophysics by quoting
The underlying methodological assumption of Econophysics is that, even if economics is a social science and has to deal with incentives and human decisions, the aggregate behavior can be described by models of statistical physics Delli Gatti et Al. (2008) Emergent Macroeconomics pg. 8
This, however, is unsatisfying as it doesn't capture the analogy that is at the heart of the inter-disciplinary application of statistical mechanics to economics, nor does it capture the different philosophical approach of falsifiability in place of the more axiomatic approach in neo-classical economics (more on that in a future post - in the meantime I recommend David Deutsch The Beginning of Infinity).
A Complex Economy
Our first definition was not enlightening to those of us unfamiliar with statistical physics. To expound on the analogy between physics and economics, lets start with the economy.
The economy overall can be seen as a complex system (W. Brian Arthurs Complexity and the Economy). That is, at a micro-level the economy can be conceptualized as a large group of heterogeneous (different / individual) agents (e.g. people, households, firms, financial institutions, governments) that interact. Macroeconomics then focuses on what happens overall when we have appropriately aggregated different magnitudes of interest (total output, trade, cashflow, employment etc.). Effectively, the complex structures that happen at the micro-level also lead to complex dynamics at the macroeconomic level.
Complexity science postulates that a lot of these systems, including the economy, cells and atoms, share common properties. Enter statistical physics, which offers tools and techniques for understanding macroscopic dynamics given the heterogeneity and interaction at the micro levels. In the words of Peter Eastman,
That is what statistical mechanics is all about: deriving high level descriptions by starting from lower level ones and then averaging out lots of details.Peter Eastman, Introduction to Statistical Mechanics, https://web.stanford.edu/~peastman/statmech/introduction.html
The most common means of which is the application of the Ising model (see Bouchaud, 2013, Crises and Collective Socio-Economic Phenomena for a great introduction) and further mean-field theory. This approach offers an mathematical description of the dynamics of various cycles of booms and busts due to the failure of all agents to perfectly coordinate.
While in some cases a mathematical approximation of the macroeconomic dynamics can be formed on the basis of such microeconomic interactions. Overall it seems that to fully realize macroeconomic dynamics we must resort to simulation of the economy via Agent Based Modelling, which at its heart is a large scale simulation of the actual agents in the economy. Agents are then typically endowed with rules of thumb that govern their behavior. Yes, it is still a subjective choice of rules, and no it can never actually model a human being entirely. However, it does allow us to recover macro and meso economic dynamics that much more closely resemble what we observe in economic timeseries.