This page is based on a market model from this paper (for economists) or this one (for math/physics people), simulated in javascript in a browser. It does not currently work in Internet Explorer, use Chrome (preferable) or Firefox. It is still being (spasmodically) updated and so if anything odd happens just hit the restart button ot reload the page. To get a feel for how the model behaves, follow the Quick Instructions immediately below the Figures.
Many thanks to Julian Todd (of scraperwiki.com) for turning my original code into Javascript so quickly and efficiently! And of course to my collaborators Michael Grinfeld, Rod Cross and Tim Seaman.
1) Don't change any of the variables yet and focus on the first picture with the blue and red circles moving within the triangle. Each circle represents an economic or financial agent who is either blue (bullish, long, optimistic) or red (bearish, short, pessimistic). The triangle itself and the coordinates of the agents within it do have an economic/trading interpretation but you can read about that later if you wish.
When an agent hits either boundary of the triangle they switch state/colour and are reinjected into the interior. Note that the agents are not colliding with each other but are simply being plotted on the same triangular region. When you are comfortable with what the model is doing, speed up the simulation by changing the `ms per day' variable from 270 to 70 and then hit the 'restart' button. Note that the red and blue agents are always pretty well mixed up and the ratio of reds to blues stays very close to 50/50. This is the kind of `equilibrium solution' that is either explicitly or implicitly assumed in nearly all the standard models of economics and finance. The agents are acting independently of each other and their net effect on global variables (such as price) cancels out. Thus they can legitimately be averaged away and then ignored using the standard assumptions of neoclassical economics and finance.
2) We shall now make the agents' behaviours change in one very simple way that corresponds to many different situations in real world socio-economic systems (see the associated write-up or my papers for full details).
Agents that are in the minority feel pressured into switching to join the majority (this herding is especially prevalent in financial markets where investment managers may lose their investment capital or even their jobs if they significantly underperform their peer group for more than a couple of reporting periods). This is simulated (as justified in the papers) by making agents in the minority position drift downwards so that they are more likely to switch, on average, than a majority agent.
To achieve this, simply change the 'Herding' value above from 0 to 300 and hit 'restart'. Watch how the equilibrium solution quickly loses stability. It is replaced with complicated far-from-equilibrium dynamics where either the red or the blue agents can slowly come to dominate the system. Then (very) rapidly the system can change via a cascading process. These cascades occur at all scales --- there are lots of smaller ones and the occasional huge one that can flip the states of almost all the agents.
Rhetorical Question: Which scenario feels more like a financial market to you?! (By the way, 300 is my best estimate of the herding parameter in real financial markets but try other values too if you like).
Almost all the standard models of economics and finance are designed so that the solution MUST be a stable, and unique, equilibrium. Far-from-equilibrium models are almost never considered even though they easily explain some important conundrums in the standard approach. As I see it there are three fundamentally incorrect assumptions underlying equilibrium modeling:
1) It is assumed (either explicitly or implicitly) that some 'invisible hand' will operate near-instantaneously to move the system back to equilibrium after some change in one of the variables. This means there is no time for competing positive feedback effects (such as herding above) to take hold. However it is this potential for competiton between positive and negative feedbacks that causes boom-and-bust behaviour and there are many effects that can prevent or slow down the operation of the invisible hand.
2) For over 100 years economists have tried to convince themselves (and everyone else!) that economics can achieve the rigour, clarity and predictive ability of the hard sciences. In particular, they have been motivated by concepts from physics such as the `balancing-of-forces' that is required for equilibrium in a physical system (in an economic system such forces represent thing like supply and demand). However, it is only in the very simplest systems that balance-of-forces implies a unique equilibrium solution and this is another error that they have made.
One example of a complex physical system that does not behave that way is an earthquake zone. The tectonic plates have an internal structure that can be in many different states/configurations which correspond to `near-equilibria'. There is a balance of forces before and after the earthquake but NOT during the earthquake which is when the internal configuration of the system suddenly changes. By the way, this analogy with economic systems is not a bad one and there are distinct similarities between the statistics of earthquakes and of financial/economic shocks.
3) The simulation above shows a realistic (albeit simplified) representaion of the internal dynamics of a financial market. Without herding the red and blue agents are just a uniform smudge that can be averaged away, and without an internal structure the balance of forces argument does indeed lead to equilibrium. Thus the third flaw is to assume that differences in behaviour/attitudes/preferences/knowledge/intelligence/constraints/time horizons/incentives etc etc between all the agents in an economic system can just be cancelled out to leave the `correct' behaviour on average. Then, having averaged away all the internal dynamics one is left with the unique equilibrium solution. It only needs one effect (such as herding but there are many others) that acts systemically rather than randomly to invalidate this averaging procedure.
This careless use of averaging occurs throughout economics and finance. You can find it on page 1 of ECON 101 in those hypothetical-but-convenient Supply-Demand curves and also baked into the DSGE models that are used by central bankers to model entire economies and determine interest rates. This is a mind-boggling inconsistency at the heart of neo-classical thinking. It is the differences between economic agents that drives most economic activity -- differences between needs/resources/expectations and so on but these are exactly the things that are being averaged away. If there is a worse example of throwing out the baby with the bathwater in academic research I have yet to come across it!
My favourite example of equilibrium thinking is this quote:
``We can model the euphoria and the fear stage of the business cycle. Their parameters are quite different. We have never successfully modelled the transition from euphoria to fear.'' Alan Greenspan, Financial Times, March 27th 2009.
What Alan Greenspan is actually admitting is that he has models that look like they are working until they suddenly don't! These unexpected transitions are exactly what you would expect when you are trying to model a far-from-equilibrium system with an internal structure by an averaged equilibrium model without one.
So why is mainstream economics still hooked on equilibrium models? This is probably a question for an economic historian or philosopher but I think there are several factors. Firstly, the flawed assumptions are so ingrained that most economists don't even think about them very much if they are even aware of them at all. And they certainly don't explain them to their students which leads to a vicious trans-generational spiral. Secondly, economists don't know very much mathematics beyond (if you're lucky) basic calculus and perhaps some elementary differential equations. In particular they have almost no experience of nonlinear systems. For example, some economists I have spoken to believe that instabilities cannot exist in economic systems because in unstable systems the mathematical quantities will fly off to infinity (or minus infinity). This is only true in LINEAR systems however. The model above is highly nonlinear (when the herding is non-zero) as I believe are most economic systems.
The concepts of nonlinear systems lead much to far more complex and difficult mathematics which is a very good reason for not wanting to believe them. Yes, to a casual observer a technical economics paper looks very impressive but the mathematical concepts are very unsophisticated (and rather dull). And in any case no amount of clever-looking math can correct bad assumptions!
Another reason is the unfortunate fact that far-from-equilibrium dynamics caused by competing negate and positive feedbacks tends to result in surpringly long-lived, apparently stable, but ultimately unsustainable trends. Or to put it another way --- tomorrow looks a lot like yesterday even when you are in the middle of a bubble! Equilibrium thinking has caused economists to focus on time-scales that are too short and when your belief system seems to be working most of the time you can usually come up with some plausible story to excuse what look like occasional hiccups. Yes Alan, I'm talking about you.
The vast majority of theoretical work in economics over the last 50 years has either been extending the equilibrium approach or introducing ad hoc modifications to explain the inexplicable without having to junk the entire life's work of many, many people. In the hard sciences researchers are forced to live with this possibility every day and have no place to hide when it happens. Not so in economics where controlled experiments are often impossible, different interpretations abound and clean data is hard to come by. Hopefully computer simulations such as the one described here can help fill this experimental gap and, at the very least, introduce economists and others to the relevant non-equilibrium concepts.