Origins of multistability in economic systems: commentary on Soros (2012)

All over the world, the same message is relentlessly hammered home--conventional economics has failed. Policy makers did not foresee the 2008 crisis--and their attempts at remediation of the unemployment situation have had effects opposite to what was intended.

Why is this? Does economics in the real world differ so much from the theoretical? And if so, why?

Let us consider how complex behaviour arises in some natural systems.

Multistability in natural systems

The global climate system is a nonlinear, nonequilibrium system involving internal time-varying mechanisms, feedbacks, and external forcing. Systems with feedbacks are commonly multistable, prone to bifurcations, and hysteresis—even when those systems are driven by invariant driving functions.

In previous posts we have seen that the phase space projections of numerous climate functions show multistability--that is they tend to evolve not to a single equilibrium, but oscillate among any number of equilibria. The reason that multiple equilibria arise is because the dynamics of the climate system include both negative and positive feedbacks.

Different forms of stability. For asymptotic stability, given a limited range of  initial 

conditions, the system evolves towards a fixed point. For Lyapunov stability, once the system

reaches a limited region of phase space (b), the system tends to remain there. 

Where negative feedbacks dominate, the system tends to be stable. In the diagram above, there are different forms of stability, but the two most important are asymptotic stability (also called a point attractor) and Lyapunov stability. It will normally not be possible to distinguish between these on the basis of observation of some system.

Positive feedbacks tend to enhance the effects of external forcing, multiplying the magnitude of the stresses brought on by forcing. The presence of both negative and positive feedbacks supports a system with multiple disjoint regions of equilibria, bounded by separatrices. 

Time evolution of a system with multiple equilibria. In actuality, the separatrices 

are likely to show fractal interfingering.

I have commented on applications of this idea to unemployment, but have not discussed the origins of the necessary feedbacks required to generate multistability. Some comments by George Soros (below) seem to shed some light on this topic.

Soros' remarks on global economy

George Soros recently spoke at the Festival of Economics in Trento, Italy. What made his remarks interesting to me were his allusions to nonlinear dynamics in the evolution of the economic system, and their effects on policy. Soros begins by remarking on the lack of success policy makers have had in predicting economic outcomes in the past few years. The reasons for these failures . . .

go back to the foundations of economic theory. Economics tried to model itself on Newtonian physics. It sought to establish universally and timelessly valid laws governing reality. But economics is a social science and there is a fundamental difference between the natural and social sciences. Social phenomena have thinking participants who base their decisions on imperfect knowledge.

Anyone reading about Austrian Economics will be familiar with the argument. Market participants will try to act in a way that maximizes benefits to themselves, but what constitutes maximum benefit may vary from one to another. A highly technical treatment of this topic can be found here (probably not of interest to most of you, except for the part about aggressive participants with a strategy of investing in risky assets increasing the likelihood of a market crash for everyone).

The market participants do not perceive the true nature of the system in which they are operating, and so many will choose suboptimal strategies. However, as they act, they also change the nature of the system, so that what would have been an optimal strategy had all participants been "rational" may become suboptimal in the real world. Likewise, strategies which would be suboptimal in a purely rational world may become optimal.

I found a two-way connection between the participants’ thinking and the situations in which they participate. On the one hand people seek to understand the situation; that is the cognitive function. On the other, they seek to make an impact on the situation; I call that the causative or manipulative function. The two functions connect the thinking agents and the situations in which they participate in opposite directions. In the cognitive function the situation is supposed to determine the participants’ views; in the causative function the participants’ views are supposed to determine the outcome. When both functions are at work at the same time they interfere with each other. The two functions form a circular relationship or feedback loop. 

For instance, under normal circumstances it would not be advantageous to rush to the bank and withdraw all of your money. However, the economic system could be altered to the point where that might turn out to be the optimal strategy after all. 

Soros goes on to describe the inflation and bursting of a bubble in terms of the interaction between positive and negative feedbacks.

I developed a model of a boom-bust process or bubble which is endogenous to financial markets, not the result of external shocks. According to my theory, financial bubbles are not a purely psychological phenomenon. They have two components: a trend that prevails in reality and a misinterpretation of that trend. A bubble can develop when the feedback is initially positive in the sense that both the trend and its biased interpretation are mutually reinforced. Eventually the gap between the trend and its biased interpretation grows so wide that it becomes unsustainable. After a twilight period both the bias and the trend are reversed and reinforce each other in the opposite direction. Bubbles are usually asymmetric in shape: booms develop slowly but the bust tends to be sudden and devastating . . .

At any moment of time there are myriads of feedback loops at work, some of which are positive, others negative. They interact with each other, producing the irregular price patterns that prevail most of the time; but on the rare occasions that bubbles develop to their full potential they tend to overshadow all other influences.

What does the phase space of a system with myriads of feedback loops look like?

The recognition of multiple equilibria in economic systems does not go far enough, in Soros's view, because the collapse of bubbles can trigger policy responses which greatly alter the workings of the system. In other words, politics can become a potent driving force, with both secular components (such as the progressive concentration of wealth and power into fewer hands over the last forty years) and singular spectacular events (such as declaration of wage and price controls, short-duration spikes in interest rates; or even irreversible decisions like detaching the dollar from gold).

The addition of the political drivers adds a dimension which has no analog in nature. It also forces us to recognize that the future evolution of the economy will be not only a function of the feedbacks and forces we consider above, but also the entire history of the economy as well. For instance, Soros argues that the present European crisis is as much a function of history as of excessive government debt . . . 

because the financial problems were reinforced by a process of political disintegration. While the European Union was being created, the leadership was in the forefront of further integration; but after the outbreak of the financial crisis the authorities became wedded to preserving the status quo. This has forced all those who consider the status quo unsustainable or intolerable into an anti-European posture. That is the political dynamic that makes the disintegration of the European Union just as self-reinforcing as its creation has been. 

Unfortunately the non-linearities in the system make prediction hazardous. But given the preliminary indicators of bank runs in Europe, South America, and Africa, as well as Oanda's recent announcement . . . errm, yes, excuse me, but I have some preparations to see to.

Innovation in earth systems poster presentation

Presented at GAC in St. Johns early last week.

It looks like it can't be enlarged in this format. Later I'll try breaking it up into different panels and posting separately. The 3-d projection at lower right will be the hardest to present.

Update:

This is just the long 3-d image set at original size. Not sure about your best viewing options.

The main issue I note is that after trying to trace particular attractors through all of the different windows all at once, my interpretation of the number of areas of Lyapunov stability is a little different than when I looked at them sequentially. I now think that the ice-minimum attractor in the Early Quaternary is the same as that in the late Quaternary, even though the range of O-18 values represented in it has drifted over the last two million years. In earlier postings I had interpreted these as different attractors on the basis of the different values.

Secular drift in the positions of attractors in phase space speaks to slow changes in governing parameters of the climate system. On the scale of two million years, likely candidates are tectonic uplift (particularly around the North Atlantic), strengthening of the modern oceanographic circulation system after the closing of the Panamanian isthmus, drawdown of atmospheric CO2 due to enhanced erosion of uplifted highlands--at least these occur to me off the top of my head.

Post St. John's

The trip Newfoundland last week was great apart from the snow. You probably didn't realize that it is still winter on the Avalon Peninsula.

It really wasn't the snow so much as the continual 60 knot winds. I don't know why they don't just build 10,000 windmills there--the wind never stops.

The garden spot of the southern Avalon Peninsula, near Trepassey.

My poster presentation on recognizing innovation in geological systems largely went unrecognized. Not exactly an overwhelming response, but due to overflow I was placed outside of the main poster area, where I mostly talked to my neighbour and his students/associates. I think that each of us had about only one paying customer.

This wasn't the worst setting I've had but it was up there. I remember at AGU several years ago being placed in a room with one other presenter, and during the entire session not a single other soul entered the room. We spent the entire time chatting. Bad as it was for me, the other fellow was J. Rial, who was already fairly well known in the field.

Fairness and mismatched incentives in education

The kids finished their EQAO exams last week. This is what passes for a provincial exam. But here's the thing. The kids are told that their marks won't count toward their evaluation. But at the same time, they are told that it is really important that they do well, although they are not told why that is the case.

Oh wait! Here's a recent news release.

TORONTO, May 31, 2012 — Starting today, Ontario’s Grade 9 students begin writing the provincial math assessment. As they do, an Education Quality and Accountability Office (EQAO) study released today shows that teachers can help them do better on the test by delivering a simple non-math message: “This test counts toward your final mark.”


EQAO’s research revealed that when teachers of academic math said they would count the assessment toward final grades, and their students were aware of that fact, 87.5% of them met or exceeded the provincial standard. By comparison, 75.9% of students in that course met the standard when they said they were not aware of their teacher’s intention to count the test—a difference of 11.6 percentage points.

What genius! Why didn't they think of that before? Over the past years I can't say how many times I have heard frustrated teachers concerned about the extra training they have to undergo if the results at their school fall below provincial expectations. They were also desperately afraid that their students would find out that their performance might doom their teachers to extra training. It certainly is possible that students might deliberately do poorly to spite their teachers.

Of course the incentives are all wrong. The incentives encourage cheating, not by students, but by teachers. What kind of example does this set for our young people?

Years ago, there really were province-wide exams. They fell out of favour some time ago for reasons that I have never heard elucidated convincingly. I have always thought it was driven by teachers who feared they would be judged against teachers at other schools where the students performed better. This was reported to be unfair because poverty, diet, and poor family situations all have a negative impact on students' performance.

At the same time, I'm pretty sure that some parents felt the province-wide exams were unfair as well. Some schools are cursed with substandard teachers whose students would be at a disadvantage in comparison to those in better schools. However, this sort of unfairness is easy to sort out--students within each school can be assigned a mark based on a Z-score (a measure of how many standard deviations above or below the mean) based on all students from their school. The province can then stipulate a mean (68% for instance) and a standard deviation (8-9%) and the Z-scores used to compute marks. The unaltered marks could still be used to determine which schools need (ahem) extra help.

The method above will level out all differences in marks between schools, but then a new source of unfairness arises. Some schools are better than others, perhaps so much so that it may be that all the students in school A, if objectively graded, should qualify for university entrance, whereas the students in school B are so abysmal that none of them should be admitted. In the test given above, an equal fraction of students from A and B will qualify for university.

I get the impression that that is a kind of unfairness that taxpayers will accept (except for the minority of soreheads whose children attend school A).

Sea level rise will not be illegal . . .

. . . just ill-advised.

A recent blog posting on SciAm states that North Carolina has declared sea-level rise to be illegal.
This could potentially be a brilliant solution, depending on your political persuasion and/or view of reality. Perhaps they can do the same for global warming.

Upon closer inspection of the legislation states something different.



(sourced from here)

It looks here like the legislation limits who can make projections about rising sea levels. Not that this isn't a serious issue--as it is possible that the "Division of Coastal Management", being a political body will provide sea level estimates that satisfy its client--but this is a far cry from declaring sea level to be illegal.

The legislation also limits the kind of projections which can be made. Never mind what the data may show, extrapolations have to be linear.

The penalty for such foolishness will be under-insured, ill-advised construction projects in soon-to-be-inundated coasts. The cure would normally be to make the General Assembly responsible--but that seems a little unfair as the penalties would simply be paid by the taxpayers of the state. Dumping the mess into the hands of the insurance companies could work--they at least have a lobby that might push the government to do the right thing (something the taxpayers lack), although they, too, would probably just get bailed out by the taxpayers.

No, the taxpayers are simply going to have to break out the torches and pitchforks.