The weather is the prime example of a system governed by Chaos Theory which means it becomes increasingly difficult to predict as one looks to the long term. Any forecaster who tells you they can predict the weather on a particular day in a year’s time is clearly taking out of their rear end.
Is the economy similar? If it is, shouldn’t our politicians stop pretending they can control it? Do governments need to realise that instead of trying to steer the economy, they should find ways to help us find shelter from it’s storms? Sold we use what we know abut Chaos Theory to inform philosophies of economics such as to stop driving the system etc?
Predicting and controlling are two different things. Take your example of weather: We can’t predict it, but we’ve been controlling it for millennia. At this spot where I’m sitting, it never rains nor snows, and it’s windy only when I want it to be, and has been that way for decades. About five feet to my right, it rains and snows distressingly often, but I don’t care about that, because that’s not where my computer is. But thanks to my walls and roof doing their jobs, the weather right here (where I spend a lot of time) is always lovely.
And yet any forecaster who tells you they can predict the weather 24 hours from now – or for a very relevant storm example, that they can predict the likely future path of a hurricane over the next week or so – is very likely telling the truth.
“Chaos” in mathematics and science doesn’t mean completely unpredictable. It doesn’t necessarily mean that we don’t understand the relevant dynamics of the system. What it means is that there is extreme sensitivity to starting conditions, which results in a limit on the useful time span of certain predictions. Specific predictions will eventually expire, they will eventually be no good, but any predictions within their useful time span are still relevant and generally reliable, with a given level of confidence. And if we give up the necessity of specific predictions, we can sometimes still say a great deal about long-term behavior in a general sense, even in a chaotic system.
The economy is without question a chaotic system.
The length of useful predictions, however, can often extend months for many relevant macro variables rather than just a couple weeks. In addition, there are exogenous variables in economic systems which humans have extensive control over. We don’t have such control over the immediate weather, for example, the energy of a hurricane is so strong that sending a nuke into the storm would accomplish essentially nothing (except for scattering fallout over an extensive area). But for the economy? We can totally nuke the economy. Pretty easy to do.
There are things we can’t control, and things we can control. There are things we can’t predict, and things we can predict.
We can’t predict GDP five years in the future, just as weather forecasters can’t predict the temperature a year from now. But we can still understand the relevant dynamics of the system. It’s simply a physical fact that certain molecules trap heat more effectively than others. We don’t know that next year’s temperature will be higher, but we do have a great deal of confidence that the temperature 20 years from now will be generally higher, in most places, if we keep pumping CO[sub]2[/sub] into the atmosphere. Likewise, we know that there are some policies that tend to encourage economic growth, and some policies that tend to retard economic growth, even if we can’t predict the next recession. We can’t stop a hurricane, but we can (potentially) lower our carbon output. We can’t predict GDP five years from now, but the central bank can absolutely set a higher nominal spending target to encourage recovery from the current recession.
Governments can enact policies that encourage long-term growth, and they also have extraordinary power to influence the economy in the short term in fairly predictable ways.
It’s beneficial to have humility. It’s beneficial to realize what the government can’t do.
But we shouldn’t be so steeped in false humility that we ignore the very real things that we know. We do have some genuine knowledge about the economy, and if feasible, we should apply that knowledge.
I am going to go out on a limb here and predict that in one year’s time, the average Canadian will have a better standard of living than the average Cambodian. I’m also going to be that the life expectancy of the average Norwegian will be longer than the life expectancy of the average Ghanaian, despite the fact that biology and health have a crazy number of variables.
Everything is governed by chaos theory, but the fact remains that things can be controlled. Argentina, one one of the richest countries in the world, no longer is. South Korea, once extremely poor, is now rich. In both cases the decisions made by politicians are largely the reason why those countries’ fortunes have changed.
Chaos theory doesn’t mean unpredictable. In fact, it means exactly predictable - only impossibly difficult to do so. Chaos theory is incredibly dependent on initial conditions. The butterfly effect - that a butterfly’s wings can start a hurricane on the other side of the planet is to show the scope and minute detail that initial conditions can boil down to. You simply can’t account for all the initial conditions though if you did, you would be able to make exact predictions.
Now as for economics? Macroeconomic factors like increasing/decreasing money supply and raising/lowering interest rates generally do help the government control trends to fit what they want. It’s when unaccounted conditions like squirrely bankers or irrational investors get together and throw a monkey wrench into the works that gunk things up.
You have to distinguish between weather and climate. Climate is an aggregate, average number. We can predict trends in climate pretty well, I’ve been told. Weather is the specific day to day variations, which are very difficult to predict even a week ahead.
“The Economy” as a term encompasses both of those concepts. So for example we can say that GDP almost always goes up. Lots of people could have predicted the 2008 recession, and many did. It was lucrative for many not to listen or to look the other way in the face of the evidence. So that is a matter of aligning incentives, not making better predictions.
Now, if you want to know whether an individual company or product will succeed or fail, that’s more akin to “weather” and you’re not going to be able to predict very well at all. Which is why only a lucky few like Warren Buffet make a killing in the stock market. It’s essentially gambling, but without the built in house advantage.
To pile on … Chaos Theory is all about making probablistic predictions. With all the popularity of “the butterfly effect” concept people pay little attention to another big Chaos Theory concept: attractor basins. The simple way to look at them is rolling a die. Stating exactly which portion is facing up at any one time is extremely difficult to do (could be this number or that, an edge or a vertex), but I can state with great confidence that over it will end up with a flat surface facing up and more so that over a large number of throws each number will come up around the same number of times. Each face landing up is an attractor basin with a probability of 1 out of 6. If the die is fair.
The issue with economics is figuring out how to weight the die.
If the economy were predictable, everyone would do it, and the benefits would become spread out over all the participants. (It’s only of real benefit if you’re the only one who knows the secret!)
Once that happened, the real speculative market would move into the unpredictable fringes of the overall (predictable) market. In much the same way, the local tv stations not only tell us the broad patterns of the weather (which is, now, more predictable than it was 30 years ago) but also go into speculation about very local “micro-climate” weather – like the difference in weather between Los Angeles and Long Beach.
Also, no matter how accurate the oddsmakers are, you can still take a flyer on a long-shot at Del Mar, and, mirabile dictu, even win once in a while. I got a hot tip from Damon Runyan on a mudder named Patagonia Patty…
I would argue the economy is actually predictable within certain limits. Most insurance companies and investment banks pay actuaries tons of money to develop probability distributions and simulations that accurately model stock returns. They don’t get paid tons of money because their final work is slipshod and guesswork.
One of the great theorems of probability tells us the sum of independent random variables approaches a normal distribution (bell curve) as the number of variables becomes arbitrarily large. In most instances in the marketplace, the political, production, demand, good will/name brand recognition, etc., inputs that determine the fair price are approximately independent, i.e. the manipulation of one doesn’t radically affect how the manipulation of another variable affects the price. So it stands to reason the confluence of all these extenuating circumstances leads to a process that is reasonably predictable.
As an example, consider the famous Black-Scholes equation. Even with its relative simplicity, it provides a good way to measure what the fair price of stock options should be. The options are actually sold in a clearing house and the price is determined by how many sellers vs. how many buyers there are. Yet, if you got on Yahoo Finance, pulled up a random stock’s option prices, found all of the relevant inputs and saw how the theoretical price differs from the market price, the absolute error usually isn’t off by much more than twenty/thirty cents, which usually translates to a 5% - 10% error.
Of course, the B-S Model isn’t great for ALL stocks, but the underlying process of the stock can be modified to accommodate probability distributions other than the normal distribution. For instance, you can introduce a Poisson counting process to model large discontinuous jumps in stock prices.
The key is understanding statistics. Sure, you can get a point estimate for the future value of a stock, but the point estimate is drawn from data that is a realization of a presumable infinite set of possible outcomes, so your estimate is skewed by the data you have. By placing some assumptions on how the set of possible outcomes is distributed, you can determine a reasonable prediction interval for the stock price in the future.
We’re pretty sure human activity is changing the climate, and we have a pretty good idea of what types of policies we can enact to steer that chaotic system toward a different trend.
We can’t predict market crashes next year, just like we can’t predict heat waves next year. But I’ll bet we can predict the trends if we put enough effort and thought into it. The better we get at analyzing it, the more accurately we can control the trends.
No type of mathematics “governs” a physical phenomenon. Mathematics is used to describe and predict behavior, but any model is only as good as its results. Having said that, just because something is best described using chaos theory doesn’t mean that it is unpredictable.
Was unexpectedly offline after I posted the question, so I just wanted to thank you for all these excellent replies. I understand that the economic system is not equivalent to the weather and out of our control. But there are some interesting insights that you have all bought up. Part of Chaos Theory as I understand it is that completely random factors - however tiny - can dramatically alter the system. And not only are these factors random they’re often unknown and unprecedented - Black Swans, as Nassim Nicholas Taleb would say.
I never hear politicians or economists talking about Chaos Theory in relation to the economy so I’m curious as to how important it is in their thinking. Of course I am neither an economist nor a mathematician - merely a curious mind.
Another mathematical model of markets (and other behaviors) is Catastrophe Theory.
Early on, it was hyped a bit too much – people said it would allow the prediction of the stock market, etc. (The same sort of hype that accompanied Neural Net programming. Useful, yes. The biggest thing since Pythagorus…no.) It didn’t live up to that level of promise, but it does have some nice explanatory power.
Re chaos theory, remember that the “butterfly effect” doesn’t apply at arbitrarily small scales. The location of one particular atom isn’t going to change the history of the world. By and large, for want of a nail, the kingdom is not lost. In practice, small causes tend to damp out and disappear into the background noise. One guy, marching in cadence, is not going to cause the bridge to fall down. 5,000 guys? Maybe.
I’ve been strongly convinced in the last year that most macroeconomists don’t think nearly as much as they should about this.
Conventional macroeconomic models are equilibrium models, where the whole system trends toward a predictable stable state, often linearized for simplicity. There are big historical and methodological reasons for this, and hey, the equilibrium linear stuff is much easier. Chaos is dynamic, non-linear, always moving, eventually unpredictable on a long enough time scale. Not so easy, this stuff.
I play around with non-equilibrium models, with potentially chaotic behavior. Damn tough to do in a convincing way. Damn tough.
Dynamic non-linear, yes. Unpredictable on a long enough time scale, again, NO. On a long term time scale predicting a family of likely outcomes is a large part of what chaos theory is about.
Actually a quick google shows that there has been some work on describing economic systems in terms of their chaotic dynamics. Note in particular the sections from 91 on on strange attractors.
The math itself is beyond me, but the concept that the models demonstrate that widely divergent paths will converge on (be attracted to) some number of predictable potential sets of solutions, is easy enough.
If I give you starting conditions for the Lorenz system, and I tell you those starting conditions have a random fluctuation of up to 0.0001 in all three dimensions, then you’ll have a good grip on the climate of the system – the dynamics are fairly easy to understand if we linearize on the three equilibrium points to see their behavior – but you still won’t have any full certainty about which of the two equilibrium attractors the system will be “orbiting” at time t=100. That is a relevant question in certain contexts, and this was the unpredictability I was referring to.
This distinction between “weather” and “climate” has been discussed many times already, including in my own first post in this thread. When we’re referring to the “unpredictability” of chaos theory, I think maybe it should be clear from this point in the thread that we’re referring to precise weather predictions a year from now, not general climate conditions.
Maybe it should be clear, but I do not think it is to most. The fact that utilizing chaos dynamics can predict that there are, say, two groups of outcomes that are most likely at t=100, and the relative probabilities of being in each one, is usually lost on most when they hear all about the unpredictability of chaotic systems.
Long term steering of the economy (the concern of policy makers) does not require knowing exactly what will be the conditions on an exact day some time a year from now or later. It does require having some sense of what the likely outcomes are, how likely, and, the tricky part, what can be done, if anything, to adjust that fractal landscape.
That’s a good point. I’ll try to be less ambiguous in the future.
I also wanted to touch on another interesting thing in response to your previous post:
The problem isn’t to create a non-linear system. Those are pretty easy to make. I’ve got a small collection littering my own library and hard drive, a few of them extremely interesting in their results.
The problem is to make the model interesting/convincing/comprehensible to conventionally trained optimization-with-equilibrium economists, the kind of people who populate prestigious universities, finance ministries, and central banks. The most popular academic macro methodology, by far, is a form of general equilibrium analysis where a single agent tries to make an optimal decision across time periods, “intertemporal maximization”. This is the academic mainstream. It tends to involve an assumption of a single steady state, and then linearizing on that steady state for simplicity. There are other common assumptions that are arguably even less realistic – rational expectations and the representative agent – but these unrealistic simplifications are needed to make the model work.
People get into journals with this methodology, refereed by others who became famous with this methodology. They get jobs based on their conventional general equilibrium publications. Eventually they become referees of conventional papers themselves, custodians of orthodox macroeconomic procedures.
How do we test which model is best? There are no macro experiments. Data comes in slowly. In fact, any divergence from theoretical prediction can be explained away with “exogenous shocks” to the system. These models have a random factor already included, so if the model output is wrong, the model might be considered still correct, because the model itself said that the model could be wrong, given the random shock. It’s right even when it’s wrong. It’s completely normal for an economist to take the standard general equilibrium model, and then hand-pick the kind of “random” shocks which would be necessary to get anywhere near the real-world experience. No experiments, so the so-called random shocks are specifically calibrated for the model to work.
So let’s suppose that a disequilibrium theory actually did a better job describing how the economy functions. Let’s suppose one of the little toys on my hard drive could one day grow up to be the single best description of the economy that we have available to us.
How long would it take for the average macroeconomist to understand and accept this novel idea?
I don’t have any firm conclusions about this, but my relative complacency about the state of macro before 2008 was completely destroyed by the general economic response to the crisis, both among professors and policy makers. Something is very wrong here, but it’s incredibly hard to say exactly what it is in a convincing manner.
Well what you describe is why we have such widely divergent schools of economic thought still around! And why the state of the art is such as you had described – able to make some reasonable predictions about the reactions to interest rates and stimulus packages in a short term, but harder pressed to look out much beyond that.
My onlooker’s understanding is that modeling a complex dynamic nonlinear system rapidly requires a whole heckuva lot of processing power to produce those fractal landscapes. Assuming we had a reasonable model what sort of processing power would be required for economic models, and testing it on past data sets? And modeling out what tweaks do what to that fractal landscape?
It just seemed to me that we had a lot more consensus before the Great Recession.
Maybe’s that just fantasy idyllic thinking on my part. Or maybe there really was a general feeling of consensus, because we required crisis to illuminate the fundamental disagreements that lay hidden below the surface.
ETA: It goes a little deeper. The average macroeconomist has genuinely forgotten a lot about money and macro that used to be known to the leading lights of previous decades. That’s just bizarre.
I wish I had a reasonable model, but I don’t, so I can’t yet say what sort of oomph it would require. The stuff I’m looking at right now is useful more in what it says qualitatively than quantitatively. The interesting stuff is the very basic dynamics of money flow, not crunching a lot of dimensions, which is to say processing power isn’t an issue yet.
I’m dipping my toes into this stuff searching for fresh perspective, but really, I’m not the person who’s going to untangle this web.