Here’s a great metaphor from Paul Krugman’s The Return of Depression Economics:
A microphone in an auditorium always generates a feedback loop: sounds picked up by the microphone are amplified by the loudspeakers; the output from the speakers is itself picked up by the microphone; and so on. But as long as the room isn’t too echoey and the gain isn’t too high, this is a "damped" process and poses no problem. Turn the dial a little too far to the right, however, and the process becomes explosive; any little sound is picked up, amplified, picked up again, and suddenly there is an earsplitting screech. What matters in another words, is not just the qualitative fact of feedback, but its quantitative strength.
Aside from the obvious parallels – feedback, the crash as an ear-splitting screech, the way everyone is always surprised – this metaphor has something else going for it. It doesn’t make a lot of sense to look for the X,Y,Z "causes" of the crash because when feedback is present X,Y,Z may not be a problem even though X,Y,Z + epsilon creates a disaster.
Mark to market is a fine example, with less dynamical complexity than acoustic feedback.
Acoustically, certain frequencies are selected out. The fastest growing instability mode in a linear system is a sinewave of some frequency, and that’s the one that shows up.
The fastest growing gravity wave across a wind shear shows up as a herring-bone clouds with that particular wavelength.
The economic case though is just a simple tipping over, with no particular mode selected out.
It’s feedback in that the output goes back into the input, but I don’t think any analogous understanding results from it. Output always goes back into the input, in economics.
i’m new at this, but it certainly looks like economists like both linear and equilibrium models, and from a mathematical point of view these are very different animals, yes. i suppose there is a certain amount of handwaving to nonlinearity (marginal not equal to average etc) but this is usually then ignored.
i have more of a control theory / dynamic systems background. naievely: when you are up against a boundary or when you have zero derivatives you will have different system behavior than you are used to if you are used to a world that is essentially locally linear. second derivatives and/or other variables will come into play than you expect. you might be looking at the wrong things.
one thing that i have wondered about: there seems to be an assumption among economists that increasing the money supply is key to fixing this problem and so the fed is printing money, recapitalizing banks, and trying to lower long term interest rates to get banks to lend thereby producing more money. however it appears there are other constraints that are making this not work, and these constraints look obvious from another point of view including high probability of increased corporate defaults due to a massive misallocation of credit in the past few years plus the concomittant increase in credit loss correlation. it seems folly to attempt to stop this — it’s MISallocation after all — but unless people can figure out how to better allocate resources in a new equilibrium that seems to be our only choice?
And that is precisely why Austrian Economics, with its lack of mathematical modeling and insistence that measurement is impossible, is a pseudoscience. Prediction of damping versus uncontrolled feedback requires measurement and mathematical models. Logorrheic insistence that certain factors are the important ones reeks of authority, not science.
Really? Alex just told us to stop looking for causes of the housing boom because it’s due to an “epsilon.” That’s more scientific than the Austrian approach of thinking economists should be able to attribute worldwide disasters to actual causes?
because it’s due to an “epsilon.”
That only changes an existing unstable mode from slightly damped to slightly growing. An unstability that is there either way is to blame. Don’t depend on small effects to be absent.
If only there was a way to model these sorts of complex systems…think man! THINK!
How long do we have to listen to the predictors with their mathematical models before they get it right?
It was several Austrians that did predict this.
It is the Austrian critique of Alan Greenspan that is now the popular narrative. Ironically, Greenspan’s association with free markets is tainting the markets instead of the acknowledgement of the free market criticism of Greenspan.
Math models seem to be best for getting grants.
The audio feedback loop analogy seems flawed, because economies reach and look forward in time. Feedback depends only on the current variables affecting the sound produced by the speakers and how it makes its way to the microphone. An economy’s current output depends on expectations of the future, which don’t exist as real variables (yet) but only as information inside of people’s minds.
In the feedback example, a decrease in volume leads to a decrease in feedback. In the economy, a decrease in demand or supply may not lead to a decrease in output, depending on people’s expectations of the future.
A better analogy might be if sound waves traveled at vastly different speeds, and sometimes destructively or constructively interfered with each other. But that looses its usefulness as an analogy because its no longer simple to understand.
Agreed viz the Austrians. Austrian macroeconomic ideas aren’t irrelevant, but there are so many balls in play when you’re talking about macroeconomics that you need to rely on mathematics to make all of your assumptions clear and derive implications from those assumptions correctly. As we’ve seen from reading the General Theory, an over-reliance on verbal reasoning leads to an accumulation of ambiguities that can be impossible to disentangle.
For my money, the embrace of algebra is the reason why macroeconomics has been able to advance so far from its state 75 years ago while Austrians haven’t made a lot of progress over that period.
Keynes was an important source of inspiration, but guys like Samuelson, Modigliani, Hansen, Hicks, Tobin and Patinkin were the ones that concretized aspects of that intuition using math. As a result, they developed a set of clear assumptions about macroeconomics that provided a basic foundational consensus for the profession to refine and elaborate.
That’s not a metaphor. The use of derivatives, including CDOs, has literally created a feedback loop in mortgage prices (and hence home prices). As babar suggests, increasing money supply only floods the feedback loop, thereby temporarily hiding instabilities. Long term, you have to introduce negative feedback to increase price stability — for example, by requiring banks to pay capital insurance, or consumers to buy insurance against off-site declines in value, or both.
Why are these feedback loops more obvious now? Derivatives are more prevalent and the damping effect of transactions costs has never been lower. Market prices were always subject to negative feedback, it’s just that the time-scale over which signals could become correlated was so much longer that equilibrium approximations looked better.
Nice to see that Krugman is still learning.
Krugman’s argument makes a poor assumption, that feedback is bad. Those of us cool enough to start listening to Sonic Youth or Jesus and Mary Chain know that’s not true.
@David
The input/output signal is price. The frequency represents the periodicity in price cycles. Most of the time, the driving forces between price variations are out of phase. But there are linkages at different time-scales that can cause them to correlate and resonate — i.e., form a bubble.
See a post I did on the subprime market a while back:
http://brokensymmetry.typepad.com/broken_symmetry/2008/05/modeling-the-su.html
Didn’t Krugger bugger write that his strength was being a history major using very simple math?
Michael,
Your assumptions are that (a) there is inherent periodicity in human action and (b) that there can exist a feedback loop where the feedback signal leads the output.
I don’t know if (a) is false but it is certainly possible for it to be false. And (b) violates causality. The amplifier metaphor breaks down.
@David
Whoops. I linked the wrong post. Here’s the one I meant to post:
http://brokensymmetry.typepad.com/broken_symmetry/2008/05/applying-contro.html
The periodicity of human activitiy is not only a hypothesis, but a testable hypothesis. If most acts of consumption or production were not repeated, then it would be useless or false or both.
I don’t understand what you’re talking about the signal leading the output. No feedback loop that I know has input that does not include output.
Michael M,
Are you certain that, “The periodicity of human activitiy is not only a hypothesis, but a testable hypothesis”? If human activity is truly periodic and measurable, then it would possible to measure fear,despair and happiness. This would mean that we would have no Free-Will, as we could figure out the first cause of all of our woes and joys, via a math model, as you suggest, based on electricity. So are you next going to tell me that Ohm’s Law is the key to understanding the world we live in, and is at the depths of the human psyche?
Your link gives some nice math about reactive/inductive capacitance; but the last time I have looked around, people do not behave like AC electricity, and I think most social scientists would agree with that.
So for an audio to economics perspective: if we carefully adjust the feedback strength and timing in a creative manner can we make the financial/economic version of a dub mix?
I wrote that the feedback leading the output violates causality. That is true. The feedback must follow the output. The conventional definition of a bubble is an irrational expectation of increasing prices. Do bubble investors live inside the amplifier, or outside?
Equating a bubble with an unstable amplifier is a fallacy for at least two reasons. First, price may increase monotonically. As it goes longer and longer without decreasing, frequency s -> 0. If your amplifier has a pole at s = 0, you are claiming that bubbles form when prices are rock steady.
Second, an unstable, oscillating amplifier is essentially ignoring its input signal, which you claim is price. Bubble investors demonstrably are not ignoring price.
Human beings are not electrons. There are no time constants.
But as long as the room isn’t too echoey and the gain isn’t too high, this is a “damped” process and poses no problem.
Or you could add in some fixed delay and noise limiting, and run the gain (nearly) as high as you want.
Yes. The answer is in the math. Any good astrologist could have predicted this crisis mathematically.
Comments on this entry are closed.