To expand a little on the point I was making the other day about mathematical models, consider Newton’s laws of motion. Newton’s first law, which you probably learned back in high school as “an object in motion tends to stay in motion, an object at rest tends to stay at rest”, while a pretty good first approximation, doesn’t really work. Why?
Because the actual statement is “Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon”. In normal terrestrial environments we’re never without a net force. In particular, friction and gravity need to be taken into account.
When it comes to actual measurable results, two bodies in a vacuum behave differently than two bodies in air. Or water. And there are environments in which viscosity is the most important determinant of motion, say, a vat of molasses.
That’s why I insist on actual measurements in evaluating how successful a model is. However elegant, models that don’t take into account all of the forces involved can be disastrously wrong and, while I’m prepared to believe that deficit spending applied with perfect timing to optimal objectives can have the predicted multiplier effect, I’m not as prepared to believe that real governments operating in real political environments aren’t counter-productive.
Using your model to compare the unemployment that would have taken place without your spending measures to the unemployment that will take place with your spending measures proves exactly nothing if the model itself is wrong. And the same is true if the numbers being produced by your model are less exact than the data that’s being used to evaluate the model.
Philosophically speaking, idealism has always been seductive, in the etymological sense of being “led away from” reality. It is always fun to see the faces of students with a mathematical bent when I say things like “In the real world there are no circles, or squares.” For them the connection between reality and abstract theory is unproblematic, and whenever reality doesn’t act the way we predicted it is because the theory was “not implemented properly” and never anything else.
Still disagree. All models are approximations of reality and hence cannot take into account all forces involved. To do so means you are quite literally modelling reality and why bother with that when we already have reality. But reality is too complicated, hence the need for simplification and abstraction. This position forces you to be come completely and totally anti-model.
Take for example your Newtonian model. For many things it is just fine in that it gets the job done. However, at speeds close to the speed of light or at or below the molecular level it doesn’t do well at all. Or consider the implication of data that is “too accurate” a very useful model might be rejected simply because the data is so accurate and minor variables are excluded from the model. Parsimony in mathematical models a good thing.
In the end, what is important to remember is that mathematical models are simplifications or realtiy and as such they may not apply in certain situations. Also, that the parameter values can change and we may not know that until after the fact. That is, in the end models can help us get insight into how reality works, but they aren’t perfect and that basing policy off them is going to entail some risk that the model is going to tell us the wrong policy.
Setting aside the economics point………
Let me be a bit pedantic and help you out on the technical side, and your analogy, which gets off base.
The problem with Newton’s equations isn’t that they don’t work because they are “wrong” or fail to account for outside forces such as friction or gravity. In fact the very essence of Newton’s equations and Newtonian mechanics is the study of how outside forces affect a body. Rather, the problem with Newtonian physics is that it ceases to work in very, very special circumstances, at high rates of speed. That is, rates of speed approaching the speed of light where things begin happening to mass. This is where special and general relativity come into play. In fact if you look at the general equations there is a mathematical term, actually the ratio of velocity squared to the speed of light squared, that becomes vanishingly small at low rates of speed (that is somewhat less than the speed of light.) So in our everyday world Newton’s equations are all but perfect approximations and work just fine. It has nothing to do with their failure to account for outside forces such as air, molasses or gravity.
I’ll save the wave particle duality stuff, quantum mechanics, for a later date.
Perhaps a better analogy would have been chaos theory, or perhaps simply the fact that there are so many variables at work that isolating one or two of them becomes almost impossible in a dynamic experiment such as the economy.
My understanding was that economists looked high then they looked low for “chaos” in economics and pretty much said, “Nope, not here.” Now maybe they are wrong, but consider that on the theoretical side if you incorporate “chaos” into your economic models all the results we are used to seeing pretty much n0 longer hold.
I’ve always thought — and I don’t offer this as an argument against modeling — that the danger, and strength, of models lies in their seductiveness. It’s quite easy to become enamored of the model because of its elegance and beauty — and its success — and begin to treat it as more real, in a sense, than the reality it was set to describe. Much the same can be said for theories, which are a kind of model. When Kuhn advanced the notion of the paradigm in The Structures of Scientific Revolutions, some took the term ‘paradigm’ to refer to a theory, or a model. But the theory, while central to the paradigm, was only one component. The theory dictates what kinds of things the investigators will count as evidence, as facts. This, in turn, dictates the kinds of experiments and so on that investigators will pursue and even the kind of instruments they will devise. This is what Kuhn called ‘normal science’. Only when the weight of experimental evidence in the negative, what he called ‘anomalies ‘, reaches a threshold will the paradigm, and its central, animating theory, be overthrown. The theory is essential, though, for without it, we couldn’t do science at all. But it’s only when someone comes along, looks at the negative results, and is able then to resist the seductive power of the old theory that a new, more adequate theory is advanced.
Steve-
Perhaps that makes my “too many variables”more to the point.
Sam-
There are a lot of themes bouncing around here. But I was always taught a pure scientist would throw out a theory if but one observation didn’t conform. Contrast that with an engineer who introduces a fudge factor or a coefficient if you will to make a theory work in the real world. After all industrial processes must move on, and they do.
Drew, I think you mean he’ll throw out an hypothesis if there’s one nonconforming observation. Theories, if they’re entrenched enough, are extremely resistant to overthrow. There’s just too much at stake. The things that Newtonian mechanics couldn’t explain, eg, the advance in the perihelion of Mercury ( General Relativity), the results of the Michelson-Morely experiments (Special Relativity) were sorta brushed aside because of the overwhelming success of Newton’s mechanics (worldview) elsewhere.
Sam –
Sorta like Global Warming theory?
;->
Yeah, just like that 🙂 I’m not going to get into it deeply here, because it’s kinda lengthy, but one of criticisms of Kuhn, especially by Popper and other advocates of the so-called layer-cake theory of scientific advancement, was that Kuhn had introduced the language of politics into the study of the history of science. Revolution, etc, etc. Now Kuhn, of course, didn’t say the science was politics, but rather that things that we normally associate with politics, consensus building, marginalization of minority views, and so on, are at work also in science as an institution. Needless to say, for some folks the very idea that Scientists, in their Relentless Search for the Truth, resemble a bunch of grubby politicians in some of the institutional aspects of the search for that truth didn’t go down too well. I tend to side with Kuhn. Just because somebody puts on a white coat doesn’t mean he or she is immune from the things that drive us nonscientific types. I took a course in biology once, a survey, intro course, and after the instructor would get done describing one of the milestones in the history of modern biology, he’d say something like, “And he got the Nobel prize for that.” He did this a number of times. Perfectly legit, they did get the prize. But I remarked on it once to a biologist friend, and he said, “Well, Jesus, Steve, after you’ve spent a year or more getting up every two hours every night to collect a set of fucking data points, you’d hope there’d be some kind of recognition. Mostly the work is borrrrring.”
Now you know what the ‘s’ stands for in ‘sam’ 🙂
So if models don’t work, we should just guess?
Steve
No, I’m just suggesting that models be adjusted when the data doesn’t conform to the models. What I see now is the models being treated as sacrosanct and the data being ignored.
That’s not empiricism. That’s either aestheticism or mysticism.
I would highly recommend this from the CBO on how they model. From this, and other papers I have seen, it sounds to me as though they are constantly adjusting the models. They almost all assume, at some level, rational behavior as the rule. I am with the behavioralists here and think that a lot of economic decisions are emotional ones. Let’s face it, we still do not have a great model for predicting bubbles.
Anyway, what they do sounds very empirical to me, they just do not yet know all they need to know. I suspect we will have to wait for Hari Seldon to resolve this.
http://www.cbo.gov/ftpdocs/106xx/doc10682/Appendix.5.1.shtml
Steve
I think the difficulty is twofold: 1) that the models being used (as necessary simplifications of a complex reality) are being treated with a degree of confidence that far exceeds their design margin, and 2) that the models themselves fail to account for the way in which emotional investment affects rational decision-making–including that done by scientists.
In other words, not only are the models making bad predictive outputs based on their exclusions of the effects of emotional processes, but the modelers/politicians themselves are also ignoring the degree to which they are emotionally invested in the results they are seeking, and doing so to the point where they are pushing the model predictions far past their reliability limits.
It seems to me that the missing element in the whole mess is a fundamental understanding of the many ways in which emotion interacts with intelligence. While I am no Hari Seldon (I’m a musician, dammit!), my sideline of research into this area is rapidly taking over center stage, to the point where I have begun to blog my thoughts on the possible connection and the ways in which it might be modeled.
http://piercello.blogspot.com/2009/02/modest-proposal.html
Alot of economic models with rational actors say you cannot predict bubbles.
If we could predict bubbles then there would never be bubbles. Pretty obvious if you think about it for a minute.
I find this kind of “test” of economics complete assinine to be quite honest. It is like saying, well now that we have a pretty damned good handle on evolutionary processes we can predict exactly speciation events.