Models clarify the logic of hypotheses, ensure that predictions indeed follow from the premises, open our eyes to counterintuitive possibilities, suggest how predictions could be tested, and enable accumulation of knowledge. The advantage of clarity that mathematical models offer scientists is nicely illustrated in the following quote from Economics Rules: “We still have endless debates today about what Karl Marx, John Maynard Keynes, or Joseph Schumpeter really meant. … By contrast, no ink has ever been spilled over what Paul Samuelson, Joe Stiglitz, or Ken Arrow had in mind when they developed the theories that won them their Nobel.” The difference? The first three formulated their theories largely in verbal form, while the latter three developed mathematical models.
Pointer from Mark Thoma.
Are you kidding me? The meaning of Arrow’s Impossibility Theorem has been endlessly debated.
With mathematical models in economics, the question is whether the conclusions of the model apply in the real world. That is something that cannot be settled mathematically. It often cannot be settled empirically.
If I had chosen to write a review of Turchin’s latest book, Ages of Discord, I would have devoted most of the review to criticism of Turchin’s statistical methods. I am quite confident that if you formulated his project as “Come up with a set of indicators that represent the concepts here,” there would be no consensus, and that almost no one would come up with the indicators that he selected. The overall thesis of the book might turn out to be right. But in terms of methods, it could be held up as the poster child of what Paul Romer calls “mathiness.”
A nice thing I learned from Deirdre McCloskey is the approach where we derive a certain finding from price theory and then look to see if it is supported or refuted by empirical observation.
One of her textbook examples (See _The applied theory of price_ ) is the sharecropping model that shows sharecropping to result in large misallocations of resources, because the sharecropper is a marginalist and stops working too soon, when his/her marginal cost = marginal benefit.
Then you look at the world and mostly you don’t see that. Cursory examination doesn’t show what the theory suggests.
The interpretation is that the sharecropper is supervised to produce roughly as much as an owner-operator. If not, the sharecropper can’t get the contract renewed.
I’m sure this is not the final word on the topic, but it was a module for teaching.
it helps when you get the delivery (at this point still by a gruff, sarcastic Donald) who says, with a sort of impatience for bad theorists.
“I have conclusively shown…*right here on this blackboard* that Capitalism Fails.”
then the “Capitalism Fails” is patiently tested against reality.
maybe you had to be there. But it was good teaching.
The style of this old paper is rather flamboyant, but the core ideas apply to economic modeling as well as warfare modeling (the immediate target of the paper): http://www.dtic.mil/dtic/tr/fulltext/u2/a100421.pdf
Math can clarify or confuse, simplify or make complex, but progress beyond description requires quantification and measurement requires math.
Yeah, as illustrations. But as Mises used to say, math models are just narrative translated into symbols. If the narrative is wrong the model will be wrong. In order to translate narratives into models, the assumptions become unrealistic and the narrative has to be simplified to a childish level. That’s why narrative economics is so much richer and realistic. Also, micro issues can be modeled fairly easily, but with macro the data just doesn’t exist for complex models.
I would say precisely the opposite: verbal narratives are just a roundabout way of construing a mathematical relationship.
And the simplicity is a *feature.* Part of the problem with narrative thinking is that it allows for too many implicit or unspoken parameters, without penalizing the implicit model. But math forces you to illustrate precisely how complex your model is and (if you’re statistically honest) to penalize models that are gratuitously complex, as is done in all natural sciences.
You may be right about the lack of sufficient data. But if the math is done right, it should then say precisely that: there isn’t enough data to resolve the parameters you’re trying to impute with any reasonable degreee of confidence. The ‘anti-math’ people seem to forget that uncertainty is itself a quantifiable thing.
Except that’s not how people think. We don’t have the model pop into our heads and then try to imagine a narrative that would explain it. Even the most mathematically dominated economist encounters the real world and develops a narrative to explain it. Only then does he have to fabricate unrealistic assumptions and make ridiculous simplifications until he can translate it into symbols.
“Part of the problem with narrative thinking is that it allows for too many implicit or unspoken parameters, without penalizing the implicit model.”
That’s because the parameters are never fixed. Anyone who had done modeling for any length of time knows that the values of the parameters change radically over short time periods. And the correlations between input variables cause the parameter values to flop around like fish on dry land when variables are added or taken away.
“But math forces you to illustrate precisely how complex your model is…”
No, it’s exactly the opposite. Check out all that has been written about complexity economics. The real world is far more complex than even the most complex models. What you refer to is the much simpler problem of adding more variables to a model just to get a higher R-square.
“But if the math is done right, it should then say precisely that: there isn’t enough data to resolve the parameters you’re trying to impute with any reasonable degreee of confidence. ”
Well if people were honest they might do that. But when have you ever read any economist write something that honest? I have never seen it. As Hayek said in his Nobel speech, instead what they do is reduce the complexity of economics to the data available and ignore any issues raised by a lack of data. That’s all part of the reduction that takes place to simply the real world to the childish level that it can be modeled.
PS, don’t think I’m anti-math and modeling. I do it all the time. My specialty is modeling the stock market. I love econometrics. I use structural equation modeling in SAS to analyze our company’s consumer satisfaction survey. I’m just aware of its limitations and the damage to economics that too much emphasis on modeling has done.
We operate, economically, with a system called pricing which only works if we collectively work the math model. Economics can only be successful when we crack the pricing function, figure out how it works.
Excellent insights! Also, could it be there is less debate about models because they are so simple?