Math can tell you where a cannonball will land, not where the economy is headed.

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How 'Mathiness' Made Me Jaded About Economics

Noah Smith is a Bloomberg View columnist. He was an assistant professor of finance at Stony Brook University, and he blogs at Noahpinion.
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Celebrated growth economist Paul Romer -- whose name is regularly shortlisted for the Nobel Prize -- recently caused a big stir with a paper in the American Economic Review Papers and Proceedings called “Mathiness in the Theory of Economic Growth.” The paper is a blast of frustration against people that Romer thinks have abused mathematical theory by failing to draw a tight link between mathematical elements and the real world. Most prominent among Romer’s targets are Nobel-winning macroeconomists Robert Lucas and Edward Prescott. 

To me, Romer’s essay shows two things. The first, and more entertaining, is just how many top-level economists have been annoyed by Lucas and Prescott. The second, and more important, is that there is a quiet crisis in macroeconomic theory as a whole. 

First, the feud. Lucas, Prescott and their large band of followers (known as the “freshwater” tribe because the places they work tend to be far from the coasts) have relentlessly pushed for theories in which there is no need for government intervention in the economy. They were known for aggressive -- though ultimately unsuccessful -- attacks on New Keynesian macroeconomics. Their disparaging of Keynesian ideas has repeatedly earned them the ire of Paul Krugman and Brad DeLong, but within the profession their influence was such that criticisms were usually whispered behind closed doors. 

No longer. Romer isn't the first mild-mannered math nerd to come out breathing fire against the freshwater folks in recent months. Back in December, Roger Farmer at UCLA denounced the freshwater folks and the paradigm that they had forced on business-cycle theory. 

So the enemies of the freshwater tribe are finally speaking out. I wonder who will be next! 

Romer’s mathiness eruption -- which owes a debt to comedian Stephen Colbert's "truthiness" -- goes far deeper than the feud with the freshwater folks. Really, it’s about the role of math in economic theory. 

Economics has a lot of math. In no other subject except mathematics itself will you see so many proofs and theorems. Some branches of econ, such as game theory, could legitimately be housed in university math departments. But even in fields such as macroeconomics, which ostensibly deal with real-world phenomena, math is central to everything that economists do. 

But the way math is used in macroeconomics isn't the same as in the hard sciences. This isn't something that most non-economists realize, so I think I had better explain. 

In physics, if you write down an equation, you expect the variables to correspond to real things that you can measure and predict. For example, if you write down an equation for the path of a cannonball, you would expect that equation to let you know how to aim your cannon in order to actually hit something. This close correspondence between math and reality is what allowed us to land spacecraft on the moon. It also allowed engineers to build your computer, your car and most of the things you use. 

Some economics is the same way, especially in microeconomics, or the study of individuals' actions -- you can predict which kind of auction will fetch the highest prices, or how many people will ride a train. But macroeconomics, which looks at the broad economy, is different. Most of the equations in the models aren’t supported by evidence. For example, something called the consumption euler equation is at the core of almost every modern macroeconomic model. It specifies a relationship between consumption growth and interest rates. But when researchers looked at real data on consumption growth and interest rates, they found that the equation gives exactly the wrong predictions! Yet it continues to be used as the core of almost every macro model. 

If you read the macro literature, you see that almost every famous, respected paper is chock full of these sort of equations that don’t match reality. This paper predicts that everyone will hold the same amount of cash. This paper predicts that people buy financial assets that only pay off if people are able to change the wage that they ask to receive. These and many other mathematical statements don't remotely correspond to observable reality, nor do they have any evidence in support of them. Yet they are thrown into big multi-equation models, and those models are then judged only on how well they fit the aggregate data (which usually isn't very well). 

That whole approach would never fly in engineering. Engineering is something you expect to work. But macroeconomists often treat their models as simply ways, in the words of David Andolfatto, vice president of the Federal Reserve Bank of St. Louis, to “organize our thinking” about the world. In other words, macroeconomists use math to make their thoughts concrete, to persuade others, and to check the internal consistency of their (sometimes preposterous) ideas, but not to actually predict things in the real world. 

Back to Romer’s complaint. He singles out Lucas, Prescott and a few others for having tenuous or sloppy links between mathematical elements and the real world. But from what I can see, such tenuous and sloppy links are the rule in macro fields. Romer says that I am “jaded” for saying that, and that it was bad apples like Lucas and Prescott who soured me on macroeconomic theory. Well, he’s right that I’m jaded, and he’s right that it was learning about models by Prescott that I first became jaded. Romer, you got me. 

But when I looked beyond those models, to older or newer models, I found what seemed to be only a difference in degree, not in kind. Macroeconomic theory is chock full of mathiness. It’s not just Lucas and Prescott, it’s the whole scientific culture of the field. 

Romer says that in the new, debased culture of macroeconomics, “empirical work is science; theory is entertainment.” Maybe that is close to the rational way to think about things. Now that information technology is providing economics with a flood of new data, the percentage of theory papers in top journals is falling. Maybe economists are starting to see mathiness for what it is, and discount it accordingly.

This column does not necessarily reflect the opinion of Bloomberg View's editorial board or Bloomberg LP, its owners and investors.

To contact the author on this story:
Noah Smith at nsmith150@bloomberg.net

To contact the editor on this story:
James Greiff at jgreiff@bloomberg.net