Economics and Mathematics

Here is an interesting article by Larry Elliott in the Guardian. He points out that economics has failed us.

As a profession, economics not only has nothing to say about what caused the world to come to the brink of financial collapse last autumn, but also a supreme lack of interest in it. If, for example, you scroll down the list of papers scheduled for publication by the Review of Economic Studies, one of the prestigious UK journals, there is not the slightest sense that the world of general equilibrium and real business cycle models has been turned upside down in the past two years. There is, on the other hand a paper on "Generalised non-parametric deconvolution with an application to earnings dynamics", which includes the insight that "Monte Carlo simulations show good finite-sample performance, less so if distributions are skewed or leptokurtic". Got that? And that's just the abstract. The full article is even more fun – if you get your kicks from fantasy economics divorced from reality.

The big divide in economics is not between Keynesians and Hayekians, but between those who are interested in looking at the world as it is and those who are interested in how it would be if it conformed to the dictates of their mathematical models. The insights that Smith, Marx and Keynes brought to economics came not from differential calculus but from an attempt to understand what was happening during the early stages of the Industrial Revolution, the expansion of the mid-19th century and the Great Slump.

To those who believe in it, general equilibrium theory is a beautiful expression of the world assuming that the price mechanism works to align demand with supply and that human beings are rational economic agents. There is no room for the idea – supported by Minsky and Schumpeter – that instability is inherent to the economy, and might be good for it.

Experiments have shown just how limited the modern approach can be. Try this one for size: you are given £100 and told to share it with a stranger. If the stranger accepts your offer you get the money, but if he rejects it neither of you get a penny. How would you divide the cash? An economist's answer is that you offer the stranger £1 and keep £99 for yourself. That way you are both better off but you maximise your benefit. But this is not what tends to happen, since it offends people's sense of fairness. Many people share the money equally.

There are economists out there battling against the mainstream. Andrew Oswald, Amartya Sen, Robert Frank – you can take your pick of those who have insights into the way we live now. Paul Ormerod has written a series of books describing how general equilibrium theory has driven economics down a blind alley.

But it should be of concern that mainstream economics is disappearing up its own fundament, with the determination to see economics as a hard science crowding out a more nuanced and ­relevant approach.

I can appreciate the argument that mathematics and models give a crispness and manipulability to economics that you don't get from an arm chair philosophical economics. But when the mathematization of economics means that it deals with minutiae and irrelevancies rather than critical economic issues of the day, that says to me that the field needs to be revamped from top to bottom.

Notice that the discussion of splitting £100 in the above excerpt is a presentation of the ultimatum game, a toy model that behavioural economics (and neuroeconomics) focuses on. This is economics that deals with humans not as homo economicus but as living breathing beings with behaviours relevant to our evolutionary past and social systems.

Here is an analysis of the problem from Steven D. Levitt of Freakonomics fame:

In my opinion, the fundamental problem is this: from a modern academic perspective, the sorts of skills that accompany having a good working knowledge of the macroeconomy are not easily measured by, and are not rewarded in, the current incentive schemes for economists. In microeconomics, at least there is an abundance of good data, so people who are good at measuring and describing things can succeed. But in macro there is not much data, so most of the rewards are for the mathematics, not the empirics.

The single easiest way to make a mark in a modern macro paper is to solve a problem that is really, really hard mathematically. Even if it is not that relevant to anything, it is seen as a sign that the author has “impressive skills,” which is enough to get a job — and even tenure sometimes — at top universities.

You might think that macro forecasting would be an important part of what academic economists would do, but in practice there is almost nothing of that sort being done. That sort of thing is left for economists at places like the Federal Reserve or private banks to do. You might think that the models that most successfully explain economic patterns would rise to the top, but in the current regime, if they are not meticulously constructed from “micro foundations,” they aren’t allowed to be considered.