It's not often one gets a chance to say this, but today the "dismal science" of economics is sexy. In the market for explaining what makes people tick, different approaches come in and out of fashion. Once it was the psychological traits supposedly hard wired into our genes from the time our ancestors lived in the African savanna. Now a raft of popular books has hit the shops arguing that economic incentives can account for some of our most surprising behaviour.

It all started, as is well known, with (economist) Steven D. Levitt and (journalist) Stephen J. Dubner's Freakonomics (2005), a book famous for divining startling links between, for example, estate agents and the Ku Klux Klan. Even a glance at publishers' catalogues reveals their desire to repeat the formula. Blurbs fire out questions that have seldom occurred to most of us (and seem to have nothing to do with economics), and then promise that an economist will pull a rabbit out of a hat to unravel the mystery. "Why is there a light in your fridge but not in your freezer?" asks the promotional copy for Robert H. Frank's The Economic Naturalist (2008). "Why do 24-hour shops bother having locks on their doors? Why did kamikaze pilots wear helmets? The answer is simple: economics."

Another skilled practitioner is Tim Harford, a Financial Times journalist who has just followed up the success of The Undercover Economist (2006) with The Logic of Life. Even at our strangest, most irrational and seemingly self-destructive, he argues, we are often responding to real incentives and disincentives. Hence his intriguing accounts of "rational crime", "rational racism" and "rational revolutions". At a time when the risks of penetrative sex have gone up and celibacy still seems unappealing, there is even such a thing as a "rational blow job". Forget about a moral panic: simple economics can explain "the teenage oral sex craze".

These books demonstrate that there is a great public appetite for economic ways of thinking when they are presented with passion and panache. Freakonomics' most celebrated and counterintuitive claim, that the huge drop in American crime rates was caused not by better policing, for example, but mainly by more liberal abortion laws - so that the babies most likely to grow up and become criminals simply weren't being born - was obviously based on heroic feats of number crunching. Yet Levitt's highly technical paper in the Journal of Economic Perspectives would hardly have attracted general interest; it was only when he got a journalist on board to "translate" it into snappy copy that it became a major talking point.

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And this, of course, raises much wider questions about academic economics. How far has the discipline become so self-enclosed and drenched in mathematical technicalities that business people and policymakers find it hard to extract the practical lessons - and the wider public, eager to learn more, doesn't get a look-in? And what are the incentives within the profession that push people in particular, and sometimes dysfunctional, directions?

Someone rather worried about the state of the discipline is Michael Kitson, lecturer in business economics at the Judge Institute of Management, University of Cambridge. He regrets the dominance of a narrow band of neoclassical mathematical economists among those consulted by policymakers and the decline of a more pluralist approach, arguing that "business schools and departments such as geography and sociology often generate more useful ideas on economic themes than university economics departments". While highly mathematical approaches can obviously be valuable, he notes, they can also "amount to an elaborate game based on very idealised and unrealistic assumptions; even when research does have useful real-world applications these are often impossible to extract".

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Arthur Marshall (1842-1924), one of the founding fathers of neoclassical economics, once set out the rules for a "good mathematical theorem": "(1) use mathematics as a shorthand language, rather than an engine of inquiry (2) keep to them till you have done (3) translate into English (4) then illustrate by examples that are important in real life (5) burn the mathematics." Today, far too often, Kitson says, "we don't get past stage (1)".

Quite apart from the issue of the emperor's new clothes ("insights" that would appear much less impressive if they were translated into plain English), Kitson fears that "the research assessment exercise and list of 'top journals' positively discourage people from writing in a way that would be comprehensible and useful".

Lord Kaldor (1908-86) was a major influence on Kitson's early career. Because he wrote very accessibly, he is now "largely ignored in the discipline and in the policy domain, while those who have taken Kaldor's insights and forced them into a mathematical straitjacket (losing much of their relevance) have risen up the academic ladder". In the meantime, Kitson adds, "leading economists such as Paul Krugman and Joseph Stiglitz have to put in decades producing highly technical papers (and/or winning Nobel prizes) before they can free themselves from the constraints of academia and make significant contributions to important issues of public concern". Since economics clearly has much to say about vital topics such as global warming and Third World poverty, this sounds like a pretty unhealthy situation.

Paul Collier, who is professor of economics and director of the Centre for the Study of African Economies at the University of Oxford, as well as the author of The Bottom Billion, shares Kitson's concerns. "Since the Nobel prize and the RAE," he argues, "the incentives have been heavily skewed towards peer-group opinion; writing for a broad audience is seen as an academic death sentence ... Of course, peer pressure has brought many good things: the lazy tail of the profession has been squeezed out, and the technology has greatly advanced. So, paradoxically, economics has more of value to contribute than a generation ago, but less incentive to do so. I fear that there is also less competence to do so: the searingly tough training involved in becoming an academic economist leaves no room for functional literacy beyond the most rudimentary level. Many economists are incapable of expressing themselves."

Some of these issues also came to the fore in the debate on "Why Economics Matters", which was held at the London School of Economics in May to mark the launch of The New Palgrave Dictionary of Economics. This immense eight-volume book, edited by Steven N. Durlauf and Lawrence E. Blume (and just published by Palgrave Macmillan at ?1,600), brings together the contributions of more than 1,500 economists as well as a few outsiders such as the Swedish zoologist who contributed an entry on "game theory and biology". Although full of diagrams and mathematics, it also bears ample witness to the way that economics has loosed its moorings and now takes in pretty much all of human life. Entries range from "addiction" and "altruism", "bribery" and "bubbles", "convict labour" and "co-operation", all the way through to "tulipmania", "user fees" and "value of life". It is precisely because economic perspectives can be applied to parenting and speed dating that there is a popular market for the subject. Yet there have also been criticisms that economics has colonised and taken over much of the other social sciences, to the detriment of both sides.

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The two panellists at the LSE debate who had contributed to the dictionary took very different lines. For Franceso Caselli, professor of economics at the LSE, books about sumo wrestlers and United Nations diplomats not paying their parking fines were all very well, but it was often the most nerdy, technical and even mind-numbing areas of economics that provide the crucial insights to improve lives. His "unsung and unlikely heroes", he said, were Alan Heston and Robert Summers, economists "who spent most of their professional lives developing - and implementing - methods to make national accounts comparable across countries, particularly, but not exclusively, by putting them on a purchasing-power-parity basis. The result of this lifetime effort was the publication of the Penn World Tables, in 1991."

While their work might sound dull and offputting - it certainly required one "to set up and solve a rather opaque set of many equations in many unknowns" that took "several hours to explain even to advanced PhD students" - it provided a set of vital practical tools. "Economists (and policymakers) used to think poor countries were poor because they invest too little, whether in physical capital or in their people, and as a result at any point in time they have too little capital," Caselli pointed out. "What the Penn World Tables allowed Chad Jones and others to do is to check these assumptions against the data - and to find that they were completely wrong ... the problem of poor countries is not that they have too little resources to produce, but that they use these resources very badly. What they need is not more investment or more schooling: they need to become more efficient." All this will make a big difference to the lives of the poor "in the same way that in medicine getting the right diagnosis for a sick patient improves his life relative to having the wrong diagnosis. Different diagnosis implies different therapy."

Although he is also a contributor to The New Palgrave Dictionary, Klaus Nielsen, professor of institutional economics at Birkbeck, University of London, was far more worried about the highly mathematised state of economics today. For a start, he suggested, technical economic arguments were often a smoke screen used to disguise quite different reasons for making decisions (as when Britain stayed out of the eurozone or aggressively bid to host the Olympic Games).

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But he also worried that the subject had become "autistic". "Mainstream economics", he has written elsewhere, "has developed too much in the direction of an excessively specialised and formalised state of de facto withdrawal from the study of the economy in favour of exercises in applied mathematics". While its language "makes dialogue with other disciplines impossible ... the self-image of the discipline makes it unnecessary".

Part of the problem, Nielsen continued, is that economics is now "based on an expansive research programme with a strong core and a flexible protection belt". All the claims of the "belt" were up for discussion, provided the core remained intact. But it was the core, unfortunately, that incorporated a lot of basic assumptions about human nature and behaviour that disciplines such as anthropology, psychology and sociology had long called into question.

When economic research is impenetrable to those outside the subject (or even outside the subdiscipline), there will always be disputes about whether its difficulty is unavoidable, given the fiendish complexities of the real world, or whether it just amounts to an arid exercise in applied mathematics. And, because every example is different, there is probably no general answer to this question. But what about cases where economists do have important insights but dress them up in jargon and formulas that only their fellow specialists can understand?

Harford of the Financial Times, who was another panellist at the LSE debate, had something to say about that. Long may academic economics remain impenetrably opaque, he declared. It left a very lucrative gap in the market for people like him to step in as "translators", taking the best ideas of the ivory tower into the airport bookshop.

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