Applying this to the stock market, it is possible to hold two apparently contradictory att.i.tudes simultaneously: the market is driven largely by endogenous processes in which previous price movements determine future price movements; and it is impossible or very difficult to predict which way the market will move, and by how much.

Much of the Fractal Markets Hypothesis is directed at critiquing the notion that price movements in the stock market are random as I noted earlier, it is primarily a way to characterize the properties of the statistics the market throws up, rather than a theory of how the market actually behaves. However, it makes one important behavioral observation that runs directly counter to the EMH's a.s.sumptions about investors.

This is that the market will be stable when it allows investors with different time horizons to trade smoothly. As a result, heterogeneity the fact that all investors are not the same is a vital part of this theory. As Peters puts it: Take a typical day trader who has an investment horizon of five minutes and is currently long in the market. The average five-minute price change in 1992 was 0.000284 per cent [it was a 'bear' market], with a standard deviation of 0.05976 per cent. If, for technical reasons, a six standard deviation drop occurred for a five minute horizon, or 0.359 per cent, our day trader could be wiped out if the fall continued. However, an inst.i.tutional investor a pension fund, for example with a weekly trading horizon, would probably consider that drop a buying opportunity because weekly returns over the past ten years have averaged 0.22 per cent with a standard deviation of 2.37 per cent. In addition, the technical drop has not changed the outlook of the weekly trader, who looks at either longer technical or fundamental information. Thus the day trader's six-sigma [standard deviation] event is a 0.15-sigma event to the weekly trader, or no big deal. The weekly trader steps in, buys, and creates liquidity. This liquidity in turn stabilizes the market. (Peters 1994) The Fractal Markets Hypothesis thus explains the stability of the market by the realistic a.s.sumption that traders differ in their time horizons. It also alleges that instability is likely to occur if all investors suddenly switch to the same time horizon.

The Fractal Markets Hypothesis is thus more consistent with stock market data, more robust, and completely untainted by any a.s.sumption that the market is in, or tends toward, equilibrium. But it still doesn't provide an answer to what is actually generating the data: what is the system behind the fractal? To answer that question, we have to return to the kind of inst.i.tutional a.n.a.lysis that Keynes provided in 1936. Two such a.n.a.lyses have been provided: by Robert Haugen in the 'Inefficient Markets Hypothesis,' and Hyman Minsky in the 'Financial Instability Hypothesis,' as discussed in Chapter 13.

The Inefficient Markets Hypothesis After a long career as an academic finance economist, Bob Haugen presents the diametrically opposite case from the Efficient Markets Hypothesis with gusto in three short books: The Beast on Wall Street, The New Finance, and The Inefficient Stock Market. Anyone who is or is thinking of speculating in the market or is suffering from having done so should read all three. Amid an extensive catalogue of data that contradicts the Efficient Markets Hypothesis, Haugen presents the alternative case for 'a noisy stock market that overreacts to past records of success and failure on the part of business firms, and prices with great imprecision' (Haugen 1999b).7 Though Haugen makes no reference to Keynes, the reasons he gives for the market behaving in this way echo the arguments Keynes made back in 1936 that in the real world of uncertainty, few if any stock market speculators trade on the basis of new information. Instead, they trade on the basis of how they think other market partic.i.p.ants will, on average, expect the market to react to news. Unlike the efficient market hypothesis, this 'news' can include the most recent movements of stock prices themselves.

In fact, in today's stock market, the major news will always be the most recent movements in stock prices, rather than 'real' news from the economy.

Haugen argues that there are three sources of volatility: event-driven, error-driven, and price-driven (the Efficient Markets Hypothesis models only the first, on the belief that the other two can't exist in the equilibrium of an efficient market). The second results from the market overreacting to news, then over-adjusting itself once the initial mistake has become obvious.

The third is the phenomenon of the market reacting to its own volatility, building price movements upon price movements, in the same way that neighborhood dogs can sometimes keep yelping almost indefinitely after one of them has started. Haugen argues that this endogenous instability accounts for over three-quarters of all volatility.

He also argues that the market's endogenous instability has a severe and deleterious impact on the functioning of a modern capitalist economy.

First, if the stock market has any role at all in directing investment funds, then its valuations will direct them very badly. Price-driven volatility will lead to some companies which will in the long term turn out to be worthless being given ma.s.sive funding which will then be wasted while potentially worthy ventures will be starved of funds. According to Haugen, the managers of a firm that has been seriously overvalued by the market over-invest: 'Consumers get what they don't want.' On the other hand, an undervalued firm 'would invest to produce a product that consumers really want, if it could raise capital at a fair price, but in this market, it can't' (Haugen 1999a). Overall, by providing too much money to ventures which, in the long run, are going to turn out not to be all that profitable, while providing too little money to those which, in the long run, will be worthwhile, the market causes the economy to grow less rapidly and less smoothly than it could.

Secondly, Haugen argues that, as well as causing investment to be badly apportioned, the stock market's endogenous volatility reduces the overall level of investment. Over the long term, the risk-free real rate of return has averaged about 1 percent, whereas the risk premium for investing in stocks has averaged about 6 percent. This means that investors have required a return of about 7 percent on their investments with the result that investments which predict a lower expected rate of return don't get funded.

Haugen argues that investors require this higher return to compensate them for the risk of investing on the market, yet most of this risk results from the endogenous instability of the market itself. Since his statistical research indicates that price-driven volatility accounts for almost 95 percent of all volatility, he argues that this risk premium would be substantially lower perhaps as low as just 0.4 percent, versus the 6 percent it has been historically (ibid.). If the risk premium could be reduced to this level, then the rate of investment would be substantially higher: 'Price-driven volatility has greatly inhibited investment spending over the years. Ultimately, it has acted, and acts, as a serious drag on economic growth' (ibid.).

At the individual level, Haugen argues that the market's tendencies to overreact to news, and to be consumed with endogenous instability in prices, provide opportunities for non-inst.i.tutional investors to profit from the market. However, at the macroeconomic level, Haugen believes, as did Keynes, that the economy would benefit if the market were restrained. His recommendation, again very similar to Keynes's, is to reduce the length of the trading day, or to limit trading to just one computer-a.s.sisted auction per day. He hopes that this would eliminate the phenomenon of price volatility driven by the market reacting to its own every move.

Econophysics Broadly speaking, Econophysics is the application of the a.n.a.lytic techniques of modern physics to the social sciences. This is rather ironic, since the founders of neocla.s.sical economics themselves aped what they thought were the methods of physicists in the nineteenth century.

What Walras and others attempted to mimic then was physics before it had developed a number of key innovations, including not merely quantum mechanics but the concept of entropy, which introduced the notion of irreversible change into physics. Mirowski coined the term 'proto-energetics' to describe the type of physics on which neocla.s.sical economic theory modeled itself: From now on I shall need a term that will serve to identify a type of physical theory that includes the law of conservation of energy and the bulk of rational mechanics, but excludes the entropy concept and most post-1860 developments in physics. This collection of a.n.a.lytical artifices is more an historical than a systematic subset of physics: it includes the formalisms of vector fields, but excludes Maxwell's equations, or even Kelvin's mechanical models of light.

Since this resembles the content of the energetics movement, I trust it will not do the phenomena too much violence to call it 'proto-energetics.' Cla.s.sical thermodynamics diverges from proto-energetics in one very critical aspect: Thermodynamic processes only change in one direction. In proto-energetics, time is isotropic, which means that no physical laws would be violated if the system ran backward or forward in time. (Mirowski 1989: 63) Since then, physics has evolved rapidly, while economics has developed rather as can the language of a group of migrants who, separated from their home country, hang on to terms that have become obsolete in the original language.

The new incursion of physics into economics is being led by physicists themselves, and motivated partly by the innate curiosity that physicists like Cheng Zhang had about economic issues, and partly by the fact that 'we'd run out of things to do in physics.'8 Though called Econophysics, a more accurate term for this school of thought at present would be 'Finaphysics' since the vast bulk of its research has concerned the behavior of financial markets, rather than the broader economy.

This orientation reflects the inherently empirical nature of physics, and the fact that its a.n.a.lytic techniques have been developed to process enormous amounts of data generated by non-equilibrium experiments in physics. Economics does not generate a sufficient volume of data, but financial markets do in abundance, with the price and volume data of financial transactions; as Joe McCauley put it, 'the concentration is on financial markets because that is where one finds the very best data for a careful empirical a.n.a.lysis' (McCauley 2004: xi).

Given that it is a relatively new field, there are numerous explanations of the volatility of financial markets within Econophysics including Power Law models of stock market movements (Gabaix, Gopikrishnan et al. 2006), Didier Sornette's earthquake-based a.n.a.lysis (Sornette 2003), Joe McCauley's empirically derived Fokker-Planck model (McCauley 2004), and Mandelbrot's fractal geometry (Mandelbrot and Hudson 2004) and it would require another book to detail them all.

A unifying theme is that the behavior of financial markets is driven by the interactions of numerous market partic.i.p.ants with each other, and these generate a highly unstable and therefore relatively unpredictable time series in financial data themselves. These characteristics resemble the behavior of fissile materials in a nuclear reactor, or tectonic plates in an earthquake zone, physical processes for which physicists have developed an enormous a.r.s.enal of mathematical a.n.a.lytic techniques in the last century. Econophysics is essentially the application of these techniques to financial data.

This Econophysics explanation of the unpredictability of finance markets is thus diametrically opposed to the explanation that neocla.s.sical economics has given of precisely the same phenomenon the difficulty of predicting the market and Econophysicists react with incredulity to the simplistic 'random disturbances to an equilibrium process' explanation that neocla.s.sical economists provide: Three states of matter solid, liquid, and gas have long been known. An a.n.a.logous distinction between three states of randomness mild, slow and wild arises from the mathematics of fractal geometry. Conventional finance theory a.s.sumes that variation of prices can be modeled by random processes that, in effect, follow the simplest 'mild' pattern, as if each uptick or downtick were determined by the toss of a coin. What fractals show [...] is that by that standard, real prices 'misbehave' very badly. A more accurate, multifractal model of wild price variation paves the way for a new, more reliable type of financial theory. (Mandelbrot and Hudson 2004: v) Economists teach that markets can be described by equilibrium. Econophysicists teach that markets are very far from equilibrium and are dynamically complex [...] equilibrium is never a good approximation [...] market equilibrium does not and cannot occur [...] (McCauley 2004: 185) Uncertainties and variabilities are the key words to describe the ever-changing environments around us. Stasis and equilibrium are illusions, whereas dynamics and out-of-equilibrium are the rule. The quest for balance and constancy will always be unsuccessful. (Sornette 2003: xv) I'll single out Didier Sornette's work here, not because it will necessarily be 'the' approach of Econophysics, but because he is making a direct challenge to one tenet of conventional finance: that the market cannot be predicted. Using his model that the behavior of stock markets follows the 'log-periodic' pattern of earthquakes, he has made predictions about future stock market crashes that can be verified after the predicted crashes have (or have not) occurred: 'The Financial Crisis Observatory (FCO) is a scientific platform aimed at testing and quantifying rigorously, in a systematic way and on a large scale, the hypothesis that financial markets exhibit a degree of inefficiency and a potential for predictability, especially during regimes when bubbles develop' (Sornette 2011).

The result of the FCO can be tracked at the website www.er.ethz.ch/fco. The voluminous literature of the Econophysics movement can be tracked from its website unifr.ch/econophysics.

Conclusion: progress versus ossification There are thus numerous vigorous alternatives to the failed paradigm of neocla.s.sical finance but students of economics are unlikely ever to learn of them, if all they do is study the textbooks of neocla.s.sical finance courses. Despite the manifest failures of the Efficient Markets Hypothesis, and the recanting of it by the very same economists who developed it in the first place (Fama and French 2004), and the numerous stock market booms and crashes of the past quarter-century that could not have happened if the EMH were correct, textbooks continue to teach that finance markets are 'efficient,' in the b.a.s.t.a.r.dized way that economists use the term. This extract from a brand-new 2011 text published seven years after the developers of the EMH concluded that 'the failure of the CAPM in empirical tests implies that most applications of the model are invalid' (ibid.: 25) is typical: A financial market is informationally efficient if prices reflect all available information [...] there are likely to be noise traders [...] who trade on information unrelated to the true value of shares. If the information they trade on is random, they will tend to cancel each other out, leading to efficient market prices. However, it is likely that they trade on similar information, so that noise trading will lead to either an undervaluation or an overvaluation [...] it would pay arbitragers to take an offsetting position [...] This process will cause share prices to stay close to their true values [...]

Academic studies usually conclude that the share market is efficient. (Valentine, Ford et al. 2011: 2457) The unwillingness and possibly even the inability of neocla.s.sical economists to admit that their paradigm has failed means that, if change is left to them alone, it will not occur.

Reforming finance?

The results of the non-neocla.s.sical theories of stock market behavior surveyed in this chapter emphasize one point: a.s.set markets perform their alleged role of the allocation of investment capital very poorly.9 In this they echo Keynes's dictum during capitalism's last major crisis, that speculation should not be allowed to dominate capital formation and allocation: Speculators may do no harm as bubbles on a steady stream of enterprise. But the position is serious when enterprise becomes the bubble on a whirlpool of speculation. When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. The measure of success attained by Wall Street, regarded as an inst.i.tution of which the proper social purpose is to direct new investment into the most profitable channels in terms of future yield, cannot be claimed as one of the outstanding triumphs of laissez-faire capitalism which is not surprising, if I am right in thinking that the best brains of Wall Street have been in fact directed towards a different object. (Keynes 1936: 159; emphasis added) Though deregulation of the financial sector was far from the sole cause of the financial crisis that began in 2007, removing the fetters from the financial sector resulted in a crisis that was more extreme than it would have been had the previous regulations been kept in place. The USA's 'shadow banking' sector could not have invented and sold nearly so many 'weapons of financial ma.s.s destruction' as it did to use Warren Buffett's evocative phrase had Gla.s.s-Steagall not been abolished during Bill Clinton's term, for example.

I expect that history will judge that signing that bill into law was a far more reckless act than anything Clinton did with Monica Lewinsky. The comments of the handful of senators who opposed its repeal back in 1999 make interesting reading today: 'I think we will look back in 10 years' time and say we should not have done this but we did because we forgot the lessons of the past, and that that which is true in the 1930's is true in 2010,' said Senator Byron L. Dorgan, Democrat of North Dakota. 'I wasn't around during the 1930's or the debate over Gla.s.s-Steagall. But I was here in the early 1980's when it was decided to allow the expansion of savings and loans. We have now decided in the name of modernization to forget the lessons of the past, of safety and of soundness.'

Senator Paul Wellstone, Democrat of Minnesota, said that Congress had 'seemed determined to unlearn the lessons from our past mistakes.'

'Scores of banks failed in the Great Depression as a result of unsound banking practices, and their failure only deepened the crisis,' Mr. Wellstone said. 'Gla.s.s-Steagall was intended to protect our financial system by insulating commercial banking from other forms of risk. It was one of several stabilizers designed to keep a similar tragedy from recurring. Now Congress is about to repeal that economic stabilizer without putting any comparable safeguard in its place.' (Labaton 1999) In contrast, the beliefs of those who campaigned to end the Act have the ring of delusion: 'The world changes, and we have to change with it,' said Senator Phil Gramm of Texas, who wrote the law that will bear his name along with the two other main Republican sponsors, Representative Jim Leach of Iowa and Representative Thomas J. Bliley Jr. of Virginia. 'We have a new century coming, and we have an opportunity to dominate that century the same way we dominated this century. Gla.s.s-Steagall, in the midst of the Great Depression, came at a time when the thinking was that the government was the answer. In this era of economic prosperity, we have decided that freedom is the answer.' (Ibid.: 2) Far from strengthening America, the financial follies that followed the repeal of Gla.s.s-Steagall have left it crippled at the start of the twenty-first century, and facing an economic eclipse by China. Far from reducing the role of the government in the US economy, the collapse of the Subprime Bubble has resulted in the government taking a larger role in the economy than it did even during the Great Depression.

Back in 2000, in the first edition of this book, I sided with the opponents of deregulation, noting that though they were 'mooted as "reforms" by their proponents, [...] they were in reality retrograde steps, which have set our financial system up for a real crisis' (Keen 2001a: 255). That real crisis duly arrived eight years after the repeal of Gla.s.s-Steagall.

However, blocking the abolition of Gla.s.s-Steagall wouldn't have prevented the crisis, since its underlying cause was a debt bubble that had already driven the USA to the brink of Great Depression debt levels by 1989. Deregulation simply allowed the debt bubble to continue growing for another two decades, from the 170 percent of GDP level it reached as the 1990s recession began, and the 200 percent level it was at when Gla.s.s-Steagall was abolished, to the 300 percent of GDP peak hit ten years later in 2009.

I also wrote in 2000 that 'I can only hope that, if the crisis is serious enough, then genuine reform to the finance sector will be contemplated' (ibid.: 256), but the first and second response of government to this crisis has been to try to restore the 'business as usual' that applied prior to the crisis.

This is to be expected. Politicians, as Keynes observed long ago, are just as beholden to the ideas of neocla.s.sical economics as are professional economists: 'Practical men, who believe themselves to be quite exempt from any intellectual influences, are usually the slaves of some defunct economist. Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back' (Keynes 1936: 383).

It takes time before a real reformer comes along and challenges, not merely the belief systems that gave rise to mistakes like the abolition of Gla.s.s-Steagall, but the beneficiaries of those belief systems as well. We await a politician who is willing to not merely try to resuscitate the financial sector but to challenge it, as Roosevelt was during the Great Depression.

[A] host of unemployed citizens face the grim problem of existence, and an equally great number toil with little return. Only a foolish optimist can deny the dark realities of the moment.

Yet our distress comes from no failure of substance [...] Plenty is at our doorstep, but a generous use of it languishes in the very sight of the supply. Primarily this is because the rulers of the exchange of mankind's goods have failed, through their own stubbornness and their own incompetence, have admitted their failure, and abdicated. Practices of the unscrupulous money changers stand indicted in the court of public opinion, rejected by the hearts and minds of men.

True they have tried, but their efforts have been cast in the pattern of an outworn tradition. Faced by failure of credit they have proposed only the lending of more money. Stripped of the lure of profit by which to induce our people to follow their false leadership, they have resorted to exhortations, pleading tearfully for restored confidence. They know only the rules of a generation of self-seekers. They have no vision, and when there is no vision the people perish.

The money changers have fled from their high seats in the temple of our civilization. We may now restore that temple to the ancient truths. The measure of the restoration lies in the extent to which we apply social values more n.o.ble than mere monetary profit. (Roosevelt 1933; emphasis added) The reforms enacted in Roosevelt's era clearly worked, but as subsequent history has indicated, the problem with real reforms of our financial system is that, if successful, they will be abolished. The era of financial tranquility they usher in will be misinterpreted particularly if economists continue to believe in the fantasy world of neocla.s.sical economics as inherent to capitalism, and not merely the product of regulations that inhibit the financial system's innate tendency to create too much debt.

Politicians who did not live through the crisis that caused these regulations to be enacted will then weaken these regulations over time, and we will be back in a crisis again.

Fundamentally, reforms of the financial sector fail because they try to constrain the sector's innate desire to create debt. They will work for a while in the aftermath to a crisis like the Great Depression or the Great Recession, where the carnage wreaked by a financial crisis is so great that the sector behaves prudently for a while. However, the incentives to create debt are so great for this sector that, over time, a debt-driven culture will replace prudence.

Inst.i.tutional control of finance is also flawed, for reasons that should be obvious from our current crisis: 'regulatory capture.' Not only are regulators slower to move than the organizations they are intended to control, they often become advocates rather than monitors of those organizations. There is little doubt that Greenspan's actions in rescuing the financial sector from itself after numerous crises, in championing the development of financial a.s.sets now universally regarded as toxic, and in restricting the development of new regulations to control new financial instruments, turned a potentially garden-variety would-be depression in 1987 into the near-death experience of the Great Recession. The regulators, by delaying the inevitable for two decades, have made this crisis more intractable than it would have been without them.10 Reforms also fail because they do not recognize that the financial system has what Kornai called a 'soft budget constraint' (Kornai, Maskin et al. 2003).11 A bank is not constrained in its lending by its reserves, but by the willingness of borrowers to take on additional debt (see Holmes 1969; Moore 1979). It therefore faces a 'soft budget constraint': to expand its operations, all it has to do is to persuade borrowers (firms and households) to borrow more money, and its income will grow as will the level of debt.

This growth in bank income and debt is in turn dependent on the willingness of borrowers to incur debt. If this is based solely on their income, then the 'hard budget constraint' that households and firms face will put a limit on the amount of debt they will take on.

If, however, a Ponzi scheme develops in some a.s.set cla.s.s so that people are willing to borrow money in the expectation of future capital gain then the amount of borrowing will no longer be constrained by incomes. While capital gains are made, the borrowers also operate with a soft budget constraint: any deficiency of revenue over costs can be covered by selling an a.s.set whose price has been inflated by the increase in leverage.

Initially banks after they have forgotten the previous crisis will be willing to fund this process, since it increases their incomes. But inevitably a crisis will result because the borrowing is adding to debt levels without increasing the capacity of the economy to service those debts. Though individuals can operate with a soft budget constraint while the price bubble lasts, the entire economy is stuck with the hard budget constraint that, in the long run, the debt must be serviced from income.12 If we are to prevent this process playing out yet again in the future, then we need to prevent the formation of Ponzi schemes in the first place. Unfortunately, the way that financial a.s.sets are currently defined contains the seeds of not one Ponzi scheme but two.

Because shares currently have an indefinite lifespan, it is quite possible for someone to a.s.sert, as Henry Blodget did about Amazon in 1998, that a given company's shares will go from $1 to $400 in a matter of a year (Blodget 2010). Faced with those hypothetical gains, ordinarily sane people are liable to succ.u.mb to the euphoria that produces them and be willing to borrow to speculate.

Because there is no effective limit to the debt that can be secured against a property, property prices reflect the leverage that people are willing to incur to buy them. When houses are bought as residences, that isn't a problem. But when they are bought as speculative a.s.sets, then again people's willingness to borrow can become unhinged from their incomes.

We therefore need not merely reforms, but changes to the incentives that encourage people into debt because so long as those incentives exist, we can be sure that at some point the financial sector will find a way to entice the public into debt, leading to yet another financial crisis.

I have two simple proposals to achieve this objective. Neither of them has any chance of being implemented immediately, but there is some prospect that they might be considered more seriously if, as I expect, this crisis causes a prolonged slump for America that resembles j.a.pan's two 'Lost Decades' since its bubble economy collapsed in the early 1990s. They are: 1 Jubilee shares: To redefine shares so that, if purchased from a company directly, they last for ever (as all shares do now), but once these shares are sold by the original owner, they last another fifty years before they expire; and 2 Property Income Limited Leverage: To limit the debt that can be secured against a property to ten times the annual rental of that property.

Jubilee shares Ninety-nine percent of all trading on the stock market involves speculators selling pre-existing shares to other speculators. Valuations are ostensibly based on the net present value of expected future dividend flows, but in reality based on the 'Greater Fool' principle, where rising debt funds the Greater Fool. Antic.i.p.ated capital gain is the real basis of valuation, and the overwhelming source of that capital gain is not increased productivity, but increased leverage. This trading adds zip to the productive capacity of society, while promoting bubbles in stock prices as leverage drives up prices, encouraging more leverage, leading to a crash after price-to-earnings ratios reach levels even the Greater Fool regards as ridiculous. When the share market crashes, prices fall but the debt that drove prices up remains.

If instead shares on the secondary market lasted only fifty years, then even the Greater Fool couldn't be enticed to buy them with borrowed money since their terminal value would be zero. Instead a buyer would purchase a share on the secondary market only in order to secure a flow of dividends for fifty years (or less). One of the two great sources of rising unproductive debt would be eliminated.

This reform would dramatically tilt the balance in favor of the raising of capital via primary share issues, force valuations to be based on prospective earnings rather than capital gain, and make leveraged speculation on the value of shares on the secondary market much less attractive.

Jubilee shares could be introduced very easily, if the political will existed something that is still years away in practice. All existing shares could be grandfathered on one date, so that they were all ordinary shares; but as soon as they were sold, they'd become Jubilee shares with an expiry date of fifty years from the date of first sale.

Property Income Limited Leverage Obviously some debt is needed to purchase a house, since the cost of building a new house far exceeds the average wage. But debt past a certain level drives not house construction, but house price bubbles: as soon as house prices start to rise because banks offer more leverage to home buyers, a positive feedback loop develops between house prices and leverage, and we end up where Australia and Canada are now, and where America was before the Subprime Bubble burst: with house prices out of reach of ordinary wage earners, and leverage at ridiculous levels so that 95 percent or more of the purchase price represents debt rather than owner equity.

Property Income Limited Leverage ('the PILL') would break the positive feedback loop that currently exists between leverage and property prices. With this reform, all would-be purchasers would be on equal footing with respect to their level of debt-financed spending, and the only way to trump another buyer would be to put more non-debt-financed money into purchasing a property.

This doesn't happen under our current system because the amount extended to a borrower is allegedly based on his/her income. During a period of economic tranquility that is initiated after a serious economic crisis has occurred and is finally over like the 1950s after the Great Depression and World War II banks set a responsible level for leverage, such as the requirement that borrowers provide 30 percent of the purchase price, so that the loan-to-valuation ratio was limited to 70 percent. But as economic tranquility continues, banks, which make money by extending debt, find that an easy way to extend more debt is to relax their lending standards, and push the loan-to-valuation ratio (LVR) to, say, 75 percent.

Borrowers are happy to let this happen, for two reasons: borrowers with lower income who take on higher debt can trump other buyers with higher incomes but lower debt in bidding on a house they desire; and the increase in debt drives up the price of houses on sale, making the sellers richer and leading all current buyers to believe that their notional wealth has also risen.

Ultimately, you get the runaway process that we saw in the USA, where leverage rises to 95 percent, 99 percent, and even beyond to the ridiculous level of 120 percent, as it did with Liar Loans at the peak of the subprime frenzy. Then it all ends in tears when prices have been driven so high that new borrowers can no longer be enticed into the market since the cost of servicing that debt can't be met out of their incomes and as existing borrowers are forced into bankruptcy by impossible repayment schedules. The housing market is then flooded by distressed sales, and the bubble bursts. The high house prices collapse, but as with shares, the debt used to purchase them remains.

If we instead based the level of debt on the income-generating capacity of the property being purchased, rather than on the income of the buyer, then we would forge a link between a.s.set prices and incomes that is currently easily punctured by rising debt. It would still be possible indeed necessary to buy a property for more than ten times its annual rental. But then the excess of the price over the loan would be genuinely the savings of the buyer, and an increase in the price of a house would mean a fall in leverage, rather than an increase in leverage as now. There would be a negative feedback loop between house prices and leverage. That hopefully would stop house price bubbles developing in the first place, and take dwellings out of the realm of speculation back into the realm of housing, where they belong.

Conclusion As the above 'bubble on a whirlpool of speculation' quote from Keynes indicates, this is not the first time that the conventional theory of finance has been attacked. What is unique about these most recent critiques is that the contribution from physicists in particular turns one of the alleged strengths of neocla.s.sical economics against it: mathematics.

In the past, neocla.s.sical economists have disparaged their critics with the a.s.sertion that they object to neocla.s.sical theory because they don't understand mathematics. This time, however, they are under attack, not merely from critics who eschew the use of mathematics, but from those to whom mathematical thinking is second nature.

The impact of this power inversion can be seen in the physicist Joe McCauley's observations about the need to reform economics education: The real problem with my proposal for the future of economics departments is that current economics and finance students typically do not know enough mathematics to understand (a) what econophysicists are doing, or (b) to evaluate the neo-cla.s.sical model (known in the trade as 'The Citadel') critically enough to see, as Alan Kirman put it, that 'No amount of attention to the walls will prevent The Citadel from being empty.'

I therefore suggest that the economists revise their curriculum and require that the following topics be taught: calculus through the advanced level, ordinary differential equations (including advanced), partial differential equations (including Green functions), cla.s.sical mechanics through modern nonlinear dynamics, statistical physics, stochastic processes (including solving SmoluchowskiFokkerPlanck equations), computer programming (C, Pascal, etc.) and, for complexity, cell biology.

Time for such cla.s.ses can be obtained in part by eliminating micro- and macro-economics cla.s.ses from the curriculum. The students will then face a much harder curriculum, and those who survive will come out ahead. So might society as a whole. (McCauley 2006: 6078) This amplifies a point that, as a critic of economics with a reasonable grounding in mathematics myself, has long set me apart from most other critics: neocla.s.sical economics is not bad because it is mathematical per se, but because it is bad mathematics.

16 | DON'T SHOOT ME, I'M ONLY THE PIANO

Why mathematics is not the problem Many critics of economics have laid the blame for its manifest failures at the feet of mathematics. Mathematics, they claim, has led to an excessive formalism in economics, which has obscured the inherently social nature of the subject.

While it is undeniable that an inordinate love of mathematical formalism has contributed to some of the intellectual excesses in economics, generally this reaction is as erroneous as blaming the piano for the discordant notes of a bad piano player. If anything should be shot, it is the pianist, not the piano.

Though mathematics has definite limitations, properly used it is a logical tool that should illuminate, rather than obscure. Economists have obscured reality using mathematics because they have practiced mathematics badly, and because they have not realized the limits of mathematics.

The kernel If you divided the world's population into those who dislike mathematics, those who like it, and those who were indifferent, I suspect that 95 percent would be in the first camp, 5 percent in the second, and 0 percent in the third. Neocla.s.sical economists come almost exclusively from the 'like it' camp, and therefore their arguments are almost always expressed in mathematical form. Most critics of economics come from the 'dislike it' camp, and frequently criticism of mathematics per se forms part of their criticism of economics.

Call me weird: I'm a critic of neocla.s.sical economics who likes mathematics. But I am not alone. There are numerous mathematically inclined critics of neocla.s.sical economics, and in many ways this book was written to convey their critiques to a non-mathematical audience. Not only is it possible to simultaneously like mathematics and dislike mainstream economics, but a sound knowledge of mathematics makes you an even more confirmed opponent because much of the mathematics in conventional economic theory is unsound.

At one level, it is unsound because conditions that economists a.s.sume contradict other conditions needed for their models, so that the theory is built on a mathematical error. For example, as shown in Chapter 4, one crucial a.s.sumption in the neocla.s.sical argument in favor of small compet.i.tive firms over monopolies violates one of the most basic rules of calculus, the Chain Rule.

At a second level, it employs the wrong mathematical tools to a.n.a.lyze the dynamic processes that characterize a market economy employing complicated comparative static equilibrium a.n.a.lysis when dynamic systems a.n.a.lysis is not only more appropriate but frankly easier.

At a third and more profound level, conventional economics is mathematically unsound because it has not learnt the lesson which true mathematicians have learnt in the last century: that there are limits to mathematical logic.

The roadmap In this chapter I argue that conventional economics has abused mathematics in two main ways: by practicing bad mathematics, and by not acknowledging the limitations of mathematics. Many economic theorems result in logical contradictions which economists fail to recognize as such, and many other theorems are derived by falsely a.s.suming that different quant.i.ties are in fact equal. Modern mathematics has also realized that there are limits to mathematical logic, but economists have evaded this realization by effectively but unintentionally isolating themselves from mainstream mathematical science.

Bad mathematics In a cla.s.sic instance of 'those who live by the sword die by the sword,' the school of economics that prides itself on being mathematical is subject to the indictment that its mathematics is erroneous. There are numerous theorems in economics that rely upon mathematically fallacious propositions. There are basically four ways in which this manifests itself in economic theory: logical contradiction, where the theory is allegedly 'saved' by an a.s.sumption which in fact contradicts what the theory purports to show; omitted variables, where an essential aspect of reality must be ignored to derive the mathematical results that economists wish to prove; false equalities, where two things that are not quite equal are treated as if they are equal; and unexplored conditions, where some relation is presumed without exploring what conditions are needed to make this relation feasible.

Logical contradiction The case outlined in Chapter 2 the failed attempt to aggregate individual preferences to form community preferences with the same properties is an excellent example of logical contradiction.

The economic theory of consumer behavior begins with the proposition that it is possible to aggregate individual demand curves to derive a market demand curve that has the same characteristics as an individual's demand curve. Economists have proved that this is possible only when the Sonnenschein-Mantel-Debreu conditions apply: (a) that all consumers have the same preference map; and (b) that preferences do not change with income.

Condition (a) effectively means that there is only one consumer. Condition (b) effectively means that there is only one commodity. Aggregation is therefore strictly possible if there is only one consumer and only one commodity.

Clearly this is not aggregation at all.

A good mathematician would recognize this as proof by contradiction (Franklin and Daoud 1988). This is a clever technique whereby, to prove a statement, you a.s.sume its opposite and then show a contradiction. Therefore the statement is true.

For example, consider the problem that confronted Pythagoras and friends when they tried to work out the length of the hypotenuse of a right-angled triangle whose other sides were both one unit long. According to Pythagoras's theorem that 'the square of the length of the hypotenuse is equal to the sum of the squares of the other sides,' this meant that the length of the hypotenuse was the square root of 2.

These Ancient Greeks initially believed that all numbers were 'rational,' which meant that any number could be expressed as the fraction of two integers: thus 1.5, for example, is the integer 3 divided by the integer 2. But they could never accurately measure the value of the square root of 2 in terms of the ratio of two integers: every more accurate measurement led to a different fraction.

The reason that they couldn't find the 'right' two integers is that the square root of 2 is an irrational number: it can't be defined as the ratio of two integers.

This can be proved quite easily using proof by contradiction. You start with the opposite a.s.sumption that it is possible to express the square root of 2 as a ratio of two integers. You then work on from this point, to show this leads to a contradiction. Therefore you show that the square root of 2 is irrational.1 The proofs which led to the Sonnenschein-Mantel-Debreu conditions can easily be described in the same fashion. You wish to prove that it is not possible to aggregate individual preferences to derive community preferences which display the same characteristics as individual preferences.

You start with the opposite a.s.sumption that it is possible to aggregate the preferences of two or more different consumers over two or more different commodities to market demand curves that have the same characteristics as individual demand curves. You then show that this is possible only if there is only one individual and only one commodity. This contradicts your starting a.s.sumption that there are multiple different consumers and different commodities. Therefore you have proved, by contradiction, that it is not possible to aggregate individual preferences to derive market demand curves that obey the 'Law' of Demand.

The trouble is that economists were hoping that they could prove that it was possible to aggregate. In this sense, they were in the same situation as the ancient Pythagoreans, who were trying to prove that all numbers were rational they were not at all pleased to find that they were wrong.

At least the Pythagoreans relented: they abandoned the belief that all numbers were rational, and accepted that there were numbers which could not be described as the ratio of two integers. Mathematics thus absorbed the existence of irrational numbers, and went on from there to many other discoveries.

Economists, on the other hand, have been unwilling to abandon their concept of rationality. Faced with an equivalent discovery that society cannot be understood as the sum of the rational individuals within it economics has instead enshrined these and similar logical contradictions as 'intuitively reasonable' (Gorman 1953) abstractions that are needed to forge a link between individual and collective utility.

This is bad mathematics. It has led to bad economics, which has avoided the more complex but richer visions of the economy that flow from coming to terms with the myriad contradictions of the simplistic notions underlying neocla.s.sical economics.

Omitted variables Bad mathematics also shows up in such hallowed economic concepts as maximizing profit by equating marginal cost and marginal revenue. As is shown in Chapter 4, this mantra of the everyday economist is false even on its own terms, but it is doubly so if we ignore time. Once time is rightly included in the a.n.a.lysis, then it is mathematically evident that, to maximize profits over time, a firm should ensure that its marginal revenue exceeds its marginal cost.

Many critics of conventional economics have previously argued that time is the most crucial variable left out of economic a.n.a.lysis, but most of these critics have then eschewed mathematics itself as a result. However, good mathematical economics incorporates time as an essential aspect of reality, and results in a type of economic a.n.a.lysis that is profoundly different from conventional neocla.s.sical economics.

Time is not the only vital factor omitted by neocla.s.sical economists, of course. Other notable examples include uncertainty, and the formation of expectations under uncertainty, and, most importantly of all, given the debt-induced crisis we are now in, money and debt. The basis of this is the so-called 'money illusion,' which is drummed into new economics students in their first year ordinarily when most are too naive about the world to see the fallacy behind it2 resulting in macroeconomic models that ignore the role of money and debt in our fundamentally credit-driven market economies.

False equalities One popular but erroneous step in conventional economic argument is to a.s.sert that something that is extremely small can be treated as zero. This is especially so when economists then pretend to 'aggregate up' from the individual firm to derive a result that applies at the aggregate level. What results is not mathematical a.n.a.lysis, but a mathematical sleight of hand the intellectual equivalent of a magician's trick.

The model of perfect compet.i.tion ill.u.s.trates this nicely. The argument starts with the market having a downward-sloping demand curve and an upward-sloping supply curve. Step one of the trick is to omit showing the downward-sloping marginal revenue curve, which must be there if the market demand curve slopes downward, and which is distinctly different from, and steeper than, the demand curve. Step two is to break the market demand curve into lots of tiny bits, each of which must also slope downwards if the whole curve slopes downwards, but to persuade the audience that the slope of each of these little lines is so flat that they can be treated as horizontal. Hence for the individual firm, the demand curve and the marginal revenue curve are identical. The final stage of the trick is to return to the market level by adding up all the individual firm's marginal cost curves, and to show that price is set by the intersection of the demand curve and the supply curve. The troublesome market marginal revenue curve has been made to disappear, and the trick is complete.

The special irony of this piece of magic is that the magician doesn't realize that a trick is being pulled. Economists are so used to presuming that an infinitesimal amount is equivalent to zero that they don't even realize they are breaching one of the fundamental rules of mathematics.

Unexplored conditions There are numerous examples of this phenomenon. The comparison of monopoly to perfect compet.i.tion presumes that the supply curve for the compet.i.tive industry is equivalent to the marginal cost curve for the monopoly. However, this is possible only if the two 'curves' are the same horizontal straight line (Keen and Standish 2010: 8991). The theory of the labor market presumes that the supply curve of labor is upward sloping; Chapter 5 showed that this is not a necessary outcome of the neocla.s.sical theory of labor supply. The a.n.a.lysis of production requires that the money value of capital is an adequate measure of the amount of capital; Chapter 6 showed that it is not, once we acknowledge that machines are produced by other machines and labor.

That these (and doubtless many other) logical conundrums exist indicates that economists do not explore the logical foundations of their beliefs. This in itself is not necessarily unscientific; as discussed in Chapter 7, it is a standard practice that scientists in a given school within a science do not challenge what Lakatos describes as the 'hard core' of their beliefs. But it is a sign of how fragile the neocla.s.sical hard core is that so many elements of it can be shown so easily to be internally inconsistent.