Note: the next section is possibly the most difficult part of this entire book. If you're satisfied with the debunking above, then you can skip this section for now and move to the next chapter. But I do recommend reading this section at some stage.

The whole box and dice.

Sraffa's technique was to eschew the initial aggregation of capital, and to say, in place of 'factors of production produce goods,' that 'goods produce goods' in concert with labor. Sraffa then used this 'a.s.sumption-free' model of production to show that the economic theories of price and of income distribution were invalid.

The essential point in his a.n.a.lysis was that capital does not exist as an easily definable ent.i.ty, yet such an existence is necessary for the simple parable that profit represents the marginal productivity of capital to be true. He made this point by constructing a series of models that directly confronted the true complexity of a system of commodity production.

Sraffa built his models up very carefully, from a simple model with very little real-world realism to a more complex model which, with one exception, was a fairly realistic rendition of a market system of production.

The exception was that Sraffa considered an economy in equilibrium, when a real-world economy is certain not to be in equilibrium. However, Sraffa's purpose was to critique economics on its own terms, and since economics a.s.sumes equilibrium, Sraffa made the same a.s.sumption. He took it to its logical conclusion, considering an economy which was not only in equilibrium now, but had been in equilibrium for the indefinite past.

Model one: production with no surplus His first model was one in which the economy was just able to reproduce itself, and in which there was no 'fixed capital' instead, all inputs were 'circulating capital' which are used up in each round of production.

In this economy, the output of each industry was just sufficient to supply the demand for its output by itself and the other industries. Labor was not explicitly treated, but it was feasible to envisage that part of the inputs to an industry represented workers receiving a subsistence wage. Sraffa's example is shown in Table 7.1.

In this hypothetical economy, combining 240 quarters of wheat, 12 tons of iron and 18 pigs in a production process results in an output of 450 quarters of wheat. Similarly, 90 quarters of wheat, 6 tons of iron and 12 pigs are used to produce 21 tons of iron; and 120 quarters of wheat, 3 tons of iron and 30 pigs are used to produce 60 pigs.

The total output of each sector just equals the amount of its output used to produce both its own output and that of all other sectors. Thus the total demand for wheat as an input is 450 quarters: 240 in wheat production, 90 in iron and 120 in pig production.

Sraffa posed the question of what would determine prices in this hypothetical economy, and the answer was not 'demand and supply,' but 'the conditions of production': each sector's price had to enable it to just purchase its inputs. Specifying this for the wheat industry, this meant that 240 times the price of wheat, plus 12 times the price of iron, plus 18 times the price of pigs, had to just equal 450 times the price of wheat.

Similar equations applied for iron and pigs, and with three equations (the price equations for each sector) and three unknowns (the prices), there was one unique set of prices which made it possible for the economy to reproduce.6 TABLE 7.1 Sraffa's hypothetical subsistence economy.

Neocla.s.sical economists might have endeavored to find this set of prices by considering the demand curves for wheat, pigs and iron, and the supply curves for wheat, pigs and iron, and solving these to find the set of relative prices that equated supply and demand in each industry. However, in this context this would have been overkill: the only prices that work for this economy are those that enable each sector to buy its inputs.

Model two: production with a surplus The next step towards realism was to consider an economy which produced a surplus: where at least one sector produced more of its output than was used up to produce itself and all other commodities. This step closer to a real market economy raises the issue of profits which weren't an issue in the first model. For this economy to be in equilibrium, the rate of profit has to be the same across all sectors even if only one sector produced a physical surplus. Otherwise, capitalists in sectors with a low rate of profit would be tempted to move to sectors with a high rate of profit, and the economy would not be in equilibrium. Sraffa used a two-sector example, as shown in Table 7.2.

TABLE 7.2 Production with a surplus.

This economy uses 280 quarters of wheat and 12 tons of iron to produce 575 quarters of wheat; another 120 quarters of wheat and 8 tons of iron are used to produce 20 tons of iron. 175 bushels of wheat are produced over and above the 400 used in production, whereas the entire 20 tons of iron are used up in producing wheat and iron.

For a uniform rate of profit r to apply, the prices in this economy must be such that the 'money' value of inputs, multiplied by (1+r), must equal the money value of its outputs. For this example economy, the price ratio is 15 bushels of wheat for 1 ton of iron, and the uniform rate of profit is 25 percent.

Model three: production with a surplus and explicit labor The economy above had to have labor in it, since nothing can be produced without labor.7 However, this was not explicitly shown. The next model added further realism by showing that output was produced by combining both commodities and labor in a production process.

This introduces the wage as an additional unknown, and establishes the first element in Sraffa's critique of the economic theory of income distribution: rather than prices determining the distribution of income, the distribution of income between wages and profits must be known before prices can be calculated.8 Sraffa then shows that there is an appropriate measuring stick (the 'standard commodity') which reveals a simple, linear relationship between the wage w, the actual rate of profit r, and the maximum feasible rate of profit for a given economy, R.9 The wage w falls linearly as the rate of profit r rises towards its maximum value R.

The example economy in Table 7.2 has a maximum rate of profit of 25 percent, and results in the wage/profit function shown in Figure 3.1. If the wage w is .8 which means that workers' wages represent 80 percent of the surplus output of this economy then the corresponding rate of profit r is 5 percent. This is shown numerically in Table 7.3.

TABLE 7.3 Relationship between maximum and actual rate of profit and the wage share of surplus.

What this table says is that if workers, for example, get a zero wage, then all of the surplus goes to the capitalists, who then make a profit of 25 percent. If, however, workers get 10 percent of the surplus as their wage, then the rate of profit falls to 23 percent (rounded up). The same linear process continues right out to the point at which workers get 100 percent of the surplus, at which point capitalists get nothing and therefore have a rate of profit of zero.

7.4 The wage/profit frontier measured using the standard commodity.

Clearly, this a.n.a.lysis is reasonably realistic, and therefore, one might think, rather innocuous. However, this apparently innocuous step sets up the coup de grace for the economic theory of income distribution.

The punchline: capital behaving badly.

The key concept in the neocla.s.sical theory of income distribution is that factors get paid in accordance with their marginal contribution to output in the context of diminishing marginal returns. This means that as the supply of a factor increases, its return should fall.

The difficulty is, as alluded to earlier, that it is not easy to see how one can add units of capital together. Workers can be aggregated by adding up the number of hours they work after notionally standardizing for different levels of productivity by multiplying the hours of skilled labor by some amount to reflect higher productivity. Land can be aggregated by adding up acres and again by adjusting numerically for varying degrees of fertility.

But machines have no apparent common property apart from price. This is in fact how economic theory aggregates capital, but this involves an obvious circularity, because the price of a machine reflects the profit expected from it, yet the rate of profit is the ratio of profit to price.

Sraffa proposed an ingenious and logically sound method of aggregation: to reduce capital to dated inputs of labor. The previous linear relationship between the wage and the rate of profit was an essential element in this a.n.a.lysis.

All items of capital are produced by other items of capital and labor. When an economy has been in equilibrium for the indefinite past, it is thus possible to regard the value of a machine as being equal to the value of the machines used to produce it, plus the value of the labor involved, times a rate of profit to reflect the pa.s.sage of time. If we notionally treat the period of production as a year, then if the equilibrium rate of profit is 5 percent, 1.05 times the value of the inputs last year should equal the value of the machine this year.

The same argument applies to all the machines and labor inputs used to produce the inputs, and to all the machines and labor that produced them, and so on.

If we repeat this process, and each time reduce machinery inputs to the machinery and labor used to produce them, then we get a set of labor terms and a declining but never zero residual of machinery inputs. Each labor input is multiplied both by the wage, and by one plus the rate of profit raised to a power which reflects how many years ago the input was made.

If, for example, we are considering a machine manufactured eleven production periods ago, then this term will be the amount of direct labor bestowed in producing all the relevant components in the twelfth year, times the wage, plus the capital input, all raised to the twelfth power. It is therefore possible to subst.i.tute an expression in terms of labor for the capital inputs used up in producing a given commodity.10 TABLE 7.4 The impact of the rate of profit on the measurement of capital.

We can now approximately11 express the value of a machine in terms of the sum of the value of the labor inputs used to produce it. Each element in this sum consists of a physical quant.i.ty of labor, multiplied by two terms: one representing the wage, and another representing the impact of acc.u.mulated profit over time.

The former term is a negative function of the rate of profit (as in Table 7.3); the latter is as a positive function of the rate of profit, raised to a power. The former will fall in size as the rate of profit rises; the latter will rise, and it will also rise more for inputs made a long time ago.

This combination of opposing effects one term that falls as r falls, the other that rises as r falls evokes the possibility that one effect can prevail for a time, only to be overwhelmed by the opposite effect at a higher rate of profit. Therefore, the individual terms that interact to determine the value of an item of capital can rise for a while as the rate of profit rises, only to fall as the rate of profit rises still further.

This can be ill.u.s.trated using Sraffa's example economy where the maximum rate of profit was 25 percent, and considering a machine which was made using one unit of labor as an input at some time in the past.

If the rate of profit was zero, then no matter how many years ago that machine was made, if a machine cost one (standard commodity) unit to make, its measured value would still be 1, as shown by the first row of Table 7.4. If the rate of profit was instead 1 percent, then the measured value of that machine falls to 0.96, if it is used today reflecting the lower value of labor in terms of Sraffa's measuring stick.

The value of the machine rises a bit if it was made two years ago, because its value is calculated to be 0.96 times 1 plus the rate of profit. This is 0.96 times 1.01, or roughly 0.97. This larger amount, though, is still less than 1, which would have been its value if the rate of profit had been zero. The same applies if the machine was used two periods ago, in which case its calculated value would be 0.98 or 0.96, multiplied by 1.01 squared.

However, if the machine was produced five years ago, then its value in terms of the standard commodity rises to 1.01. This is because, while one part of the overall term has fallen to 0.96, the other has risen to 1.01 multiplied by itself five times which roughly equals 1.05 and 1.05 times 0.96 gives us 1.01.

The same effect applies across the row of the table, showing that as the rate of profit rises, the measured value of this capital input rises. The second term, 1.06, is 0.96 times 1.05 raised to the 10th; the third, 0.96 times 1.05 raised to the 15th; and so on.

The measured value of the machine therefore falls because of a higher rate of profit, but then rises if it was used many years ago. And the table has even more complications.

Notice that as we go down the table so that the rate of profit increases the value of a machine input today falls smoothly. However, the value of a machine applied five years ago rises for a while, but then falls. This accurate picture is a lot more complicated than economists a.s.sumed it to be, and these complications rule out the simple correspondence economists believed existed between the 'amount' of capital and the rate of profit.

The complications arise because the two different effects in Sraffa's accurate measure of capital don't cancel each other out. The first is the value of a wage unit, given the rate of profit r. On the first row, that is 1 (reflecting a zero rate of profit); on the second, 0.96 (at a 1 percent rate of profit); the third, 0.92 (at a 2 percent profit rate); and so on. But the second effect is 1+r, raised to a power of 5, reflecting how many years ago the input was made. On the first row, that term is 1 because the rate of profit is zero and 1 times 1 is 1. On the second row, it is 0.96 times 1.05, which is 1.01 raised to the fifth power. This is roughly 1.01, so the measured value of the machine has risen. On the third row, it has risen further to 1.02 which is 0.92 times 1.1, which is 1.02 raised to the 5th. On the fourth, it is roughly the same 0.88 times 1.16, which is 1.03 raised to the 5th.

But by the time we get to a 10 percent rate of profit, the value goes down to 0.97: here we have 0.6 times 1.61, which is 1.10 raised to the 10th. The impact of the falling value of the first term now outweighs the impact of the rising value of the second. By the time we get to a rate of profit of 20 percent, the value of this machine (in terms of the standard commodity) has fallen to just 0.5, having been as high as 1.02 at lower rates of profit.

So the measured value of a machine rises and then falls as the rate of profit rises, and also rises and then falls as the time at which the machine was used to produce a commodity becomes farther in the past.

This is not exactly how economists think about capital as a factor of production. They had hoped that the rate of profit would fall smoothly as the amount of capital used in production rose, so that capital, like labor, would manifest diminishing marginal productivity. But Sraffa instead showed that not only was there no uniform relationship between the rate of profit and the amount of capital, but also the direction of causation was the opposite of what economists wanted. Rather than the rate of profit depending on the 'amount' of capital, the measured amount of capital actually depended on the rate of profit. This makes it impossible to argue that the rate of profit is determined by the marginal productivity of capital, and so this second leg of the economic theory of income distribution collapses.

Not only that, but the perverse relationship that exists between the measurement of capital and the rate of profit is going to cause perverse effects in production. A rising rate of profit might for a while make one method of producing a commodity cheaper than alternatives, but then at a still higher rate of profit, it might make it more expensive.

Sraffa provides one ill.u.s.tration of this by comparing the price of two commodities which start out equal when the rate of profit is zero, and where one becomes more expensive than the other as the rate of profit rises, only to have the other become more expensive as the rate of profit rises farther still. One product has relatively more 'direct labor' applied to its production in the recent past, while the other has more direct labor applied in the far distant past. Sraffa likens the latter to wine produced by being aged in a barrel; the former could be regarded as producing wine of identical quality using advanced chemical processes.12 The latter process would be regarded as 'capital intensive,' since so much machinery is used directly in its production, while the former would be called perhaps 'time intensive' (or labor intensive if you imagine the barrels being tended over the years by cellar masters).

At a zero rate of profit, the cost of each barrel of wine equals simply the sum of the wages paid to produce the wine and for both methods of production to exist in equilibrium, the cost of the two techniques must be identical.

As the rate of profit rises from zero to a moderate uniform rate, the far distant application of labor needed to produce the barrel has comparatively little impact, so that the wine produced using modern technology is more expensive. In this range of the rate of profit, production using modern technology would cease, since it would be uncompet.i.tive with wine produced using the aging process.

However, as the rate of profit becomes higher still, the effect of compounding the rate of profit on the making of the cask becomes enormous, so that the aged wine becomes more expensive than its ma.s.s-produced cousin. Ma.s.s production would take over again we would switch back to the apparently more 'capital intensive' means of production.

Finally, when the rate of profit reaches its maximum value and wages fall to zero, the cost of wine falls to simply the cost of the irreducible commodity components (the original grapes, etc.), and the price of the two types of wine could again coincide.

Subsequent economists used Sraffa's building blocks to ill.u.s.trate that a method of production could start out superior to all others at a zero profit rate, become less profitable than some other methods at a higher rate, only to once again become the most profitable at a higher rate still.

This phenomenon of 'reswitching' destroyed the simple proposition that the rate of return on capital represented the marginal product of capital. If a particular production technique had lost primacy to others at one rate of profit, then it could not regain that primacy at a higher rate of profit still, unless for a period it benefited from increasing marginal product. But if marginal product could alternately rise and fall, then there was no necessity that the market for capital should be well behaved. Demand curves could slope up as well as down, supply curves down as well as up, and no unique equilibrium position could be defined.

The causes of this apparent paradox are that the concept of capital as a h.o.m.ogeneous substance is an illusion, and that what is capital intensive depends on the rate of profit. If the rate of profit is low, then the labor embodied in an ancient wine barrel is of little consequence, and the process of aging wine may well appear to be labor intensive. But if the rate of profit is high, then compounding of this high rate of profit makes that ancient wine barrel of great value and the process could be described as capital intensive. Rather than the rate of profit depending on the quant.i.ty of capital, the quant.i.ty of capital (in terms of its value measured in embodied labor value) depends upon the rate of profit.

The intricate and interdependent processes of production thus generate many opportunities for factor returns to move one way and then the other as factor intensities rise. There is therefore no consistent relationship between factor productivity and factor incomes. Instead, the distribution of income between wages and profits is largely independent of the system of production. The distribution of income is a social phenomenon.

Economists fought against this conclusion, but every apparent victory was shown to be invalid. Ironically, the reb.u.t.tals to economic rejoinders often showed that the only conditions under which the economic position could hold would be if the ratio of capital to output was the same in all industries. This is the same condition needed to make Marx's labor theory of value hold, yet the neocla.s.sical revolution which gave us modern economic theory was supposedly free of the nonsense conditions needed by its Marxian rival.

So what?

Just as Chapter 6 showed that the wage can't be explained as the marginal product of labor, this chapter has established that economic theory cannot justify the existing rate of profit as somehow reflecting the marginal productivity of capital. Instead, the rate of profit reflects relative power in our society, as well as the technical capabilities of factories and the success or otherwise of recent waves of investment. It is clearly possible for the rate of profit to be 'too high' or 'too low,' but conventional economics is of no use in establishing either level.

Ignorance is bliss.

Of course, the average economist would never tell you that economic theory had suffered such a devastating blow. This is because the average young economist doesn't even know that this intellectual bout took place the concepts in this debate don't make it onto the curriculum for either undergraduate or postgraduate students. Older economists cannot avoid some knowledge of the war, but they either erroneously believe that their camp won, or they dismiss the issue completely.

Today, economic theory continues to use exactly the same concepts which Sraffa's critique showed to be completely invalid capital as an amorphous ma.s.s that can be costlessly moved from producing any commodity to any other, whose return reflects its marginal productivity, and which can be aggregated by adding up its price times quant.i.ty.

There are few better signs of the intellectual bankruptcy of economics than this.

However, this madness is often justified by an appeal to a methodological precept that the absurdity of a theory's a.s.sumptions is irrelevant all that matters is that the theory's predictions accord with reality. We now turn to consider this popular but false defense of economics.

8 | THERE IS MADNESS IN THEIR METHOD.

Why a.s.sumptions do matter, and why economics is so different from the true sciences.

Economics would have us believe that it is a science, fully able to stand tall beside the more conventional physical sciences and mathematics.

After the preceding chapters, you should be inclined to reject that belief. Surely, whatever 'science' is, one might hope that it is undertaken with more impartiality, regard for the facts and logical consistency than economics has displayed.

However, the critiques of conventional economics which form the substance of this book were devised by critical economists (and sometimes, inadvertently, by conventional economists themselves) and some of these critiques have been acknowledged as valid by some conventional economists. There is also a small but robust minority working on other approaches to economic a.n.a.lysis, as you'll find in Chapter 18. There are thus some systematic and logical aspects to what economists in general do, which could qualify as scientific behavior.

The position I now favor is that economics is a pre-science, rather like astronomy before Copernicus, Brahe and Galileo. I still hold out hope of better behavior in the future, but given the travesties of logic and anti-empiricism that have been committed in its name, it would be an insult to the other sciences to give economics even a tentative membership of that field.1 Before better behavior can take widespread root, economics will have to wean itself from a methodological myth. This is the proposition, first put by Milton Friedman, that a theory cannot be judged by its a.s.sumptions, but only by the accuracy of its predictions.

Leaving aside the question of whether economics has ever accurately predicted anything, the argument that 'the more significant the theory, the more unrealistic [are] the a.s.sumptions' is simply bad philosophy.

The kernel.

Have you heard the joke about the chemist, the physicist and the economist who get wrecked on a desert isle, with a huge supply of canned baked beans as their only food? The chemist says that he can start a fire using the neighboring palm trees, and calculate the temperature at which a can will explode. The physicist says that she can work out the trajectory of each of the baked beans, so that they can be collected and eaten. The economist says, 'Hang on, guys, you're doing it the hard way. Let's a.s.sume we have a can opener.'2 That a.s.sumption is not too different from the type of a.s.sumption that economists routinely make, and yet they defend themselves on the apparently convincing grounds that the a.s.sumptions don't matter a theory can be evaluated only on the basis of the accuracy of its predictions.

This methodological defense is invalid, because it confuses 'negligibility' a.s.sumptions, which argue that some minor details can be ignored, with 'domain' a.s.sumptions, which determine the range of applicability of a given theory. a.s.sumptions also do matter to economists, in that they genuinely believe that their theories describe reality, and they reject economic argument that is not based upon their preferred set of a.s.sumptions.

The roadmap.

In this chapter I outline the paper in which Friedman introduced the notion that 'a.s.sumptions don't matter.' Following Musgrave, I cla.s.sify a.s.sumptions under three headings: negligibility a.s.sumptions, domain a.s.sumptions, and heuristic a.s.sumptions. Friedman's paradoxical statement that 'the more significant the theory, the more unrealistic the a.s.sumptions' is only partially true of the first cla.s.s of a.s.sumptions, and manifestly untrue of the latter two cla.s.ses. Finally, I detail the many ways in which a.s.sumptions do matter to economists.

A paradoxical proposition.

There would be few if any academic economists who have not had a lecture disturbed by some recalcitrant student, interjecting that the a.s.sumptions of the model being discussed are unrealistic. Fortunately, there is a simple weapon at hand: an appeal to the authority of Milton Friedman that a theory can't be judged by its a.s.sumptions, but only by how well its predictions accord with reality.

In fact, Friedman's case went farther: he argued that unrealistic a.s.sumptions were the hallmark of good theory. In what Paul Samuelson later dubbed 'the F-twist,' Friedman argued that Truly important and significant hypotheses will be found to have 'a.s.sumptions' that are wildly inaccurate descriptive representations of reality, and, in general, the more significant the theory, the more unrealistic the a.s.sumptions (in this sense). The reason is simple. A hypothesis is important if it 'explains' much by little, that is, if it abstracts the common and crucial elements from the ma.s.s of complex and detailed circ.u.mstances surrounding the phenomena to be explained and permits valid predictions on the basis of them alone. To be important, therefore, a hypothesis must be descriptively false in its a.s.sumptions; it takes account of, and accounts for, none of the many other attendant circ.u.mstances, since its very success shows them to be irrelevant for the phenomena to be explained.

To put this point less paradoxically, the relevant question to ask about the 'a.s.sumptions' of a theory is not whether they are descriptively 'realistic,' for they never are, but whether they are sufficiently good approximations for the purpose in hand. And this question can be answered only by seeing whether the theory works, which means whether it yields sufficiently accurate predictions. (Friedman 1953) The proposition that a theory is not regarded as a description of reality, but merely as a way of predicting the future, is known as 'instrumentalism.' This position is superficially appealing, and sufficiently persuasive to quieten the average interjector. It appears scientific, in that most scientists would admit that their theories can never exactly describe reality. It also implies a healthy dose of theoretical agnosticism, in that the economist is purportedly detached from his theory, and is only really interested in 'the facts.'

However, despite its superficial appeal, instrumentalism suffers from several flaws, which were clearly set out by the philosopher Alan Musgrave in 1981. Musgrave argued that there were three cla.s.ses of a.s.sumptions, and that Friedman's dictum was only partially true in the least important of them.

Negligibility a.s.sumptions Negligibility a.s.sumptions state that some aspect of reality has little or no effect on the phenomenon under investigation. Friedman's paper made heavy use of the example of a ball being dropped near the earth, which fell very nearly 'as if' it had been dropped in a vacuum. In this instance it was valid to a.s.sume that the ball was falling in a vacuum, since air resistance has negligible impact on the ball's fall. However, the same was obviously not true of a feather dropped under the same circ.u.mstances.

Friedman argued that though it was unrealistic to say 'a.s.sume the ball was dropped in a vacuum,' the theory of gravity had great explanatory power: it explained much (the acceleration of bodies in free fall close to the earth) with very little (a gravitational constant and simple calculus). This theory should be dropped in favor of another only if a rival is at least as accurate and equally acceptable on other grounds, or 'when there exists a theory that is known to yield better predictions but only at a greater cost' (Friedman 1953).

Musgrave argued that many of Friedman's musings were reasonable in this domain, but that even here his 'dialectical' proposition that 'the more significant the theory, the more unrealistic the a.s.sumptions' is overblown. In fact, it is possible to rephrase these 'unrealistic' statements as 'realistic' ones: for example, it is realistic to say that air resistance is negligible for dense bodies falling from rest over short distances. As Musgrave put it, these a.s.sumptions: are not necessarily 'descriptively false,' for they do not a.s.sert that present factors are absent but rather that they are 'irrelevant for the phenomena to be explained' [...] Galileo's a.s.sumption that air-resistance was negligible for the phenomena he investigated was a true statement about reality, and an important part of the explanation Galileo gave of those phenomena. (Musgrave 1981) However, negligibility a.s.sumptions are the minnows of the a.s.sumptions family. Far more important are domain a.s.sumptions, and it is these to which rightly troubled students often object.

Domain a.s.sumptions A domain a.s.sumption specifies the conditions under which a particular theory will apply. If those conditions do not apply, then neither does the theory.

An economic example of this is the a.s.sumption that risk can be used as a proxy for uncertainty an a.s.sumption that permeates the conventional theories of macroeconomics and finance, which we will investigate in Chapters 10 and 11.

Risk applies to situations in which the regularity of past events is a reliable guide to the course of future events. Gambling gives us many such examples: if a tossed coin is seen to land showing heads roughly half the time, then you can reliably bet that there will be a 50:50 chance of heads in the future. If anyone bet you that heads would in future come up only 40 percent of the time, it would be sensible to take the bet. A risky event will have a probability a.s.sociated with it, and a variance of outcomes around those probabilities, which can be reliably estimated using the techniques of statistics.

Uncertainty applies when the past provides no reliable guide to future events. Though the fact that we cannot predict the future is the essence of the human condition, the very nebulousness of uncertainty means that many people and certainly the vast majority of economists have difficulty grasping the concept. As a result, they act as if the quantifiable concept of risk can be safely subst.i.tuted for unquantifiable uncertainty.

A somewhat intimate example might ill.u.s.trate the fallacy of identifying uncertainty with risk.3 Imagine that you are very attracted to a particular individual, and that you know this person has gone out with 20 percent of those who have asked him or her out in the past. Does this mean that you have a 20 percent chance of being lucky if you 'pop the question'?

Of course not. Each instance of attraction between two people is a unique event, and the past behavior of the object of your desires provides no guide as to how your advances will be received. How he or she will react cannot be reduced to some statistical prediction based on past apparent regularities. From your perspective, their reaction is truly uncertain and this uncertainty is at the root of much of the angst that romantic attraction generates.

A similar observation can be made about each new business investment. Even if similar investments have been made in the past, the economic environment of a new investment differs from those which have gone before. Past trends therefore cannot be confidently extrapolated to predict future performance but this procedure is the essential a.s.sumption behind using statistics to calculate risk.

The a.s.sumption that risk can be used as a proxy for uncertainty when evaluating investments is therefore unrealistic. A theory that makes such an a.s.sumption is quite clearly not better than an alternative one which does not quite the opposite in fact. This a.s.sumption says that the domain of relevance of the theory is a world in which the future is simply subject to chance.

Since there is no such world, the domain of applicability of theories which make such an unrealistic a.s.sumption is 'nowhere.' Yet a.s.sumptions of this type abound in economic theory (especially, it must be said, in the work of Milton Friedman).

Such an a.s.sumption should be made only if it fits into Musgrave's third cla.s.s, the heuristic a.s.sumption.

Heuristic a.s.sumptions A heuristic a.s.sumption is one which is known to be false, but which is made as a first step towards a more general theory. Musgrave gives the example of Newton's a.s.sumption that the solar system consisted only of the sun and the earth. This gave rise to the theory that planets would follow elliptical orbits (which is a reasonable medium-term guide to actual planetary orbits in our solar system).

The next major step came with Poincare in 1899, when he tried to develop a formula describing planetary motion in a system with more than one planet. His proof that there was no such formula and that the actual orbits would interact in wildly unpredictable ways ushered in what is now known as 'chaos theory' or 'complexity theory' (though it lay dormant for sixty-eight years until modern computers allowed its accidental rediscovery).