Friday, 5 July 2013

Moralised Markets

This is an extract from a draft paper A Context for Financial Economics: Ethics in the Face of Uncertainty  I have placed on SSRN.  It forms the basis of the case I will present as part of The Cabaret of Dangerous Ideas at the Edinburgh Festival Fringe on 18 August.

Determining what is is part of epistemology, and Thagard and Beam have noted,
Epistemological theories can be classified into foundational or coherentist. Foundational theories attempt to ground knowledge in a solid base such as sense experience [Empiricism] or a priori reasoning [Realism]. In contrast, coherentists [Pragmatists] argue that there are no foundations for our beliefs, whose justification derives from how well they fit together with each other.[Thagard and Beam2004]
Realism argues that there are immutable truths in an ‘intelligible’ universe and a ‘sensible’ universe that is actually experienced. ‘Truth’ transcends experience and can be established only through abstract thinking (Rationality). Realism, in the Christian and Islamic traditions, goes back to Plato’s Theory of Forms (or Ideas) and was central to Descartes and Kant’s philosophy. In this framework, there is a hierarchy of knowledge with mathematics being closer to ‘truth’ than experimentation. Greek beliefs in the immutability and indubitability of mathematics became embedded in western philosophy with the Neo-Platonists, such as Augustine of Hippo who associated mathematics to a transcendental deity [Augustine of Hippo1993, p 46].
Empiricism argues that there are two types of truth: tautologies, established through formal mathematics or logic; and factual statements that can be verified by employing the ‘scientific method’ to guide observation and analysis. A principal of Empiricism is that while ‘truth’ might be unachievable, the scientific method will converge towards a close approximation of true facts. European Empiricism has its roots in Greek Epicureanism and became dominant in British philosophy through Francis Bacon, John Locke, David Hume and J. S. Mill. Logical Positivism, a form of Empiricism, emerged in Vienna in the early twentieth century and became significant in North America in the 1940s following the emigration from Nazi Germany of, amongst many others, Hans Reichenbach and Rudolph Carnap.
The Empiricists rejected the metaphysics of Realism, but generally did not challenge the status of mathematics and created a special class of truth related to Hilbert’s Formalism. To appreciate the distinction between Realism and Empiricism, a Realist might claim that “2 + 2 = 4 was true at the time of the dinosaurs”, implying the mathematics is independent of human thought (synthetic a priori); an Empiricist would claim the statement is a tautology: 2 := 1 + 1, 4 := 1 + 1 + 1 + 1 and so 2 + 2 = (1 + 1) + (1 + 1) = 4 (analytic a posterior).
Within economics, Realism is associated with Neo-classical theories that employ equilibrium and rationality and resort to ceteris paribus arguments to explain why economic facts (what is experienced) rarely conform to Neo-classical theory [Arnold and Maier-Rigaud2012]. Contemporary economics in the ‘Logical positivist’ spirit includes experimental and behavioural economics (Vernon Smith, Daniel Kahneman) with the field of neuroeconomics being an emerging exemplar [Camerer et al.2005].
Realism and Empiricism, foundational theories, are both built on the idea that ‘truth’ is a static relationship to some reality that is external to the thinker. Pragmatism, on the other hand, argues that ‘truth’ is just ‘warranted assertability’, what ‘competent, rational enquiry’ produces and it is pointless to try and identify some ultimate indubitable and immutable ‘Truth’.
For example, Poincaré argued that if the Earth was covered in thick clouds, so that the stars were never visible, at some point a Copernicus will “come at last” to argue that
It is more convenient to suppose the earth turns round, because the laws of mechanics are thus expressed in much more simple language. [Poincaré1902 (2001), pp 89—91]
and then he goes on to say
these two propositions “the earth turns round,” and “it is more convenient to suppose that the earth turns round,” have one and the same meaning. [Poincaré1902 (2001), p 91]
Pragmatists deal with the contingency of ‘truth’ by adhering to the principle of ‘fallibilism’, an acceptance that we can be wrong in our beliefs and we can be justified in being wrong. Fallibilism is balanced by the principle of ‘experimentalism’; problems can be resolved by trying out different approaches to their solution. The process involves discourse, amongst those who might disagree, so pluralism is admired and ‘Theory’ does not take precedence over ‘Practice’, as it often does with foundational approaches. Critical in preventing Pragmatism from becoming an instrument to attain ends, is that it is not only means that might change as a result of Pragmatic reflection, but also ends. ([Danisch2007] [Putnam2002, pp 97—134])
Pragmatism emerged in the late nineteenth century with Charles Peirce, William James and John Dewey and was revived in the 1970s by Richard Rorty, Hilary Putnam and Robert Brandom. While closely associated with American philosophy, there have been Pragmatic strands in French thought, sometimes associated with Greek Sophism, notably the ‘occasional Pragmatism’ of Henri Poincaré [Heinzmann2010] and Émile Durkheim acknowledged the usefulness of Pragmatism in destroying “the cult of truth” [Laufer2009], [Durkheim and Allcock1983, pp 69-72]. Pragmatism overlaps Empiricism (e.g. Charles W. Morris, W.V.O. Quine) in its criticism of Realism, and Realism (e.g. C.S. Peirce, Hilary Putnam) in its criticism of Empiricism [Rorty1982, pp xvi—xvii].
There are two metaphors discussed by Thagard and Beam [Thagard and Beam2004] that are useful when approaching Pragmatism. Peirce challenged classical Realism by arguing that ‘reasoning’ was not a chain of deductions that is reliant on the ‘weakest link’ holding, but rather a body of knowledge is like a cable with each fibre of the cable representing a belief: if a fibre fails the cable remains in place. Otto Neurath challenged Empiricism by presenting a body of knowledge as a ship and scientists (sailors) must maintain the ship (revise beliefs) at sea, they do not have the opportunity to completely rebuild the ship.
Pragmatism does not assign a special status to mathematics, in the way that Realism and Empiricism do, meaning that mathematics is more tightly integrated into the approach. This is characterised by the fact that a number of significant Pragmatists, such as Peirce, Poincaré and Putnam, were also prominent mathematicians. Putnam argues that
we learn what mathematical truth is by learning the practices and standards of mathematics itself, including the practices of applying mathematics. [Putnam2004, p 66]
Important advocates of a what might be described as a Pragmatic approach to mathematics, challenging both Realism and Formalism and acknowledging the social nature of mathematics, are Philip Davis, Reuben Hersh (e.g. [Davis and Hersh1990], [Hersh1998]) and Sal Restivo [Restivo and Bauchspies2006].
Pragmatism is being associated with a revival of ‘classical economics’ [Martins2011], is close to Pasinetti’s description of the Cambridge School of Keynesian Economics [Pasinetti2005], relates to Deirdre McCloskey’s economics founded on rhetoric (discourse) [McCloskey2010], has been linked to behavioural economics [Khalil2004] and institutional economics [Barbalet2008]. Pragmatic approaches are distinguished by acknowledging ethical features of economic behaviour and place a greater emphasis on uncertainty ([James1896 (2009], [Dewey2005]). For example, Friedman’s argument in The Methodology of Positive Economics appears to share principles of Pragmatism [Khalil2004, p 2]: “[Positive economics’] performance is to be judged by the precision, scope, and conformity with experience” [Friedman1953, p 4]. However, Friedman’s rejection of a normative dimension to economics and a faith in the ability to verify stable economic theories makes it incompatible with mainstream Pragmatism.
Putnam’s criticises the Fact/Value Dichotomy [Putnam2002] with the observation that when Empiricists insist on the distinction, they are exclusive in associating values with ethics. Concepts such as ‘coherence’, ‘plausibility’, ‘simplicity’, and so forth, are also values and Empiricists implicitly regard these values as objective, raising the question whether ethical values are also objective. Central to this observation is the belief that values are embedded in scientific processes; they are so much part of life that we cannot avoid them.
Ethical frameworks, in the Western tradition, are usually classed as being either Deontological, Consequentialist or Virtuous. Deontology can be typified as “Thou shalt / shalt not” and guides action on the basis of laws, rule or principles. Since an individual cannot be subject to a law unless it has been promulgated, Deontology is linked to with philosophical systems that are based on ‘divine’ or ‘natural’ law, such as Realism and Stoicism [Anscombe1958, p 14]. The practical problem with Deontological Ethics is that basic rules such as “Thou shalt not kill” have caveats while other prohibitions become redundant, or need revising, as society evolves. In the context of contemporary economics, Deontological Ethics has been employed in financial regulation (Pillars I & II of Basel II) and has been criticised for being over-bureaucratic and rigid while susceptible to ‘gaming’, adhering to the letter of the law but not the spirit. [Van Staveren2007, pp 23—26]
Consequentialism attempts to judge the value of an action in terms of its consequences. This approach has its roots in ancient Chinese Mohism and Greek Epicureanism, developed in opposition to Platonism and Stoicism. The approach became fully developed in the nineteenth century with a trio of British philosophers, Bentham, Mill and Sedgewick, who argued that one should “Act always in such a way as to promote the greatest happiness to the greatest number”.
On the basis of Consequentialism and David Hume’s distinction of ‘what is’ and ‘what ought to be’, ‘value—neutrality’ was established in economics: since we have ‘objective access’ to the empirical world’ and are ‘rational beings’, we are able to calculate the consequences of our economic actions [Wilber and Hoksbergen1986]. A problem with this value-neutrality, described by Robert Heilbroner, is that it misses the critical fact that
the objects observed by the social scientist all possess an attribute that is lacking in the objects of natural universe. This is the attribute of consciousness — of cognition, of “calculation”, of volition [Heilbroner1973, p 133]
The importance of ‘volition’ had been recognised by Oskar Morgenstern, who objected to perfect foresight based on calculation because
always there is exhibited an endless chain of reciprocally conjectural reactions and counter-reactions. This chain can never be broken by an act of knowledge but always through an arbitrary act — a resolution. [Mirowski1992, quoting Mogernstern on p 129]
Practically this means that while we could incorporate the possibility of a Japanese earthquake into the modelling of asset prices, it would be impossible to account for the behaviour of Nick Leeson in destroying Barings’ Bank.
As well as questioning the basic ability to predict in an social context, Consequentialism has been criticised because obviously immoral acts, such as the execution of the innocent, could be justified either by the hope of good consequences or the fear of bad [Anscombe1958, p 14]. In response to these problems, many argue that ethics should focus on the judgement of the agent taking the action that has consequences, or Virtue Ethics.
Virtue Ethics, in the European tradition, is associated with Aristotle, in particular Nicomachean Ethics in which virtues are the “characteristics that enable individuals to live well in communities” [Pojam1998, p 247]. Aristotle’s ethics do not distinguish reason and emotion, as Hume did in the eighteenth century, nor do they define absolute standards, rather Virtue is a consequence of personal reflection [Van Staveren2001, pp 6—8]. This opens Virtue Ethics to the criticism that it cannot be codified into a set of rules that any person could apply to determine ethical action in any situation. However, this criticism assumes such a reduction is possible, and implicit in this is that the environment is stable and predictable. The advantage of Virtue Ethics is precisely that it can accommodate unforeseen circumstances.
However, Virtue Ethics is open to the criticism of Relativism. For example, Abelard, who was the first western European to highlight the tripartite classification of ethics in Dialogue of the Philosopher with the Jew and the Christian, was condemned as a heretic on the basis that he argued that those who were responsible for the crucifixion of Jesus Christ were not necessarily doing wrong if they believed they were fulfilling their social obligations [Luscombe1997, p 53].
Medieval Scholars approached Virtue Ethics using the same framework that they used to study physics or medicine, by blending elements, or humours, in the right manner. They identified seven elements of morality, the four ‘Cardinal’ virtues; Courage; Justice; Temperance; and Prudence, and three, so-called, ‘Christian’ virtues: Faith; Hope; and Charity. For example, blending (tempering) Justice, Courage and Faith result in honesty [McCloskey2007, p 361]. An ethical life was one that exhibited all, not just some, of the virtues and anyone, priest prince or merchant, was virtuous providing they got the balance right.
While Virtue Ethics is often associated with Catholicism, all seven virtues, including Faith, Hope and Charity, existed in pre-Christian Greek and Roman philosophy, which influenced both Judaic and Islamic thought. Chinese and Indian philosophy both have their own versions of Virtue Ethics that can be mapped onto the Catholic framework. Particularly relevant is the first century Mahayana Buddhist Vimalakirti Sutra that tells the story of how a virtuous merchant instructs both kings and monks.
While it is conventional to associate Deontology with Realism and Consequentialism with Empiricism, it is not so well established to associate Virtue Ethics with Pragmatism, but there are links.
Aristotle notes that intellectual excellence develops with teaching while excellence of character [ethike] derives from ‘habituation’ [ěthos] [Broadie and Rowe2011, 1103a15—20]. This can be related to the technical term ‘Pragmatism’, which is derived from the Greek word describing ‘deed, act, affair, matter, business’ [pragma] and both words are more closely associated with ‘practice’ rather than ‘theory’,
Khalil notes that “true [Pragmatic] inquiry cannot take place in an ivory tower” [Khalil2004, p 2] and discourse is central to Pragmatism. Putnam admires Jürgen Habermas’ position on ‘communicative action’. Habermas defines a ‘norm’ as a “universally valid statement of obligation”, where as a ‘values’ are culturally specific. The “binding universal norm” is ‘communicative action’, “norms of communication governed by the ideal of rational discourse” and the ideal of rational discourse is governed by
the norm of sincerity, the norm of truth-telling, and the norm of asserting only what is rationally warranted †[and] is contrasted with manipulation. [Putnam2002, pp 113-114]
Putnam goes on to say
assuming we have a community of human beings who do regard the ends of others as important, and who do not assume that there own ends should override — Habermas’s approach is to assume that disagreement about what ethical life concretely requires of us is a fact of life, something that will not go away. [Putnam2002, p 115]
Ethics in Pragmatism is not dependent on an act or its outcome, but the agent performing an act which may have unforeseen consequences.
Albert Hirschman has provided a description of four different views on the relationship between markets and morality: doux-commerce, self-destruction, feudal-shackles and feudal-benefits [Hirschman1982].
The idea that commerce improved society was prevalent throughout the eighteenth century. In 1704 technical text on commerce argues “Commerce attaches [men] to one another through mutual utility”, while in The Rights of Man (1792) Thomas Paine writes “[Commerce is a pacific system, operating to cordialise mankind”. In the intervening years Montesquieu, Hume, Condorcet and Adam Smith all agreed that commerce was a powerful civilising agent, promoting honesty, industriousness, probity, punctuality, and frugality, in contrast to the excesses of absolute monarchies.
Following the Industrial Revolution, these attitudes all but disappeared and were replaced by views that blamed the collapse of morality on the influence of capitalism. Commerce was seen as commodifying human interaction, “custom is replaced by contract”, and on this basis Romantics saw capitalism as being un-natural, undermining conservative hierarchies while Marxists believed that the alienation of the proletariat along with capitalism’s instabilities would lead to revolution. Others believed that the success of capitalism, founded on frugality and probity, would eventually be so great that society would become dissolute, seeking instant gratification, echoing the rise of Republican Rome and the fall of Imperial Rome.
Both the doux and self-destructive views of commerce represented capitalism as a powerful force driving social change. When capitalism did not collapse, the emphasis changed and capitalism was not seen as strong but weak: the bourgeoisie were unable to escape traditional social forces. Marx, while arguing that English capitalism would destroy itself, also argued that German capitalism was hindered by antiquated social and political structures. For Schumpeter, in The Sociology of Imperialisms written during World War I, Weber’s ‘spirit of capitalism’ was no where in the warmongering of the age. Schumpeter’s views contrasted to the optimism of the pre-war sociologists Durkheim and Simmel who both saw echoes the ties that bound traditional societies in contemporary commercial relations.
The United States of America, not bound by “feudal—shackles” seemed to have an advantage over Europe between 1914 and the sixties. Capitalism, led by America, seemed to rediscover its confidence in solving society’s problems after the Second World War. But this confidence was lost with the mass movements of the late sixties and the subsequent economic malaise of the seventies. The problem had been foreseen by Louis Hartz in The Liberal Tradition in America (1955): because America did not have the feudal past of Europe it did not have social and ideological diversity and so reforms, such as Roosevelt’s New Deal, were vulnerable to a “tyranny of the majority”; America missed the feudal—blessings.
The doux-commerce thesis is a powerful argument in favour of markets yet rarely figures in neo-classical economics and Hirschman explains this omission by pointing out that the neo-classical program depends will not accommodate sociological considerations. Hirschman does acknowledge that economics was changing in the early 1980s, with the introduction of behavioural economics, in particular results such as Prisoner’s Dilemma that highlighted the role of co-operation in economic affairs.
Marion Fourcade and Kieran Healy [Fourcade and Healy2007] have recently returned to Hirschman’s characterisation and argue that it is still valid today, but have added a fifth characterisation: Moralized Markets.
Fourcade and Healy identify four strands of the doux-commerce thesis in recent scholarship. Deirdre McCloskey argues that markets nurture “bourgeois virtues” and summarise this view with the observation that
Commerce teaches ethics mainly through its communicative dimension, that is, by promoting conversations among equals and exchange between strangers. [Fourcade and Healy2007, p 287]
Seabright and researchers performing empirical studies on the Ultimatum Game (introduced the year of Hirschman’s thesis, [Güth et al.1982]), argue that commerce fosters co-operation, particularity amongst strangers while others support Hayek’s argument that “Capitalism makes you free”. Finally, some economists look for evidence that markets are the best motor for innovation. In opposition to these strands, economists are arguing that instead of virtue we have envy, instead of co-operation there is coercion, freedom does not equate to populism and creativity is being stifled by copyright.
While economists seem to focus on the robust nature of markets, able to create or destroy society, sociologists tend to study the feebleness of markets. Following Weber, some authors argue that markets are consequences of cultural legacy, of institutions, or that Capitalism takes on different forms in different societies. The Moralized Markets thesis goes further, it characterises markets as ‘cultures’, not simply a consequence of culture, which “are explicitly moral projects, saturated with normativity.” [Fourcade and Healy2007, pp 299-300].
Fourcade and Healy identify three strands of the Moralized Markets thesis. Firstly, there is the view that markets have a role in creating moral boundaries, as McCloskey argues. This approach follows Durkheim, who argued that morality is not fixed by some ‘Ontological’ ethical standard (that is, one fixed and derived from a single issue [Putnam2004, p 19]), rather, morality is defined by the group. This is problematic in that it is virtually impossible to evaluate the role of markets neutrally.
The second strand builds on the first by turning to the sociology of science, where an emphasis is placed on impartiality in evaluating scientific knowledge (i.e. it studies failures as well as successes). A key theme in this approach is to study what Michael Callon called the ‘performativity of markets’, that economic theory drives economic behaviour, rather than economic theory describes economic behaviour (in the words of Donald MacKenzie, financial economics is “An engine not a camera”).
While the second strand focuses on behaviour at the micro level, the third strand considers economic rules at the macro level and how they are saturated with normative considerations. For example, when Friedman made the case for positive economics it was “to make correct predictions” [Friedman1953, p 4] he ignored the question of what determines ‘correct’, and this driven by mutable normative values. For example determining ‘correctness’ has changed with the emergence of the value ‘efficiency’ and the decline of ‘social cohesion’.
Gambling is today regarded as profane, but this was not always the case. For the Greeks, the brothers Zeus, Poseidon and Hades cast lots to divide up the universe. The Hindus believe the world was a game of dice played between Shiva and his wife and at the heart of the epic tale Mahabharata is an, unfair, dice game between the Kauravas and the Pandavas.([Sahlins1972 (2003), p 27], [Brenner and Brenner1990, p 1—5]). Divination by casting lots played an important role in Judaism and the Bible refers to the ‘judgement’ of Urim and Thurim, which scholars today think were two dice ( Exodus 28:30, Leviticus 27:20-21, Samuel I 14:41 see [Brenner and Brenner1990, p 2]).
Gambling was often associated with sacrificial practises that were widespread and are generally known by their Native American name, potlach. Potlach involved the destruction of goods, and seems to have evolved in nomadic groups because they could not store what was not needed and gambling was a means avoiding waste by re-distributing goods before any excess was destroyed. Similar ceremonies are described in Vedic scriptures ([Keynes1936, pp17-19], [Graeber2011, p 56]).
The role gambling plays in archaic societies has been studied by Jon Altman and William Mitchell. Altman studied an Australian aboriginal group around 1980 [Altman1985]. The community had access to social security payments and there was often a surplus left over after essentials had been bought. However, some individuals were excluded from social security payments by the government and there was an “inter—household variability in access to cash”. This variability was seen as a subjective discrimination within the community by the Australian government and gambling “acted effectively to both redistribute cash †[and] provided a means for people with no access income to gain cash” [Altman1985, pp 60-61]. This was important in non-hierarchical communities because it meant that one arbitrary bestowal of money was not corrected by another subjective distribution, such as redistribution by a chief. William Mitchell has considered the role that gambling plays in disrupting hierarchical social structures, such as the Indian caste system, by studying the Wape in New Guinea [Mitchell1988]. The conclusion was that the non-hierarchical society of the Wape was maintained through gambling.
The pervasive nature of gambling in archaic communities, appearing in the Vedic scriptures, potlach ceremonies, aboriginal Australia and New Guinea and the Hazda [Sahlins1972 (2003), p 27] can be explained because it is an objective, ‘fair’, mechanism for the redistribution of wealth. What needs to be recognised is that this process remains valid only so long as no single entity accumulates enough wealth that it can bankrupt all the others.
Gambling had been outlawed in the medieval period, usually because time spent gambling could be better used [Brenner and Brenner1990, p 58]. However, building on Roman practice, lotteries began to be used as means of raising public-finance in the later Medieval period. The first private lottery appeared in the sixteenth century in Italy and the mechanism spread to France and England [Brenner et al.2008, pp 133—138]. The practice culminated in The Million Adventure lottery set up by the English government and drawn in November 1694 [Murphy2009, p 34].
The seventeenth century economist, William Petty, observed that lotteries were “a tax upon unfortunate, self-conceited fools” and from the start of the eighteenth century gambling became increasingly associated with “the waste of time and money; the neglect of familial and business duties; the erosion of social trust; and the severed link between hard work, talent and gain.” [Daston1998, p 161]. However, by the end of the century ‘gambling’, in the form of insurance, had become a legitimate practice if based on rational foundations ([Zelizer1979], [Daston1987]) and in 1774 the Life Assurance Act distinguished between legitimate insurance and illicit gambling and became known as the Gambling Act.
Gabrielle and Reuven Brenner argue that the de-legitimisation of lotteries, and gambling in general, comes about because during the seventeenth and eighteenth centuries there was significant social and economic change. In this environment gambling and speculation provided the ‘lower classes’ with a means to climb up the social ladder [Brenner et al.2008, pp 98—104]. While the lotteries enabled this disruptive social mobility, they were a necessary tool of public finance that prevented the stagnation and crises suffered by states reliant on taxation [Nash2000]. By the start of the nineteenth century, finance had developed to such an extent that governments could tax more effectively, notably the incomes of the middle classes, or to borrow from the middle and upper classes. The working classes could be excluded from the opportunities to get rich that participating in public-finance provided.
The prohibitions on gambling had an important impact on the development of finance. In 1851, following a dispute between two counterparties in a forward contract, English law established that there needed to be ‘intent to deliver’ for a derivative to avoid being classed as an illegitimate gamble [Swan1999, pp 211—213]. While English courts avoided becoming involved in derivative markets, U.S. courts were much more active in restricting speculative behaviour and were vigorous in prosecuting “idlers who made profit even while they slept” [de Goede2005, p 62, quoting Fabian]. One case, brought by the Chicago Board of Trade (CBOT)against Christie-Street Commission Company, which was offering its customers bets on the grain futures prices published by the CBOT, eventually reached the U. S. Supreme Court, who ruled in 1905 that
People will endeavour to forecast the future, and to make agreements according to their prophecy. Speculation of this kind by competent men is the self—adjustment of society to the probable. [de Goede2005, p 71]
Hirschman presents the ‘Industrial Revolution’ as being the “most plausible explanation for the eclipse of the doux-commerce thesis” [Hirschman1982, p 1470]. However, there have been similar societal changes that did not lead to similar attitudinal changes, raising the question as to whether there is a more specific explanation to the eclipse of the doux-commerce thesis.
In 1932 Lionel Robbins defined economics as “the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses”. This can be traced back to John Stuart Mill’s 1836 definition of political economy as being
concerned with [man] solely as a being who desires to possess wealth, and who is capable of judging of the comparative efficacy of means for obtaining that end. [Mill1967]
Mill defended Thomas Malthus’ An Essay on the Principle of Population, which focused on scarcity, in Principles of Political Economy of 1848. Mill was writing at a time when Europe was struck by the Cholera pandemic of 1829—1851 and the famines of 1845—1851 and while Alfred, Lord Tennyson, was describing nature as “red in tooth and claw”.
Between Mill and Robbins is Alfred Marshall who synthesised Mill’s approach to economics with Darwinian metaphors of competition ([Backhouse1985, 10.1], [Thomas1991]). Malthus, Darwin and Mill all worked in culture infused with a belief that chance was being defeated and Aristotle’s class of events that were unpredictable was becoming empty. While contemporary Darwinists reject the idea that evolution is random [Kiontke et al.], in the presence of uncertainty economics becomes an exercise in optimisation, such as of maximising utility. Even when it is acknowledged that there is uncertainty in the future, the economic system is assumed to be ergodic, to have stable parameters, and the economic exercise is one of maximising expected utility. This is a strong assumption with wide implications [Feller1949, p 417—418].
A confidence in determinism has been challenged by the Pragmatists and financial events since the Nixon Shock. In the 26 years between 1945 and autumn 1971, the Bank of England changed its lending rate 41 times, with 30% of these changes occurring between 1966 and 1971. In the 26 years after 1971, it changed them 216 times. After the collapse of Bretton—Woods, a key economic factor had gone from being fairly stable to being a random process. What links contemporary culture with that before 1700 is the understanding that uncertainty has to be accommodated. What characterised much of the nineteenth and twentieth century was a confidence in uncertainty and a concern for scarcity.
We refine Hirschmann’s explanation that the ‘Industrial Revolution’ was responsible for the decline in the doux-commerce thesis by identifying the emergence in a faith in determinism and certainty coinciding with a concern for scarcity. This is not a new observation, Moses ben Maimon (Maimonides) argued that God’s punishment after the Fall of Man was not so much about scarcity but uncertainty in his Guide for the Perplexed, written in 1190 and an influence on the Scholastics. In the Garden of Eden humans had perfect knowledge, which was lost with the Fall, and it is the loss of this knowledge which is at the root of suffering: if we know what will happen we can manage scarcity [Perlman1997].
The relationship between uncertainty and scarcity is a component of the distinction between legitimate investment and illicit speculation. In an attempt to understand this moral distinction Gabrielle and Reuven Brenner identify the three types of market participant, facing the problems of scarcity and uncertainty. Investors are preoccupied with scarcity and defer income. Because uncertainty exposes the investor to the risk of loss, investors wish to minimise uncertainty at the cost of potential profits. Gamblers will bet on an outcome taking odds that have been agreed on by society such as with a sporting bet or in a casino. Gambling is rational in two circumstances, when the gambler has an excess of resources and can afford to lose the stake: on course betting for the rich has never been restricted, or when the gambler is facing certain ruin/extinction and so they have nothing to lose but much to gain by taking the gamble. ‘Speculators’ bet on a mis-calculation of the odds quoted by society and explains why speculators are regarded as socially questionable: they have opinions that are explicitly at odds with the consensus, they are practitioners who rebel against a theoretical ‘Truth’ ([Brenner and Brenner1990, p 91], [Beunza and Stark2012, p 394]). This is captured in Arjun Appadurai argument that the leading agents in modern finance
believe in their capacity to channel the workings of chance to win in the games dominated by cultures of control †[they] are not those who wish to “tame chance” but those who wish to use chance to animate the otherwise deterministic play of risk [quantifiable uncertainty]”. [Appadurai2011, p 533-534]
The philosophical antecedents of the modern speculators, betting against determinism can be found in medieval Franciscans such as Pierre Jean Olivi and John Duns Scotus. The Dominican, empirical rationalist, Aquinas argued that knowledge rested on reason and revelation and so God could be understood by rational examination of nature. The fideist Scotus argued that this placed unjustifiable restrictions on God, who could interfere with nature at will: God, and nature, could be capricious [Luscombe1997, p 127].
Appadurai was motivated to study finance by Marcel Mauss’ essay Le Don (‘The Gift’), exploring the moral force behind reciprocity in primitive and archaic societies. The relationship between fairness, reciprocity and markets has been studied in the context of the so—called ‘Ultimatum Game’ [Thaler1988]. The ‘Golden Rule’ of reciprocity appears to be behaviour learnt in the social context of market exchange and is fundamental to human civilisation ([Murnighan and Saxon1998], [Henrich et al.2004], [Henrich et al.2006], [Jensen et al.2007]).
Appadurai notes that the contemporary financial speculator is “betting on the obligation of return” [Appadurai2011, p 535]. The role of this balanced reciprocity in finance can be seen as an axiom in that it lays the foundation for subsequent analysis, it can also be seen as a simplifying assumption: if the future is uncertain what mechanism ensures that agreements will be honoured. When Daniel Beunza and David Stark observe, echoing Ramsey, that in finance “to be opportunistic you must be principled, i.e. you must commit to an evaluative metric” [Beunza and Stark2004, p 372], the assumption in reciprocity is part of this evaluative framework.
David Graeber also recognises the fundamental position reciprocity has in finance [Graeber2011], but where as Appadurai recognises the importance of reciprocity in the presence of uncertainty, Graeber essentially ignores this fundamental issue in his analysis that ends with the conclusion that “we don’t ‘all’ have to pay our debts” [Graeber2011, p 391]. In advocating that reciprocity need not be honoured, Graeber is not just challenging contemporary capitalism but also the foundations of civil society in the Golden Rule, based on equality and reciprocity [Graafland2010, p 235].
In the presence of uncertainty, society needs reciprocity, if there is no certainty in what the future holds we need to trust that our debts, whether physical or metaphysical, are going to be repaid. Determinism emerged as the dominant scientific principle, initially with the Augustinian probabilists of the seventeenth century, then with the post Revolutionary science of Laplace. As life became predictable, an emphasis of dealing with uncertainty was replaced by one of dealing with scarcity and the fact/value dichotomy became embedded into culture.

References

   J. Altman. Gambling as a mode ofredistributing and accumulating cash among Aborigines: a case studyfrom Arnhem Land. In G. Caldwell, M. Dickerson, B. Haig, and L. Sylvan, editors, Gambling in Australia, pages 50—67. Croom Helm, 1985.
   G. E. M. Anscombe. Modern moralphilosophy. Philosophy, 33(124):1—19, 1958.
   A. Appadurai. The ghost in the financial machine. Public Culture, 23(3):517—539, 2011.
   D. Arnold and F. Maier-Rigaud. The enduring relevance of the model Platonism critique for economics and public policy. Journal of Institutional Economics, 8:289—294, 2012. 
   Augustine of Hippo. On Free Choice of the Will translated by T. Williams. Hackett, 1993.
   R. Backhouse. A History of Modern Economic Analysis. Blackwell, 1985.
   J. Barbalet. Pragmatism and economics: William James’ contribution. Cambridge Journal of Economics, 32(5):797—810, 2008.
   D. Beunza and D. Stark. Tools of the trade: the socio-technology of arbitrage in a Wall Street tradingroom. Industrial & Corporate Change, 13(2):369—400, 2004.
   D. Beunza and D. Stark. From dissonanceto resonance: cognitive interdependence in quantitative finance. Economy and Society, 41(3):383—417, 2012.
   R. Brenner and G. A. Brenner. Gambling and Speculation: A theory, a history and a future of some human decisions. Cambridge University Press, 1990.
   R. Brenner, G. A. Brenner, and A. Brown. A World of Chance, Betting on Religion, Games, Wall Street. Cambridge University Press, 2008.
   S. Broadie and C. Rowe. Aristotle: Nicomachean Ethics: Translation, Introduction, Commentary. Oxford University Press, 2011.
   C. Camerer, G. Loewenstein, and Drazen Prelec. Neuroeconomics: How neuroscience can inform economics. Journal of Economic Literature, 43(1):9—64, 2005.
   R. Danisch. Pragmatism, Democracy, and the Necessity of Rhetoric. University of South Carolina Press, 2007.
   L. J. Daston. The Domestication of Risk: Mathematical probability and insurance 1650—1830. In L. Kruger, L. J. Daston, and M. Heidelberger, editors, The Probabilistic Revolution: Volume 1: Ideas in History. MIT Press, 1987.
   L. J. Daston. Classical Probability in the Enlightenment. Princeton University Press, 1998.
   P. J. Davis and R. Hersh. The Mathematical Experience. Penguin, 1990.
   M. de Goede. Virtue, Fortune and Faith. University of Minnesota Press, 2005.
   J. Dewey. The Quest for Certainty: A Study of the Relation of Knowledge And Action. Kessinger Publishing, 2005.
   É.D. Durkheim and J.B. Allcock. Pragmatism and Sociology. Cambridge University Press, 1983.
   W. Feller. On the theory of stochastic processes, with particular reference to applications. In J. Neyman, editor, Proceedings of the First (1945/46) Berkeley Symposium on Mathematical Statistics and Probability, pages 403—432. University of California Press, 1949.
   M. Fourcade and K. Healy. Moral views ofmarket society. Annual Review of Sociology, 33:285—311, 2007.
   M. Friedman. The methodology of positive economics. In M. Friedman, editor, Essays In Positive Economics, pages 3—43. Univ. of Chicago Press, 1953.
   J. J. Graafland. Do markets crowd out virtues ? An Aristotelian framework. Journal of Business Ethics, 91:1—19, 2009.
   J. J. Graafland. Calvins restrictions on interest: Guidelines for the credit crisis. Journal of Business Ethics, 96(2):233—248, 2010.
   D. Graeber. Debt: The first 5,000 years. Melville House, 2011.
   W. Güth, R. Schmittberger, and B. Schwarze. An experimental analysis of ultimatum bargaining. Journal of Economic Behavior & Organization, 3(4):367 — 388, 1982.
   R. L. Heilbroner. Economics as a ‘Value-Free’ science. Social Research, 40(1):129—143, 1973.
   G. Heinzmann. Henri Poincaré’s and his thoughts on the philosophy of science. In E. Charpentier, E. Ghys, and A. Lesne, editors, The Scientific Legacy of Poincaré. American Mathematical Society / London Mathematical Society, 2010.
   J. Henrich, R. Boyd, S. Bowles, C. Camerer, E. Fehr, and H. Gintis. Foundations of Human Sociality. Oxford University Press, 2004.
   J. Henrich, R. McElreath, A. Barr, J. Ensminger, C. Barrett, A. Bolyanatz, J. C. Cardenas, M. Gurven, E. Gwako, N. Henrich, C. Lesorogol, F. Marlowe, D. Tracer, and J. Ziker. Costly punishment across human societies. Science, 312:1767—1770, 2006.
   R. Hersh. What Is Mathematics, Really? Vintage, 1998.
   A. O. Hirschman. Rival interpretations of market society: Civilizing, destructive, or feeble? Journal of Economic Literature, 20(4):1463—1484, 1982.
   W. James. The dilemma of determinism. In W. James, editor, The Will to Believe and Other Essays in Popular Philosophy, pages 145—183. Longmans Green & Co. (Project Gutenburg), 1896 (2009).
   K. Jensen, J. Call, and M. Tomasello. Chimpanzees are rational maximizers in an ultimatum game. Science, 318:107—108, 2007.
   J. M. Keynes. The general theory of employment, interest and money. Macmillian, 1936.
   E.L. Khalil. Dewey, Pragmatism, and Economic Methodology. Routledge /Chapman & Hall, 2004.
   K. Kiontke, A. Barrière, I. Kolotuev, B. Podbilewicz, R. Sommer, D. H. A. Fitch, and M.-A. Félix. Trends, stasis, and drift in the evolution of nematode vulva development. Current Biology, 17(22):1925 — 1937.
   R. Laufer. New rhetoric’s empire: Pragmatism, dogmatism, and sophism. Philosophy and Rhetoric, 42(1):326—348, 2009.
   D.E. Luscombe. Medieval Thought. Oxford University Press, 1997.
   N. Martins. The revival of classical political economy and the cambridge tradition: From scarcity theory to surplus theory. Review of Political Economy, 23(1):111—131, 2011.
   D. N. McCloskey. The Bourgeois Virtues: Ethics for an Age of Commerce. University of Chicago Press, 2007.
   D. N. McCloskey. Bourgeois Dignity: Why economics Can’t Explain the Modern World. University of Chicago Press, 2010.
   J. S. Mill. On the definition of political economy; and on the method of investigation proper to it. In J. M. Robson, editor, The Collected Works of John Stuart Mill, Volume IV - Essays on Economics and Society Part I,. Routledge, 1967.
   P. Mirowski. What were von Neumannn and Morgenstern trying to accomplish?. In E. R. Weintraub, editor, Toward a History of Game Theory, pages 113—150. Duke University Press, 1992.
   W. E. Mitchell. The defeat of hierarchy: Gambling as exchange in a Sepik society. American Ethnologist, 15(4):638—657, 1988.
   J. K. Murnighan and M. S. Saxon. Ultimatum bargaining by children and adults. Journal of Economic Psychology, 19:415—445, 1998.
   A. L. Murphy. The Origins of English Financial Markets. Cambridge University Press, 2009.
   R. C. Nash. The economy. In J. Bergin, editor, The Seventeenth Century: Europe 1598-1715. Oxford University Press, 2000.
   L. L. Pasinetti. The Cambridge School of Keynesian Economics. Cambridge Journal of Economics, 29(6):837—848, 2005.
   M. Perlman. Looking for ourselves in the mirror of the past. In B. B. Price, editor, Ancient Economic Thought, chapter 3, pages 61—75. Routledge Studies in theHistory of Economics, 1997.
   H. Poincaré. Science and hypothesis. In S. J. Gould, editor, The Value of Science: Essential Writing of Henri Poincaré. Modern Library, 1902 (2001).
   L. P. Pojam. Classics of Philosophy. Oxford University Press, 1998.
   H. Putnam. Ethics without Ontology. Harvard University Press, 2004.
   Hilary Putnam. The Collapse of the Fact/Value Dichotomy and Other Essays. Harvard University Press, 2002.
   S. Restivo and W. Bauchspies. The will to mathematics: Minds, morals, and numbers. Foundations of Science, 11:197—215, 2006.
   R. Rorty. The Consequences of Pragmatism: Essays, 1972-1980. University of Minnesota, 1982.
   M. Sahlins. Stone Age Economics. (Routledge), 1972 (2003).
   E. J. Swan. Building the Global Market: A 4000 year history of derivatives. Kluwer Law, 1999.
   P. Thagard and C. Beam. Epistemological metaphors and the nature of philosophy. Metaphilosophy, 35(4):504—516, 2004.
   R. H. Thaler. Anomalies: The ultimatum game. The Journal of Economic Perspectives, 2(4):195—206, 1988.
   B. Thomas. Alfred Marshall on economic biology. Journal of Financial Intermediation, 3 (1):1—14, 1991.
   I. Van Staveren. The Values of Economics: An Aristotelian Perspective. Routledge, 2001.
   I. Van Staveren. Beyond utilitarianism and deontology: Ethics in economics. Review of Political Economy, 19(1):21—35, 2007.
   C. K. Wilber and R. Hoksbergen. Ethical values and economic theory: A survey. Religious Studies Review, 12(3/4):208—214, 1986.
    V.A.R. Zelizer. Morals and Markets: The Development of Life Insurance in    the United States. Columbia University Press, 1979.  

Tuesday, 2 April 2013

Enlightenment Exchange: forecasting the future


I was due to be participating in the Edinburgh International Science Festival as part of the  Enlightenment Exchange on forecasting the future, however I am recovering from surgery and so will not make it.  This is an outline of what I planned to talk about.

Needham’s Question is why did the development technology in western European accelerate much faster than in China after 1600.

The issue that Needham wanted to tackle was that China had the physical   and intellectual resources, mathematics, alchemy, astrology and magic, just as Renaissance Europe did, but it did not develop science as Europe did.

One key distinguishing feature between the science that emerged in western Europe in the seventeenth century and other scientific cultures was the use of mathematics.  Aristotle, and his heirs, did not think that physics was reducible to mathematics, similarly the Chinese and Indians did not apply maths to solving scientific problems in the way Newton and Clerk Maxwell did.

One answer to why European science adopted mathematics lies in medieval European finance.  Medieval Western Europe was unique in having to deal simultaneously with a heterogeneity of currency and prohibitions of usury. Muslims had the usury prohibitions but homogeneous currency, the Chinese were lax on usury and generally had homogeneous currencies..

In Western Europe, any local lord would mint their own coin, as soon as they had the power to do so, Italy had 28 currencies in the High Middle Ages while the single authority that ruled the Kingdom of France used  three currencies.  Meanwhile, merchants were prevented from charging for the use of money, usury, but they could ask for compensation for risk, interest.  The skill came in treading a fine line between usury and interest under the scrutiny of the Catholic Church.

As a consequence medieval finance was not simple, on the contrary, having to deal with uncertainty and a complex regulatory system, it was highly sophisticated.  The “modern” financial techniques, such as asset backed securities, collateralisation - “slicing and dicing” - and credit default swaps, were all developed by Europe’s merchants between Charlemagne’s reign and the discovery of North America.

The solution to the problems that Medieval European merchants faced was mathematics, specifically the mathematics Fibonacci described in his 1202 text, the Liber Abaci.  Fibonacci’s mathematics revolutionised European commercial practice.  Prior to the Liber Abaci, merchants would perform a calculation, using an abacus, and then record the result.  The introduction of Hindu/Arabic numbers in the Liber enabled merchants to “show their working” as an algorithm, and these algorithms could be discussed and improved upon.  Essentially after Fibonacci mathematics ceased to be simply a technique of calculation but became a rhetorical device, a language of debate.

The Liber, and the abacco schools that emerged across Europe to train merchants, separate to  the Universities, disseminated and developed practical mathematics and the influence of this training was profound.  The “Merton Calculator” Thomas Bradwardine, who  would have been familiar with medieval mercantile practice and would leave Oxford to to work for the Treasurer of England before becoming the Archbishop of Canterbury  wrote in 1323
 “[Mathematics] is the revealer of genuine truth, for it knows every hidden secret and bears the key to every subtlety of letters. Whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.”
Copernicus, who wrote on money before he wrote on planets, Simon Stevin, the founder of the Dutch Mathematical School that inspired Descartes, Thomas Gresham, Francis Bacon’s influential uncle who established  the first Chair in Mathematics in England and laid the foundations for the Royal Society,  were all trained in the abbaco tradition.

Newton, who spent as much time as Master of the Mint as he did as an academic, stood on the shoulders of merchants.  His derivation of calculus comes from writing a function as a polynomial, mimicking Stevin’s representation of a number as a decimal fraction.

Between 1650 and 1713 extraordinary advances were made in the the mathematical theory of chance in the context of the “fair” pricing of commercial contracts in the context of Christian morality: Faith was associated with statistics, Hope with probability.  The modern conception of probability theory as being based on performing repeatable experiments was simultaneously presented in 1713 by de Moivre and Montmort, this was taken up by Laplace a hundred years later when he argued that nothing was random, it was just humans lacked knowledge to appreciate the links between cause and effect.
“We look upon something as the effect of chance when it exhibits nothing regular,or when we ignore its causes”
To Laplace and scientists that came after him, the problem of uncertainty could be resolved by gathering more data, the mathematics of chance, which developed in the context of ethical finance before calculus was developed in the context of physics, was reduced to the Law of Large Numbers.  Economics developed in the context of deterministic models based on analogies from physics or biology.

The significance of randomness in physics started to emerge in the second half of the nineteenth century in the context of thermodynamics, leading to Einstein’s analysis of Brownian motion, which explained random behaviour of pollen particles in terms of “invisible” atoms, and then in the 1920s with the Copenhagen Interpretation of Quantum Mechanics, prompting Einstein to state that he did not believe God played dice.  Meanwhile, in biology, R A Fisher synthesised Darwinian evolution with Mendelian genetics and in the process revolutionised statistics, the analysis of data.  Meanwhile  economists, such as the American Frank Knight and John Maynard Keynes, started placing uncertainty at the heart of Economics.

At the outbreak of the war in 1939 the vast majority of soldiers and politicians would not have thought mathematicians had much to offer the military effort, an orthodox attitude amongst the military is still that “war is a human activity that cannot be reduced to mathematical formulae”.  However, operational researchers  laid the foundations for Britain's survival in the dark days of 1940-1941. Code-breakers transformed seemingly random streams of letters into messages that enabled the allies to keep one step ahead of the Nazis while Allied scientists had ensured that the scarce resources of men and arms were effectively allocated to achieving their military objectives. By the end of the war General Eisenhower was calling for more scientists to support the military.

During the war many economists had worked alongside mathematicians solving military problems, such as Paul Samuelson.  In the post war decades mainstream economics transformed itself from a discursive discipline into a mathematical science.  However the biggest change in the field came in 1972 with the Nixon Shock and the collapse of the Bretton-Woods system of exchange rates.  Overnight finance transformed from a broadly deterministic system, fixed exchange rates, static interest rates and constant commodity prices, into a stochastic system.  As exchange rates fluctuated, interest rates started changing monthly and the commodity prices became a random processes.

The markets evolved quickly in response to the changed environment.  Financial instruments that had not been a feature of financial economics since 1914 re-appeared, and over the next decades techniques that would have been familiar to Renaissance bankers like the Fuggers, such as securitisation, emerged to cope with the fundamental uncertainty of the markets.

Mathematics enables science without experiments, the Large Hadron Collider was built on the basis of a mathematical theory, and so is essential in the markets that are too dynamic for experimentation.  The question is, was the post-Laplacian science, with an implicit rejection of randomness, up to the task of  dealing with the fundamentally uncertain markets?

The UK’s Financial Services Authority in their 2009 review of the Financial Crisis of 2007-2009 identified a “mis-placed reliance on sophisticated mathematics” as a root cause of the Crisis.  Last June, the Director of Financial Stability at the Bank of England, identified basic flaws in mathematical understanding as a “top 5 but not top 3” cause of the crisis, more significant was the fact that Banks were not maintaining adequate records of their loan portfolios.  The Financial Crises since 2007 have been less to do with fancy finance backed up by even fancier maths, it was more to do with banks, and their regulators, not keeping an eye on their core business of lending prudentially.  It is worth noting that Fred Goodwin at RBS and Andy Horner at HBOS both came from outside banking.

But the facts are dull, it is more interesting, and convenient for many, to talk about the slicing and dicing of loan portfolios as the cause of the Crisis.  In the aftermath of the Crisis, the technology magazine Wired identified the “Formula that Destroyed Wall Street”, the Gaussian Copula.  The formula is a function that captures the distribution of loan defaults in an abstract  portfolio of infinitely many infinitesimally small loans based on a single parameter,rho,  representing the dependence of loans in the portfolio failing.  If rho=0 then the loans were completely independent, one default would not affect any other loan,  if rho=1.0 they were completely dependent, one default would lead to all the loans to default.  This formula was applied to Mortgage Backed Securities across investment banks with rho set at 0.3.  This choice of rho was based on historical data based on the defaults of corporate bonds, and it resulted in low chances of significant portfolio defaults.  (For a full analysis see MacKenzie and MacKenzie and Spears)

What is most significant about the Gaussian Copula is that it was popularised in investment banking by J.P. Morgan, a very old fashioned bank, who relied on the moral character of their employees and employed a lot of good mathematicians.  J.P. Morgan did not create, distribute or invest in many Mortgage Backed Securities.  The reason is described in Gillian Tett’s book on the crisis, Fool’s Gold.  The mathematicians at Morgan’s reverse engineered prices of traded MBS and deduced that they were generally based on rho=0.3, the bankers then asked themselves was this reasonable, and decided that since corporations where different to mortgage borrowers, it was not.  rho should be higher indicating a greater probability that if one homeowner defaulted, another would.  On this basis, of a rho=0.5,  there was no chance of making a profit on MBS.  J.P. Morgan were right, other banks, who relied on rho=0.3, were wrong.

Were the failed banks bad scientists as well as bad bankers?  While the banks that chose rho=0.3 were wrong, their behaviour was not too different from that encountered in more traditional branches of science and engineering.  Official assessments of the probability of a serious failure of a nuclear power plant do not match the empirical evidence that the have been 5 major failures of commercial, not just experimental, nuclear power plants, most recently at Fukushima.  Similarly, in the 1980s, the official NASA assessment of  the probability of a Shuttle failure was 1 in 10,000, while engineers on the shopfloor reckoned it to be 1 in 200.  In fact, reading Richard Feynman’s Appendix to the Rogers’ Commission Report on the Challenger Failure is interesting in context of the banking failures.

A common feature of the under-reporting of the chances of failure in nuclear engineering, NASA and banking has been a belief in “perfect” systems so that data that can be extrapolated from the known into the unknown.  Today, as “big data” becomes the current buzz-word, with Wired declaring in 2008 the “end of theory”, the power of data enables the scientific method, that searches for coherence and causality, to be replaced by the identification of correlations.

To understand why this is relevant, observe that the Financial Crisis on 2007-2009 was not a global event, whatever Gordon Brown says.  While British and American banks failed, German, and particularly French, banks did not.  At the time there was anger in the Anglo-Saxon banking community, who knew their Continental colleagues were involved in exactly the same practices but did not report the staggering losses.  When a prominent mathematician at a major French bank was asked about this, his response was candid and logical: “We thought the pricing models were weak before the crisis, we knew they were wrong during the crisis.  Why ruin the bank by reporting numbers we knew were wrong?”.  In 2009, The Economist, a tub-thumper for Anglo-Saxon culture, reported with glee on the problems at Societe General caused by the fraud of Jerome Kerviel.  They observed that the problem with French risk managers is that their attitude is ‘That is all very well in practice, but what about the theory”.  It was precisely this belief in placing data in the context of a theory that prevented the failure of French banks, the more empirical, pragmatic Anglo-Saxon approach led to disaster.

The malevolent impact of “social physics”, aggregating a data set into a representative point on which decisions are based, ignoring the distribution, is particularly resonant for me at the moment.  SInce January I had been suffering gastric problems.  Based on my symptoms the initial assessment was that I had gallstones, a prognosis that was confirmed by ultrasound.  However, this evidence, when presented to a consultant,  was contradicted by a brute fact that it is unusual for men in my condition to be troubled by gallstones.  Within 10 days of this assessment, I was admitted to hospital as an emergency, with a gallstone blocking my bile duct,  and have had two operations in the past two weeks.  I proved not to be the “average man”.

I suspect that “on average” the consultant made the right, money saving, decision.  However in making this decision there was a risk of a greater loss, I had two complicated procedures instead of one and spent 5 nights in hospital instead of none.

Nassim Taleb might observe that my consultant was Fooled by Randomness, or had experienced a “rare event”, what Taleb calls a “Black Swan Event”.  But Taleb’s definition of a Black Swan event is novel.

The concept of the Black Swan emerged in the late thirteenth and early fourteenth centuries, at a time when scholars were introducing mathematics into physics.  The concept was part of a vigorous debate between Realists, in the Platonic sense, such as Thomas Aquinas,  who believed that by observing nature its rules and mechanisms could be gleaned.  Opposed to the Realists were Nominalists, who rejected the idea that there was a hidden Reality of nature, the rules and mechanisms were constructed by the men observing them.  Nominalists included Franciscans such as John Duns Scotus and William of Ockham, who rejected a mechanistic universe and believed if God wished to create a Black Swan, He could. The fact that only white swans had been observed did not preclude the fact that a Black Swan could exist.  Of course, the Nominalists were proved right when Black Swans were discovered in Australia.

A good financier is a Nominalist: they recognise that their models are man-made constructions that are a simple approximation of the nature of markets.  On this basis a financier does not attempt to predict the future, and is circumspect about their ability to “beat the market”.  A good financier is often distinguished by their obsession with attempting to handle the risks they might encounter rather than exploit the opportunities that might arise.  We cannot predict an earthquake but we can plan for them.

There is nothing new in suggesting that applied science should broaden its outlook to consider distributions rather than focus on expectations.  However I think finance tells us something more, we need to be sceptical about the very models that produce our distributions.

For example, the debate about climate change is not a dispute between good and evil, or between idealists and empiricists, but more a disagreement between two approaches to modelling.  It is not the data that is disputed but the modelling framework used to interpret the data.  I feel the reason the Climate Debate is so intractable is that popular science, as distinct from mainstream science as practised by the majority of scholars, cannot accommodate the idea that there can be competing theories and this is a consequence of the pervasive belief that science has a Real  basis, rather than being a social construction.  A Realist will always believe that, given enough effort, the secrets of the universe can be uncovered and the future predicted and controlled. A Nominalist is far more humble.

So none of this is new, but in the context of the Enlightenment Exchange, it is worth noting that some people argue that Quetelet, with his social physics based on the average man, put an end to the Enlightenment's focus on the rational man.

Wednesday, 6 March 2013

The Perils of Physics Imperialism

 My undergraduate degree was in physics, then sixteen years working in oil exploration led me to doubt the certainties that I was taught at Imperial and I became a mathematician interested in uncertainty. The domain for mathematicians interested in uncertainty are the social sciences and I have the fervour of a convert in condemning my old faith and promoting my new faith. While you might not think my beliefs are particularly relevant, I do think a contributory factor in the credit crisis was the wholesale adoption of the culture of the physical sciences by modern finance.

In December there was discussion prompted by the particle physicists Brian Cox and the comedian Robin Ince arguing that policy makers should place scientific advice at the heart of government policy making. My experience of using science to advise policy (in an industrial context) means I think this position is fundamentally mis-guided, but beyond that it relies on the belief that 'science' is indubitable and immutable. My experience is that science and mathematics is definitely not indubitable and immutable, and in fact I belief it has moved backwards in regard to understanding uncertainty in the eighteenth century and is only now recovering. This piece covers an example of what I mean. To me, the example highlights the disproportionate faith people, from all walks of life, have in what physicists say, which is usually grounded in a set of assumptions that cannot be transferred from the physical sciences into the social sciences.

Towards the end of 2012 I came across a paper 'The time resolution of the St. Petersburg paradox' published in the Philosophical Transactions of the Royal Society A on the subject of 'Handling Uncertainty in Science' by a physicist, Ole Peters. The abstract is as follows
A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoullis resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.
The Petersburg paradox was first recorded in 1713 in correspondence between Rémond de Montmort, a gentleman mathematician, and Nicolas Bernoulli, the nephew of James Bernoulli who posthumously published his uncle's Ars Conjectandi and whose own thesis was De Usu Artis Conjectandi in Jure ('The Use of the Art of Conjecturing in Law'). It is worth mentioning that the pair, along with James, first Earl Waldegrave (ancestor of the 1990s UK Science Minister, William Waldegrave) were the first people to identify 'mixed strategy' solutions in game theory, some two hundred years before the twentieth century re-discovery of game theory. The Petersburg game is described as follows
Given a (fair ) game of Heads and Tails, A tosses a coin and gives B 1 coin if a Heads comes up, if a Tails comes up, the coin is tossed again and if a Head turns up, A gives B 2 coins, if a Tails comes up, the coin is tossed again and if a Heads comes up A gives B 4 coins. In general the coin is tossed until a Tail comes up, and, if the first Tail occurs on the nth toss, then A gives B 2n-1 coins. How much should B offer to pay A to play the game?
The problem for Bernoulli and Montmort was that it had been established that a game should be valued by adding together all possible products of the games winnings and the chance of the winning, the mathematical expectation. There is a 1 in 2 chance of winning 1 coin, a 1 in 2 chance of getting a Head on the first toss. B wins 2 coins by there being a Head and then a Tail, with a 1 in 4 chance, there is a 1 in 8 chance of winning 4 coins and so on. In general the mathematical expectation of the game is

However, nobody would stake more than 20 coins to play the game and typically they would offer 4-6 coins to play. Mathematical expectation seemed to be wrong.

The Petersburg game is generally thought to have been resolved by Nicolas' cousin Daniel Bernoulli, who is today known for his contributions to physics, in a paper he presented to the Imperial Academy of Sciences of St Petersburg (hence its name) in 1731 (it was published in 1738). Economists (good reviews can be found in Basset or Cowen and High) see Daniel's solution as being the earliest expression of the mathematical conception of utility, Daniel writes that "Any gain, however small, brings always a utility (emolumentum) inversely proportional to the whole wealth" and described this in terms of a differential equation, which was the rage at the time in physics, with u being utility and x being wealth, and k a constant, the equation is

The solution to this equation is that u = k log(x), that utility is the logarithm of wealth. On this basis Daniel was able to calculate a reasonable value of the game, which was dependent on B's initial wealth.

Daniel's solution appealed to nineteenth century economists as utility theory took hold of the discipline following Bentham, Mill, Walras and Menger. In particular, logarithmic utility would be given a biological, as distinct from mathematical, justification with the identification of the Weber-Fechner law that showed that the brain responded to stimuli in a logarithmic fashion. By the late twentieth century the recieved wisdom, captured in Peter Bernstein's Against the Gods (p 107) was that the paradox appears, is solved by Daniel in 1731/1738, it was briefly mentioned by Keynes in a Treatise on Probability and was picked up by von Neumann and Morgenstern.

Peters' highlights the role of fairness in the development of early probability, but in saying "was no universal agreement on the relevant concept of fairness" is mistaken: the concept was understood, the mathematical formulation was problematic. But when it comes to the issue of the Petersburg game, he falls in step with the mainstream account of the story. However, his main thrust is in the direction of ergodicity. The word ergodic was coined by the physicists Boltzmann in relation to his study of gases and derives from the Greek for 'work' and 'way'. Today, in physics, it relates the average time a gas particle is in some point of space (which can be the phase space, not necessarily a simple location) with the relative size of the space. However, this is a manifestation of a more general mathematical concept, that a random dynamical system is ergodic if it will eventually have a stable distribution independent of the initial state. For example, if a deck of cards is shuffled enough times, we would expect the eventual distribution to be uniform, whatever the initial state of the deck was (i.e the ace of spades is equally likely to be at any point in the deck). Generally speaking a dynamical system with constant coefficients is ergodic.

Peters argues that the problem with the Petersburg Game is that the system is not ergodic, in that the classical expectation of considering all possible winnings along with their space (chance of occurring) was not the same as the time averaged expectation. This is a physicists view of ergodicity, the association of time averages and space averages.  From the perspective of mathematics, the game is clearly ergodic, it is a stable system with unchanging parameters and in this respect the game is also ergodic in the terms that economists would understand.  Peters' interpretation of the game challenges a physicists understanding of ergodicity but does not really address economists' concerns in the area.Peters then analyses the game in the context of time, with the game being an investment in an asset that offers a high return along with the chance of bankruptcy. On this basis he derives and expression that equates to Daniel's logarithmic utility and goes on to criticise Menger's objections to Daniel's solution.

My objection to Peters' paper is not that it is wrong, it isn't, but its assumption that the paper presents a new novel resolution of the Paradox because he has a naive understanding of the history and importance of the Game.

The most detailed scholarly analysis of the game can be found in an article, "The Saint Petersburg Paradox 1713-1937" by the French philosopher and historian of science Gerard Jorland. The article is difficult to read, because it only exists in a book and is French philosophy written in English.

Jorland argues that the paradox was resolved in the late eighteenth century by Condorcet. Jorland comes to this conclusion by discussing the various attempts to resolve the problem which he categorises into two explanations that emerged as soon as the problem was identified. Nicolas Bernoulli, following his uncle's lead, argued that events with very low chance were 'morally impossible', chances less than 1 in 10,000 could be ignored. A colleague of Nicolas', Cramer, argued that while "Mathematicians value money in proportion to its quantity, commonsense men proportion it to its use" (i.e. utility) and introduced the concept of moral expectation, rather than summing the products of gains and probability, the gains should be raised to the power of the probability and then multiplied, formally
and so the logarithm of the moral expectation is the mathematical expectation of the log utility of the game.

Throughout the eighteenth century French (mathematicians) debated whether the Petersburg game should be resolved by taking a lower bound on probabilities, following Nicolas, or an upper bound on gains, following Cramer, as Daniel did. The issue was resolved in 1785 by Condorcet who took the view that the expectation did not 'really' exist: if someone has a 1 in 2 chance of winning 2 and a 1 in 2 chance of winning 0, the mathematical expectation is 1, but they would never win 1. In the Petersburg game the only way someone will win an infinite amount is if the game continued for an infinite number of rounds, which in reality is impossible. Today, this  is incorporated into stochastic control in finance by the incorporation of the transversality condition  that the discounted value of payoffs at infinite time should be zero.

This view, that infinite payoffs are meaningless, became standard in the nineteenth century, and and developed into the position that mathematical expectation is only valid for repeatable events, when the law of large numbers can come into play. Laplace, who did not believe in randomness, only ignorance, accepted the idea of moral expectation and realised that it equated to mathematical expectation if the number of possible payoffs was infinite (and the division of risks could be infinite). This was the basis of insurance, individuals have a finite number of risks and so employ moral expectation where as insurance companies, with a portfolio of risks, employ mathematical expectation. The physicist EmanuelCzuber noted in 1882 that classical mathematical expectation was meaningless for single events.
Peters approaches his solution to the problem by observing that
To the individual who decides whether to purchase a ticket in the lottery, it is irrelevant how he may fare in a parallel universe. Huygens (or Fermats) ensemble average is thus not immediately relevant to the problem.
This point was appreciated by Condorcet, Laplace and Czuber, it is not new.

Peters actually employs Cramer (and Daniel Bernoulli's) idea of moral expectation by considering the time evolution of the game. He assumes that there is a 'growth rate' for each round of the game r such that the value of the game increases by er each round. This is a cheat, acknowledged by Peters to facilitate the comparison with Bernoulli. In fact, a more appropriate formulation was presented by Durrand in 1957 and more recently by Szelkey and Richards.

Peters argues that Menger's criticism of Daniel Bernoulli's resolution of the Petersburg Game in the context of logarithmic utility was wrong. Menger argued that a Petersburg Game could be constructed that offered infinite payoff even using moral expectation/logarithmic utility, and so the only resolution of the Paradox was to use bounded utility functions, not just logarithmic utility functions. It is not clear why Peters thinks Menger was wrong, this is not surprising since Menger was not wrong, if B wins e2n instead of 2n logarithmic utility does not solve the problem. What Peters fails to appreciate was that Menger was conforming to the resolution provided by Condorcet, the game cannot proceed for an infinite number of rounds, which is were the resolution to the Paradox really lies.

In fact the Comte de Buffon (of Buffon's needle) did a very un-French thing and resolved the Paradox empirically.  He asked a young boy to conduct 2,048 experiments of the Game and tabulated the results.  He found that the experimental results closely matched the theoretical results based on the Binomial Distribution and that the total payout (to B) of the 2,048 games was a little over 10,057 coins  resulting in a fair price for the Game of around 5, close to the original observation of Nicolas Bernoulli and Montmort (in fact if you consider 2n trials of the game, the expected value of the game is n/2, and so if you consider events of chance less than 1 in 10,000 to be "morally impossible", this corresponds to it being "impossible" to see 14 heads in a row, you would value the game around 6.5-7).

Buffon's result employs ensemble averages to arrive at a sensible answer.  There seems little value in Peters approach employing contemporary ideas in physics.

Peters is challenging the concept of ergodicity in finance, ergodicity was introduced into finance from physics (Mirowski has written on this) along side utility theory. This was done in the context of post-Laplacian science, when there was no such thing as randomness, only a lack of information. Pre-Laplacian, and pre-Smithian ideas relating mathematics to the uncertainties of finance were lost. Peter is not just re-inventing the wheel by presenting his resolution of th ePetersburg papradox, his attack on Menger disguises the real solution to the problem, which is that mathematical expectation is not really relevant to economic affairs, because there is n stability in the dynamical system (a lack or ergodicity) and parallel universes don't really exist.

Peters paper has been well received, particularly by those who believe the solutions to the problems of finance lie in physics or in heterodox economics. Unfortunately, the well regarded actuarial consultancy Towers Watson has also succumbed to the allure of physics, shame on them.

Friday, 15 February 2013

Food and Finance

It seems, from the cheap seats at least, that the Eurozone crisis has abated, so now the media is filled with a food crisis. For anyone not following the story, despite food being an important issue of public discourse, following the emergence of BSE twenty years ago and the GMO debate, it turns out things are not as transparent as one would hope and when Europeans have been paying for processed beef they have ended up eating dead horses.  This is no great surprise to someone who has occasionally bought a burger for £1.50.

I started thinking about the relationship between the food crisis and finance when a non-academic colleague asked me to explain the difference between a new Master's in Financial Engineering we have introduced and our existing programmes in Risk Management and Financial Mathematics.  My explanation was as follows
In the past, investors did the equivalent of buying tomatoes, onions, meat and pasta.  Today financial engineers sell investors ready made lasagne.  Risk managers make sure it is correctly labelled (the traffic lights/no horsemeat instead of beef) while financial mathematicians put a price on the lasagne.
This got me thinking about the failures of food regulation and financial regulation.   The changes in finance that have occurred over the past forty years mirror those in food.  In the 1960s investors had a limited choice of where they could put there money - the job of an investment manager at a life insurance company involved buying government bonds, and if you were particularly daring, Ford or Exxon stock. When Bretton-Woods collapsed in 1971 this benign environment became perilous, exchange rates fluctuated and governments responded by adjusting their interest rates while commodity prices became volatile.  The work of fund managers ceased to be sedate and became something of a high wire juggling act.  To make the juggling act easier, hedge funds, and then banks, started processing the volatile raw assets into investment vehicles designed to meet the needs of the fund manager.

Pretty much contemporaneous with these developments in finance, the UK food industry was making similar innovations.  As society changed and housewives went out to work the food industry started selling processed ready-meals.  Apart from convenience, ready meals are sometimes seen as being important in developing consumer tastes - the British menu is today much more varied than the traditional "meat and two veg" of the sixties.  The downside has been concerns as to the nutritional value of ready meals, and as a result there has been more and more regulation on the industry, particularly relating to labelling.

My problem is that despite significant effort (and expenditure) by regulators, the consumer does not seem to have been well protected.  This statement could apply to either food or finance.

In the aftermath of the Credit Crisis, the then Science Minister, Lord Drayson asked me to collate views from leading mathematicians working in finance what the causes of the crisis were. One academic (asked to be anonymous)  commented as follows
I was involved in a meeting to discuss new financial regulation. As a mathematician, I had anticipated that the discussion would be on the robustness of the underlying models being used. In fact the discussion focused on the processes to ensure financial institutions complied with the letter of the regulation.

What the academic observed was that as a result of detailed regulations, bankers stopped "thinking" about their models and processes and resorted to a "box ticking" exercise.  The regulations were so detailed that they responded by focusing on the legal issues around the regulations and not the substance  of their business.  One wonders if something similar has happened in the food industry.  If we pass the "traffic lights" all is well with our ready meal.

This issue was raised by Andy Haldane in his "The Dog and the Frisbee" paper presented last year when he argued that "less is more" in banking regulation.  If the regulations are too detailed, bankers can lose sight of the key issues. However, Haldane's arguments do not square with the views of his new boss, the Bank's Governor designate, Mark Carney.

In the conversations I had with bankers who were involved in Credit Derivatives after the crisis, the point was made that the emphasis in the business was "knowing the components" of a structured product (a ready meal) rather than having a whizz-bang pricing model (efficient food processing).  One suspects the food industry will start taking a closer look at its supply chain as well, now.

Just as EU bureaucrats discuss the Food Crisis, their colleagues are proposing new regulations on finance.  The Financial Transaction Tax that the EU are looking to implement has three objectives:

  • To tackle fragmentation of the Single Market that an uncoordinated patchwork of national financial transaction taxes would create;
  • To ensure that the financial sector makes a fair and substantial contribution to public finances and covering the cost of the crisis, particularly as it is currently under-taxed compared to other sectors;
  • To create appropriate disincentives for financial transactions which do not contribute to the efficiency of financial markets or to the real economy
The EU food labelling regulations share the first objective, but Europe does not tax salt-sugar-fat in processed foods and does not seek to hinder the development of innovative food products, even if they do not contribute to the nutritional well being of EU citizens.

Food and financial regulation are extremely important to the well being of Europe's citizens.  While Food Regulation will be developed in public, and as a result I do not expect the EU to implement a Food Transaction Tax.  However Financial Regulation is rarely considered outside the specialist media.  As a result, I worry that ill considered regulations will be implemented that do more harm than good.