Friday, 30 August 2013

Insincerity in climate science

This post is concerned with the idea that truth does not exist and the best science can do is be honest.  The argument emerged because I read a Tweet from @Jackstilgoe, a science and technology studies lecturer at UCL,
I love the first sentence of this abstract. A paper on what climate models can tell us. (via )
Intrigued I followed the link to the paper, whose title is  "Climate Change Policy: What do models tell us?" and the first sentence is "Not very much." What caught my attention beyond the simple humor was it was written by Robert Pindyck who has had an influence on my academic career.  In the late 1990s I was working for a US oil company struggling in an environment of $15/bbl - orange juice was more valuable at the time.  Representatives from a well known consultancy proposed employing a new technique to value the company's undeveloped resources that would enhance the firm's balance sheet, the technique was known as "Real Options", and employed ideas from stochastic control to assess the value of real assets.  During the course of the presentation the engineering director asked the questions "So when would it be optimal to develop the fields" and the consultant replied "Either immediately or just before expiry of the exploration license".  This made no sense to the managers and I was asked to explain why the highly paid consultant came up with such as seemingly dumb (and actually dumb) answer and the standard text at the time was Pindyck's book.  While Pindyck moved swiftly on from Real Options theory I became interested in the underlying mathematics and my PhD was substantially on how the structure of the payoff, discounting  and driving stochastic process determine the structure of the optimal control strategy.

Because I had this association with Pindyck I read the meat of the paper.  What I discovered was that economic assessment of climate change comes down to calculating a "social cost of carbon" and this typically involves building "integrated assessment models" of the future impact of current green-house gas emissions, and in doing this the IAMs "discount" the future "cost" of climate change to give it a current value.

This is bread and butter to a financial mathematician: how do we value an asset with an uncertain value in the future, and I found Pindyck's discussion interesting because it touched on a number of topics I ponder on
We can begin by asking what is the “correct” value for the rate of time preference, (delta)? This parameter is crucial because the effects of climate change occur over very long time horizons (50 to 200 years), so a value of (delta) above 2 percent would make it hard to justify even a very moderate abatement policy. Financial data reflecting investor behavior and macroeconomic data reflecting consumer and firm behavior suggest that is in the range of 2 to 5 percent. While a rate in this range might reflect the preferences of investors and consumers, should it also reflect intergenerational preferences and thus apply to time horizons greater than 50 years? Some economists (e.g., Stern (2008) and Heal (2009)) have argued that on ethical grounds (delta) should be zero for such horizons, i.e., that it is unethical to discount the welfare of future generations relative to our own welfare. But why is it unethical? Putting aside their personal views, economists have little to say about that question. I would argue that the rate of time preference is a policy parameter, i.e., it reflects the choices of policy makers, who might or might not believe (or care) that their policy decisions reflect the values of voters. As a policy parameter, the rate of time preference might be positive, zero, or even negative. The problem is that if we can’t pin down (delta) , an IAM can’t tell us much; any given IAM will give a wide range of values for the SCC, depending on the chosen value of  (delta) .   
Firstly I am interested in how choices made by modelers determine the answer: a good mathematician is one who instinctively knows how to formulate a problem so that it is tractable, for example exponential and power utilities are often preferred to log utility for the reason that they are more likely to result in closed form solutions. But more resonant to me was the discussion of the ethics of the discount rate (the "time preference", delta).  In Dixit and Pindyck the advice is to determine the discount rate based on the Capital Asset Pricing Model (CAPM), essentially the discount rate is a linear function of the standard deviation of asset returns: high discount rates (bad) are associated with very uncertain returns (bad, also .

 The roots of CAPM are in Markowitz's theory which trades off returns for uncertainty represented by the mathematical operator "variance".  Markowitz's choice of variance was novel, but not unique.  Simultaneously a less well known British mathematician, A. D. Roy, came up with p the same idea, but Roy's background is revealing in why variance (uncertainty) was regarded as a "bad thing".  Roy had originally entered Cambridge to study mathematics just before the start of the Second World War. His studies were interrupted by his service in the Royal Artillery, and he fought at the Battle of Imphal in Burma - Britain's Stalingrad, contracting jaundice and being invalided out with what would now be regarded as post traumatic stress disorder.  In his Econometrica (Markowitz published the same year in Journal of Finance) article titled Safety First and the Holding of Assets Roy  explicitly observed, in language that is poignant coming from someone who had been besieged in a Burmese town for about four months in 1944, that
Decisions taken in practice are less concerned with whether a little more of this or of that will yield the largest net increase in satisfaction than with avoiding known rocks of uncertain position or with deploying forces so that, if there is an ambush round the next corner, total disaster is avoided.
The question of portfolio selection was one of balancing the risks of disaster against the opportunities for reward.  This approach is now canaonical but I do not think it is particualry rational: opportunity (and threats) lie in uncertainty; this is why the poor gamble.

In this contemporary paper Pindyck does not explicitly recommend, as others do, that the discount rate should be set by the 'market', though he does quote the market rate.  Rather, in rejecting the 'ethical' position that the discount rate should be set to zero, he suggests the rate is a "policy parameter" that can be set arbitrarily by policy makers.  In making this observation Pindyck is presenting himself as what Roger Pielke Jnr defines as a "Pure Scientist", someone who stands above the murky process of policy decisions, and in doing so presents climate science as something of a forlorn exercise:
IAMs are of little or no value for evaluating alternative climate change policies and estimating the SCC. On the contrary, an IAM-based analysis suggests a level of knowledge and precision that is nonexistent, and allows the modeler to obtain almost any desired result because key inputs can be chosen arbitrarily.
while the climate economist "Pure Scientist" Pindyck describes  the "discount rate" is the "rate of time preference",  the "Science Arbiter" Nicholas Stern, descibes it as

 simply (sic) the proportionate rate of fall of the value of the numeraire used in the policy evaluation. 
...number of general conclusions follow immediately from these basic definitions. First,[discount rate] depend on a given reference path for future growth in consumption and will be different for different paths. Second, the discount rate will vary over time. Third, with uncertainty, there will be a different discount rate for each possible sequence of outcomes. Fourth, there will be a different discount rate for different choices of numeraire. In imperfect economies, the social value of a unit of private consumption may be different from the social value of a unit of private investment, which may be different from the social value of a unit of public investment. And the rates of changes of these values may be different too.
A further key element for understanding discount rates is the notion of optimality of investments and decisions. For each capital good, if resources can be allocated without constraint between consuming the good in question and its use in accumulation, we have, for that good, the result that the social rate of return on investment (the marginal productivity of this type of good at shadow prices), ...
And it goes on, while people complain about mathematicians obscurifying economic intuition!  This text is part of a section entitled Ethics and gives a "positive" justification for a conclusion that I hope to arrive at in an simpler and quicker manner than Stern.

I believe financial economics emerged as an expression of virtue ethics in the face of uncertainty, specifically it is about establishing equality between what is given and what is returned in a reciprocal relationship.  In this context I explain interest rates  using Poisson's 'Law of Rare Events'.
 
Possion worked on many of the topics pioneered by the great Revolutionary physicists, Laplace and Lagrange, and ventured into physics, working on heat, electricity and magnetism. In respect to probability, and keeping to Laplace’s division between physical and social sciences, in 1837 Poisson wrote Recherches sur la probabilité des jugements en matiére criminelle et en matiére civile (‘Research on the Probability of Judgements in Criminal and Civil Matters’). Despite its title, most of Possion’s book was a development of ‘probability calculus’, and according to the historian of probability, Ivo Schneider, after its publication “there was hardly anything left that could justify a young mathematician from taking up probability theory” [2, p 203].
The heart of Recherches was a single chapter on determining the probability of someone being convicted in a court, by a majority of twelve jurors, each of whom is “is subject to a given probability of not being wrong” and taking into account the police’s assessment of the accused’s guilt [2, p 196]. In order to answer this problem, Poisson needed to understand what has become known as the ‘Law of Rare Events’, in contrast to the Law of Large Numbers [1]. Poisson’s starting point was the Binomial Model, based on two possible outcomes such as the toss of a coin, or the establishment of innocence or guilt. De Moivre had considered what would happen as the number of steps in the ‘random walk’ of the Binomial Model became very large, with the probability of a success being about half. Poisson considered what would happen if, as the number of steps increased, the chance of a success decreased simultaneously, so that it became very small.
On this basis, Poisson worked out that if the rate of a rare events occurring, the number of wins per round, was lambda, then the chance of there being k wins in n rounds was given by

  The Poisson distribution. Apart from being one of the key models in probability, along with the Binomial and the Normal, the Poisson distribution has an important financial interpretation.
Consider a someone lending a sum of money, L. The lender is concerned that the borrower does not default, which is hopefully a rare event, and will eventually pay back the loan. Say the banker assesses that the borrower will default at a rate of lambda defaults a day, and the loan will last T days. The banker might also assume that they will get all their money back, providing the borrower makes no defaults in the T days, and nothing if the borrower makes one or more defaults. On this basis the lender’s mathematical expectation of the value of the loan is 
using the Law of Rare Events, we can ignore the second expression, since it is zero, and for the first, we have that, the probability of no defaults is given when k = 0,
so
The lender is handing over L with the expectation of only getting
 
back. To make the initial loan amount equal the expected repayment, the lender needs to inflate the repayment by 
 
to make it equal to the loan amount, 
James Bernoulli had identified the number e in 1683 by considering how a bank account grew and as the time between interest payments became infinitesimally small, and in the process solved the fundamental differential equation of science
Notice that neither the number e, the fundamental differential equation nor the Poission distribution came out of the physical sciences, they all emerged out of the analysis of social sciences and humanities.
This argument explains why a lender charges interest at a rate of lambda a day: the lender is not charging for the use of money, they are equating what they lend with what they expect to get back, just a Pierre Jean Olivi had argued in the thirteenth century [3, p 19], a fact that is crystal clear through the use of Poisson's mathematics, but had escaped philosophers since Aristotle.

I think this mathematical explanation is simpler than Stern's discursive one, but what does it imply for the discount rate employed in climate science? In my formulation the discount rate is determined by the chance that a borrower might default, and it makes the expected amount returned equal to the amount taken.  In the case of climate science, the default probability is the chance that humanity is not present to benefit from sacrifices made today, i.e the discount rate is related to the extinction of human beings.  Stern, eventually, makes the same point but via a rather precipitous route that eventually justifies it on the basis that other great men have recommended it in the past.

But that is not really the point of this post, the point is as follows.  Pindyck adheres to the fact value dichotomy, but in doing so ends up arguing, as far as I can see, that science is impotent to answer the important problems of society.  I think an issue related to this position is the belief that "Pure Science" is about Truth, and anything that cannot establish "truth" is not a suitable topic of "Scientific" debate.

I take the Pragmatic position: Truth does not exist.  In the face of this fact science is about establishing consensus through communicative action.  In this setting science must be sincere (that is it OED 4 "Characterized by the absence of all dissimulation or pretence; honest, straightforward:"). It is at this point I diverge with Stern who I think ties himself in knots (in my humble opinion) because he does not wish to stand up and declare we cannot separate what is from what ought to be.

The popular alternative to Stern's advocacy of a low discount rate and Pindyck's rejection of modelling is to choose a 'market rate'.  This is more disingenuous than either Stern's or Pindyck's arguments because while Stern struggles to integrate ethics into the argument, 'market forces' advocates claim to be objective, ignoring the fact that choosing money as the determinant of value is, in itself, highly subjective.  Fairness is a more universal concept than money.

 In the Pragmatic context, mathematics is not the determiner of truth, but a rhetorical device that assists discourse. This view goes back to Fibonacci's Liber Abaci, which can be seen as being successful because it gave merchants the tools, in Arabic/Hindu numbers and the concept of the algorithm, to communicate the best way of solving commercial problems.  This is at the heart of my objection to what I see as Pindyck's approach, he sees the models as useless because they do not provide an accurate answer, I see the models as useful if they are regarded as the focii of discussions about what is important in climate science.
 

References

[1]    I. J. Good. Some statistical applications of Poisson’s work. Statistical Science, 1(2):157—170, 1986.
[2]    I. Schneider. The Probability Calculus in the Nineteenth Century. In L. Kruger, L. J. Daston, and M. Heidelberger, editors, The Probabilistic Revolution: Volume 1: Ideas in History. MIT Press, 1987.
[3]    E. D. Sylla. Commercial arithmetic, theology and the intellectual foundations of Jacob Bernoulli’s Art of Conjecturing. In G. Poitras, editor, Pioneers of Financial Economics: contributions prior to Irving Fisher, pages 11—45. Edward Elgar, 2006.



Friday, 23 August 2013

Oedipus and the difficult relationship between maths and economics

Noah Smith recently wrote a “rant” on maths in (macro)economics, which elicited a swift response from Paul Krugman, which in turn prompted Bryan Caplan to argue that “Economath fails the cost benefit analysis”. As a mathematician (i.e. someone who is employed by a maths department of a university) I think all the commentators make valuable points but, maybe somewhat surprisingly, my strongest affinity is with Bryan Caplan’s position that maths is failing economics. What I intend to do in this post is present an argument that, historically, `physics maths' has been driven by economic intuition and the contemporary problems in economics are that it is adopting maths from the physical science rather than generating a more insightful mathematics of its own. In the context of Noah’s original article, econmath is not enjoyable in the same way that ill fitting clothes are not enjoyable, or playing football in tennis shoes can be painful Metaphorically, maths is Oedipus and economics is King Laius: maths does not recognise its father, father does not recognise child, and tragedy follows.  
In a recent post Caplan challenges Krugman to “Name three important economic insights you think we owe to economath.”, I will support my case by naming three critical developments in “physics math” that come out of economic intuition.
The mathematisation of physics
Aristotle, and his successors such as the medieval Islamic scientists, did not think that maths had anything to offer physics, probably similar to Caplan’s view that maths has little to offer economics. Maths had nothing to say about causes, what was important in understanding nature were the qualities of objects, whether they were heavy or light, hot or cold, wet or dry, hard or soft. Since mathematics is concerned with precision, numbers and proportions, it could not give any insight into these qualities; “boulders were never perfectly spherical nor were pyramids perfectly pyramidal, so what was the use of treating them as such” [7, p 16]. The critical distinction for Greek science and its descendants was that mathematicians dealt with pure abstract objects while natural philosophers and engineers work with the concrete, messy, qualities of physical objects [9, p 65]. This approach was not just Greek, other cultures, such as the Chinese, took a similar line on the usefulness of maths to science [11, p 53].
Approaching physics through mathematics was uniquely European and was first recorded by the ‘Merton Calculator’ Thomas Bradwardine in
[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 [13, p 176]
Bradwardine had entered Merton College in 1323 and twelve years later went on work for the Bishop of Durham, who was the Treasurer and Chancellor of England, was eventually appointed Archbishop of Canterbury shortly before his death in 1349.
Arguing that physics was inseparable from mathematics was revolutionary because it completely broke with Aristotle’s approach to physics. From this point ‘Latin’ science would take a very different path to Islamic science, which was based on the same Hellenistic tradition. Bradwardine put this theory into practice by looking for a mathematical description of Aristotle’s laws of motions in his 1328 book De proportione velocitatum in motibus (‘Concerning the ratio of speeds in movement’), he achieved this, but being based on Aristotle’s incorrect principles, it was wrong. The ideas were developed by subsequent Calculators and the French philosophers Jean Buridan, who identified the concept of inertia, and Nicolas Oresme, who identified the mean speed theorem.
Key to unlocking the laws of motion was the realisation that speed was the ratio of distance divided by time. This seems obvious today but was not to Aristotle who had investigated measurement in Physics and Metaphysics, parts of the Organon where he claimed that a measure is always the minimum unit of the thing being measured. The measure shares the same substance as the subject of measurement. For example, numbers are measured by the smallest number, ‘1’, distances are measured by the smallest length of distance, say an inch, while liquids are measure in pints and so forth. This is not conceptually unnatural, the Chinese language still incorporates ‘measure words’ when quantifying objects. When Aristotle measured physical objects, as Richard Hadden has noted, “he [was] careful not to mix quantities differing in kind in the same expression” [12, p 75], he, and scientists in the Greek tradition could not get their heads around the very concept of ‘metres per second’ or ‘foot—pound’.
So why did Bradwardine ‘get it’? Joel Kaye has argued that the 45 Fellows at Merton were not just occupied in academic activities but were involved in the daily management of the College’s extensive resources
The three bursars who had collective responsibility for the college’s monies, the warden who headed the yearly audit and visited the far-flung manors at harvest time to assess the year’s taxation, in money or in kind, [others] oversaw the books and calculated the profits of the college’s many properties [17, p 33]
The point is Bradwardine would have developed his mathematical skills through economic application. But this is insignificant on its own, what was critical was the change in the conception of measurement that had occurred when Albert the Great studied Aristotle’s Nicomachean Ethics, in the 1250s after it had been translated into Latin in 1248/9.
Book V of Nicomachean Ethics considers the justice of economic exchange, and as a philosophical text it is disjointed and hard to follow. However, what is clear is that Aristotle sees reciprocal, fair, exchange in the market as being fundamental to a well functioning society since it binds individuals together [17, p 51]. Since Nicomachean Ethics was concerned with justice, Aristotle needed to identify under what conditions economic exchange was ‘just’ and he did this by insisting that there needed to be an equality between the goods being exchanged [17, p 45]. Aristotle identified that for equality to be established there needed to be a measure of the value of the goods, and this measure, the price, was provided by money.
all things that are exchanged must somehow be comparable. It is for this end that money has been introduced, and it becomes in a sense an intermediate; for it measures all things, and therefore the excess and the defect — how many shoes are equal to a house or to a given amount of food [17, p 47 quoting Ethics]
In his translation, Grosseteste described money as the medium of exchange. Today we interpret this in the sense that money is a physical token, however this is a modern interpretation. For the medieval scholar the Latin word medium was more commonly used in the sense of a mediator or intermediary, money is a neutral agent that links two distinctive commodities, such as shoes and houses.
Albert realised that if Aristotle was right about money being a measure he could not be right about a measure sharing the substance of the measured. This insight enabled Albert, and his successors, to revolutionise the concept of measurement, in a way that contemporary Muslim scholars did not. In particular students of Albert were able to reject Aristotle’s theories of measurement and consider concepts like metres per second or kilograms—metres per second (momentum). [17, p 67]
The mathematisation of Western Science is a consequence of the ethical assessment of an en economic activity.
The development of calculus
Bertrand Russell (amongst others) stresses the fundamental role probability (and statistics) has in science [21, page 301], it is less well known that probability emerges out of the ethical assessment of commercial contracts following Aristotelian concepts of Justice. Even less well known is the role financial practice and theory had in the genesis of Newton’s calculus on which his physics is based.
Many people appreciate that Arabic (Hindu) numbers were introduced into Europe through Fibonacci’s Liber Abaci, a financial text book. But Fibonacci employed fractions, not decimals. The significance of the decimal notation was highlighted by the Flemish mathematician Simon Stevin in his 1585 text , De Thiende (‘The tenths’). Stevin had not invented decimal fractions, they had been used by the Arabs and Chinese and first appear in Europe in a German text on algebra of 1525, but the audience for De Thiende was ‘practical men’ and Stevin pointed out that ‘all computations that are met in business may be performed’ using his notation. Stevin’s notation was in fact a bit cumbersome, decimal fractions as we know them appear in English in 1616. [2, p 316—317] Its also worth pointing out that the ‘=’ sign was introduced in The Whetstone of Witte written by Robert Recorde who controlled the English Mint).
The significance of decimal fractions to calculus is in how Newton tackled the problem of motion, building on Oresme’s work. While in Lincolnshire avoiding the 1666 Plague, Newton thought about how a point turned into a line by moving in an infinitesimal moment, for example how a pencil-line is drawn on a piece of paper. Newton called the resulting curve a fluent and he called the velocity of how the fluent grew in a moment its fluxion. For example a fluent could be the distance of a cannon ball from a cannon, the fluxion its velocity, or a force (the product of mass and acceleration) on cannon ball was the fluxion and its momentum (the product of mass and velocity) the fluent. Despite coming up with these ideas before 1667, Newton only circulated them in 1671 in Tractatus de methodis serierum et fluxionum (‘A Treatise on the Methods of Series and Fluxions’) [16, p 462].
Following Descartes’ Newton was comfortable in describing the distance travelled by an object with a function, and following Buridan and Oresme he understood the fluxion was the rate of change of the fluent, but in order to solve problems in general he needed to develop a way of deriving a function for a fluxion from a function for a fluent.
The key to unlocking this puzzle lay in decimal notation. before Stevin, numbers were generally written as composed or continued fractions. For example, as a composed fraction the sum of money five pounds, seven shillings and nine pence £5 and 149 pence, or 5would be written as a composed fraction,
as a continued fraction,
while in decimal notation it is
Newton realised this was the same as writing
and was interested in whether a similar approach could be taken with functions.
Newton’s approach, to write a function as a series
was not unheard of. Independently Indian mathematicians had considered writing functions as power series as early as the fourteenth century while in 1688 Nicolas Mercator considered power series for logarithms. (Mercator was German and originally called Niklaus Kauffman, he Latinised his name to Mercator; both Mercator and Kaufmann mean ‘merchant’). If a decimal number, written as a continued fraction, never ends it is an ‘irrational’ number rather than a ‘rational’ one. If a function when written as a power series/polynomial has a finite number of terms it is ‘algebraic’, if it has an infinite number of terms it transcends algebraic functions, it is transcendental, and usually given a name, such as sin, log, exp, etc.
Having realised that he could write a function as a power-series, working out how the function changed could be resolved if he could work out how a simple power changes, by establishing
What follows are two supreme achievements of Western science, Newtonian mechanics and Mathematical Analysis.
At this point it is worth observing that the diagrams in Noah’s original blog post are both directly related to these first two examples.

The Bachelier myth
Paul Samuelson tells the story of how
In the early 1950s I was able to locate by chance this unknown book by a French graduate student in 1900 rotting in the library of the University of Paris and when I opened it up it was as if a whole new world was laid out before me. [4, 13:00]
The book Samuelson refers to is Louis Bachelier’s thesis Théorie de la spéculation. The story that Samuelson tells, and has been disseminated, associates Bachelier’s work with Einstein’s work on Brownian motion rather than the pre-existing theories around finance. The alignment of Bachelier’s work with theoretical physics, rather than highlighting how the practice of applying mathematics to economics informs the development of mathematics, is an example of the tendency of academics to elevate theory over practice [10, Chapter IV].
Bachelier’s work had nothing to do with the physical process of Brownian motion, which Einstein was interested in, but was part of a long (French) tradition of employing the Binomial random walk model in finance. The canonical origins of mathematical probability are in the Pascal-Fermat solution to the Problem of Points, which introduced the model in 1654, a decade before calculus appears. Vernacular research into the subject includes French actuary Emmanuel-Etienne Duvillard’s Rechererches sur les rentes, les emprunts et les remboursements (‘Researches on annuities, loans and refunding’) [23] and Jules Regnault’s Calcul des Chances et Philosophie de la Bourse (‘Probability and the science of the markets’) of 1863 [15, .] In 1870, Henri Lefèvre de Chateaudun, an actuary who had been the private secretary of Baron de Rothschild [14] published Traité des valeurs mobilières et des opérations de Bourse: Placement et spéculation (‘Treatise of financial securities and stock exchange operations’)” [20]. In 1875 the Danish actuary and astronomer Thorvald Thiele introduced the concept of the random walk to model observational errors, incorporating a dynamic component to Gauss’ earlier work [18]. In 1894 Poincaré, France’s greatest mathematician of the time, chose to teach probability over all other subjects. At the time it was traditional for lecture courses by prominent mathematicians to be edited and published. In the case of Poincaré’s Calcul des Probabilitités, the editing of the lectures was carried out Albert Quiquet, an actuary working for the La Nationale insurance company, and not a university student, as was usual [3, p 279], highlighting the active interest of practising financiers in theoretical probability.
It was into this tradition that Bachelier was drawn. On account of his parents’ early deaths, Bachelier had been unable to enter university after school, and had worked initially for the family’s firm in Normandy and then moved to Paris where he traded rentes (i.e. consols) while studying mathematics at the University of Sorbonne, eventually taking his doctorate nominally under Poincaré ([6], [22]). Bachelier’s thesis is known for extending the discrete time Binomial random walk model into a continuous time model (i.e. it is a descendant of Newton’s work on calculus), and this is the aspect Samuelson picked up on.
Bachelier was not a succesful academic. It is rather obscure how Bachelier earned his living in the following decade, he obtained a few scholarships and in 1909 became a ‘free’ (unpaid) lecturer at the Sorbonne, lecturing on probability theory applied to finance. [6] In 1912 he published Calcul des Probabilitiés (‘Probability Calculus’) and then in 1914, Le Jeu, la Chance et le Hasard (‘Game, Chance and Randomness’). That same year, on the verge of being permanently appointed to the University of Paris, he, along with every other fit young Frenchman, was conscripted, as a private, into the army. He survived the cataclysm of the war, finishing it as a lieutenant, and in 1919 he took up a temporary post at the University of Besançon. He had further temporary positions at Dijon, between 1922 and 1925 and Rennes between 1925 and 1927.
In 1926 a permanent position had become available at Dijon, which Bachelier applied for. His application was reviewed by a professor at Dijon who was not familiar with Bachelier’s work but believed an important article published in 1913 contained a ‘gross error’. The referee wrote to a young ‘doctoral brother’ (student of the same doctoral adviser) who was developing a reputation in probability, Paul Pierre Lévy, to comment on Bachelier’s work. Unlike Bachelier’s unconventional pathe into academia, Lévy was the son of an academic at the École Polytechnique, where he studied and published his first paper at the age of 19 in 1905 becoming a professor at the École Nationale Supérieure des Mines in 1913, and spent the war doing research for the French artillery. In 1920 he was appointed to the École Polytechnique and it was on the basis of his 1925 book Calcul des Probabilitiés that he was asked to report on Bachelier.
Lévy checked the page that contained the suspected error and agreed with the referee, Bachelier was blackballed. The issue that the referee and Lévy had with the paper was that it appeared to contradict a feature of Weiner’s 1921 formulation of Brownian Motion, the fact was it didn’t if you followed the approach Bachelier had been taking since his dissertation. The reviewer’s were unfamiliar with this work and so the 1913 paper was ambiguous and appeared wrong. Though the blackballing was painful to Bachelier, in 1927, at the age of 57, he finally secured a permanent position at Besançon where he would remain until his retirement in 1937. He wrote two more books on probability in retirement, and died in 1946 in Brittany.
While Bachelier was never appointed to one of the great French universities, perhaps because his vocational background did not conform to France’s Rational ideal, he had a successful academic career and to suggest his thesis was ‘rotting’ in a library ignores the significant contribution Bachelier made to mathematics. Notably his idea that probability was dynamic which was a significant conceptual leap at the time and was taken up by Kolmogorov when laying the foundations of modern probability.
In his thesis Bachelier discusses what he calls Rayonnement de la probibilité (‘Radiation of probability’) [1, p 46—47], [8, p 41], the idea that a probability density evolves in time. This was revolutionary, up until Bachelier had made his observation in his thesis it had been assumed that probabilities were static, even Bayesian approaches assumed the probability density was static but you learnt more about it in time. The idea emerged in physics following Einstein’s work in 1913 as the Fokker-Planck equation.
Kolmogorov became familiar with Bachelier’s work, and when Lévy this he realised also that if he had looked into the Bachelier’s work in 1927 when he refereed his application to Dijon, he might have come to Kolmogorov’s conclusions before the Russian and be famous today for laying the foundations of modern probability. Lévy apologised to Bachelier and publicly acknowledged Bachelier’s priority, not just over Wiener in the mathematical study of Brownian motion, but also over over Kolmogorov in linking Brownian motion to Fourier’s heat equation, and over himself in establishing certain properties of the Wiener process. [22, pp 20—21]
I think the Bachelier myth is incredibly important in demonstrating how academics, from Lévy in 1927 to Samuelson in 1999, denigrate the significance of economic phenomena in generating mathematical ideas that have profound impact in the physical sciences.
Conclusions
I sympathise with Bryan Caplan’s claim that modern mathematics obscures economic intuition. I think Noah Smith’s point that econmath is unappealing is because the mathematics developed in response to physical problems is not suited to economic problems.  
The observation that economists could do better with mathematics is nothing new, the mathematician Augustin Cournot did not think that economics was susceptible to precise quantification, in fact he was wary of attempts to ‘arithmetise’ economics
There are authors, like [Adam] Smith and Say, who, in writing on Political Economy, have preserved all the beauties of a purely literary style; but there are others, like [David] Ricardo, who, when treating the most abstract questions, or when seeking great accuracy, have not been able to avoid algebra, and have only disguised it under arithmetical calculations of tiresome length. Any one who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labour and pains.
I propose to show in this essay that the solution of the general questions which arise from the theory of wealth, depends essentially not on elementary algebra, but on that branch of analysis which comprises arbitrary functions, which are merely restricted to satisfying certain conditions. [5, p 4—5]
More recently John von Neumann refused to write a review for Samuelson’s Foundations of Economic Analysis in 1947 because “one would think the book about contemporary with Newton”, like many mathematicians who look at economics, on Neumann believed economics needed better maths than it was being offered [19, p 134].
Paul Krugman is right in emphasising the usefulness of mathematics as a rhetorical device, the problem is that he does not recognise that it is difficult to describe the Spitsbergen in winter in Arabic or the pleasures of a desert oasis in Sami.
My plea is that economists stop using existing mathematics and start commissioning new mathematics. I can see no resolution of the problem of econmath until there is the sort of relationship between economics and mathematics that mathematicians have with physical scientists and mathematicians work with economists to create a mathematics that enables the clear discussion of economic intuition.

In the Oedipus myth, although Oedipus does not realise he has killed his father, the murderer of Laius has to be brought to justice to end famine and pestilence in the kingdom.  Ultimately it is mathematics that needs to correct the wrongs to economics.

References

[1] L. Bachelier. Théorie de la spéculation. In Annales scientifiques de l’É. N. S. 3e série, tome 17 (1900), pages 21—86. École normale supérieure, 1900.
[2] C. B. Boyer and U. T. Merzbach. A History of Mathematics. John Wiley and Sons, 1991.
[3] P. Cartier. Poincaré’s Calcul des Probabilitités. In E. Charpentier, E. Ghys, and A. Lesne, editors, The Scientific Legacy of Poincaré. American Mathematical Society / London Mathematical Society, 2010.
[4] M. Clark. The Midas Formula (the Trillion Dollar Bet). BBC Horizon, 1999.
[5] A. A. Cournot. Researches into the mathematical principles of the theory of wealth (trans. N. T. Bacon). Macmillian, 1897. www. archive. org/details/researchesintom00fishgoog.
[6] J-L. Courtault, Y. Kabanov, B. Bru, P. Crépel, I. Lebon, and A. Le Marchand. Louis Bachelier on the centenary of Théorie de la Spéculation. Mathematical Finance, 10(3):339—353, 2000.
[7] A. W. Crosby. The Measure of Reality. Cambridge University Press, 1997.
[8] M. H. A. Davis and A. Etheridge. Louis Bachelier’s Theory of Speculation. Princeton University Press, 2006.
[9] P. Dear. Revolutionizing the Sciences. Palgrave, 2001.
[10] J. Dewey. The Quest for Certainty: A Study of the Relation of Knowledge And Action. Kessinger Publishing, 2005.
[11] P. Fara. Science: a four thousand year history. OUP, 2009.
[12] R. W. Hadden. On the Shoulders of Merchants: Exchange and the Mathematical Conception of Nature in Early Modern Europe. State University of New York Press, 1994.
[13] J. Hannam. God’s Philosophers: How the medieval world laid the foundations of modern science. Icon Books, 2009.
[14] F. Jovanovic. Was there a “vernacular science of financial markets” in france during the 19th century? History of Political Economy, 38(3):531—545, 2006.
[15] F. Jovanovic and P. Le Gall. Does god practice a random walk? the ’financial physics’ of a nineteenth-century forerunner, Jules Regnault. The European Journal of the History of Economic Thought, 8(3):332—362, 2001.
[16] V. J. Katz. A History of Mathematics: An Introduction. Haper Collins, 1993.
[17] J. Kaye. Economy and Nature in the Fourteenth Century. Cambridge University Press, 1998.
[18] S. L. Lauritzen. Time series analysis in 1880: A discussion of contributions made by T. N. Thiele. International Statistical Review, 49(3):319—331, 1981.
[19] 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.
[20] A. Preda. Informative prices, rational investors: The emergence of the Random Walk Hypothesis and the Nineteenth-century ‘science of financial investments’. History of Political Economy, 36(2):351—386, 2004.
[21] B. Russell. An Outline of Philosophy. George Allen & Unwin (Routledge), 1927 (2009).
[22] M. S. Taqqu. Bachelier and his times: A conversation with Bernard Bru. Finance and Stochastics, 5(1):3—32, 2001.

 [23] Y. Biondi (trans J. d’Avingnon and G. Poitras). Duvillard’s Recherches sur les rents (1787) and the modified internal rate of return: a comparitive analysis. In G. Poitras, editor, Pioneers of Financial Economics: contributions prior to Irving Fisher, pages 116—148. Edward Elgar, 2006.  

Tuesday, 20 August 2013

Faith, Hope and Charity in the genesis of actuarial science

Before the crisis caused by the South Sea Company, Daniel Defoe had written in 1719 that he “hoped that mathematicians might cure the reckless of their passion for cards and dice with a strong dose of calculation” Gigerenzer [1989, p 19], and after the Bubble he returned to the theme in Complete English Tradesman in which he observed
A tradesman’s books are his repeating clock, which upon all occasions are to tell him how he goes on, and how things stand with him in the world: there he will know when it is time to go on, or when it is time to give over; and upon his regular keeping, and fully acquainting himself with his books, depends at least the comfort of his trade, if not the very trade itself. If they are not duly posted, and if every thing is not carefully entered in them, the debtor’s accounts kept even, the cash constantly balanced, and the credits all stated, the tradesman is like a ship at sea, steered without a helm; he is all in confusion, and knows not what he does, or where he is; he may be a rich man, or a bankrupt—for, in a word, he can give no account of himself to himself, much less to any body else. Defoe [1726, Chapter I]
Defoe seems to be endorsing Locke’s empiricism, with a nice dose of Puritan Prudence, with respect to finance. It was not English tradesmen who would demonstrate the usefulness of Defoe’s advice, to employ mathematics built on Locke’s philosophy, but Scottish clergymen.
When the Scottish Church was reformed in 1560, so that married men could be ministers, it became necessary to provide for ministers’ widows and their children. In 1672 the Scottish Parliament passed the ‘Law of Ann’ which legislated that widows were entitled to half a year’s stipend from their husband’s parish, with half of that going to any children. By the 1730s this one-off payment was regarded as insufficient, and the Church of Scotland should set up a ‘general fund’ from which pensions for widows could be drawn and in 1742 a scheme was proposed by two Edinburgh ministers, Robert Wallace, born in 1697 in Kincardine, and Alexander Webster, born in 1708 in Edinburgh.
Despite the reputation that Scottish Presbyterians sometimes have, Wallace and Webster appear to be convivial characters. Wallace was a founder member of a university ‘debating’ (drinking) club, the Rankenians, and it was said of Webster that it was “hardly in the power of strong liquor to affect Dr Webster’s understanding of his limbs” Ferguson [2008, p192]. Both clergymen were popular preachers, in fact Webster was considered so eloquent that a friend asked him approach a wealthy young lady, Mary Erskine, concerning the friend marrying Mary. Webster was a little to good at persuasion and Mary said to him “You would come better speed, Sandy, if you spoke for yourself”. Alexander and Mary lived happily ever after Dow [1992, p 27]. (Mary’s sister was the mother of James Boswell, Samuel Johnson’s friend.)
Wallace and Webster were also skilled mathematicians, and Wallace was part of a group which founded the Philosophical Society in 1735, which then became the Royal Society of Edinburgh in 1783. This group was led by the mathematician Colin Maclaurin who was regarded as the United Kingdom’s leading mathematician after Newton died in 1727. In 1742 Maclaurin wrote a Treatise of Fluxions in defence of Newton’s ideas around rates of change, which Newton called fluxions Boyer and Merzbach [1991, p 397] and underpinned the physics in his Principia. He wrote his Treatise in order to put Newton’s ideas on a firm basis, not because of any doubt coming from scientific circles but because they had been attacked by Bishop George Berkeley in 1734 in a tract called The Analyst. Berkeley was a Tory, an opponent of the Whigs Defoe and Locke, who “had been nettled on having a sick friend refuse spiritual consolation” Boyer and Merzbach [1991, p430] because the astronomer, Edmund Halley, had convinced him that Christian dogma was untenable. The subtitle to The Analyst was
Or a Discourse Addressed to an Infidel Mathematician Wherein It Is Examined Whether the Objects, Principles, and Inferences of the Modern Analysis are More Distinctly Conceived, or More Evidently Deduced, than Religious Mysteries and Points of Faith. “First Cast the Bean Out of Thine Own Eye: and Then Shalt Thou See Clearly to Cast Out the Mote Out of Thy Brother’s Eye.” Boyer and Merzbach [1991, p 430]
The problem was, Bishop Berkeley had a valid mathematical criticism of fluxions, which Maclaurin needed to address, and would not be resolved for another hundred years.
In response to the problem of funding widows’ pensions, in 1741 Webster wrote to all the presbyteries (parishes) of the Church of Scotland asking for statistics on ministers’ deaths and their dependants, alive and dead, for the period March 1722 to March 1742. Meanwhile, Wallace tackled the theory behind the problem using information provided by that “Infidel Mathematician” Edmund Halley. In 1693 Halley had been asked by the Royal Society to analyse data relating to births and deaths from the German city of Breslau (Wroclaw) for the period 1687 to 1691 which Leibnitz had provided Poitras [2000, p 197]. This data enabled Halley to construct a more precise life-table than Graunt’s, which had estimated the ages of deaths, and using this data, Halley solved the problem of valuing an annuity independently of Jan de Witt.
In 1743 Wallace compared the data gathered by Webster to that in Halley’s work and realised the ministers were less likely to die young than the general population of Breslau. Wallace then calculated what premiums, paid by the ministers when they were alive, could yield annuities, pensions, to the widows. Wallace calculated the premium rates for four different classes of pensions as Hare and Scott [1992, p 59]
Class
Widows’ Annual Annuity
Ministers’ Contribution
1
£10
£2 . 12s . 06d
2
£15
£3 . 18s . 09d
3
£20
£5 . 05s . 00d
4
£25
£6 . 11s . 03d
The next set of calculations Wallace undertook were concerned with the cashflows in the early years of the fund. It would take time for the fund to build reserves from which to pay out to the widows and Wallace needed to make sure the fund did not fail within a few years of its establishment, and the fund would be founded on the basis of a one-off ‘marriage tax’, charged to all married ministers who joined the fund.
Wallace assumed that all 930 married ministers would join the scheme, all be it in different classes, and 800 ministers would pay the marriage tax in the first year. This would establish the fund with £7,560 and after the annuity payments, would be worth £5,900 at the end of the first year Hare and Scott [1992, p 64]. Wallace then asked Maclaurin to check his figures, more to give them authority than because he had any doubts, though Maclaurin did spot and correct an error. The trio, based as much on their faith in mathematics as their faith in God, were confident that the fund was structured in such a way that it would not fail.
Wallace travelled to London to get the Scottish MPs at the United Parliament to pass an Act establishing the Fund in March 1744 and it was a great success. Up until 1778 the fund’s capital never deviated by more than 5% from estimates calculated in 1748 Dunlop [1992, p 18]. Wallace moved on to be an important figure in the Church of Scotland but did not involve himself with its further development, which was managed by Webster. Maclaurin was not so fortunate, he was active in the opposition to the Young Pretender and fled south to England to avoid the rebels and the stress of the flight is believed to have caused his death in summer 1746.
The Scottish Ministers’ Widows’ Fund was the first fund covering insurance liabilities, either in general insurance or in life insurance, to be managed on a mathematical basis Hare and Scott [1992]. The Scottish Ministers’ Widows’ Fund was copied in the Presbyterian’s Ministers Fund of Philadelphia in 1761 and the following year the English Equitable Company was founded, the oldest public life insurance company until its failure in 2000.
The story of the establishment of the Scottish Ministers’ Widows Fund is a story of the triumph of British Empiricism. However, it can be more than that, it can be seen as an expression of the ‘Christian’ (misnamed they were evident in pre-Christian Rome and Greece) virtues of Faith, Hope and Charity. The fund was clearly Charitable, in the sense that the Church is concerned for the welfare of the Widows of its dead Ministers. Faith is the ability to believe without seeing, and the Latin root is fides captures the concept of trust. In this case the Minister’s had Faith in the data, as advocated by Defoe. Today Science rests on Statistics, which provides a formalisation of when we can trust data: it creates ‘knowledge’ out of data. While Faith looks backwards, Hope looks forwards and in mathematics is represented by Probability through the operation of Expectation. While the link between Probability and the virtue Hope is obscure in English, it is explicit in French using the word espérance, ‘hope’, when referring to mathematical expectation. The root of espérance is in the Roman goddess Spes, usually depicted with a cornucopia and flowers, and is linked to the Greek daimon Elpis, which was the spirit of hope left in Pandora’s Box.
Deirdre McCloskey, in her examination of the Bourgeois Virtues, challenges Hume’s fact/value dichotomy McCloskey [2007, p 265]
Does it contain any abstract reasoning concerning quantity or number?, No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it to the flames: for it can contain nothing but sophistry and illusion
McCloskey asks
No theology: no natural law: no ethics. We are only to have mathematics on the one hand and on the other the “sciences”
My point is that while the establishment of the Scottish Ministers’ Widows’ Fund is mathematical and scientific, it was also moral, and by separating fact from value we lose something of the meaning of the Fund.

References

C. B. Boyer and U. T. Merzbach. A History of Mathematics. John Wiley and Sons, 1991.
D. Defoe. The Complete English Tradesman. Project Gutenburg, 1726. www.gutenberg.org/files/14444.
J. Bremner Dow. Early Actuarial Work in Eighteenth Century Scotland. In A. I. Dunop, editor, The Scottish Ministers’ Widows’ Fund 1743—1993. St. Andrews Press, 1992.
A. I. Dunlop. Provision for Ministers’ Widows in Scotland — Eighteenth Century. In A. I. Dunop, editor, The Scottish Ministers’ Widows’ Fund 1743—1993. St. Andrews Press, 1992.
N. Ferguson. The Ascent of Money: A Financial History of the World. Allen Lane, 2008.
G. Gigerenzer. The Empire of Chance: how probability changed science and everyday life. Cambridge University Press, 1989.
D. J. P. Hare and W. F. Scott. The Scottish Ministers’ Widows’ Fund of 1744. In A. I. Dunop, editor, The Scottish Ministers’ Widows’ Fund 1743—1993. St. Andrews Press, 1992.
D. N. McCloskey. The Bourgeois Virtues: Ethics for an Age of Commerce. University of Chicago Press, 2007.

    G. Poitras. The Early History of Financial Economics, 1478—1776. Edward Elgar, 2000.  

Friday, 16 August 2013

Lady Credit

Economics is can be seen as being primarily concerned with managing resources when faced with scarcity; the maximisation of expected utility. An alternative view is that aspects of economics, particularly finance, are concerned with managing resources when faced with uncertainty. This distinction is not new, Moses ben Maimon, Maimonides, argued that the suffering of mankind is not because they were expelled from the Garden of Eden into a world of scarcity but because they were expelled into a world of uncertainty. 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
The first definition of economics is conventional, and as far as I can work out goes back to John Stuart Mill’s argument that
[Political economy] is concerned with [mankind] 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. It predicts only such of the phenomena of the social state as take place in consequence of the pursuit of wealth. It makes entire abstraction of every other human passion or motive; except those which may be regarded as perpetually antagonizing principles to the desire of wealth, namely, aversion to labour, and desire of the present enjoyment of costly indulgences.
and the subsequent definition that Economics is
The science which traces the laws of such of the phenomena of society as arise from the combined operations of mankind for the production of wealth, in so far as those phenomena are not modified by the pursuit of any other object.
Mill distinguished the ‘science’ of economics from the “art’ of ethics, and at the end of the nineteenth century, John Neville Keynes (Maynard Keynes’ father) argued that there were two sides to economics, the ‘positive, abstract, deductive' science of Mill, and the 'an ethical, realistic, and inductive science', of the German Historical School, and the choice of approach was determined by the nature of the question. Fifty years later, Lionel Robbins, a robust opponent of Maynard Keynes, offered the following definition
Economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses
Robbins adheres to the English tradition (as described by Neville Keynes) of separating the ‘science’ of economics from the 'art’ of ethics but this distinction grew into a dichotomy in the second half of the twentieth century.
The second definition, less conventional, is related to John Dewey’s argument for Pragmatism: that traditional philosophies had focussed on a forlorn ‘Quest for Certainty’ in an attempt to replace ‘belief’ (or judgement) with 'knowledge’. In doing this, abstract, deductive approaches dominated knowledge generated in practice. Whereas academic scholarship attempted to ignore the issue of uncertainty and randomness, vernacular knowledge had to face the brute fact head on. In the context of economics the effect was to start with a 'rational agent' handling physically tangible objects and then deduce hypotheses independent of ethical considerations. These hypotheses rarely stood up to empirical testing, resulting in the emergence of Behavioural Economics in the final quarter of the century. The Pragmatic approach to economics is that it should start with society, infused with morals, and then look to see how society could be improved. It is because I adopt a Pragmatic approach based on the axiom that the world is uncertain that I think Credit (associated with belief, trust), rather than Money (associated with minting coin), should be at the heart of finance.
These observations are made as a preamble to my case to support the proposition that Credit should be the central topic of Finance, not Money.  A while ago I posted a piece on the lack of financial activism, this was read as a case for Credit, which was an afterthought in the original piece.
Theories of money can be categorised into two classes: commodity theories or representative. theories Commodity theories hold that money derives its value from some object with intrinsic value (gold, silver, copper, iron, cigarettes, wheat, etc). In the European tradition this idea goes back to Aristotle (at least) who argued that money emerged to facilitate exchange and to overcome ‘the double coincidence of wants’; that in order for exchange to take place the two parties must desire what the other has. In neo-classical economics ‘money’ is simply a technical device that facilitates transactions and does not represent any single commodity, or even the labour that goes into a product, but all components of the economy. As such, while it is all’ commodities it is also totally separate from the ‘real’ economy (it is as if money is deified, everywhere but nowhere). Money should be controlled because it represents a measure; allowing it to grow or shrink is as problematic for economics as allowing the ‘standard metre’ to grow or shrink would have to physics; this quantity theory of money dominated the monetarist rhetoric of Margaret Thatcher and Ronald Reagan.
The narrative that money emerges out of barter has become part of received wisdom and as with most ‘common sense’, it has no basis in fact. Just as astrophysicists use telescopes to look back in time, anthropologists visit isolated communities to see how society evolved, and the evidence of this research is summarised by Caroline Humphrey (a.k.a. Lady Rees of Ludlow)
Barter is at once a cornerstone of modern economic theory and an ancient subject of debate about political justice, from Plato and Aristotle onwards. In both discourses, which are distinct though related, barter provides the imagined preconditions for the emergence of money ...[however] No example of a barter economy, pure and simple, has ever been described, let alone the emergence from it of money; all available ethnography suggests that there never has been such a thing. [Humphrey, 1985, p 48]
What actually happens in practice is that when individuals knew each other, exchange was based on reciprocity; a gift would be given in the anticipation of it being reciprocated in the future (when they don’t know each other there is barter, but in such situations money cannot emerge because cowrie shells might be important in one society, and gold in another). One of the most famous stories illustrating the role of reciprocal exchange has concerns an anthropologist who after spending some time with bushmen, gave one of them his knife. When visiting the group some years later, anthropologists discovered that the knife had been owned, at some point in time, by every member of the community. The knife had not been communally owned, its ownership had passed from one person to the next and its passage was evidence of a social network in the community, just as the motion of planets is evidence of an, otherwise invisible, gravitational field.
One of the most studied examples of these sorts of systems was that of indigenous people around Vancouver in Canada. A young man would lend five blankets to an older, richer person, for a year and they would be repaid with ten blankets (going to an American school in the 1970s I learnt the pejorative term ‘Indian giving’). A similar situation existed in the Southwestern Pacific were strings of shells, whose value was purely ceremonial, were lent by a young man, sometimes to an unwilling borrower, at very high rates of interest Homer and Sylla [1996, pp 22—23]. Many cultures had similar systems where by a gift had to be reciprocated by a greater gift in return these systems played a critical role in gluing society together by establishing bonds between the rich and poor, the old and young.
One particular manifestation of gift giving is sacrifice. Just as gift giving amongst humans creates a contract between them, giving a gift to a god obliges the deity to return the favour. Sahlins [1972 (2003)], Mauss [1924 (2001] At about the same time as cities began to appear people started making ornaments out of electrum (an alloy of gold and silver), copper and gold, metals found naturally in nature. Metals have an almost unique, natural, physical property; they reflect light. The only other material that stone-age humans would have come across that reflected light would have been water, which along with sunlight is the basis of life Diamond [1998, pp 362—363], Betz [1995], Landes [1999, pp 70—73]. The first time a human spotted a nugget of gold sparkling in a river bed they must have experienced a sense of awe, here was an object that seemed to capture life-giving sunlight and water.
Religiously significant metals became important as temple offerings and temples began accumulate large reserves. Followers of the religion would look to acquire the metal, to enable them to make an offering to the gods, and so the metal became the commodity in the most demand. The Ancient Egyptians, who had easy access to gold, used Cypriot copper for their religious offerings while the Cypriots used Egyptian gold. In Mesopotamia, the metal of choice was silver. Pryor [1985], Eagleton and Williams [1997]. When ‘Currency Cranks’ or ‘Bullionists’ argue that the economy would be improved by reverting to a Gold Standard because gold has an ‘inherent value’ they need to explain where is the value in gold, apart from its inherent symbolic, representative, value.
We don’t know much about economics in the ancient cities apart from for Mesopotamia, which has left hordes of clay tablets describing financial transactions. The economy was dominated by the temples who received rents and tribute, provided religious services and loans. The cuneiform tablets recorded the debits and credits associated with these activities. The transactions were denominated in shekels, crude bars of silver. Coins, metal tokens, rarely, if ever, actually changed hands. Later, we read in Homer that the Greeks priced goods in terms of oxen, the animal that was reserved for sacrifices to the gods, and then the treasury of Athens, the richest Greek city after the Persian Wars, was in the Temple of Athena and Jesus cast the money-lenders, exchanging worldly Roman money for divine shekels, out of the Temple.
As states emerged money became defined by the state, fiat money or chartalism. Fiat money is central to Modern Monetary Theory that argues money is created when governments pay for services using tokens, which it then redeems through taxation. This theory contradicts Monetarism in arguing that national deficits are not necessarily detrimental to the economy.
There is firm evidence to support money being a state creation. Money appears in Europe at the time the Greek city states became reliant on mercenary armies. Cities paid soldiers in gold to conquer some community, the soldiers then spent the gold in the colonised lands and the state recovered the gold by taxing the colonised merchants and innkeepers using the tokens that the soldiers had paid for food and lodgings. Greek and Roman citizens never paid tax, only the conquered paid for the privilege and were bound to the conqueror by having to exchange their resources for the Imperial currency. The model would survive and drive colonialism in the modern age, in the 1920s the British taxed Kenya at a rate of about 75% of wages, forcing the colonised to grow cash-crops to be consumed by the colonisers. The Belgians did not tax the Congo — they relied on forced, rather than ‘free’ wage labour Ingham [2004, p 76].
Monetarists have long argued that the fall of the Roman Empire was facilitated by an economic collapse caused by a dilution of the currency resulting in inflation. The Monetarist explanation is that the Emperors’ needed more coins to pay their armies and since they had a fixed amount of gold bullion to make coins, the coins had to be debased. Since the ‘gold price’ of goods was fixed, the ‘money (coin) price’ had to rise, because with debasement more coins were needed to deliver a fixed quantity of gold. Advocate of fiat money theories counter argue that the Emperors raised taxes in the core provinces of Gaul, Spain and the Middle-East, and spent these taxes in Rome (public entertainment) and the frontier provinces (on the army). The core provinces obtained coins, tokens that enabled them to pay taxes, by selling goods to Rome. As long as this circulation was maintained all was well. However a combination of factors, over-reach by the Empire, natural famine and a decline in the supply of slaves — the main means of production— began to disrupt the circulation. Since the state still had to pay the army, coin flowed into the system, but taxes did not drain it out again and more money chased fewer goods, resulting in the inflation Ingham [2004, pp101—104].

Charlemagne reinvented the Roman empire in the West, and part of this process was the re-introduction of the Roman monetary system into an 'un-monetised' feudal economy where exchange was rare, that is one without currency circulating.  Because coin was scarce, Charlemagne's bureaucrats specified the exchange rate between common goods and money in order that the taxpayers could pay there tax.  If you were a small holder and had been assessed for one shilling tax, if you did not engage in the market economy you would not have a shilling, so the government told you a shilling equated to a cow.  This fixed the prices of cows, an unintended consequence, since Charlemagne's bureaucrats  probably couldn't care less about what was happening in the market place.  However the impact was enormous - there was no incentive to move goods from places of abundance to places of scarcity.
Fiat money is representative money but not necessarily credit money. In the Roman Empire banks did not exist, and the state could not fund its activity by borrowing from the market, as states started to do in the medieval period. There was a credit-debt type relation in the Roman economy, the state was buying goods with IOUs, in the form of the coin, which it redeemed through the tax system. If you were living on the Danube and felt the presence of the Goths more keenly than the Legions, you might well not bother to trade your produce for Roman tokens, causing scaricty at the centre and disrupting the circulation of currency.
Credit theories argue that buying and selling is about exchanging a good for credit. When I do work my employer gives me an IOU (ideally in the form of fiat money, which is in demand because I must pay taxes), I then offer this IOU to a grocer for food. If the grocer trusts the credit’ of the writer of the IOU, they will accept the IOU. The government can print as many IOUs as it likes, but if it issues too many, the grocer may lose faith in the Government’s fidelity to repay its IOU. If the grocer thinks there is a 50:50 chance of repayment, they might ask for twice as many IOUs. If the Chines feel the US government will not honour its promises, the USD/REN exchange rate will fall, an inflation will appear in the US and Chinese growth will slow.
I may want to buy something, like a house, that requires a more money than I have, I do not have enough IOUs to hand. In this case I can go to a bank, which can be seen as a technology that converts my own credit’ into money: banks make tangible an agent’s intangible credit Keynes [1971, chapter 2] just as machines make energy tangible as heat or motion. Governments have a role in this process by regulating the interest rate it will demand to realise banks’ credit, and banks use their realised credit to realise their customers’ credit.
Banks, in realising their customers’ credit, are often seen as feminine institutions
They create the new money which sets the wheels of production turning again. But they cannot procreate without a spouse. The newly born money must have a father as well as a mother. Someone must take the active, positive role of borrowing, spending, and employing, or the banks will remain barren. Winder [1959, p 81] quoting Strachey
In the early eighteenth century this identification of femininity with the concept of credit was widespread, and described in detail by Daniel Defoe. Between 1706 and 1709 Defoe published various articles on Lady Credit in his periodical, the Review of the State of the English. In 1706 he introduces her as
Money has a younger sister, a very useful and officious Servant in Trade ...Her name in our Language is call’d CREDIT ...
This is a coy Lass ...a most necessary, useful, industrious creature: ...[and] a World of Good People lose her Favour, before they well know her Name; others are courting her all their days to no purpose and can never come into her books.
If once she is disoblig’d, she’s the most difficult to be Friends again with us de Goede [2005, p28 ]quoting Defoe, 1706
Today, Defoe’s imagery may appear quaint, but he captures the elusive nature of ‘credit’.
The use of gender imagery to represent concepts like ‘credit’ is nothing new, the Greeks represented luck as the feminine, and unstable, Tyche and the Romans developed the idea into the unpredictable Fortuna, with luck, or good fortune, becoming associated with wealth. This imagery developed with the sixth-century, Christian, philosopher, Boethius writing in his Consolation of Philosophy
I know how Fortune is ever most friendly and alluring to those whom she strives to deceive, until she overwhelms them with grief beyond bearing, by deserting them when least expected Boethius [(2010, Book II]
Defoe’s Lady Credit is as fickle as Fortuna but has a particular feature, her coyness; the more you chase her, the less likely she is to respond,
for as once to want her, is entirely to lose her; so once to be free from Need of her, is absolutely to posses her. de Goede [2005, p29] quoting Defoe, 1709
In 1709 Defoe describes how stock-jobbers, the most speculative of animals, treated Lady Credit,
The first Violence they committed was downright Rape ...these new-fashion’d thieves seiz’d upon her, took her Prisoner, toss’d her in a Blanket, ravish’d her, and in short us’d her barbarously, and had almost murther’d her de Goede [2005, p34 ] quoting Defoe, 1709
Commodity theories are more popular than representative theories because they are perceived as simpler, and hence have the veneer of common sense logic. It is obvious that if money is a tangible, physical asset its quantity should correspond to some calculation of tangible of tangible objects. Since the physical planet is a closed system money is scarce and in this framework Ayn Rand’s argument that selfishness, the dominance of one’s own interests, is a virtue and altruism a vice, is inevitable.
For me, commodity theories are on an intellectual par with flat-earth theories and the enigma is why they persist. Society accepts that energy’ exists and its existence is manifested in heat and work, but are queasy that credit’ exists and is manifested in money. I think the issue is that most of us are taught about energy from an early age, there is a widely held coherent story that has developed over 150 years that we can tell our children. No such consensus exists with regard to the nature of money, and I think this is because science’ is uncomfortable about discussing the idea of credit, which seems tied up with moral ideology, it is much easier to talk about tangible things’. One observation a scientist might make is that the problem is energy is conserved whereas credit is not, but the obvious point to make to parents is is the love for children conserved (i.e. if a second child is born, does the familial love divide between the two with a corresponding loss of welfare)? If science accepts that everything is ideological but this is not the central issue: a consensus, which is objective by not being subjective, is what is needed, and consensus is developed through rational discourse (or Habermas’ communicative action).
That is the theory, now the practice. Why did Long Term Capital Management fail? LTCM had a simple business model, speculate on mis-pricings in the market and then borrow money in anticipation of the prices correcting themselves. The obvious risk in this model is that you are not as smart as you think you are, and that the market gets the prices right and you are wrong. The less obvious risk is that Lady Credit will abandon you in your hour of need. Donald MacKenzie MacKenzie [2003] summaries five explanations
  1. The partners in LTCM were guilty of greed and gambling (consciously reckless risk-taking); 
  2. LTCM’s partners had blind faith in the accuracy of finance theory’s mathematical models. 
  3. LTCM was over-levered too high a proportion of its positions were financed by borrowing, rather than by LTCM’s own capital. This third hypothesis, however, explains at most LTCM’s vulnerability to the events of August and September 1998: it does not explain those events. The most common explanation of them is: 
  4. On 17 August 1998, Russia defaulted on its rouble-denominated bonds and devalued the rouble. However, superimposed on the flight-to-quality, and sometimes cutting against it, was a process of a different, more directly sociological kind: 
  5. LTCM’s success led to widespread imitation, and the imitation led to a superportfolio’ of partially overlapping arbitrage positions.
   Most of these narratives of the failure of LTCM focus on the obvious risk, that the managers were dumb (which encompasses reckless and imprudent in borrowing). MacKenzie’s own explanation focuses on the markets as a complex network, and it was the interactions in the network that caused the problems.
MacKenzie highlights a fax that LTCM sent to its investors on 2 September
the opportunity set in these trades at this time is believed to be among the best that LTCM has ever seen. But, as we have seen, good convergence trades can diverge further. In August, many of them diverged at a speed and to an extent that had not been seen before. LTCM thus believes that it is prudent and opportunistic to increase the level of the Fund’s capital to take full advantage of this unusually attractive environment.
LTCM were acknowledging that they had made losses but in the crisis there was opportunity. Unfortunately this private e-mail became public and all that was communicated by it was that LTCM was making losses. This had the immediate effect that any assets that LTCM had a large holding of were sold in anticipation of a fire sale by LTCM, this depressed the value of LTCM’s holdings further. Speculators simultaneously started betting on LTCM’s failure, further depressing the value of their assets. As a result LTCM’s credit evaporated, the market lost its faith in the firm to repaid its loans and the firm could no longer fund its positions and collapsed. LTCM’s strategy was fine, the assets it held were mis-priced and eventually converged, but LTCM went bankrupt before the doubling strategy, the martingale, paid out.
Because the popular narrative, which created the consensus amongst the public, policy makers and practitioners alike, focused on the stupidity of LTCM rather than the collapse of credit in a social network, a decade later the Financial Crisis occured. Many commentators argued at the time that the Crisis of 2007-2009 was unusual in that it was a solvency crisis, not a liquidity crises, but I think this is a bit naive. French and German banks should have suffered similar losses to US/UK banks at the time but they did not, probably because they threw away their models that told them they had made losses. As a result they did not appear insolvent, and so retained some of their credit. Today finance is placing greater emphasis on credit risk, but the mainstream has responded to the Crisis more by a lurch to the empiricism of behavioural finance rather than engage with the metaphysics of faith, hope and charity around Lady Credit.

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