Humans are inherently risk averse. When offered a coin toss with a reward of $10,000 for heads but a loss of $10,000 for tails, most people would decline. They would likely agree to pay a significant sum to avoid the gamble, despite the expected value of the gamble being zero.

When economists describe the preferences of a person, they often build in some form of risk aversion. A risk averse person will always prefer a sum with certainty than a gamble with that expected value. One way that economists do this is by describing the preferences of a person as logarithmic. This means that the level of utility that an individual gets from, say, a sum of money increases at a diminishing rate. They might value an increase in their wealth from $1 to $10 the same as an increase from $10 to $100. These preferences then shape the choices that the person makes. For example, they might value of 50-50 gamble between $1 and $100 at only $10, despite the expected value of the gamble being slightly above $50.

Beyond the extensive research on preferences in the behavioural economics literature, the use of logarithmic preferences to approximate decision-making has some support in empirical work on how we view numbers in our minds. In 2008, Stanislas Dehaene and colleagues made a useful contribution to this area through their examination of whether our mental mapping of numbers was inherent or trained.

First, some background. As noted by the authors, there have been a number of experiments that showed that children mapped numbers to space in a logarithmic fashion. They noted that:

When asked to point toward the correct location for a spoken number word onto a line segment labeled with 0 at left and 100 at right, even kindergarteners understand the task and behave nonrandomly, systematically placing smaller numbers at left and larger numbers at right. They do not distribute the numbers evenly, however, and instead devote more space to small numbers, imposing a compressed logarithmic mapping. For instance, they might place number 10 near the middle of the 0-to-100 segment.

This logarithmic view of the world does not last. Between first and fourth grade children start to move from logarithmic to a more linear mapping of numbers. This transition is most pronounced across small numbers, and moves to higher numbers as they age. Some logarithmic mapping persists for very large numbers.

Dehaene and colleagues contributed to this picture through their examination of whether the move from logarithmic to linear mapping was a result of formal schooling or a natural process of brain maturation. To study this, they undertook some number-mapping exercises with the Mundurucu, an Amazonian group with little access to education or other instruments that may affect their perception of numbers (such as maps and rulers).

To test how they map numbers, the participants were given a line with one dot at one end and 10 or 100 dots at the other. They were then given a number of dots between either one and 10 or one and 100 and were asked to place them at the proper place on the line.

This exercise showed that logarithmic mapping persisted into adulthood for the Mundurucu. This was even the case for numbers between one and ten. These findings suggest that it is the experience of children who receive formal education in mathematics that shifts their mental mapping to a linear way. This could be through either through the formal education itself or some other cultural cause.

This study raises a number of implications for the way people’s risk preferences are formed. If people perceive quantities in a logarithmic fashion, they will tend to be risk averse. As they move to a more linear way of mapping numbers, this could coincide with a reduction in risk aversion. Does the education of children in mathematics tend to increase their risk tolerance through changing the way they see numbers?

This could be argued to have a number of follow-on effects. A reduction in risk aversion would naturally see an increase in risk taking activity. They will weight the possibility of great wealth higher and be willing to accept the risk of a larger loss to make it. An economy full of people with a greater risk tolerance could have more entrepreneurial activity, greater wealth (with some unlucky losers) and a larger tendency to chase wealth.

From a historical perspective, the questions become more interesting. Could the increasing degree of education over the last few hundred years have been training children to be more risk seeking in their activities? If so, could we argue that an environmental cue is part of the reason modern economies look the way they do?

An additional implication from the study is the manner in which large numbers are dealt with. From a logarithmic scale, large numbers appear closer together. If functioning with large numbers in an accurate fashion is important (for example, if it matters whether I pay you $100 or $110), the shift to a linear way of thinking will reap some important dividends. This is not so much a question of risk aversion but the ability to differentiate when numbers get large.

Time preference is a measure of one’s future orientation. It has been linked with long-term individual outcomes (as was shown by Mischel’s marshmallows) and influences macroeconomic outcomes such as the level of saving and investment.

Time preference is not consistent across countries. This was shown in a working paper by Wang, Rieger and Hens, who examined variation in time preference across 45 countries. They found significant cross-country variation in time preference and further, that it could not be explained by differences in interest rates or inflation. Instead, evidence was found for the variation being based on cultural factors, risk preferences (such the degree of loss aversion) and macroeconomic variables. I found the raw results interesting, and a contribution in themselves, but as I note below, it would be good to further tease out the explanations for the variation.

The paper was based on surveys conducted on university students in 45 countries. The first question on time preference was whether the subject would prefer to receive $3,400 now or $3,800 one month into the future (a wait-or-not question). The responses to this question showed a large degree of variation, ranging from 8 per cent of Nigerians who were willing to wait for the $3,800 versus 89 per cent of Germans. Austria, Switzerland, Denmark and Norway also had well over 80 per cent of the survey subjects who choose to wait (amusingly, some students in Norway complained the question was ridiculous as everybody would choose to wait). When the groups were split by cultural groups, Germanic-Nordic and Anglo groups demonstrated the highest level of patience, while the African group was the lowest.

The students were also asked a one-year and ten-year matching question, where they state what sum they would need to receive in one or ten years to be indifferent between that payment and payment of $100 now. The results to these questions showed that most people discounted the near future more than the far future, indicating that the classical consistent approach to risk does not hold. As a result, the authors calculated rates of time preference from the survey questions using the implicit risk and hyperbolic discounting approaches. The implicit risk approach is based on the idea that risk and time are conceptually separate. There is an implicit risk that the delayed outcome will not occur, so people try to avoid delaying positive consequences. Hyperbolic discounting results in people discounting the pay-off  by a large amount for small delays, but with a decreasing level of discounting as the pay-off moves further into the future. The implicit risk approach is mathematically equivalent to a quasi-hyperbolic discounting model, which is a tractable approximation of hyperbolic discounting based on a large initial discount for any delay, and then a constant lower discount rate beyond that point. Despite that mathematical equivalence, the implicit risk approach is typically treated as a rational response, while quasi-hyperbolic discounting is usually based on concepts such as lack of self-control.

Across the sample, the authors calculated a mean value of β (the risk or self-control part of the discounting) of 0.60. This means that for a delay, the mean respondent would value the pay-off at 60 per cent of what they would if they received the pay-off immediately. The United States had a value of 0.77, Japan of 0.70 and Germany of 0.60. The countries with the lowest values were former Eastern-bloc countries such as Georgia, Estonia, Russia and Bosnia and Herzegovina. Splitting the countries into cultural groups, East Europe (β=0.38) and Africa (β=0.43) had the strongest present bias, Anglo cultures the least (0.76) while the others cluster around 0.60. All cultural groups had a roughly similar long-term discount factor of between 0.77 and 0.84 per year, so after the initial impatience or risk response, there is less difference between groups.

The questionnaire also included questions to calculate the students’ degree of risk aversion, largely through lottery based questions, and some questions that sought to measure cultural dimensions such as individualism, uncertainty avoidance and long-term orientation. The authors regressed the waiting tendency results from the first question and present bias and long-term discount rate from the second question against the cultural measures obtained from the survey, their risk preferences and some other factors including age, gender and whether they were an economics major. They found that cultural factors such as individualism and long-term orientation had a significant effect. Higher risk aversion and loss aversion were also found to be statistically significant factors. (Is this link between risk and time preference a causal link, or are the attitudes to risk and rate of time preference subject to some other underlying variable?)

But despite the findings of statistical significance, it is hard to argue that these measures are important. The regression showed that, at best, 10.9 per cent, 12.2 per cent and 4.6 per cent of the variation in waiting tendency, present bias and the long-term discount rate can be explained by these factors combined. Many variables may be statistically significant, but as a predictive measure, they are not important.

Further, for some of the statistically significant findings, I would like to see the potential underlying factors teased out. What is the causal relationship between economic growth and time preference? While the regressions included whether the subject was “native”, immigration could be useful in teasing out the link between time preference and cultural factors, the external environment and inherent characteristics. Even though there are some similarities between the countries included in the survey, there is no substitute for comparing different cultures in the same environment. Immigrants who have been in the country for several generations could be used to examine any inherent characteristics.

Links this week:

1. Biology, behaviour and obesity.
2. Eric Crampton on the heritability of political preferences.
3. Polywater (HT: Joe Pickrell).
4. Matt Zwolinski defends the morality of markets.
5. Jason Potts on funding the arts.

I’m going to be away in the Malay Archipelago the next two weeks. I’ve scheduled some old posts (with accompanying promotional tweet) from my early blogging days for while I am away, but otherwise, it will be electronic silence from me. If you want to find me, try looking here:

Despite the massive influence of Richard Nelson and Sidney Winter’s An Evolutionary Theory of Economic Change within evolutionary economic circles, the book and the body of work it inspired has had a limited effect through mainstream economics. I believe there are a few reasons for this, but I’ve always thought that this 1996 speech by Paul Krugman to a bunch of evolutionary economists captures one of them:

To read the real thing in evolution – to read, say, John Maynard Smith’s Evolution and the Theory of Games, or William Hamilton’s new book of collected papers, Narrow Roads in Gene Land, is a startling experience to someone whose previous idea of evolution comes from magazine articles and popular books. The field does not look at all like the stories. What it does look like, to a remarkable degree, is – dare I say it? – neoclassical economics. And it offers very little comfort to those who want a refuge from the harsh discipline of maximization and equilibrium. … Evolutionary theorists, even though they have a framework that fundamentally tells them that you cannot safely assume maximization-and-equilibrium, make use of maximization and equilibrium as modelling devices – as useful fictions about the world that allow them to cut through the complexities. And evolutionists have found these fictions so useful that they dominate analysis in evolution almost as completely as the same fictions dominate economic theory.

Krugman illustrates his point with an example:

William Hamilton’s wonderfully named paper “Geometry for the Selfish Herd” imagines a group of frogs sitting at the edge of a circular pond, from which a snake may emerge – and he supposes that the snake will grab and eat the nearest frog. Where will the frogs sit? To compress his argument, Hamilton points out that if there are two groups of frogs around the pool, each group has an equal chance of being targeted, and so does each frog within each group – which means that the chance of being eaten is less if you are a frog in the larger group. Thus if you are a frog trying to maximize your choice of survival, you will want to be part of the larger group; and the equilibrium must involve clumping of all the frogs as close together as possible. Notice what is missing from this analysis. Hamilton does not talk about the evolutionary dynamics by which frogs might acquire a sit-with-the-other-frogs instinct; he does not take us through the intermediate steps along the evolutionary path in which frogs had not yet completely “realized” that they should stay with the herd. Why not? Because to do so would involve him in enormous complications that are basically irrelevant to his point, whereas – ahem – leapfrogging straight over these difficulties to look at the equilibrium in which all frogs maximize their chances given what the other frogs do is a very parsimonious, sharp-edged way of gaining insight.

It was an interesting paper to select for the example. While Hamilton did assume the frogs had a fixed instinct for wanting to minimise their chances of being eaten, Hamilton ran a simulation to show his point rather than solving a set of equations for an equilibrium. Krugman continues:

Now some people would say that this kind of creation of useful fictions is a thing of the past, because now we can study complex dynamics using computer simulations. But anyone who has tried that sort of thing – and I have, at great length – eventually comes to realize just what a wonderful tool paper-and-pencil analysis based on maximization and equilibrium really is. By all means let us use simulation to push out the boundaries of our understanding; but just running a lot of simulations and seeing what happens is a frustrating and finally unproductive exercise unless you can somehow create a “model of the model” that lets you understand what is going on.

I take Krugman’s argument to be a call for heterogeneity of approach. And in evolutionary biology, multiple approaches are often used. If we stick with William Hamilton, his famous 1981 Science paper with Robert Axelrod on the evolution of cooperation uses a dynamic out-of-equilibrium approach to examine how cooperation could initially emerge in a population of defectors. For that purpose, a maximisation and equilibrium approach is insufficient. However, this work was not done in a vacuum, and there was a lot of work using a maximisation and equilibrium approach that informed it.

Today, simulation and other methods of examining dynamic processes are becoming more prevalent in evolutionary research. Computers have come some way since Krugman’s speech in 1996. Much of the theoretical research on the evolution of handicaps or Fisherian runaway selection is now simulation based. However, although they are important and their use is growing, I’m tempted to agree with Krugman’s assessment that “evolutionary” approaches are not the dominant approach in evolutionary biology.

Given this, it is a challenge to argue that economics should be “evolutionary” when an evolutionary approach is not the dominant paradigm in the field that bears its name. One of the stronger signs of the lack of the “evolutionary” approach in evolutionary biology is that most of Nelson and Winter’s evolutionary models are not sourced from evolutionary biologists. There was not a body of work that could easily be transferred across.

I will, however, stop well short of saying that the use of evolutionary approaches is currently at the right level in either economics or evolutionary biology. Krugman goes on to criticise those who see maximisation and equilibrium as truths and not as useful fictions to discard when the time is right. There is certainly space for an evolutionary approach in economics.

For me, the strongest case for a more evolutionary approach in economics comes from the timeframes with which economics is engaged. In evolutionary biology, maximisation and equilibrium approaches typically assume plenty of time for the traits of interest to have evolved. Economics is more interested in short-term dynamics, possibly more in the style of ecological models where dynamic modelling is the norm. In that case, there may be a stronger case for evolutionary economics than for “evolutionary” evolutionary biology. *I’ve posted about other parts of this Krugman article before – here and here.

Richard Nelson and Sidney Winter’s An Evolutionary Theory of Economic Change is the book on which modern “evolutionary economics” is built. Published in 1982, Nelson and Winter took the ideas expressed by Armen Alchian and Joseph Schumpeter decades earlier and presented a direct evolutionary challenge to mainstream approaches to economic growth, technological progress and competition between firms.

Nelson and Winter’s conception of firms is a collection of heterogeneous organisations guided by routines, the evolutionary economic equivalent of genes. Firms search for innovative (or imitative) solution to improve their profits, with successful firms growing at the expense of the less successful. The process is fundamentally dynamic, as firms interact and create the relative competitive environment that each faces. That firms may not be able to find the best technological solutions, nor seek to optimise profit perfectly, further separates the evolutionary and orthodox approaches.

When Nelson and Winter describe their approach as evolutionary, it is not necessarily “evolution by natural selection” in a strict Darwinian sense. The “evolutionary” label relates to the focus on dynamic change, and even though they make suggestions such as viewing routines as genes, they do not seek to pin their approach precisely to the biology (Geoffrey Hodgson and Thorbjørn Knudsen, who advocate a Darwinian approach, seek to increase this precision). I don’t necessarily think this is problematic, as in a transparently specified model we can see how the dynamics work, be they Darwinian or not. Issues generally arise later when people generalise those results verbally, with a lack of precision then causing confusion.

There are a lot of things to like about this book. First, it is an example of a criticism of economics done right (although in some parts the criticism is a bit dated, in others as current as it ever was). Where Nelson and Winter have a specific criticism, they identify the mainstream economic approach, note the outcomes of that approach, undertake the analysis with their own approach and then show how the approaches produce different results. They then argue why their approach is superior. Whether you buy their arguments or not, its transparent and leads to a productive discussion.

For example, early in the book they take on Milton Friedman’s claim in “The Methodology of Positive Economics” in which Friedman states:

Let the apparent immediate determinant of business behavior be any­ thing at all – habitual reaction, random chance or what not. When­ ever this determinant happens to lead to behavior consistent with rational and informed maximization of returns, the business will prosper and acquire resources with which to expand; whenever it does not the business will tend to lose resources and can be kept in existence only by the addition of resources from outside. The process of natural selection helps to validate the hypothesis [of maximization of returns] – or, rather, given natural selection, acceptance of the hypothesis can be based largely on the judgment that it sum­marizes appropriately the conditions for survival

To test this, Nelson and Winter create a basic model of firm interaction, analyse it using an orthodox equilibrium approach as Friedman suggests can be done, and then examine it as a dynamic selection process between firms. They show that the orthodox and selection equilibriums do not correspond with each other, as in the selection approach nonoptimal rules may survive in equilibrium due to path dependency, novel environments may be created as the mix of firms changes (which changes what the optimal rules are, effectively creating an evolutionary mismatch), and firms may fail to discover the optimal rules.

Another part of the book I enjoyed was their analysis of skills. In the past, I have been critical of the level at which some evolutionary economic analysis occurs – this being generally at the firm level and not the level of the people within the firm (or even deeper, their genes). But in the chapter on skills, Nelson and Winter spend a lot of time asking how the people in a firm shape the behaviour of that firm. In later chapters and models, the limitations of firms in searching for new technologies or attempting to achieve their objectives are informed by this more atomistic analysis of the people in the firm. Nelson and Winter’s focus on the level of firms is a conscious choice of the most useful level of analysis rather than ignorance that the lower levels might matter.

Their discussion of the competition policy implications of some of their models was also interesting. Depending on the assumptions used, monopolies may drive faster technological progress and deliver greater benefits to consumers as they are able to capitalise on any innovations through their large market shares. This is particularly the case if imitation is easy, with imitators eroding the benefits that an innovator can obtain in the market. Conversely, a monopoly might then be the only source of innovation, which is problematic if it satisfices or has other decision rules that limit its investment in innovation when times are good. While producing at times ambiguous results, an evolutionary analysis could form the base for a decent critique of competition policy.

I’d read parts of the book before, but this was my first time reading it right through. For someone broadly interested in the topic but lacking a desire to play with specific models, I would recommend reading the first five and last two chapters. There is a lot of great material in it. The rest of the book is also useful, although harder work for the rewards delivered.

As an endnote, it is interesting how little effect this book has had on mainstream economics, despite the massive influence of this book in evolutionary economic (and to a lesser extent organisational theory) circles. I’ve posted about why this might be the case here.

Links this week:

1. Gary Marcus takes on John Horgan over the achievements of science.
2. The medicalisation of normality.
3. On neuroeconomics – we need to understand the processes underlying decisions to get microeconomics right.
4. Andrew Gelman on statistical significance: “A serious researcher can easily get statistical significance when nothing is going on at all …. And this can happen without the researcher even trying, just from doing an analysis that seems reasonable for the data at hand…So, given all this, the focus on p=.04 or .06 or .10 seems to be beside the point. It’s worth looking at … but what it’s focusing on is the least of our problems.”
5. A piece by Robert Shiller where, among other things, he defends the use of mathematics in economics.
6. A few more pieces of criticising economics – Chris Dillow, Alex Marsh and Diane Coyle.

From Boyd and Richerson’s The Origin and Evolution of Cultures (references removed):

The proposal that human intelligence is at the root of human cooperation is difficult to evaluate because of the ambiguity in what we might mean by intelligence in a comparative context. As the Tasmanian Effect [the loss of their toolkit in a small population] illustrates, individual human intelligence is only a part, and perhaps only a small part, of being able to create complex adaptive behaviors. In fact, we think ‘‘intelligence’’ plays little role in the emergence of many human complex adaptations. Instead, humans seem to depend upon socially learned strategies to finesse the shortcomings of their cognitive capabilities. The details of human cognitive abilities apparently vary substantially across cultures because culturally transmitted cognitive styles differ. Although we share the common intuition that humans are individually more intelligent than even our very clever fellow apes, we are not aware of any experiments that sufficiently control for our cultural repertoires to be sure that it is correct. The concept of ‘‘intelligence’’ in individual humans perhaps makes little sense apart from their cultural repertoires: humans are smart in part because they can bring a variety of ‘‘cultural tools’’ (e.g., numbers, symbols, maps, various kinematic models) to bear on problems. A hunter-gatherer would seem an incredibly stupid college professor, but college professors would seem equally dense if forced to try to survive as hunter- gatherers (a few knowledgeable anthropologists aside). Even abilities as seemingly basic as those related directly to visual perception vary across cultures. Second, intelligence implies a means to an end, not an end in itself. Individual intelligence ought to serve the ends of both cooperation and defection. We suspect that actually defection, requiring trickery and deception, is better served by intelligence than cooperation. Game theorists assuming perfect, but selfish, rationality predict that humans should defect in the one-shot anonymous prisoner’s dilemma, just as evolutionary biologists predict that dumb beasts using evolved predispositions will.

I’ve sat on that passage for a while now, contemplating turning it into a larger blog post. But for the moment, the abstract for this paper from Garett Jones points to the crux of my response:

Are more intelligent groups better at cooperating? A meta-study of repeated prisoner’s dilemma experiments run at numerous universities suggests that students cooperate 5–8% more often for every 100-point increase in the school’s average SAT score. This result survives a variety of robustness tests. Axelrod [Axelrod, R., 1984. The Evolution of Cooperation. Basic Books, New York] recommends that the way to create cooperation is to encourage players to be patient and perceptive; experimental evidence suggests that more intelligent groups implicitly follow this advice.

There is some evidence that patience is enough when the game is not particularly cognitively demanding (noting that patience and cognitive ability are positively correlated in most studies). But beyond a certain point, intelligence and cooperation appear to go hand-in-hand.

In the process of listening to audio versions of some of the less arduous books on my reading list, I have just listened to Richard Thaler and Cass Sunstein’s Nudge.

The ideas in the book have been discussed in the public realm often enough that the book didn’t contain any surprises, although the emphasis in the book is a touch different from that in public debate. That difference in emphasis largely relates to the first word of Thaler and Sunstein’s philosophy, “libertarian paternalism”, and how nudges could be used to increase freedom.

Unlike public policy discussion of nudges which always seem to be on top of existing regulation, Sunstein and Thaler discuss how nudging could be used to wind back government involvement and increase freedom. They cover, among other things, school choice, getting the state out of marriage, allowing waiver of the ability to sue for medical negligence and allowing people to ride motorcycles without a helmet if they choose to opt out after suitable warnings.

Their discussion of how nudges could apply to marriage was the most interesting part of the book. They suggest that marriage should be the domain of private institutions, with the role of the state to set default rules that apply if there is no agreement to the contrary. If a couple splits, how much support should someone provide to their partner who has low career prospects due to the time they spent raising children? Appropriate default rules would give protection as they would likely stick (particularly as most people do not expect to divorce) and if they are amended, there will need to be transparent agreement between the parties. This nudge could provide protection to the vulnerable member of a couple and get the government out of marriage.

I’m not convinced by the “slippery slope” argument against nudges, as the slope toward regulation is already well oiled, and would like to see nudges used as a push toward sliding the other way. What about legalising a range of drugs with warnings? Or an ability to opt out of government provided services in exchange for tax breaks after you are nudged through, say, financial advice requirements (Bryan Caplan makes some of these arguments)? Libertarians should be more aggressive in seeing how nudges can wind back hard regulation.

And as an end note, this is another book that I’m glad I did via audiobook. If you’re familiar with much of the behavioural science literature, the book covers a lot of stuff you already know. And when you come to the chapters on money where Thaler and Sunstein tell “econs” to skip those sections, do it. You really won’t learn anything. That said, I am sure there are a lot of bureaucrats and politicians who, among others, should read the whole book.

Links this week:

1. David Dobbs on progress in genetics.
2. Steve Horwitz on what makes libertarians cry.
3. The uncertain biological basis of morality.
4. Eugene Fama on his Nobel.
5. A great story of an amateur pulling apart a psychological theory (an exception to the psychology equivalent of Sign 1 of a good critique).
6. The great interviews on the origin of the Human Behavior and Evolution Society continue. This time, Napoleon Chagnon:

In the comments, Rory Sutherland writes:

One favour to ask. I completely agree with you that Behavioural Economics should be called Behavioural Science. But

1) We don’t really to decide what things are called. Darwin only used the word “evolution” a handful of times.

2) It is a very valuable term as a Trojan Horse. If I want to get people studying for MBAs, say, or people in finance, to take behavioural science seriously, anything with the word “economics” in it will get their attention: anything with the word “psychology” in it, by contrast, will probably make them think of couches and hypnosis.

3) Since economics has become a dominant ideology in business and policy-making, and since one pressing job for behavioural science is to encourage people in such positions of influence to incorporate behavioural science into their thinking, any name which suggests that their pre-existing model (in which they have already invested an immense amount of thought and effort) needs be *improved* will be more successful than any head-on assault which suggests their model is wrong and needs to be *replaced*. After all, loss aversion and the endowment effect apply to ideas as well as things. There is hence nothing wrong with sugaring this pill if it helps people swallow it. It is simply easier to switch from “economics” to “behavioural economics” than it is to give up “economics” entirely – just as it is easier to switch from cigarettes to e-cigarettes than it is to give up smoking completely.

So, As a definition, “behavioural economics” is rather dodgy; but as a rebranding effort, it is genius.

I work in advertising not academia. For a mixture of principled and self-interested reasons I would like behavioural science to have an influence commensurate with its importance. If that means it’s sometimes called something different, it’s a trade-off I can easily accept. But it is monstrously unfair to those people in psychology and behavioural science who must sometimes feel the baton has being snatched from them within sight of the finishing line.

That’s a fairly important “but”. How much of what I do is enabled in economics faculties because there is a body of work labelled “behavioural economics”?