Links this week:
In a new article by Eduardo Undurraga and colleagues (HT: Neuroskeptic):
Math skills and market and non-market outcomes: Evidence from an Amazonian society of forager-farmers.
Research in industrial nations suggests that formal math skills are associated with improvements in market and non-market outcomes. But do these associations also hold in a highly autarkic setting with a limited formal labor market? We examined this question using observational annual panel data (2008 and 2009) from 1,121 adults in a native Amazonian society of forager-farmers in Bolivia (Tsimane’). Formal math skills were associated with an increase in wealth in durable market goods and in total wealth between data collection rounds, and with improved indicators of own reported perceived stress and child health. These associations did not vary significantly by people’s Spanish skills or proximity to town. We conclude that the positive association between math skills and market and non-market outcomes extends beyond industrial nations to even highly autarkic settings.
One nice element of this study is that the effect of math skills on economic outcomes is not through a “sheepskin effect”, whereby the benefits accrue to a degree or diploma, as there is no formal labour market where signals of that kind are used. In modern economies, it is hard to separate sheepskin effects from gains due to skills. In this case, the absence of a sheepskin effect means that it is the math skills themselves (or the general intelligence underlying those skills) that are paying off.
Links this week:
From Richard Posner (HT: Ryan Murphy):
[Behavioral economics] is undertheorized because of its residual, and in consequence purely empirical, character. Behavioral economics is defined by its subject rather than by its method and its subject is merely the set of phenomena that the most elementary, stripped down rational-choice models do not explain. It would not be surprising if many of these phenomena turned out to be unrelated to each other, just as the set of things that are not edible by man include stones, toadstools, thunder-claps, and the Pythagorean theorem. Describing, specifying, and classifying the empirical failures of a theory is a valid and important scholarly activity. But it is not an alternative theory. …
The behavioralists’ lack of interest in, and indeed hostility to, evolutionary theory is an example of their lack of theoretical ambition. But it is more. Most though by no means all behavioralists are political liberals. The use of evolutionary theory to explain human social rather than merely physical traits, the use that goes by the name “sociobiology” (recently renamed by its proponents “evolutionary ecology” because of the negative connotations that “sociobiology” had acquired among the politically correct) is anathema to liberals – as, indeed, is economics; and much of “behavioral economics” is really anti-economics. Political bias is especially conspicuous in the neglect by the behavioralists of vengeance, though it is the best attested example of the “fairness” instinct. Liberals do not like vengeance and prefer to think that our instinct for fairness is dominated by altruistic concerns that might provide a foundation for organizing society along socialist or collectivist rather than free-market lines.
The rest of the article is worth a read, although Posner’s defence of rationality is a touch too much.
Links this week:
Otherwise, I’m now back from holidays and almost over some tropical fever I managed to pick up, so regular blogging should recommence in the next few days.
An interesting idea in Herb Gintis’s review of The Origin of Wealth (pdf):
One of the ironies of history is that if the Walrasian model were plausible, there would be no need for real markets, real competition, or even capitalism itself. Socialism, consisting of a bureau of technocrats implementing the Walrasian auctioneer, could harness the general equilibrium system to a system of public ownership of wealth. This aspect of the general equilibrium model was clearly understood by Oskar Lange, F. M. Taylor, and Enrico Barone in their famous defense of market socialism (Barone 1935, Lange and Taylor 1938). This defense was so successful that it induced Josef Schumpeter to predict the imminent demise of capitalism (Schumpeter 1942), and led Friedrich von Hayek to rethink, and finally abandon, his commitment to neoclassical theory (Hayek 1945).
Ironically, however, Neoclassical theory has been an unrelenting defender of capitalism, and by casting its lot with real-world “competition” and real-world “markets”, it has thereby made a strategic choice that ensured its victory over the Socialists, the Syndicalists, the Institutionalists, the Populists, the Anarchists, the Communalists, and the other various movements that proposed alternatives to capitalism. Nevertheless, neoclassical theory is quite incapable of explaining what role “competition” and “markets” in fact play in a successful economy, since the terms refer to completely different concepts in Walrasian theory and in economic reality.
In the academic literature at the intersection of economics and evolutionary biology, evolution of time preference (patience) is one area that has received much attention. This makes some sense, as most economic models that consider decisions over time include time preference. Time preference is normally included in the model through a discount rate of a fixed value, so an evolutionary analysis might help in determining what that value is.
One of the first articles to ask what rate of time preference might be expected to evolve was by Ingemar Hansson and Charles Stuart, who examined the intergenerational rate of time preference. Intergenerational time preference is reflected in the rate of saving of one generation for the benefit of following generations. The first generation sacrifices their own consumption for consumption of their descendants.
This paper is another of those that, at least for the headline result, should strike one as obvious. Time preference would evolve such that when the person seeks to maximise utility (in an economic sense), they will also be maximising fitness. In this case, they would follow the “golden rule” of saving, which is the rate of saving that maximises the steady-state level of consumption across generations.
This outcome contrasts with empirical evidence that the golden rule tends not to be followed, with savings rate in developed, Western countries well below the golden rule. Savings rates are somewhat closer to (and sometimes argued to be higher) than the golden rule level in Asian countries. Why there is this departure requires consideration of other factors, such as aggregate risk (as Robson and Samuelson consider in this paper).
Hansson and Stuart determined that, if people followed the golden rule of saving, the discount rate would reflect the long-term population growth rate. This requires that no generation be weighted less than any other generation, which indicates a strong concern about future generations.
Based on population growth in a number of European countries since 1500, Hansson and Stuart suggested that the discount rate implied by their model would lie between zero and a few per cent per year, or between zero and one per generation. While they selected population growth rates since 1500 largely due to the lack of earlier demographic data, their upper bound estimate implicitly assumes that evolution of time preference can be relatively rapid to reflect recent population growth rates. In this case, it would also suggest that discount rates are increasing. As population growth increases, one should cut saving and focus on consumption today.
Moving beyond the headline result, an interesting part of the paper is when Hansson and Stuart ask what are the consequences of their model for economic growth. A harsh environment may increase the marginal benefit of consumption (the benefit from each additional unit) and decrease population density, which will in turn increase the level of labour that each person produces. As labour supply increases, this in turn increases the productivity of and the level of capital.
Following this logic, the authors suggest that harsh natural environments select for genotypes that have a stronger preference for saving, leading to an equilibrium with low population density and high per-capita capital. Selected traits include a preference for work and accumulation of physical capital. Hansson and Stuart suggest that this might explain why humans left the Malthusian state first in regions with harsh winters.
This results seems intuitive, although it is an interesting contrast with a Malthusian model of the economy. In a Malthusian model, high levels of technology and productivity are reflected in high population densities. To reconcile Hansson and Stuart’s thinly populated, harsh environment with this Malthusian picture, it might be necessary to imply that preferences were shaped when the first populations entered the harsh regions, and that preferences have not significantly changed despite these previously unpopulated environments now having much higher population densities.
One interesting comment in the paper refers to a methodological argument by Stigler and Becker, who stated that it is worth assuming that preferences do not differ importantly between people. Hansson and Stuart suggest that this is the case where the population to be modelled consisted of a homogeneous people from a given environment, but that this would not be as applicable in a “melting pot” such as the United States.
It seems obvious that having multiple wives is a good thing for the fitness of a man. Similarly, having the women in a population monopolised by a small number of men is not good for the fitness of those men who miss out on a mate. In such a society, the large difference in fitness between the haves and the have-nots would be expected to result in strong sexual selection.
Having noted the obvious, an article in Evolution and Human Behavior by Moorad and colleagues presents an interesting illustration of this situation. They examined the strength of sexual selection in a population of Utah men born between 1830 and 1894, with the rate of polygamy among married men dropping from over 17 per cent among some year groups born in the 1930s to less than 1 per cent among those born at the latest dates. These men faced a ban on polygamy in 1862, among other increasing social pressures against multiple marriages. The authors’ analysis of the population data allowed them to estimate the strength of sexual selection over this period and to isolate which factors contributed to reproductive success.
The headline finding from the study is that between 1830 and 1894, the strength of sexual selection in this population dropped by 58 per cent. This authors calculated this reduction from changes in Crow’s Index, which sets an upper limit on the rate of evolutionary change. Crow’s index is an upper limit as, first, not all differences in fitness may be due to phenotype. An environmental or random cause may be relevant. Second, phenotypic selection is only genetic to the extent that the genotype associated with the higher fitness is passed to the next generation.
Moorad and colleagues do not attempt to tease out the phenotypic or genetic selection in this sample. I am not sure how they could. However, it is reasonable to assume that changes in total selection are closely related to changes in the underlying level of genotypic and phenotypic selection.
The authors also made estimates of the costs and benefits of the polygamous mating system for men and women. They did this by examining the Bateman gradients, which are a measure of the change in reproductive success for a given change in mating success. In the 1830s, the Bateman gradient for men was 5.87, meaning that for each extra mate a male could expect almost six extra offspring. By the 1890s, this had dropped to 1.92. For women the gradient was slightly positive, increasing from 0.195 to 0.671 over the course of the study period.
The authors made a more interesting use of the Bateman gradient when they determined the gradient for women for each additional mate that a man has. This comes back to the classic trade-off question – do the reduced resources available to a woman from having to share the male’s resources with more wives outweigh the potentially higher quality of the man that a woman can obtain in the polygamous system? The answer to this question was yes (at least in terms of number of children) – there was a slightly negative gradient in the 1830s (starting at -0.06), which dropped to a low of -1.36, before ending at -1.11 in the 1890s. In the 1890s, each additional wife resulted in the other wives having, on average, one child less. The woman would want to hope that they are particularly high quality children.
A further piece of information that Moorad and colleagues teased out was how much a man’s increased fitness, due to additional wives, comes from increased reproductive rate or from a lengthened reproductive tenure. At the beginning of the sample, increasing the number of wives increased both the rate and tenure of reproduction. This switched towards the 1890s however, with increased wives only extending the tenure and coming at the cost of the rate of reproduction. This reflects the fact that towards the end of the sample, additional wives were normally the product of serial monogamy. For the few polygamists around at that stage, they still had the benefit of both an increased reproductive rate and tenure.
I enjoy studies like this. Even though they sometimes seem to be demonstrating the obvious, an empirical illustration adds some colour and robustness to the theory. Given my research interests around the economic consequences of evolutionary change in humans, illustrations of the rate of evolution in human populations are always useful. Could change genetically in a time period short enough to have economic significance. This study does not answer this, but it is another useful example.
In a recent post, I discussed Gianni De Fraja’s paper in which he proposed that sexual selection shaped the nature of conspicuous consumption by men. In his model, conspicuous consumption by men serves as a fitness indicator to women. Low and high quality men signal their differing wealth “honestly” (under certain conditions) as the consumption level of the high quality men is too large a handicap for the low quality men to copy.
One of the unsatisfying elements of the paper (although through no fault of De Fraja’s) was that the conditions under which high and low quality men signal honestly were not readily interpretable. The mathematics were too ugly.
De Fraja based his model on two models developed by Grafen (here and here), which were in turn the first mathematical demonstration that Zahavi’s handicap principle was theoretically sound and could work as a stand-alone process. Grafen’s first model was a simple game theoretic model for which he found the equilibrium. The second model was a population genetic model that built on the first by being explicit on how women used the information they obtained about the males’ quality. It also, as the name suggests, incorporated a genetic basis. Despite the differences in the two models, Grafen considered that the results from the population genetic model supported the use of the simpler game theoretic model and that the extra complications in the population genetic model did not negate the results of the other.
One virtue of Grafen’s game theoretic model is that it is possible to interpret the conditions under which it works. So, instead of trying to pull the conditions from the complicated mathematics of De Fraja’s model (for the moment), the conditions of Grafen’s game theoretic model are worth a look.
Putting Grafen’s model into human terms, it had three elements. First, men vary in quality (say, wealth), which women cannot observe. If they could see it, women would use it as a basis for their choice. Second, men vary in their level of conspicuous consumption, which is a function of their quality. Third, women infer the man’s quality from the level of conspicuous consumption and use it to decide their choice of mate. The fitness of a male depends on his true quality, his level of advertising (which is costly) and the woman’s perception of his quality. A woman’s fitness will depend simply on how accurate she is in inferring true quality.
Grafen showed that in this model an equilibrium exists where higher quality men advertise more than low quality men and the women use this information to correctly infer their quality. The condition for this equilibrium is that the marginal cost of advertising should be higher for worse males.
The question becomes whether this condition could exist in the conspicuous consumption example? On the one hand, a BMW costs the same to anyone who buys it. The marginal cost appears the same to both low and high quality men. But suppose that the rich man can buy the BMW with cash. The poor man needs to take out a loan, max out his credit card and hock his watch. He will be paying high interest on the loan and credit card and will need to pay extra to get his watch back. As a result, even though they are both buying the same advertising, the BMW, the marginal cost of that advertising, is higher for the poor man. This condition for the handicap could hold. The condition also holds where the poor man cannot afford the BMW no matter what he does. His marginal cost at that point is effectively infinite. In equilibrium, the rich guy will pick a level of advertising that will simply be too much for the poor chap to match.
This condition is important. Previous mathematical attempts to explain the handicap principle had generally not succeeded as they had not incorporated this higher cost of the handicap for lower quality males. In this interview, John Maynard Smith explains how his earlier work on the handicap principle had failed to support Zahavi’s claims for this reason.
There is actually an economics model which mirrors this situation (and pre-dates Grafen’s model by 17 years) – the job market signalling model of Michael Spence. The model works similarly. Suppose there are low and high quality employees and they need to signal their unobservable quality to an employer. Spence showed that there could be a separating equilibrium where each signals their quality accurately through their level of education. The condition for this is that education must be more costly for low quality people. This makes sense – it is easier to learn something and pass the tests if the person is higher quality.
Since Thorstein Veblen’s 1899 book Theory of the Leisure Class, the economics profession has taken a somewhat mixed approach to consumption. In areas such signalling theory, Veblen’s argument that conspicuous consumption must be wasteful and expensive to be a reliable signal of wealth is well recognised. Conspicuous consumption has a purpose as a signal. However, the typical economic model is built on the simple concept that more consumption brings more utility. There is no benefit beyond consumption itself.
The absence of a rationale for consumption appears even less satisfactory when considered from an evolutionary perspective. If people trade consumption against the use of resources for survival or reproduction, why does a trait which involves excessive consumption exist in the population? An individual could boost their fitness if they reallocated resources to increasing their fertility.
In this light, Gianni De Fraja’s explanation (ungated working paper here) of conspicuous consumption through an evolutionary lens is a useful addition to the literature. Using a modified version of Grafen’s model on the use of biological signals as handicaps (see also), De Fraja showed that under certain conditions conspicuous consumption could be explained as a signal to the opposite sex. De Fraja further described how utility maximisation (as used by economists) is formally equivalent to the maximisation of fitness through signalling. This provides a biological basis for economists to include consumption in utility functions.
De Fraja’s model incorporated two sexes that mate during a mating season that consists of two “periods” (although the result could be extrapolated to more periods). De Fraja assumed that men make no investment in offspring, so they are free to mate in both periods, while if a woman mates in either period, they are removed from the mating population for the rest of the season. On this basis, men are willing to mate with any woman they are paired with, while women are choosy.
The choosiness of women is with good reason, as men vary in quality. With a mate of higher quality, the female can expect more of her children to survive to adulthood. Females do not vary in quality, but they face a chance of death in each period. In the first period, men and women are matched one-to-one. Given the varying quality of the men, the women need to decide whether the man they are paired with is of high enough quality to mate with, or whether they should take their chances and wait until the next period in the hope of finding a better mate. If their chance of death is high, the woman may drop her standards.
This choice is complicated, however, as male quality is not directly observable. What women can see is the man’s level of conspicuous consumption. Putting this in terms of choices we face today, and ignoring the possible approach of bringing your bank statement or pay slip to the dinner date, total wealth is unobservable. Instead it is conspicuous consumption on the car you drive to the date, your clothes, your watch and the cost of the restaurant that will show one’s wealth. The question the woman must address is whether the signal from the man as to his wealth is reliable. Has he arrived in a BMW that he will also have to sleep in tonight as he has no resources left for accommodation? Or is he actually wealthy?
To make this choice, the woman needs to infer the man’s level of quality. In De Fraja’s model, the strategy employed by the women is heritable. In equilibrium, all women would adopt the same strategy (a function of the perceived quality of the male and their chance of death), as no alternative strategy would be able to increase the female’s fertility.
The choice faced by men is how divide resources between conspicuous consumption and survival activities, which reduce the male’s chance of death. De Fraja assumes that investment in survival activities is unobservable, leaving consumption as the only feature that the female can see. A higher quality male will have more resources to allocate between consumption and investment in survival activities. In the model, the way men allocate resources to consumption (their signalling strategy) is genetically inherited. Quality itself is not inherited but randomly allocated to each new generation.
So, how does this work out? De Fraja did not study the dynamics of the model but, as is the case of most consideration of preferences in economics, the model was solved for the steady state population equilibrium. In the first period of the steady state, a female will agree to mate with a man only if they above a perceived quality, with that threshold level of quality decreasing as the woman’s chance of death increases. In the second period, the women will mate with whoever they are matched with as there are no further breeding opportunities.
For the men, De Fraja found that for certain combinations of environmental constraints, men would split into a separating equilibrium, whereby men of above a certain quality would signal that they are of high quality (those who meet this threshold all signal at the same level of consumption). Those below that level do not signal. Put simply, the lower quality men will sacrifice too much investment in survival if they tried to match the high quality male’s level of conspicuous consumption. As a result, low quality men do not engage in conspicuous consumption and focus on surviving. If the BMW will have low quality men starving and sleeping on the streets, a low quality male will not buy it and ownership of a BMW will be a signal that women can rely on.
In this equilibrium, the strategy by women of believing the signal, and by men of signalling true quality (that is, low or high quality) was found to be stable as neither the men nor women can use an alternative strategy and increase their level of fitness.
I would like to say more about the conditions under which this separating equilibrium holds, but as De Fraja notes, the mathematical proof of the separating equilibrium is not readily interpretable. Even after solving through the equations, it is not clear to me how feasible the required conditions are.
Once De Fraja establishes his separating equilibrium result and provides an evolutionary basis for conspicuous consumption, he moves to explaining whether this result is consistent with the utility maximising approach of economics. Is the maximisation of utility subject to a budget constraint equivalent to maximising fitness subject to environmental constraints? Under conditions of similar mathematical opacity to those for the separating equilibrium, De Fraja showed that they could be equivalent. The common strategy of all men could be thought of as common indifference curves, which in economics are the bundles of goods (in this case, consumption and survival activities) between which the man is indifferent. What determines where the man is on the indifference curves (his choice of consumption and survival activities) varies according to his quality. As a result, and assuming the conditions held, a model which involves a basic utility function that has utility increasing with consumption could be said to be biologically sound.
De Fraja’s paper left me with a number of questions. The most obvious one was why no-one had done this before. This issue had been known at least since the time of Veblen, and Grafen had laid the mathematical framework in 1990. I can only suggest that most economists are not overly concerned about the biological basis of their models, particularly if they have reasonable predictive power.
The second question relates to the range of conditions under which a separating equilibrium can arise and whether these are broad enough to be realistic. Having not got to the bottom of De Fraja’s mathematics, I am not sure of whether an alternative mathematical approach might yield more intuitive and easier to interpret results. Perhaps simulation could be used as a starting point to get a feel for how specific these conditions are.
A further issue relates to dynamics. While De Fraja’s work should allow economists who use consumption in utility functions to argue that their approach is biologically consistent, this is restricted to static situations. Can we learn anything further from the dynamic processes that lead to equilibrium (if a dynamic process would lead to equilibrium)? Take Galor and Moav’s argument of natural selection being a trigger for economic growth. While natural selection is at the core of their model, the model’s agents’ desire to consume above subsistence levels is not subject to selection and has no biological justification. This leaves some scope for extensions to the model, or indeed any other long-term growth model that represents a period sufficiently long for selection to occur.
That links to the question I always ask when I see a static model which explains the equilibrium of preferences shaped by natural or sexual selection. What are the macroeconomic effects of the move to equilibrium? For example, suppose there was initially no conspicuous consumption but the separating equilibrium proposed by De Fraja evolved over a few thousand (or tens of thousands of) years. Does a preference for conspicuous consumption drive us to gather more resources, which in turn increases in economic growth? This is nothing but speculation (at this stage), but it is a question that could yield interesting answers. (Since I first wrote this post, I have developed a dynamic scenario building of De Fraja’s work.)
