technological progress

Population, technological progress and the evolution of innovative potential

In his seminal paper Population Growth and Technological Change: One Million B.C. to 1990, Michael Kremer combined two basic concepts to explain the greater than exponential population growth in human populations over the last million years.

The first concept is that more people means more ideas. A larger population will generate more ideas to feed technological progress.

The second concept is that, in a Malthusian world, population is constrained by income, with income a function of technology. Population can only increase if there is technological progress, with any increase in income generated by technological progress rapidly consumed by population growth.

When you combine these two concepts, a larger population generates more ideas, which in turn eases the constraint on additional population growth, which further accelerates the production of ideas. The result is population growth being in proportion to the population size. The following diagram illustrates the feedback loop.

Kremer model

When I first read Kremer’s paper, the title caught my attention, particularly the reference to One Million B.C. Humans have evolved markedly in the last one million years. One million years ago, Homo sapiens did not exist as a distinct species, with Homo erectus found in Africa, Europe and Asia. Since then, cranial capacity (a proxy for brain size) has increased from around 900 cubic centimeters to 1,350 cubic centimeters. And not only have humans evolved, but adaptive human evolution appears to be accelerating. As more people means more mutations, natural selection has greater material on which it can act.

It was this consideration that forms the basis of my latest working paper, Population, Technological Progress and the Evolution of Innovative Potential, co-authored with my supervisors Juerg Weber and Boris Baer.

In the spirit of Kremer’s original paper, we develop a model of population growth and technological progress, but add an extra element, which we call “innovative potential”. Innovative potential is any trait that results in the production of ideas that advance the technological frontier. Innovative potential might incorporate IQ, willingness to invest in innovation, participation in productive activities in which innovation may occur, risk preference, time preference and so on. At this stage, we do not specify the precise trait, but it is not hard to see what the likely traits are.

As more people means more mutations, mutations that increase the innovative potential of the population will occur with greater frequency in a larger population. As the population grows, so too does the rate of evolution of innovative potential.

Incorporating the evolution of innovative potential into the model creates a second element to the feedback loop, as is shown below. Population growth is now proportional to both the size and innovative potential of the population.

Collins et al model

One of the more interesting results of the model can be seen when we partition the drivers of the acceleration of population growth between increasing population size and the increasing innovative potential of the population. As the population evolves, the relative contribution of continuing growth in innovative potential to the acceleration of population growth declines. Continuing population growth becomes the main driver of technological progress and further population growth. However, this does not mean that innovative potential is not important, as the level of innovative potential continues to have a material effect. Populations with higher innovative potential will have much faster population growth.

The reason this change occurs is that population growth is driven by both increasing population size and the increasing innovative potential of the population, whereas innovative potential only increases with population size. As the innovative potential reaches a higher level, each new person is more innovative and generates more ideas, but they will only generate the same number of mutations as they always have.

One issue with introducing innovative potential into a model of this kind is that ideas are non-excludable. Suppose I invent some new technology that increases my ability to procure resources. If someone else sees and copies this idea, I wont have an evolutionary edge. In the first version of the model presented in the paper, we handwave around this issue, and suggest that innovative people may have higher fitness due to prestige, the ability to keep secrets or some other avenue of reaping the benefits of the innovation. Although this handwaving likely has an element of truth, we introduced a version of the model in which those who are more innovative are also more productive in using those ideas. The results are robust to inclusion of this element.

One other observation from the model is the robustness of the population to technological shocks. Through human history, population did not undergo a simple increase, but underwent shocks and bottlenecks. For example, a change in climate could reduce the carrying capacity of the land (through reducing the effective level of technology), reducing population size.

In Kremer’s model, shocks of this nature are a strong setback to population growth and technological progress. As the population is smaller, idea production will be slower. In fact, population growth and technological progress will resemble the levels of growth when the population was last of that size. A population experiencing consistent technological shocks may never grow to a substantial size.

Where there is evolution of innovative potential, a technological shock is a setback to population growth, but the clock is not fully wound back to the time when the population was last of that size. The population now has higher innovative potential and the population recovers faster from each successive technological shock. This effect is particularly strong where higher innovative potential also increases the productivity of the population in using the new technologies.

Finally, two assumptions that we include in the model are that population instantaneously adjusts to the carrying capacity of the land, and that the spread of mutations is instantaneous. The first is a weak assumption given the time spans over which the model operates. The second is much stronger. As a result, we also consider the time it takes for a mutation to spread through the population in a dynamic model and an agent-based simulation. Delaying the spread of a mutation does not substantively change the model results, although it prevents an explosion in the innovative potential of the population at the time that the population explodes. But as noted above, even where mutations spread instantaneously, the contribution of continuing evolution of innovative potential to the acceleration of population growth drops to near zero when the population explodes. The delay in the spread of mutations simply strengthens that result.

If you would like to play with the agent-based model, code for the model is contained at the end of the working paper, or you can download the model here. I developed the model in NetLogo, an open source agent-based programming environment, which you can download from here.

As is always the case, I would appreciate any comments, ideas or criticisms about the working paper.

More people means more ideas AND mutations

A core ideas in economics is that more people means more ideas. To take an extreme case, you would expect a population of one person to generate fewer ideas that a population of one million people. The precise relationship between population and ideas depends on factors such as the fishing-out of ideas, network effects, the composition of the population and the like, but it would seem to be strongly positive.

When you combine this assumption with the Malthusian concept that the level of technology constrains population, a larger population grows faster than a smaller population as a larger population generates more ideas to ease this Malthusian constraint. Michael Kremer used this argument to explain the greater than exponential population growth of the last million or so years (although that pattern has broken down since 1950).

This argument has a counterpart in evolutionary biology. More people means more mutations. From R.A. Fisher (1930):

The great contrast between abundant and rare species lies in the number of individuals available in each generation as possible mutants. The actual number of mutations in each generation must therefore be proportional to the population of the species. With mutations having appreciable mutation rates, this makes no difference, for these will reach an equilibrium with counterselection at the same proportional incidence. The importance of the contrast lies with the extremely rare mutations, in which the number of new mutations occurring must increase proportionately to the number of individuals available. It is to this class, as has been shown, that the beneficial mutations must be confined, and the advantage of the more abundant species in this respect is especially conspicuous.

The greater number of mutations then provides more variation on which natural selection can act. Larger groups will, other things being equal, experience faster evolutionary change. Fisher again:

The theoretical deduction that the actual number of a species is an important factor in determining the amount of variance which it displays, thus seems to be justified by such observations as are at present available. Its principal consequence for evolutionary theory seems to be that already inferred by Darwin, that abundant species will, ceteris paribus, make the most rapid evolutionary progress, and will tend to supplant less abundant groups with which they come into competition. We may infer that in the ordinary condition of the earth’s inhabitants a large number of less abundant species will be decreasing in numbers, while a smaller number of more abundant species will be increasing …

Combining these two concepts – more people means more ideas and more mutations – gives larger human populations a double advantage over a long-term horizon. The higher level of production of ideas and beneficial mutations provides two avenues from which large populations can continue to grow.

Using the Malthusian model to measure technology

TomasMaltusUnderlying much of Ashraf and Galor’s analysis of genetic diversity and economic development is a Malthusian model of the world. The Malthusian model, as the name suggests, originates in the work of Thomas Malthus (pictured). Malthus had the misfortune of providing an excellent description of the world across millennia, just at the point at which the model (apparently) lost much of its predictive power.

The Malthusian model rests on the assumption that any increase in income generates population growth. This ultimately prevents increases in technology from translating into increases in living standards. The greater resource productivity must now be  shared between more people. Of course, the reason people state that the Malthusian model no longer applies is that since 1800 many parts of the world have experienced substantial increases in per person income as population growth did not match technological progress.

The Malthusian model generates a couple of important predictions. First, any increase in productivity will generate population growth, not income growth. Secondly, differences in productivity between regions will be reflected in different population densities, not income differences.

This last point is important. It allows economists to use population density as a measure of technology and productivity in a Malthusian world. Since measuring technology is difficult but we have many measures of population density across time and societies, the Malthusian model provides a basis for conducting comparative economic analysis between countries and regions for times before 1800.

Ashraf and Galor use population density as a measure of technology for most of their analysis of genetic diversity and economic development, following a long line of economists who have done the same. But until recently, whether population density is a reasonable measure had not been properly tested.

In 2009, Ashraf and Galor published in the American Economic Review (ungated version here) an empirical examination of this hypothesis for the period 1 to 1500 CE (originating from Ashraf’s PhD thesis, as did the paper on genetic diversity and economic growth). The problem they faced was how to untangle population and technology when the two are so closely intertwined. Economists use the population density measure because technology is hard to measure and each flows directly into the other (more people leads to more ideas).

To untie the two, Ashraf and Galor use the timing of the onset of the Neolithic Revolution in different regions as a proxy for technology. The Neolithic Revolution occurred when populations moved from hunting and gathering to agricultural activities. If we accept Jared Diamond’s thesis that countries with favourable biogeographical factors gained a technological head start through the advent of agriculture that they maintain through to today, the timing of the Neolithic Revolution in different societies could be a proxy for technology and productivity.

Using this proxy, Ashraf and Galor found that, consistent with Malthusian theory, technology and productivity had a positive effect on population density, but no effect on per person income levels for the period 1 to 1500 CE. The result is robust to a range of controls including geographic and climactic factors, and holds when they use a more direct (but possibly less reliable) measure of technology.

There are two particularly interesting observations that Ashraf and Galor draw from their work. The first is that despite income stagnation, pre-Industrial times could be very dynamic. It is just that the Malthusian dynamics mask the effect of technological changes.

Secondly, their finding can be interpreted as supporting Jared Diamond’s hypothesis (or at least, it is not inconsistent with it). Those societies that first experienced the Neolithic Revolution had the highest population densities, suggesting a persistent advantage to an early start.

However, this support for the Malthusian model is not a ticket to use any population density data as a measure of technological progress. One of the more interesting points in the critique of Ashraf and Galor’s genetic diversity work published in Current Anthropology was the way some of the population density estimates used by Ashraf and Galor were developed.

McEvedy and Jones (1978:292) argue that the total population in Mexico in 1500 CE was no more than 5 million. They do so based on data from Rosenblat (1945, 1967), a source that uses problematic postconquest records. In fact, scholars contemporary with McEvedy and Jones (1978) proposed estimates in the 5–6 million range for the area corresponding only to the Aztec empire (e.g., Sanders and Price 1968). The Aztecs controlled a territory that covered no more than one quarter of contemporary Mexico and that excluded all of northwest Mexico and the Yucatan. Even while, at the time McEvedy and Jones (1978) were writing, other estimates for Mexico’s population were set at around 18–30 million (Cook and Borah 1971), McEvedy and Jones (1978: 272) discredit those estimates on the puzzling claim that they were not in line with those of other populations at “comparable levels of culture.”

Given that McEvedy and Jones are allowing the level of culture to colour their population estimates, those population estimates cannot be considered a sound basis for measuring technology. Population data shaped by the Malthusian model is not ideal to use as a measure of development. I don’t expect that changing the population density numbers substantially change Ashraf and Galor’s results (although the data is online if you want to check this), but we should use the numbers with some caution.

My posts on Ashraf and Galor’s paper on genetic diversity and economic growth are as follows:

  1. A summary of the paper methodology and findings
  2. Does genetic diversity increase innovation?
  3. Does genetic diversity increase conflict?
  4. Is genetic diversity a proxy for phenotypic diversity?
  5. Is population density a good measure of technological progress? (this post)
  6. What are the policy implications of the effects of genetic diversity on economic development?
  7. Should this paper have been published?

Earlier debate on this paper can also be found hereherehere and here.

Ashraf, Q., & Galor, O. (2011). Dynamics and Stagnation in the Malthusian Epoch American Economic Review, 101 (5), 2003-2041 DOI: 10.1257/aer.101.5.2003

Population, connectivity and innovation

Near the close of his acceptance speech for the Competitive Enterprise Institute’s Julian Simon Memorial Award, Matt Ridley suggests that the total number of people is not the major driver of technological progress:

[W]hat counts is not how many people there are but how well they are communicating. … [I]t’s trade and exchange that breeds innovation, through the meeting and mating of ideas. That the lonely inspired genius is a myth, promulgated by Nobel prizes and the patent system. This means that stupid people are just as important as clever ones; that the collective intelligence that gives us incredible improvements in living standards depends on people’s ideas meeting and mating, more than on how many people there are. That’s why a little country like Athens or Genoa or Holland can suddenly lead the world.

Bryan Caplan takes on Ridley’s argument:

Isn’t the correct position clearly that both population and communication matter?  A two-person world linked by Skype wouldn’t be very creative.  Neither would a world of a trillion people in solitary confinement.  Creativity requires minds to generate ideas, and mouths to share them. …

I agree that we need to consider both population and communication, but there is a third element: quality. Caplan nods to this in his response to Ridley’s statement that stupid people are just as important as clever ones:

This is frankly an absurd leap.  Geniuses are overrated?  Maybe.  Stupid people are “just as important” for progress as clever ones?  Come on.  Question for Ridley: Whose the most creative person alive with an IQ under 100?  Under 80?

Without quality, quantity or connectivity, technological progress of the type we see today would not be possible.

Take an example Ridley uses in the speech – that the internet and mobile telephony had no inventor. True, they were collective enterprises involving many networked people using many accumulated technologies. But what was the average IQ of the inventors of the technology used in creating them? Or the average level of education?

Or consider the comment on Caplan’s post where Ridley notes the success of Athens, Genoa, Holland, New York, San Jose, Singapore and Hong Kong. They do not look like a random sample. They comprise intelligent, educated populations.

Ridley’s agnosticism about whether people are smart is reflected in his recent post dismissing concern about shrinking brains. As I mentioned then, there are few better predictors of a country’s wealth than the IQ of the population. There are significant benefits to a high average IQ.

Finally, connectivity is at least partly a consequence of quality. Higher IQ people are more trusting and more likely to trade. Those with higher IQ are more likely to be connected and share the ideas they have created.