Malthusian

Galor's Unified Growth Theory

Galor Unified Growth TheoryIn 1798, Thomas Malthus described a world where technological progress did not increase per person income. Any additional income was consumed by population growth. It appeared a solid explanation of the world to that point, but Malthus had the misfortune of describing the “Malthusian world” just when some parts of that world were breaking their Malthusian shackles. This left Malthus with a somewhat tarnished reputation (I consider undeservedly), with the Malthusian model failing to offer an explanation for why it no longer seemed to apply.

Conversely, modern economic theories such as the neoclassical growth model and endogenous growth theory, while being useful in understanding some elements of economic growth, do a poor job of explaining the nature of the Malthusian state that existed for most of human history.

Unified growth theory seeks to overcome the limitations of these approaches by presenting a coherent, single framework that captures the Malthusian era, the transition to higher growth and the modern growth state. The process of moving from one state to the next originates within unified growth models, with the seeds of the transition growing during the Malthusian era. As such, the Malthusian state is not an equilibrium, but a dynamic process leading to its own end. The benchmark for unified growth models is that they capture the patterns in income, technology and population through these various states and generate the transition between them.

Unified growth theory was first proposed and has largely been developed in the work of Oded Galor, who with his co-authors has put together the building blocks of the theory. In his book Unified Growth Theory, Galor catalogues his work in the area and demonstrates the strength of the foundation he has built.

The book is an academic book that Galor has largely constructed from his published papers. Some chapters are heavy on the mathematics, although Galor is a clear writer and it is possible to get a sense of unified growth theory without working through the models. The first chapter, in which Galor works through some of the core features of economic history, would provide a useful grounding for any intelligent lay reader, as would his discussion of the causes of the demographic transition.

I have posted about some of the papers that form book chapters before, so I won’t give a blow-by-blow account of the book. And if you are familiar with his papers, you won’t find many surprises. But what becomes clear from reading this work in a single collection is how coherently Galor’s work fits together (and that is from the perspective of someone who is skeptical of unified growth models as potentially trying to explain too much). While a couple of the chapters present full unified growth models, other chapters examine in detail particular elements of the theory. Galor examines the relationship between population, income and technology in the Malthusian state. He steps through the triggers of the demographic transition and examines which causes are plausible. He examines the accumulation of human capital across populations and how this coincides with changes in growth (the accumulation of human capital in response to technological progress is the core driver of the transition in Galor’s models). Put together, the case the Galor is building becomes clear.

In past posts I have focused on Galor’s work examining the interaction between evolutionary factors and economic growth. These evolutionary considerations are among the more peripheral parts of unified growth theory. Unified growth theory could survive without them. But what Galor emphasises is the range of theories that can be accommodated within a unified growth framework. For example, the effect of genetic diversity on innovation and cooperation could be taken to affect the population’s ability to accrue human capital. This then generates the divergence in economic outcomes within the unified growth framework, as one population accumulates enough human capital for a take-off in growth before the other. In this context, unified growth theory does not explain every facet of economic growth, but provides a framework under which much analysis can occur.

That said, it will be interesting to see which elements of Galor’s unified growth models stand the test of time, even if unified growth theory itself becomes a more broadly used approach. What is the nature of the trade-off between quantity and quality of children? What were the evolutionary changes during the Malthusian state? How do the models stand up when we examine specific questions under their lens, such as asking why England and not, say, China first experienced the take-off in economic growth? There is a lot of potential to put more flesh on the framework of unified growth theory and the models that Galor has developed within it.

So for those economists interested in the deep causes of economic growth, I would recommend Galor’s book, even if you are generally familiar with his work. Having that body of work systematically laid out in one piece gives it a strength not apparent when each part is taken alone.

And for those who are interested on some of my earlier posts on Galor’s work (with the corresponding book chapter in brackets):

  1. Dynamics and Stagnation in the Malthusian Epoch (chapter 3)
  2. The Neolithic Revolution and Comparative Development (chapters 6.4.1)
  3. The “Out of Africa” Hypothesis, Human Genetic Diversity, and Comparative Economic Development (chapter 6.4.2)
  4. Natural selection and the origin of economic growth (chapter 7)
  5. Evolution of Life Expectancy and Economic Growth (chapter 7.7.2) [post forthcoming]

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.

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

Agriculture and population growth

Over the last few months, I have heard the phrase “agriculture creates excess population” or other words to that effect from several sources. The latest is at Evolvify, where Andrew references Richard Manning and writes:

Agriculture creates excess population. The argument that we need more agriculture to support higher population fails to recognize its inherently circular nature.

While I have some sympathy to the argument about the destructiveness of agriculture for the ecosystems it supplants, I would prefer to frame the argument differently.

If we take the Malthusian model as a description of human history, for most of that history populations were at subsistence level. The constraint on population was the level of technology. Improved technology did not increase living standards as population would simply increase to match the rise in technology (making population density a crude measure of technology). Some populations managed to briefly have higher living standards by imposing society-wide checks on fertility, or through higher death rates due to disease or violence, but subsistence was the norm.

Thus, in hunter-gatherer societies, population was constrained by the technologies available to them. A technology that allowed more game to be caught may briefly raise living standards, but population would soon increase to take advantage of the additional resources. Population could also increase where new land was entered, such as the entry of humans into the Americas 12,000 years ago.

With the advent of agriculture, the new technology allowed even higher populations. However, up to the 18th century, population generally grew in line with technology and most of the population remained at subsistence levels. New land would at times be opened up to agriculture with accompanying population growth, such as with the European settlement of the Americas, but the Malthusian constraint remained.

Thus, it is not agriculture in itself that creates excess population. The very nature of the Malthusian state – which was the state of human populations for most of their history – is excess population.

Then, around the time of the Industrial Revolution, incomes started to grow faster than population. Populations where this occurred were now able to obtain incomes above subsistence. The twist in the tail was that those with higher incomes lowered their fertility, allowing per person income to grow even faster. So, although population has grown quickly since the Industrial Revolution and on the back of agriculture, it has not grown as fast as the loosened Malthusian constraints would allow. In that sense, there is not overpopulation. We could even argue by this measure that many parts of the world have never been less crowded.

One obvious response is to ask whether the current use of land for agriculture is destroying future capital. Is agricultural productivity ephemeral, as today’s income is coming at the cost of income at the future? In that scenario, it could be argued that there is excess population, but the current population is able to temporarily ward off the Malthusian constraint at the cost of future populations. Even if this were the case, however, I would prefer to frame that argument in terms of the nature of the technology than in terms of “excess population”. A state of excess population is the norm, not a particular result of agriculture or any other technology of the day.