February 6: Malthus and the Malthusian Economy

Clark claims that "the real income in Malthusian economies [ all World economies before 1800] was determined from the birth rate and death rate schedules alone." (p. 28) Does this mean that mankind was powerless to improve its material conditions via factors such as technology, social organization, population control, etc.?

Comments

[Thorstein Veblen]

Somebody needs to show the Diamond article below to Acemoglu, so he'll stop embarrassing the profession by using urbanization rates as a proxy for income-per-capita in Malthusian economies... Hunter n' gatherer societies, after all, are often thought not to have very large urban centers...

[Mitchell Hoffman]

A formal model of Malthusian economic growth is often considered a special case of the standard Solow growth model. Instead of capital being allowed to grow via investment or shrink via depreciation, in the Malthusian model, capital is assumed fixed (for this reason, it is often renamed as “land”). That is, output is determined exclusively by the amount of labor/population and technology: Y=Z*F(K fixed, L). The growth rate of the population/labor force, i.e., the birth rate, is no longer given exogenously, but varies positively with the amount of income/consumption per person. Frequently, there is no steady-state equilibrium. Instead, the economy fluctuates between a low population, high per capita income, high population growth rate economy and a high population, low per capita income, low population economy. The highest income per person is generally achieved at a level of population below the low population, high per capita income, high population growth state.
Thus, according to theory, lowering the birth-rate via population control would likely increase income per capita in a Malthusian economy, though this cannot cause permanent growth (as income per capita as maximized at a given amount of labor). Permanent growth can come through growth in technology, exactly as in the Solow model. Good institutions might be viewed as able to get people to provide more effective labor per person, as people may be unwilling to work hard if the government is extracting output via corruption or waste. Because the amount of capital is fixed, institutions in this sense could only temporarily increase output per person.
Perhaps a more interesting question for economists, though, is whether real-world economies before 1800 could’ve been able to increase technology, improve social organization, and limit population control. I will start with population control. As discussed in the article by Ronald Lee, most economic models of fertility assume that parents care about the number of their children that survive, not about births. This is true whether most of the utility from having children is added labor and old-age income support (definitely important for most agricultural economies, including agricultural economies today), or whether it derives from other aspects of child-bearing (e.g. the fun/joy of having children). Given low life expectancies and mortality rates in the pre-1800 world, high fertility may have been entirely individually rational (if not collectively so) for parents. Second, effectively controlling fertility requires knowledge, particularly by women, and is non-trivial when artificial contraceptives are not available. Thus, given individual incentives and the lack of artificial contraceptives and education for women, I am skeptical that Malthusian economies could’ve reduced fertility. The paper by Passell and Atack lays out the hypothesis that West-East differences in 19th century American fertility reflect differences in the efficacy of bequests (more land in the West equals more efficient bequests), assuming that fertility is controllable and not a simple function of income per person, as in the Malthusian model. Though not the focus of their paper, their argument does not address the fact that industry was rising in the Eastern United States in the early-mid 19th century, so, as capital was not fixed, the economy was not really Malthusian.
The readings had much less say about whether people before 1800 could’ve actually improved their institutions or have improved technology. It is useful to recall William Baumol’s article from last week which argues that technological progress is greatly affected by the incentives for entrepreneurship, and that bad incentives for technology will drive entrepreneurs into socially-harmful innovation. This argument holds whether the economy is Malthusian or not. There does not seem to be any unique constraints against institutional progress in Malthusian economies, except that because they occurred earlier in time, there was less democracy and more powerful elites to insist on their economic privileges.

[Monica J. Deza O.]

According to the Malthusian theory, before 1800 the economy was merely determined by the balance between birth and death rates. If the birth rate was low, income per capita would be higher, as well as the individual’s living standards. In a Malthusian economy, the key is to maintain a certain population level. I am very doubtful about believing that people before the 1800 would use contraceptives efficiently. Even nowadays, population growth is uncontrollable in some parts of the world regardless of the government’s efforts to promote birth control.
Another way population would achieve its balanced point would be as follows: if population level is too high, then income per capita as well as living standards would lower, which would cause death rates to increase until the population level reaches its equilibrium point. The reverse would happen if the population level is to low, in which population would increase until achieving its equilibrium level since now the elder would live longer due to higher income per capita and higher living standards.
After learning about current macroeconomic models, it seems very hard to believe that the entire society’s economy would be based on population growth. The Malthusian economies also had developed some technology, which might have played a role in their growth. I understand that the only amount of capital was the land, which remained constant; however, throughout the years, they must have developed different ways to utilize that land, different ways to build their homes and even the contraceptives they used are part of their technology. Thus, they had a source for permanent growth.
For a population to be in complete control of their birth to death rates, external factors such as epidemics and wars would have to be assumed constant, which is impossible. For this reason, humans would have been unable to improve their well-being through population control.

[Josh Hausman]

Even in economies before 1800 – Malthusian economies – mankind was not “powerless to improve its material conditions ”. I shall first outline how population control and technology affect income per capita in Clark’s (2007) model. I shall then question whether Clark’s model fits the United States’ economy before 1800.

(1) Population control: In Clark’s model, anything that decreases the number of births or increases the number of deaths (at a given level of income per capita) will raise the equilibrium level of income per capita. Thus societal norms, sanitation, and degree of urbanization could have dramatic effects on income through their effects on the birth and death rate schedules. Lee (2003), for example, reports that before 1800, women in western Europe married on average at age 25. Relatively late marriages lowered fertility rates. In Clark’s model, this would have raised income per capita by shifting out the birth rate schedule. Many other factors also moved the birth rate schedule. For the U.S., Passell and Atack (1997) report much higher birth rates in rural than in urban areas in 1800. Thus, within Clark’s model, a larger urban population would have increased U.S. income per capita.

(2) Technological advance: The reason for dividing economies into those before 1800, and those after is partly that the rate of technological progress prior to 1800 was so slow. Furthermore, in Clark’s model, any technological progress that did occur had only temporary effects. Income gains from technological progress would disappear as the birth rate rose and the death rate fell. Unfortunately, Clark does not say how long it would take for the income effects of a positive technology shock to disappear. If, for example, the effects lasted ten generations, technological progress may have had historically significant impacts on income per capita.

(3) The U.S.: Central to Clark’s model is the assumption that a larger population will be accompanied by lower income per capita. Clark must have in mind an economy in which land and labor are the primary factors of production and all fertile land is being used. This does not fit the U.S. historical experience. In the U.S., the population expanded in part by moving west to previously unfarmed land. The white settler population grew from half a million in the 1720’s to ten million in the 1820’s. As writers from Thomas Jefferson to Richard Easterlin understood, it was the availability of land that made this population growth possible (Passell and Atack).

Presumably it was not only the U.S. that prior to 1800 had an abundance of fertile, unfarmed land. Clark’s model must be an equally poor guide to the pre-1800 economies of Canada, Australia, and Argentina.

[Mauricio Larrain]

For many centuries, the world experienced important technological improvements, such as the discovery of agriculture or the invention of writing and science. Despite these advances, it seems that increases in total output were roughly matched by increases in population. In the late 18th century, Thomas Malthus developed a powerful framework that linked better technology development with no improvements in material conditions. Was society at that time condemned to live in a world with constant living standards or could it have done something to initiate a process of increasing output growth and slowing population growth, leading to a dramatic raise in income per capita?

From the literature of endogenous growth theory, we know that the role of institutions, such as property rights, is fundamental in the process of per-capita income growth. In an interesting paper, Jones (2001, Advances in Macroeconomics) combines an idea-based theory of growth in which people are a key input into the production of new ideas with a model of endogenous fertility and mortality. The internal dynamics provided by his model are able to produce thousands of years of virtually no sustained growth in standards of living despite increases in both technology and population, followed by the emergence of rapid growth and a demographic transition. His main point is that the establishment of institutions that encourage the discovery and widespread use of new ideas can lead societies to outstrip Malthusian forces. When a society has well defined property rights, once an idea is discovered, income and fertility rises, producing a rise in population growth. More people are then available to find new ideas, and the next new idea is discovered more quickly. This feedback leads to accelerating rates of population growth and per-capita income growth.

In his paper, Jones makes a counterfactual experiment that suggests that absent the large improvements in innovation-promoting institutions measured to have occurred in the 20th century, the Industrial Revolution would have been delayed by more than 300 years. So we can ask ourselves, what would have happened with the standards of living had the improvements of institutions been made before the 20th century?

[Wayne Feng]

Clark’s analysis of the world economy before the 1800’s is correct as within the Malthusian framework real income was determined by birth and death rate schedules alone. However, this does not mean mankind is not able to improve via other factors such as technology, etc., later (which we actually do see).

Clark does a good job describing the Malthusian theory as well as analysis of living conditions in the 1800’s versus the past. Using this analysis the conclusion is that before 1800 the world economy did not have the proper forces to break out of the Malthusian equilibrium. Malthus would even go as far as to say that world income would not change with technological developments due to the increase in labor supply. Clark and Lee points out that technology will increase the real income and Lee even analyzes the complexities of industrializing and the effect on mortality, fertility, and labor. Jones, on the other end, argues that it is in fact institutions that are primarily responsible for the advances in real income (and the economy as a whole).

Back to the original question, it is quite convincing that before the 1800’s Malthusian theory is correct. Any changes in real income would be temporary. However, with the industrial revolution there has been an increase in real income and the new question is not whether or not mankind is powerless to improve its material conditions but rather how mankind was able to get that power post-1800.

Jones would quickly argue that institutions are responsible, but what about Lee’s commentary about governmental incentives to demographic changes resulting from industrializing? The main issue with Malthusian analysis is that while labor supply increased due to industrialization, so did labor demand. From the “bonus phase” analysis we see that it is possible for increasing material conditions due to technological advancements (or other factors). With institutions the progress may be fully recognized and advanced with incentives. It can also be reasonable to say that there can be institutions which can negate advancements from industrialization. Whether or not development can occur without the existence of institutions is debatable.

Another question may be how different factors interact with each other under this framework of industrialization (technological) improvement improving real income and escaping Malthusian equilibrium. Did global climate change lead to the swings in the fourteenth to eighteenth centuries (Lee)? Will we return to some set equilibrium or enter into a Malthusian trap? It would seem as if land expansion and technological development may be limited. Maybe climate change or war can increase wages, but at what cost? Analysis of these will be important for the developing countries and governments in terms of supporting demographic change (as pointed out by Lee).

[Eva Vivalt]

Clark describes a diagram connecting population and material income, with the curve connecting the two termed the “technology schedule” (2005). He justifies the downward slope of this curve by the “Law of Diminishing Returns”, holding that the main inputs to production are land, capital, and labour, and implying that it is predominantly labour which has the capability to increase.

Yet, just as the standard response to Malthusian population growth concerns is to point to technological developments, so, too, can we accuse Clark of not adequately taking into account the role that technology has to play in production. To his credit, Clark does mention the advances of the Industrial Revolution as an example of technological progress, but the constraints of his model assume that population will always increase to offset any gains in income.

This model is clearly unrealistic in the present day, but what about in world economies before 1800?

Changes in technology and social organization did play a role in increasing income before 1800. One can think of innovations in raising livestock or in cultivation, for example, as sometimes increasing production without a concomitant increase in labour; the grains or cattle themselves may simply become more productive, as in the spread of maize.

Faced with this, Clark would claim that population growth offsets any gains. Yet the assumption that with an increase in income, population will grow to just offset any gains is patently false; population can rise or fall based on any number of factors. Even before 1800, people had incentives to raise children partially based on their potential contributions to household income (Passell and Atack, 1997). If we can thus assume that children were a valuable commodity pre-1800 whether or not income was rising (perhaps making exceptions in absolute disasters), then the Malthusian link between income, labour and technological progress is broken and we can evaluate technological progress on its own merits. After all, if population is predisposed to rise even in poor economies, as we see in present day Liberia or Burundi, then improved technology would only help so long as the improvements do not raise the population size even more.

Thus, a better question to ask might be whether technological progress is apt to increase the population size more than it contributes to income, pre-1800. On the one hand, innovations in healthcare could increase lifespan, although this is a predominantly modern phenomenon and it seems that income has had a larger effect on mortality rates (e.g. McKeown cited in Passell and Atack, 1997). People living longer would seem to increase the population, if it is not completely offset by people having fewer children, and we have no reason to think that it would, especially if some of the main reasons people have children are to increase the labour available to the household, to guard against destitution in old age, and for social reasons. On the other hand, it’s unclear that technology itself as opposed to higher income levels is to blame for longer lifespans, and technology would seem to reduce the incentives to have children. Thus, only where low income truly constrained people from having more children would we expect that technology would increase population.

[F. Gerard]

Francois GERARD

Memo 2: Malthus

The Malthusian model, despite an apparently high power of description, has a severe drawback. Indeed, except for the death rate locus, it presents a deep lack of (micro- and macro-) foundations and therefore a complete inability to explain the curse for mankind it is predicting and the “accidental” exception that started after 1800. Why was the birth rate unaffected by the level of income? Why was technological progress unusual and temporary rather than sustained? Those two questions are calling another one even more relevant: What happened around 1800 that broke down the infernal mechanism? To address those issues it is useful to recall last week articles and an important conclusion: the fate of a society is affected by the incentives structure it is providing (social norms, security…). Let’s try to answer at least partially our three questions above for the European history.
Both Lee (2003) and Passel and Atack (1997) present economics model assuming that the number of children is a decision variable. Can those models explain the absence of birth control and declining birth rate with income in Europe before 1800? On the one hand, the “child default” model suggests that the driving forces for fertility reduction are the opportunities offered to children outside their family/community. The absence of any significant high-productivity non-agricultural sector and the immobile structure of classes deterring ambition and entrepreneurship that prevailed until the end of the eighteenth century in Europe were certainly enough to weaken the negotiation power of children. On the other hand, the “target bequest” model supposes that the number of children is determined by the rule of multigeniture. But in Europe primogeniture rather that multigeniture was the usual rule. Therefore, nothing in the bequest norms prevailing in European societies encouraged birth control or birth decision adaptation to wealth variations.
Concerning technological progress and entrepreneurship, I will not repeat the argumentation of last week but just underline that the immobile structure of classes, the few numbers of agricultural workers that actually owned land and the lack of guarantees for the protection of business and property can easily explain the absence of any sustained growth.
Then, what happened around 1800? The industrial revolution! Yes, but not only. We can modify the Malthusian model to explain such a revolution. Suppose again that we have a subsistence level of income and that technological progress is only accidental. But let’s add a kind of Big Push argument: if a technological accident moves the economy beyond a particular level of income, the structure of the model is modified: technological progress becomes endogenous (increasing returns or evolution linked with the growth in income). But doing so, I must also confess a complete lack of foundations. There comes my favorite argument: the industrial revolution required an incentive revolution and this is exactly what happened in the same period. Indeed, the French and the American revolutions contested the structure of the old regime and disseminated the diabolic ideas of liberty and equality into the rigid Europe: ambition, entrepreneurship and ingenuity were no longer hopeless to move along the social ladder. And even the primogeniture norm, with a significant delay, was ruled out giving to the “target bequest” model a chance to explain a new birth rate locus decreasing with the level of income.

[Gabriel Chodorow-Reich]

Clark’s model of Malthusian economies fits the available data well. Incomes appear to have been stagnant for thousands of years, while population growth proceeded at a low rate. In Clark’s model, these facts result from the assumptions of a fixed birth rate and limited technological progress that raised the number of inhabitants that production could support while leaving per capita consumption unchanged.
We know little about the stylized facts of the ancient world at a more disaggregated level. Did some societies flourish while others suffered? In that case, technological progress may have abounded in localized civilizations.
Consider an economy which introduced reforms that shifted the technology curve to the right. Call that economy Rome. As income rises, the death rate in “Rome” falls leading to population growth. In Clark’s framework, the population growth will eventually lead the economy back to its original equilibrium at a higher level of population. Suppose instead that “Rome” wages war on its neighbors, conquering new land and killing the native population in order to provide resources for the increased Roman population. In other words, conquest prevents the onset of diminishing returns in the Roman mode of production. In this case the technology schedule in Clark’s framework is vertical; the increase in population is fully absorbed at the higher level of income.
Two caveats apply to this story. First, at a global level the technological increase is augmented by the increase in the death rate of the conquered population. Second, since following the conquest Rome’s birthrate remains above its death rate, the population will continue to grow. Hence Rome will have to conquer new territory in the future or income will eventually decline to the level that stabilizes the population.
Still, these transition dynamics may take time. In the interim, technological progress greatly benefits Roman citizens, albeit at the expense of the conquered civilizations. Also, as noted in the previous reading by Baumol, the requirement of conquest to preserve the benefits of technological progress may create institutional impediments to such progress occurring at all.
The story of the young United States also comports with the conquest framework. With a seemingly endless amount of fertile land available, and militarily weak tribes of Native Americans the only inhabitants, the laws of diminishing returns may have had much less bite in America at the onset of the nineteenth century than they had in previous societies. With a steeper technology curve, technological progress could begin to have long-lasting effects on incomes. Indeed, in a model where the birth rate begins to decline at a threshold level of income, this effect could explain how the United States moved beyond that level, thus triggering a decline in the birth rate observed empirically in our reading on the United States.

[Lemin Wu]

No, it doesn’t. 1) According to Clark, such factors as technology, social organization and population control can at least influence the birth rate and death rate to affect the equilibrium material conditions. 2) Beyond some threshold of speed of change, the changes in these factors may push the economy into post-Malthusian state, in the process of which, 3) the threshold itself is a function of such variables.
1) The birth rate depends on culture which involves the impact of both social organization and population control. The religious abstinence is an example of both the factors. Kinship family, an important social organization in China, should also greatly impact Chinese people’s birth decisions since the idea of keeping line of gens unbroken prevails almost all across China. Generally, grandparents are more eager for children than parents. Given the difference of the influential power of grandparents on the family management, I expect the birth rate will be higher in the areas where grandparents more often live together with their children, ceteris paribus, like the southern provinces such as Zhe-jiang and Fu-jian. However, this by now is merely my conjecture. Be it the case, it should be another example of the impact of social organization on the determination of birth rate. As for the death rate, the position of the schedule of the death rate is a function of technology, social organization, etc. The progress in the relevant medical technology can greatly enhance the survival rate of infants given a constant level of real income per capita. So can the establishment of such charity institutes that adopt the abandoned children (not sure whether it’s true or not). Similar institutional establishments also include the introduction of risk-sharing agencies like pawnshops.

2) If the progress of technology is fast enough in a continuous period, it may overcome the negative effect of population growth and push the economy into post-Malthusian equilibrium, the hope of which lies in people’s diminishing inclination to bear children with higher real income. The technological take-off has to be fueled by supportive social structure.

3) The blessing of the post-Malthusian has a threshold of the change rate of technology. A continuous series of positive technological shocks not frequent and powerful enough to exceed the growth of population merely brings more and more dense population with almost constant and even lower real income per person. The threshold is also dependent on the factors of interest. For example, for sensible reasons, in some domain, birth rate tends to increase with higher real income per person, in which a higher sensibility of birth rate to real income means a higher threshold for technological progress to push the economy into new state. The sensibility is about culture by a large extent. This may partially explain the failure of ancient China to get into post-Malthusian era spontaneously when comparing ancient China with Europe.