population and economic change (summarize notes)
Econ/background to week 12.doc
Introduction to Migration
Migration is defined as any permanent change in residence from one region to another. In-migration (immigration) and out-migration (emigration) are the fastest ways in which a population can change its size and composition. Such rapid change can pose many challenges, including the challenge of socially integrating people from different backgrounds.
Governments do not usually keep track of emigration. They keep track of immigration, but some immigration is illegal and escapes detection. In this way both immigration and emigration pose measurement challenges.
The Net Migration rate (NMR) = 1000 x (immigrants – emigrants)/mid-year population.
If migration data are lacking, you can estimate the NMR using the demographic equation. If you know the change in population and births and deaths, you can infer the rate of increase due to net migration. If further you know the immigration rate, you can infer the emigration rate.
Another way the NMR can be estimated is by using a lifetable to predict the number of people in an age category on the basis of existing population and age-specific mortality rates. If the actual number of people is different from the prediction, and you have no cause to believe foul play, you can attribute the difference to net immigration or net emigration.
The migration ratio = (net immigration)/(natural increase) .
Migration Factors
People migrate because they are PUSHed out of their old place of residence and/or PULLed into their new place of residence.
PUSH factors include:
-imminent personal danger
-environmental degradation
-threat of destruction or confiscation of property
-discrimination, oppression against one’s religious, political, ethnic group etc.
-economic hardship
-military draft
-forced marriage
-indebtedness
-deception, enslavement, forced relocation
PULL factors include:
-higher wages, greater economic opportunity
-gifts of land
-greater safety and freedom
-adventure
Depending on the push or pull factors, those who migrate may share certain characteristics.
Leah Boustan and Ran Abramitzky studied men who migrated from Norway to the United States who had non-emigrating brothers. They found that men who migrated from rural areas did 93% better financially than their brothers, whereas men from urban areas made a 42% rate of return. They found that households with poorer economic prospects were more likely to send migrants to the US, and that within households, men with poorer prospects were more likely to migrate.
Simone Wegge has studied data on over 1000 villages in the German principality of Hesse-Cassel, for the years 1852-1857. Her data suggest that, up to a certain point of wealth, people with more money were more likely to immigrate than those without. After all, the trip to New York from Hamburg cost twice the yearly wage of a labourer. But at the highest levels of wealth, there was not the incentive to emigrate. The villages that experienced the most emigration were those with that practised unigeniture (first son gets entire farm), and those that had higher emigration flows in the past, fewer factories, and more religious minorities.
When migration is voluntary, the people most likely to migrate are possibly:
· The most entrepreneurial. (The check mark indicates this is a good thing for the recipient country)
· The most willing to change
· People with marketable education and skills
· People with existing connections to the new place
· People not desperately poor
· Young adults and retirees versus working age people
· Those who were minorities in their own nation
? Newly-weds versus longer married
x Those not wealthy
It is important to anticipate how an immigration policy and a global situation will select for a particular kind of immigrant.
Migration Policy
There is a lot of scope for migration policy, first because citizens have traditionally supported government's interference in matters of migration, and second, because economic factors – which governments can manipulate - are among the strongest push and pull factors governing migration.
Migration Policy is wide-ranging. Are citizens allowed to emigrate freely? Are aliens allowed to immigrate freely? If not, what kind of immigrant is permitted? How are immigrants treated? What programs and incentives are available to them? How do we deal with illegal immigrants? What measures do we take against human trafficking?
In the following chapters we will touch on all of these issues. As usual, a successful policy is well targeted, deals with binding constraints, attacks the relevant margin, and is conscious of the incidence of taxes and subsidies.
Consequences of Migration
Consequences of Emigration
Those who voluntarily emigrate must be doing so because they perceive that their lives will be improved by doing so. Unless they have been misinformed or have made wrong assumptions, they will benefit from emigration. The population left behind may also benefit from the emigration if its economy is characterized by a low capital:labor ratio. Wages will rise. Land and capital prices may fall. The population left behind may also benefit from remittances of cash which the emigrants mail back home. Before the current financial crisis, remittance flows exceed international aid donations by a factor of three.
The population left behind may be hurt by the emigration if the emigrants were better educated than average. This phenomenon is referred to as brain-drain. Canada is considered to suffer from brain drain to the United States. The country of origin can also be hurt if it loses citizens who were harder-working, richer, or more politically active than average. Finally, spouses, children, and parents of emigrants will miss their family members.
Consequences of Immigration
If they can realize their ambitions, immigrants benefit from the move. However, many are disappointed by the limited opportunity to use their skills in the new country. Countries like Canada impose serious restrictions on teachers, doctors, and other professionals. Many immigrants must pin their hopes for making a better life on their children.
The citizens in the host country can benefit from immigration if the immigrants bring scarce skills, scarce positive attitudes, entrepreneurship, new cultural pleasures such as recipes, and new technologies.
Immigrants may be welcomed for their help supporting an aging population. The idea is that immigrants decrease the age dependency ratio and pay taxes that support social programs. Whether this is true depends on immigrants not having large families that will increase the nation’s child dependency ratio, and on immigrants providing a net fiscal benefit i.e. paying more in taxes than they consume in services. In Canada, immigrants are eligible for free language training and free health care and public education. After one year of residence they may apply for welfare and subsidized housing. Grubel (2005) found that immigrants arriving in 1990 and 2002 cost the government 1.36 billion more than they paid in taxes. Immigrants also share use of the infrastructure and other public goods which they have not paid for.
The host country may have concerns about immigrants’ ability and willingness to integrate. We will discuss this in a later chapter.
By far the greatest concern regarding immigrants is their impact on the local wage. I suspect that much of the motivation behind the work restrictions placed on professional immigrants to Canada is the desire to protect the salaries of Canadian professionals.
How immigrants impact the standard of living in the host country
The standard of living, defined only in the simplest, material way, is Y/N, GDP per person. Y/N can be broken down into two components: Y/L, labour productivity, and L/N, which is the inverse of a dependency rate that ignores ages and focuses on participation in the workforce. Multiply productivity by L/N and you have GDP per person.
When the population increases, either by natural increase or by immigration, the consequence for the standard of living depends on the impact of the population increase on labour productivity and on dependency.
Labour productivity, like the wage, will rise if efficiency rises or if the capital:labour ratio improves.
Let Y = A K1/3L2/3, where A is efficiency, other wise known as "multifactor productivity"; L is raw labour, measured in person hours; and K is any kind of capital, including human capital like education, that workers can use.
Dividing Y by L we see that labour productivity Y/L = A (K/L)1/3.
The wage is very similar. The wage is equal to the derivative of Y with respect to L, multiplied by the price of the output. Or we could say that the real wage is equal to the derivative of Y with respect to L, which is 2/3 A (K/L)1/3.
Since the wage that employers desire to pay is inversely related to L, we can draw the labour demand curve – the horizontal summation of individual employers' demands for labour – as a downward sloping line in real wage/person-hours space. See Figure 36-1.
Figure 36-1. Labour Market with Immigration
Since Labour Demand is a function of efficiency (A) and the capital:labour ratio (K/L), any improvements in A or K will shift the Labour Demand curve to the right, resulting in higher employment.
We see in Figure 36-1 that, when the raw labour supply increases due to immigration or some other factor, such as women joining the workforce for the first time, the wage will fall. When immigrants join a labour market, native workers competing for the same jobs are hurt.
We are assuming that all workers compete with one another. However, in reality there are many occupations. Any category of worker that is complementary, rather than substitutable, with the immigrants’ skill types will actually find its wage rise with immigration. For example, translators and language instructors will no doubt benefit.
Let's have a closer look at Figure 36-1 again, where native-born and immigrant workers compete with one another. Before immigration took place, native workers earned the "old wage" and earned surplus equal to the two coloured triangles. (To calculate producer surplus, find the difference between the wage received and the lowest price the producer would have accepted, as registered on the supply curve. Producer surplus is the difference between the wage received and the lowest acceptable wage, for the entire quantity supplied at that received wage.)
Once immigrants join the labour market, the wage falls to "new wage". Where does the new wage meet the native supply curve? They meet at a lower level of employment, indicating that some native workers are not willing to work at the new wage. Those who are willing earn a lower wage, and their surplus falls to just the red triangle.
Employers are pleased with this lower wage. So are consumers, who pay lower prices for goods and services.
Refer to Figure 36-1. Now that the wage has fallen, employer/consumer surplus rises from triangle A-B-old wage to triangle A-C-new wage. In other words, consumer surplus rises by turquoise chunk and the dark blue triangle shown in Figure 36-2. Meanwhile, workers lost the turquoise chunk. There is a net gain to the host country, and that net gain is the dark blue triangle. The new money going to immigrant workers is shown in green.
Figure 36-2. Changes Due to Labour Supply Expansion
Hope for original workers
Although an increase in the supply of raw labour depresses the real wage, it is possible that the new workers bring with them some capital K or some new ideas A. In this case, labour demand will rise, mitigating the effects of a rising labour supply.
Even if the new workers do not have any K or A with them, K can be accumulated over time through education or investment. The following factors will help speed the real wage's recovery:
- access to affordable education
-subsidies for research and innovation
-ease of starting new businesses: few regulations and fees.
-access to affordable loans
-ease of hiring and firing
Like the real wage, labour productivity rises with increases in A or in K/L. Labour productivity grows at the same rate as the wage, for the two are proportional to one another.
The standard of living, Y/N, which applies to both immigrants and natives, depends on labour productivity and on dependency. Thus, immigration is most likely to be beneficial to the standard of living if a) immigrants bring new ideas and technologies with them, and a better work ethic; b) immigrants bring capital with them; and c) immigrants bring few dependents with them.
Table 36-1. Short Run Economic Consequences of Immigration
|
|
SHORT RUN EFFECTS OF IMMIGRATION |
|
Native workers |
Some workers quit. Remaining workers earn a lower wage. |
|
Immigrants |
Earn the new, lower wage. |
|
Employers |
Benefit from the new, lower wage |
|
Consumers |
Benefit from falling prices for goods and services |
|
GDP |
Rises because there is more labour input. |
|
GDP per worker |
Unclear because labour productivity depends on capital per worker (most likely DOWN) and efficiency (often UP). |
|
GDP per person |
Depends on the change in GDP per worker and the change in dependency rate N/L. Recall Y/N = Y/L * L/N |
The change in population size due to immigration can mean a change of scale in production which can have either beneficial or harmful effects, or both. We discuss the economic consequences of population size and market scale in Chapter 36.
Case Study: Illegal migration to the United States
It is estimated that 500,000 illegal migrants enter the US each year, most from Central and South America, for a total of 12 million illegals, about 5 % of the civilian labour force (Hanson, 2009). In 2008, illegals made up 25% of farm workers, 19% of cleaners, and 17% of construction workers (Hanson, 2009). Politicians would like to extend privileges to those who are already here, to help with health care and education needs, but they are worried that this will encourage more illegal immigration. Senator Harry Reid is expected to propose a "Development, Relief and Education for Alien Minors Act" intended to help illegals who came to the US as children become citizens and obtain student loans, if they agree to attend university or enter the military (Illegal immigrants pin hopes on Dream Act, Globe and Mail, December 7, 2010).
In a 2007 paper, Gordon Hanson suggested that illegal immigrants willing to work in low-skilled jobs may be meeting a need: since 1960, the share of native-born workers with less than a high-school diploma has fallen from 50% to 12%. The counterargument is that, if less-skilled labor is scarce, wages for less-skilled work will rise, attracting more native-born Americans to those jobs. The rebuttal is that there is a stigma to those jobs. The counter-rebuttal is that high-paying jobs usually lose their stigma.
Professor Hanson argued that illegal immigrants are more likely than legal immigrants to be financially beneficial to natives because:
-they improve the dependency ratio. Most are of working age, and come only to work.
-they come and go according to the demand for their services
-their wages tend to be low, so their share of what they produce is not high
-they are ineligible for many public programs
-they end up paying taxes such as payroll, sales, and property.
Hanson estimated that illegal immigration costs native-born Americans less than 0.07% of GDP, a 0.10 percent fiscal cost set against a 0.03 percent GDP gain to native-born americans from the work of illegals. This is less than the cost of keeping illegals out, which is about 0.1 % of GDP. He does not estimate benefits of immigrants or the costs that might occur if the border was not patrolled.
Hanson has calculated the short run benefits of immigration to the host nation using a simple formula attributed to Borjas (1999). He multiplies labor’s share of GDP by the wage elasticity (the percent drop in wages due to a one percent increase in labor supply) and by the share of immigrants in the labor force squared and by 0.5. This works out exactly equal to the triangle of net gains to the host economy from an expanded labour supply, i.e. the dark blue triangle in Figure 43-b. It measures the gains of employers minus the losses of native workers. There will be a net gain since GDP rises when labour expands.
In a 2009 paper Hanson repeated these claims and recommended that the government expand the legal immigration opportunities for low skilled workers. The numbers admitted should rise and fall with the business cycle. He also suggested that employers or the immigrants themselves be taxed to help pay for their use of public services.
Canada’s Immigration Policy
In Canada today, 1 in 5 people is foreign-born. While this number is trending up, it is not yet so high as it was 1911-1931. Immigration today is much more inclusive of different ethnicities. In the late nineteenth century, visible minorities were not welcome, but tolerated if needed to perform work others would not do. For example, Chinese people were permitted to enter Canada to work on railway construction, but had to pay a $500 head tax from 1885 to 1923, after which time only special categories of Chinese, such as business people and students, were allowed to immigrate. To protect jobs during the Great Depression, Canada passed a law in 1931 that limited immigration to American citizens, British subjects, and agriculturalists with money. Clearly, the racism so prevalent at the time played a role in shaping this policy. After World War II, immigration rules were relaxed, until in 1967, discrimination on the basis of race was forbidden. For more detail, see the Canadian Council for Refugees' excellent summary article, "A hundred years of immigration to Canada 1900-1999."
Figure 38-1. Proportion of foreign-born population by projection scenario, Canada, 1871-2031.
Source: Statistics Canada
Canada today admits roughly four categories of immigrants: refugees, family members of Canadians, skilled workers and professionals, and business people. In 2007, 12% of immigrants were refugees and 28% were family members.
The skilled professionals are subject to a points system. Applicants are graded out of 100 points, where up to 25 points are given for English and French proficiency, 25 for education, 20 for years of work experience, 10 for age, 10 for "adaptability", and 10 for pre-arranged employment in Canada. 67 points is a passing grade.
The business category of immigrant is intended to attract immigrants who will become employers, rather than employees, providing capital and ideas and shifting labour demand to the right. In 2011 there were three categories of business people: investors who make an $800,000 interest-free loan to Citizenship and Immigration Canada, to be repaid after five years; entrepreneurs, who have $300,000 and business experience to back it up; and the self-employed, who have experience in culture, recreation, or agriculture.
In contrast to Hanson’s recommendations, Canada has made it more difficult for lower skilled people to immigrate to Canada. Concerned about worsening immigrant poverty in the 1980s and 1990s, Canada actively selected higher skilled immigrants beginning in 1993. In 1992, only 17% of immigrants had a university degree, but by 2004 the number was 45%. The skilled worker class accounted for 29% of immigrants in 1992 but 51% in 2004. Unfortunately, the program was not successful in reducing poverty, as a 2007 study reported. In 1992, immigrants in Canada 10 years or less were twice as likely to have low income than native-born. In 2004 the ratio was even worse, with immigrants about 2.5 times more likely to have low income. In fact, by 2000 the skilled worker class of immigrant was more likely to experience low income and chronic low income than was the family class of immigrant. University-educated immigrants were earning no more than the high school-educated. Clearly, skilled workers have difficulty translating their skills into employment. They also may lack the social support that immigrants in the family class enjoy.
Others have suggested that the way the ethnicity of immigrants has changed -fewer European and more Asian – accounts for some of the difficulty finding employment. Language acquisition or social adaptation may be more difficult. Racism may also be a factor. Another important issue is that university degrees earned in Asian universities are discounted by Canadian employers and professional associations.
Figure 38-2. Canada’s Immigrants
Data Source: Statistics Canada, population censuses, 1971-2001
While immigrants to Canada have higher poverty rates than the Canadian-born, immigrants' children typically fare better than Canadian-born. 2001 Census data indicate that second-generation immigrants 25 to 37 years of age are, on average, more highly educated and earn more income than non-immigrants.
Rural-Urban Migration
Migration is not all international. Besides cross-border migration, we have patterns of migrations within countries, such as settlement of new areas, establishment of retirement havens, rural-urban migration, and flight [from the inner city] to the suburbs.
The most obvious intra-national pattern, common to all countries, is urbanization. In 1900, about 90% of the world’s population lived in rural areas, compared to 50 % today. The UN expects the urban population to grow at 1.8% in the next twenty years, compared to 1% for the rural population.
Figure 39-1. Proportion of Canadians living in rural areas.
Source: Statistics Canada, population censuses 1851-2001.
Though Canada is increasingly urban, this does not mean that Canada’s rural areas are not also growing in absolute population size. As reported by Martin Mittelstaedt in the Globe and Mail (“Paradise Lost”, December 19, 2009), between the last two censuses Ontario, Quebec, Manitoba and Alberta’s rural populations have grown significantly. Ontario’s rural population grew 33% since 1971; Alberta’s, 36%.
What is “urban”? John Weeks defines an urban area as a spatial concentration of people whose lives are organized around non-agricultural activities.
Urban areas grow by natural increase, international immigration, and domestic migration, as well as amalgamation, which is more of a technical matter. Between 2005-6, about 22% of Calgary’s population growth came from net migration within Canada. See also http://www.statcan.gc.ca/pub/91-214-x/2006000/4181349-eng.htm for a visual breakdown of the components of population change for other Canadian cities.
Figure 39-2. Calgary’s Population Growth, by Process
Data source: City of Calgary, 2009 Civic Census Overview.
The same push and pull factors that drive international migration drive rural-urban migration. The most usual motive is the pull of higher wages in the city.
Wages are usually higher in the city. As described by their champion and defender, Jane Jacobs, cities are engines of economic growth. Normally located at crossroads, borders, and ports, they serve as trading depots, transportation hubs, information hubs, education hubs, financial centres, and centres of experimentation and innovation. Firms in the city can benefit from internal economies of scale, which means their average costs fall as they expand their production lines to serve more customers. Firms can also achieve external economies of scale, which means their average costs fall because they can take advantage of the infrastructure, suppliers, and employment markets already set up for similar industries in the city. With more customers and middlemen, there are more opportunities for trade and specialization. With denser location, there is more opportunity for brainstorming, competition, and cooperation.
Firms locate in the city to achieve these advantage. Their access to technology, ideas, and loans in the city means there is more capital for each worker to work with, making the worker more productive.
The rural area, by contrast, may be stuck in a Malthusian trap where output per person stagnates at a low equilibrium level. Perhaps the residents have no personal identification or title to their land, and so cannot get loans. Perhaps it is the isolation and transportation costs that explain their low levels of capita per worker and lack of innovation.
The expected real wage
It is not enough to know that the average city wage is higher than the average rural wage. A would-be migrant must multiply the average city wage by the probability (less than one) that he or she will succeed in finding a job. The migrant calculates the
expected real wage, formed by multiplying each possible real wage by the probability of achieving it, and summing the total. By real wage, we mean the wage divided by an index of the cost of living.
Consider a hypothetical city in which there are two sectors, a formal sector where wages are recorded and taxes are paid, and an informal sector. Let e1 be the probability that the migrant can find work in the formal sector. Sometimes we just use the employment rate in the formal sector, i.e. the fraction of the labour force that is employed in the formal sector. Similarly, let e2 be the probability the migrant can find work in the informal sector. The unemployment rate is 1-e1-e2.
Workers going to the city earn the formal sector real wage -net of taxes- multiplied by e1, plus the informal sector real wage multiplied by e2, plus nothing at all or some welfare payment multiplied by the probability of not finding a job in either sectors (1-e1-e2). Workers will be motivated to flow to the city as long as this expected wage exceeds the after-tax rural area wage.
As workers stream into the city looking for work, the employment rate in each sector is likely to fall, and the wages are likely to fall as the capital:labor ratio falls. Thus the expected urban wage will fall until it is equal to the rural wage. If the actual wage cannot go that low, perhaps because of legislation or unionization, there will be unemployment in the city. The unemployment rate drives down the expected wage in the city, because the expected wage is a function of the employment rate.
If two cities have the same employment rate and the same wage, but one of the cities has a much large labour force than the other, your expected wage is higher in the larger city, because the presence of a new arrival does not change the employment rate as much in a larger city. If the large city is 10x the size of the small city, 10x as many people will migrate to the larger city to keep expected wage the same. The unemployment rate in each city will then be the same.
If one city offers higher average wages, the unemployment rate in that city must be higher or else migration to that city will continue.
Consequences of rural-urban migration
The consequences of rural-urban migration are the same as those discussed for international migration, but there are some special considerations:
· The geographic concentration/ population density implied by urbanization may overwhelm the infrastructure.
· The population density makes unemployment or underemployment more visible.
· There may be no legal way to prevent the migration. It is more difficult to keep people out of a city than out of a nation.
How could one stem a tide of rural migrants? Force is sometimes used. Since 1958 China has had a system of residency permits called "hukou". The permits specify from which region you are allowed to enjoy schooling, housing, medical, and other subsidies. Permits for major cities are highly sought after , but usually only temporary residence permits can be obtained, with which it is not possible to have one's children schooled or to have the same quality of life as permanent residents. In 2009, when per capita income in China was about $2,000 USD, the black market price of a Beijing hukou was $5,900 USD.
Using instead a market approach to discourage rural:urban migration would require the city to be made less attractive to migrants, or the rural area more attractive.
Cities can be made less attractive by removing wage supports such as the minimum wage, and by increasing taxes. Municipal services could also be reduced. Rural areas could be made more attractive by lowering taxes, improving infrastructure, improving access to loans, and improving government services.
The government of Canada effectively pays citizens to live “up north”. The Northern Residents Deduction (see Canada Revenue Agency Form T2222) is an income tax rebate for people living in qualifying areas. The federal government also provides home heating subsidies to seniors and others in northern communities.
Similarly, tying treaty benefits to residence on a reserve serves to keep First Nations Canadians on the reserves, for better or for worse.
Urbanization, Economic Development, and Population Growth
We have described some of the labour productivity benefits of cities. Indeed, urbanization is correlated with economic development and prosperity. Which comes first? Economic development or urbanization? The traditional view is that, at a certain level of development and population growth, settling down and specializing tasks becomes possible. But Jane Jacobs (1969) argues eloquently that only in cities will economic development occur. The traditional view says that when agriculture is productive and yields a surplus over and above needs, then urbanization can begin. Jacobs is convinced that innovations in agriculture began in cities.
Urbanization is not all good. Cities are crowded. Contagion and conflict are likely. Only in cities can pandemic disease agents survive and evolve. Sanitation and pollution are likely. It is believed that during the early years of the Industrial Revolution, population growth was less than it otherwise could have been because the concurrent urbanization compromised health and safety.
Population growth may give greater impetus to city growth. City growth leads to innovation and improvements in the standard of living, but also adds mortality risk factors such as disease and crime. Fertility rates tend to be lower in cities.
Domar's Hypothesis
We must not neglect to study the dark side of migration: forced migration or forced confinement. Throughout history various groups have had their movements controlled, with economic and demographic consequences for them and other groups.
Evsey Domar (1970) examined the history of Russian serfdom and hypothesized that the following three things cannot co-exist: free land, free peasants, and an upper class that does not work. Where there is free land and an upper class that wants to make its living by owning the means of production, there will be servitude and slavery. Basically, free land means that holding land is not profitable; profit is found in the relatively scarce workers, who become the objects of the upper classes’ profit motive.
As Domar describes it, in the late 1400s, the Russian government was at war and
facing a shortage of soldiers and arms. It decided to give lands away in return for men
and weapons The new landowners lent money to peasants to work the land and pay rent, but they found that the incomes earned by peasants from land, and the rents that could be charged, were too low, given the abundance of land being offered for rent. “Hence it was the ownership of peasants and not of land that could yield an income to the servitors or to any non-working landowning class.”
The Russian government gradually restricted the freedom of the debt-ridden peasants until they were enserfed by the mid 1600s. Though serfs could not be sold, they
were tied to property which could be sold. However, they had the right to life, the right
to marry and have families, and the right to own personal property.
In opposition to Domar’s hypothesis, European peasants gained rights after the Black Death (see Chapter 17) made labour very much more scarce relative to land. Domar believes that political developments were the reason. We might also add that European
peasants were less isolated than Russian serfs, and better able to assert their wishes.
Another factor may be that, although the number of workers per acre of land declined, the number of workers per landlord may not have declined: landlords too died in the plague.
The case of the Egba in Nigeria
Fenske (2009) describes the case of the Egba of south-western Nigeria and finds it fits with Domar’s hypothesis. Indenture and slavery were present in this land-abundant economy. Fenske also makes a connection between land-abundance and lack of credit.
The Egba are Yoruba-speaking Nigerians who first settled their current territory in 1830. Their military success expanded their base so much that, by 1911, population density was still only 142 people per square mile.
Between 1830 and 1914 the Egba followed a system of extensive agriculture which involved clearing forest, farming the land for five or six years without fertilizer, and moving on to new land. Land, especially land far from settlement and without many palm, kola, or cocoa trees, could be acquired for very little if any payment. Property rights over cleared land were loosely defined and rarely permanent. In 1914, the British were renting over 26,000 acres from the Egba at less than one shilling per acre.
Since every Egba man could have all the land he required, no Egba man was willing to work for another farmer and earn less than his total product. Since the technology was very simple, and there were no large fixed costs to farming, there were no economies of scale to make a farm with many workers more productive than a farm with one worker. Consequently, wage labor was rare. Wage labour became stigmatized.
The second consequence of land abundance was that land was not very valuable and did not serve well as collateral. It was difficult for the Egba to get loans. The record shows that people pawned themselves and their children in exchange for loans, and that people took draconian measures to achieve payback from their borrowers.
In a society without credit and without a social safety net, when all you have is yourself and your family, slavery is a way to escape starvation. It is a way to pay debt, including debt to a community because of crime. When someone saves your life, you may have no means to repay this person other than by paying this "life debt" with a life of service. In a way, a life of service is the one inalienable thing each human being has to offer in trade. Perhaps this is why slavery was accepted as an institution for thousands of years. In ancient Israel, where lending at interest to a fellow Israelite was forbidden, buying an Israelite slave or taking a debtor as a slave was permissible for up to 6 years. The Lord Jesus did not preach against slavery – or any other institution - in particular, and the writings of St. Paul recommended for the Christian community mutual respect between master and slave.
In their situation of land abundance, labour scarcity, and credit scarcity, the Egba accepted slavery and pawning. They also practiced polygyny and brideprice. Polygyny is the practice of having multiple wives. When land is cheap, and when women work the land, there is little cost to having more wives. In fact, wives are a net material benefit as agricultural workers, and command a bride price, a payment from the groom’s family to the bride’s family at marriage.
Slaves may have made up as much as one fifth of the population. They were generally strangers who were captured in war, sold to pay debt, or criminals being punished. Slaves provided scarce labor, reduced the uncertainty around labour availability at harvest time, and also served as productive “assets” in an economy where there were few opportunities to save or invest.
Fenske writes, “Understanding the existence of forced labor is of particular relevance to Africa, given the large-scale export of human beings from an under-populated region - a trade which had the effect of keeping the continent’s population stagnant over the course of several centuries.” Usually, an economy exports goods which make intensive use of whatever resource the country has in abundance. In the case of Africa, heat-loving crops, gold, or ivory would be obvious choices. But the very fact that Africa was under-populated meant that humans were the most valuable thing around and vulnerable to disenfranchisement and commoditization by one another. Another, more important factor was the demand by Europeans for crops grown in plantation style, which required gang labour. We discuss this more in Chapter 41.
The Economics of Bondage
We have seen that slavery is likely to arise when labour is scarce relative to other factors.
Slavery is also associated with a particular kind of work, namely, work that is intense and demeaning.
Work that is particularly intense and demeaning is work that no one wants to do. The wage offered may be higher than the average wage, but the non-pecuniary factors cause individuals to feel better off without that kind of employment. Plantation-style agricultural work, manufacturing under sweatshop conditions, mining in hazardous conditions, and prostitution come to mind as examples of work that many people will not do unless coerced.
When this kind of work is profitable, there is an incentive for humans to be trafficked to provide the labour. Ironically, bondage sometimes increases the material welfare of the person bonded, but it takes its toll in shame, restricted opportunities, and vulnerability to the caprices of the master and the master’s class.
African Slaves in the United States
Between 1500-1660, about 9.5 million Africans were enslaved and brought to the
Americas. 57% went to Latin America, 40% to the Caribbean, and only 6% to the \
United States. Most of these slaves were employed on sugar plantations, except in the
United States, where sugarcane was not grown.
Eventually, the United States became the major holder of slaves and opponent of
abolition, owning 36% of all slaves in the West. This was not because of high importation of slaves but because of a high rate of natural increase in the slave population (25% per decade).
In the Caribbean, by contrast, the slave population was not able to maintain itself
because of harsh treatment, poor food, diseases, a high sex ratio (1.5) among new slaves,
and disruption to private life. Not until the 1800s did the fertility rate equal the mortality rate. Until then, the rate of natural increase was about -20% per decade.
Indentured Europeans were brought to the West Indies to work sugar fields shortly after Columbus arrived However, indentured Europeans defected in response to the difficult work, hot weather, and tropical disease, and new recruits could not be persuaded to come in great numbers.
Financial aspects of the African slave trade.
In the Caribbean, the material benefit from owning an unskilled slave depended was the slave's output in sugar and the price of any children a female slave might be expected to bear. Demand for slaves and slave prices rose much more rapidly than did the price of sugar, suggesting that the productivity of slaves in sugar production grew strongly.
The supply of slaves was fairly responsive to slave prices except for the 1750-1775 period, and after 1791.
Fogel and Engelman (1974) argue that slavery was associated not with agriculture in general, but with plantation agriculture -large scale and labour-intensive - in particular. They claim that plantation-style agriculture was about 50% more productive than other methods of growing sugar and cotton. However, nowhere could free men be induced to work on plantations, not even for 50% higher wages. “For it was only by force that it was possible to get blacks to accept gang labor without having to pay a premium that was in excess of the gains from economies of scale…After the slaves were freed, many planters attempted to reconstruct their work gangs on the basis of wage payments. But such attempts generally foundered, despite the fact that the wages offered to freedmen exceeded the incomes they had received as slaves by more than 100 percent.”
The treatment of African slaves in the United States
Fogel and Engerman argue that, while force was necessary to get gang-style labour, the use of force had its costs, and there were diminishing returns to using force. That is why slaves also earned money. They claim that the average U.S. field hand earned 15% more than a free agricultural worker (but had to endure the gang-style labour and loss of freedom). Slaves “shared” in the gains from the economies of scale. What the slaves were paid was, of course, not enough to compensate them for the unpleasantness of their working situation. Fogel and Engerman write: “For every dollar gained by a typical consumer of cotton cloth [in lower cotton prices], there was a slave laboring somewhere under the hot southern sun who would lose at least $400 [in non-pecuniary costs].”
Fogel and Engerman believe that cruelty to slaves was not the norm. According to the 1850 US Census, maternal mortality was less for slaves than for southern white women. The infant mortality rate was roughly the same. Fogel and Engerman provide evidence that slaves had 10% more calories in their diet than the average white. They also argue that 90% of slaves’ earnings were returned to them in the form of maintenance or cash. However, this contradicts their report that freedmen were offered wages 100% higher than what they had received as slaves. If slaves were already paid 90% of their earnings, offering freedmen 180% of earnings would bankrupt employers.
The ban on trading in slaves, which came before the ban on slavery, was not a trivial step toward freedom, but may have done much to improve their treatment, forcing would-be owners to compete for slaves, raising the price of slaves, and raising the incentive to treat them well.
When slaves are freed, they are able to choose work more amenable to them…if they are not prevented by racism. The system of slavery was predicated on a disdain for blacks that restricted their opportunities after emancipation, such that they were worse off economically. After emancipation, black nutrition, health, and life expectancy declined. Whereas slaveowners had put blacks in jobs where they were most productive, after emancipation blacks were pushed out of skilled trades, and their wages relative to southern whites declined.
The demographic consquences of slavery include the settlement of blacks in the Americas, and resettlements such as Caribbean blacks in New Orleans and American blacks in Liberia. The legacies of these migrations include racial bullying by both whites (USA and Canada) and light-skinned elites (Haiti and Liberia), unrest and inequality, but also, eventually, understanding and cultural enrichment.
The British "Home Children" in Canada
As described by Joy Parr, in the late nineteenth century about 30% of the
British population lived in poverty. In city slums the infant mortality rate was
25%, and life expectancy at birth was about 36. In the event of a financial crisis, children were sometimes brought to the parish authorities. Administrators of the Poor Law placed children in apprenticeships, rural factories (restricted after 1830), industrial schools, or workhouse s. The workhouses became increasingly crowded after the Irish Potato Famine (late 1840s) and the recession of the late 1860s.
In response to lobbying efforts, the government agreed to allow children to be
sent to Canada. Most were sent by municipalities, about 20% by evangelical
church groups who had spearheaded the lobbying, and the rest by other religious denominations or charities. Sometimes children were sent abroad against the wishes of their parents. The first two distributional homes were at Niagara-on-the-Lake and Belleville, Ontario. Other major centres were Toronto, Peterborough, Brockville, Ottawa, Montreal, Sherbrooke, and Halifax. There is a reference to a “Barnardo boy” in the classic novel Anne of Green Gables. A total of 80,000 British children were compelled to come to Canada between 1868-1925.
What motivated the forced migration of these children? Besides a desire to help them, there must have been a belief that land-rich Canada, with a scarcity of labour, would welcome these children for the labour that they could provide. And indeed, for children over 8 years old, that seemed all that Canada was willing to do. Joy Parr argues that, for these children, a formal work obligation helped protect them.
Very young children were placed in trial adoptions, but the placement agencies
found that children over the age of 8 were usually not accepted as part of the
family. Because of this, indenture seemed preferable to an attempted adoptive relationship, because indenture defined the rights of the child and spared them fantasies of achieving birth child status in the family. Parr writes, “Formal apprenticeship indentures did more to define the rights of British immigrant children than to extinguish their liberties.”
What transpired is that children 6-10 were boarded out for a fee paid by the
agencies. Between 11-14 children usually boarded for free in return for their
chores, and between 15-18 they were indentured to work for pay that the agency collected.
Younger children were more popular in isolated areas, where there was little
off-farm opportunity for the farmwife, and where it was more difficult to market
farm produce for cash. “Home children” would bring in cash and could be fed on
farm produce. As children grew in skill and stature, they were relocated to more
prosperous areas which could offer more pay. In one sample, boys were moved
an average of 3 times, girls even more frequently. This must have been
disruptive to their development.
Human trafficking today
We have seen that slavery and forced migration is more likely when labor and credit are scarce. Human trafficking is likely in industries where workers’ conditions are intense and dangerous. Slaves welcome liberty, but sometimes their material standard of living deteriorates once they are freed.
In the world today, humans are trafficked to supply sex, to work in sweatshops, and to work on plantations (e.g. cocoa farms in West Africa). Some victims are conned by people offering to sneak them into a better country. Others are duped by pimps acting as friends, and brought from rural areas or reservations to big cities within the same country. A 2004 RCMP publication estimated that 600-800 people are trafficked into Canada per year, and 1,500-2,000 pass through Canada to the United States. Countries of origin include Eastern Europe, China, Southeast Asia, and Latin America. The US believes that 80% of people trafficked into the US are female.
A dear friend of mine came all by herself from Hong Kong to Vancouver in the 1980s to attend high school. Her contact was a former piano teacher, with whom she stayed. This woman soon had my friend doing household chores. She then began to bring men around the house and make suggestions. Before anything worse happened, my friend, penniless and in tears, boarded a bus and blurted out one of the few English words she knew: “YMCA”. I’m happy to say that things took a turn for the better at that point.
This story illustrates the sad reality that often, when a group is exploited, one of its own members is collaborating.
To combat human trafficking we need to uncover and prosecute it. It is also important to understand the push and pull factors.
Push Factors
-unemployment and poverty
-lack of credit and opportunities to improve one’s life
-abuse in the home or the home community
-ignorance and credulity
Pull Factors
-deceit and predation
-profits for the trafficker due to demand for gang-style labour
-lack of concern in the host community, possibly due to racism.
-lack of detection in the host community, possibly due to race and class differences.
To fight human trafficking we need to educate potential victims and potential host communities. We must ensure that people have a fair chance to develop their potential, and to safely move to areas where they have more economic opportunity. We must also spend resources finding human traffickers. Traffickers must then be given a significant punishment.
Criminalization
Criminalization of an activity raises the costs of that activity. Costs include the fines and jail time that are incurred with various probabilities, and the cost of avoiding detection. The two main results of these higher costs are that 1) the activity is discouraged; and 2) the activity is driven underground.
There is no question that criminalizing an activity will reduce its incidence. When costs rise, the supply curve shifts toward the origin. Higher prices are charged to cover the higher costs, and this discourages use. If suppliers fight among themselves for control of the market, and one succeeds in monopolizing the market, prices will rise even more, and output will fall even more. Monopolists always keep prices above the free market price.
So far so good. But we have not addressed the consequences of the activity being driven underground. This gives rise to all kinds of negative external costs. As previously mentioned, the suppliers are able to conduct turf wars underground, and violent crime is likely to escalate, at least among the criminal class. The criminals who succeed may use their monopoly profits to branch into other criminal activities or to corrupt politics.
Another consequence of an activity being driven underground is that the activity can change. Buyers can suffer if sellers contaminate the product, which is unregulated. And workers will suffer if they are forced into more isolated and less safe working environments.
Prostitution is an especially tough case. Legalizing brothels will lead to more prostitution. But criminalizing brothels forces prostitutes into the cars of potentially murderous strangers. Criminalization must be paired with a program to protect prostitutes and help them leave the trade if that is what they want.
Human trafficking is something so simply exploitative that we cannot legalize it without tearing the heart out of our society. However we must recognize that as long as the push:pull factors are there, human trafficking will be hiding somewhere.
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Box 40-1. Polygyny in Canada. A polygamous community in southeastern British Columbia came into the spotlight in 2007, when a senior leader was charged with being an accomplice to rape of a minor but was later discharged for lack of evidence. It seemed that the two groups which comprise this community would continue their illegal marital practices - underage marriage, polygyny, and the probable coercion of brides - in their remote location. Now, however, changes to property rights are developing that could change the incentives faced by powerful men in this community. The land used by this branch of the Fundamentalist Church of Jesus Christ of Latter-Day Saints (FLDS) is owned in trust by FLDS leadership in Utah, but the Canadians want to hold their land in their own names. So the State of Utah has appointed a trustee to privatize the land. This would involve putting names on leases and property titles. The trustee is looking for names of all wives, and finding it difficult to collect the information, but he intends to make all spouses equally owners of any land a husband has claim to. If there is a chance that the women might actually make use of these ownership rights, men’s incentive to have multiple wives will be reduced. (“Wives to be named on leases”, Robert Matas, Globe and Mail, July 11, 2009)
� Labour’s share of GDP is wL/GDP. Wage elasticity is dw/dL multiplied by L/w. Let dL = the number of immigrants.
� For the latest regulations, see � HYPERLINK "http://www.cic.gc.ca/english/immigrate/index.asp" ��http://www.cic.gc.ca/english/immigrate/index.asp�
� Canadian Council for Refugees, � HYPERLINK "http://www.ccrweb.ca/en/hundre-years-immigration-canada-1900-1999" ��ccrweb.ca/en/hundre-years-immigration-canada-1900-1999� Downloaded July 28, 2011.
� Statistics Canada, Report on the Demographic Situation in Canada, 2005 and 2006, Table 4.2.
� "Canada's changing immigration checklist: Youthful trades workers wanted." Globe and mail, Feburary 18, 2011.
� Picot et al. (2007)
� M. Corak (2008)
� "China's outdated residence permit system", UPI Asia.com, Feb 20, 2009, downloaded March 3, 2011.
� Workhouses were not usually places of hard work but were places where the poor could be housed. They were usually crowded and provided minimal food. There were attempts to find employment for residents of workhouses, and sometimes the working-age residents were forced to do work at the workhouse itself.
� RCMP (2004).
� Stewart and Gajic-Veljanoski (2005)
� US Department of State (2004), as reported in Stewart and Gajic-Veljanoski (2005).
�A report based on 2003 data found that East Asian homestay students in British Columbia were at greater risk for abuse and self-harm than immigrants and Canadian-born students of East Asian heritage. See Wong et al. (2010)
_1141059243.
_1141059244.
Econ/Background to week 1.docx
What is Economic Demography?
Economics is the study of material trade-offs, of costs and benefits. Demography is the study of human population changes. Can these social sciences be combined without producing a monster?
The answer is Yes – if we understand the limits of economic science. Economics does not provide ultimate, absolute, or intrinsic values for goods, services, the environment, or human life. It merely computes the relative value of these things in terms of other things. In economics, the value of something is what must be given up in exchange for one more unit of it. To be specific, economics measures the value-in-trade of the marginal unit to this generation of market participants.
The value-in-trade does not tell us what to buy or do as much as it tells us what it will cost to do so. Economics is the study of the trade-offs between competing activities. Thus Economic Demography gives us an understanding of the economic consequences of demographic changes. We will also study the demographic consequences of economic conditions. Economic demography provides us with some of the information we need to support those social outcomes we believe are best.
The interplay between the economy and the population
As described by J R Weeks (1989), population affects the economy by the impact of its absolute size, by how quickly it grows or shrinks, and by its composition e.g. its age structure. The population’s size, growth, and composition affect the supply and demand of different resources. As prices and wages change, financial pressures build.
These financial pressures lead to changes in birth rates, death rates, and migration patterns. Fertility, mortality, and migration are the three drivers of population change. Via these processes, financial pressures affect population size, growth, and composition. So we come full circle.
Figure 2-1. Economics and Demography
Since economics and demography affect one another, there is the possibility of feedback loops.
If the relationship between population growth (or shrinkage) and economic growth (or shrinkage) could be completely described by a single positive or negative feedback loop, society would not be able to find a demographic or economic equilibrium. An equilibrium is a resting place, a stable situation from which there is no tendency to move. If a randomly occurring phenomenon from outside economic or demography, that is to say, some phenomenon exogenous to the model were to upset an equilibrium, the equilibrium would eventually re-emerge.
Sources of demographic data
The principal sources of demographic data are vital statistics registries, and surveys.
Vital Statistics
In developing countries today, many people are born and live their lives without being officially registered. This interferes with their ability to vote, own land, and receive loans. In the western world, until the twentieth century, only churches kept detailed records of births, marriages, and deaths.
In Canada every citizen must report birth, marriage, divorce, and death information to the provincial government. Statistics Canada collects this information as well as vital statistics for Canadians living in some American states. Statistics Canada Health Statistics Division collects pregnancy, miscarriage, and abortion information from other agencies such as the Canadian Institute for Health Information.
Unfortunately, in July 2011 Statistics Canada stopped compiling marriage and divorce data at the national level, citing budget cuts and the "changing nature of relationships" ( www.theglobeandmail.com , "Statistics Canada to stop tracking marriage and divorce rates," July 20, 2011.)
Citizenship and Immigration Canada documents immigration and citizenship, but not emigration. Emigration data must be inferred from other data.
Surveys
A survey is a questionnaire or interview. The survey can be broad in scope or can target a particular group. The survey can follow the same group of people over time, or can be repeated over time with a randomly selected group of people. A survey that follows the same group over time is called a longitudinal survey. Some fabulous surveys to study are available online, including the USA's Panel Study of Income Dynamics, which tracks individual households from 1968 on. Canada's Survey of Labour and Income Dynamics begins in 1993. This and other Canadian longitudinal surveys – such as the National Population Health Survey (NPHS) - are found at http://datalib/chass/utoronto.ca/major/long.htm
International agencies conduct many informative surveys, especially in developing countries. Currently funded by USAID, the Demographic and Health Surveys Program collects demographic data in 205 developing countries. This began as the World Fertility Survey in 1972.
The opposite of a longitudinal survey is a cross-sectional survey which is a snapshot of a population at one particular point in time. The most famous cross-sectional survey is the Census.
Census
A census (latin root: censere, to assess ) in its simplest form is an enumeration of the population. These go back to ancient times. The Canadian Census is conducted by Statistics Canada ( www.statscan.ca ) every 5 years. Information from the 1986 and more recent censuses is available at Stats Can’s website. Each household is mailed a form which must be filled out and mailed back. (Online responses are also accepted). The form contains several questions having to do with the persons in the household: their names, ages, gender, first language, and how they are related. Formerly, a longer form census was sent to some households. It included many more questions, including questions about race, occupation, income, who pays the rent, and the condition of the house. In 2010, the Canadian government announced that the questions on the longer form were too intrusive and that filling in the longer form should not be mandatory. Consequently the longer form census has been replaced by a voluntary "National Household Survey" which asks the same questions.
In 2010 Prime Minister Harper decided that the long form census was too intrusive. While the short form census is still mandatory, the long form census is being replaced by a voluntary "National Household Survey" which will be mailed to 4.5 million Canadians.
One of the questions will ask people to waive their right to privacy after 92 years, at which point their responses will become part of the National Archives after 92 years.
Censuses suffer from overcoverage when they include people who should not be covered or when they count the same persons twice. They also suffer from not managing to include everyone who should be included (undercoverage). It is estimated that the 2006 had undercoverage of 1.5 % and overcoverage of 4 %.
Combining Census Information with Vital Statistics
Birth and death statistics tells us who should be living in Canada; the census tells us who actually is living in Canada. The difference is migration. With immigration data from Citizenship and Immigration Data, we can infer emigration. With birth and death information from Vital Statistics, and overall population numbers from the census, we can compute birth rates and death rates for the population. In its Quarterly Demographic Estimates, Statistics Canada publishes updated summary information on Canadian birth, death, and immigration rates.
Statistics Canada
Statistics Canada is a federal agency which conducts our census as well as most of our surveys. It also collects information from the provinces' Vital Statistics offices and from hospitals. Most of its information is free to students using the university's web portal.
National Identity Registers.
To avoid the need to estimate or cobble together statistics, some countries maintain up-to-date population registers that list all individuals with their vital events including change of residence. These are expensive, and raise concerns about privacy and personal freedom. Britain has a “National Identity Register”. Canada and the USA do not.
Historic Data
Much detective work and deduction must be applied to the limited historical record. For Canadian historical data up to the 1970s, see http://www.statcan.ca/english/freepub/11-516-XIE/ and go on the library website to CANSIM II.
The Malthusian Equilibrium
The most famous model of economics and demography is the one that was presented by Thomas Robert Malthus (born 1766) in his various editions of An Essay on the Principle of Population as it Affects the Future Improvement of Society (1798). The Malthusian model is famous because it has an equilibrium, an equilibrium that is credible and feared.
Malthus’ model achieves equilibrium because population size affects the amount of food per person in a simplistic and rigid way, and the amount of food per person affects the population in a simplistic and rigid way that is exactly opposite. Since the forces are opposing, no positive or negative feedback loops will form.
The Malthusian model assumes two things. First, Malthus believed that food production could grow by a fixed amount every year. This is called “arithmetic growth”. Second, Malthus believed that population always grows when food per person rises, and shrinks when food per person falls. Moreover, the growth in population is exponential, quickly outstripping any growth in food supply.
In Malthus’ formulation, the higher the standard of living (i.e. food per person), the higher the the birth rate and the lower the death rate would be, leading to population growth. Although Malthus agreed that people could restrict fertility by delaying marriage, he did not think that this or other “preventive checks” on population growth would be significant. Instead, population would grow in good times until “positive checks” (what a misnomer!) such as food scarcity, disease, criminality, and warfare resulted.
Food per person
Birth rate
Death rate
Fig. 3. The “Malthusian Scissors”
S
Rates
Be very careful with Figure 3 above. The birth rate line is NOT a supply curve. It does not shift to the right when the birth rate rises at every standard of living. It shifts up vertically in that case. The death rate line also shifts up vertically with an increase in death rates, and shifts down vertically when they fall.
Figure 3 shows us that population growth is zero only when food-per-person = S. Malthus called this equilibrium level of food-per-person “subsistence”. However, S does not have to be as low as a subsistence diet. S is simply that level of food per person that is compatible with zero net population growth. Different societies can have different S, different levels of food per person that result in zero net population growth.
In class we shall play around with this diagram, and with Figure 6 below.
Figure 6. The “technology schedule”.
Popn size
Food per person
SSAS
Old technology
New technology
SBig
NBig
N
What happens when food-producing technology improves, and the technology schedule shifts up? Using Malthusian arguments, the population becomes larger but the standard of living reverts to Ss.
Note: the technology schedule does not refer to birth control technology or medical technology. It refers to technology that affects only the ability of people to procure their standard of living from the resources around them.
Malthus and others have concluded from this analysis that it is pointless to help the poor. We will debate this in class.
Economic Consequences of the Black Death
The Black Death was a pandemic of bubonic plague that, in its most famous outbreak, swept across Europe during the fourteenth century, killing roughly a third of the population. Bubonic plague is caused by the bacterium Yersinia pestis. Swollen lymph nodes and gangrene of the extremities of the body are two of its symptoms. The bacterium is transmitted by fleas usually found on mice and rats. This could be a very old disease; the Biblical record has the ancient Philistines, afflicted by some kind of plague, offering golden rats and golden boils as penance[footnoteRef:1]. We do not know when bubonic plague began, but it has not yet been eradicated. One case was reported in California in 2006. [1: . (approximately 1140 BC, as recorded in 1st Samuel 6). ]
The Black Death was of course a time of intense human suffering and wasted potential. That so many died was a reflection of the prevailing low levels of nutrition, sanitation, and medical knowledge.
What happened to the standard of living? Apparently, wages rose as labour became scare relative to land and equipment. Ehrenberg and Smith (2003) report that a thresher earning 2.5 pence per day in 1348 earned 4.5 pence just two years later. Mowers receiving 5 pence per acre in 1348 received 9 pence in 1350. However, Munro (2004)[footnoteRef:2] has found that increases in the overall price level eroded the value of these wage gains so that real wages actually fell. Why would there have been inflation? Munro quotes Herlihy (1967) saying “men were dying, but coins were not”. [2: http://www.economics.utoronto.ca/public/workingPapers/UT-ECIPA-MUNRO-04-04.pdf]
A look at Munro’s detailed study of medieval wages and prices shows how little reliable data we have on which to base our conclusions about the economic consequences of the Black Death.
Demographic History before 1750 AD
What has been the relationship between population and the economy in human history?
The human population of our planet grew slowly between 9000 BC (estimate) and AD 0, with many reversals. The net growth that occurred was equivalent to that which would have occurred if the population had grown since 9000 BC at a constant exponential rate of 1/20th of one percent.
By AD 0 total population was about 300 million. After AD 0 the population continued to grow at the same modest pace, resulting in a population of about 790 million in 1750.
Prior to 1750, economic growth was extremely slow. The standard of living hardly changed. In 1700, most people lived in poorly heated homes, experienced periods of famine, and died young.
The slow rate of population growth prior to 1750 is attributed to
· Low rates of technological change or productivity improvements
· A standard of living so low that it left the population vulnerable to crises such as crop failure, pandemic disease, and war.
· High chronic mortality rates
· Fertility rates significantly less than the maximum biologically possible
Mortality rates
The fact that mortality rates were high in pre-industrial times is no surprise. We all know how little technological and medical assistance was available to people then. They made do with crude clothing, housing, and sanitation. They gave birth and tried to breastfeed without ultrasound, hand-washing, or sterilizing of equipment. They worked at manual labour using crude tools and bulky livestock. Most people were employed in weather-dependent agriculture without benefit of insurance. It is estimated that life expectancy at birth was, on average, between 20 and 40 years.
In those times there was little sense that the government should work for peaceful international relations, provide for the poor, or stimulate the economy. There were more frequent violent conflicts between individuals, tribes, and nations.[footnoteRef:3] [3: For evidence that violence has declined, see S. Pinker’s The Better Angels of our Nature. New York: Viking, 2011.]
Fertility Rates
Because we observe today that nations with higher incomes have lower fertility rates (fewer children per woman), we might suppose that fertility was high in the pre-industrial era. It was indeed higher than today, but not as high as you might expect. Certainly fertility was NOT normally near 15 children per woman, which is the maximum biologically possible, known as total fecundity. For one thing, many women and men did not get married. Think back only 100 years in Canada, and you will recall from novels you may have read the many more “spinsters”, “bachelors”, priests and nuns. Poverty, social isolation of farming men, strict social norms around courtship and engagement, and high mortality rates for men in war and work meant that many potential couples did not unite.
Even within marriage, infertility, poor nutrition, length of time breastfeeding, women’s deaths in childbirth, and early widowhood (death of husband) conspired to keep fertility rates lower than total fecundity.
Estimates of pre-industrial fertility differ. Clark (2007, Table 4-2) estimates that the average woman in England in before 1790 gave birth to 4.9 children. Clark and Hamilton (2012) have data to show that the average married man in New France (now Quebec) had 9 offspring, only 4.36 of which actually survived to have children of their own.
The Meaning of Life Expectancy
“Life expectancy” usually refers to how many years a newborn can be expected to live. In demography, we would call that expected life years remaining at birth. We will also learn to calculate expected life years remaining for a person of any age.
Basically, the number of life years remaining depends on the risk of dying in each of those remaining years. A person’s expectation of life years remaining at birth depends on the mortality rates its cohort will be exposed to from the moment of birth on.
(A cohort is a group of people born at the same time, either in the same year or over a longer time period. In the case of life expectancy calculations, we study people born in the same year.)
Econ/background to week 11 (1).doc
Effect of Population’s Age Structure on the Economy
Earlier in the course we learned that economically growing nations pass through a Demographic Transition whereby their age structure changes from a youth-heavy distribution to an age-heavy distribution. In between is a period of time when total dependency is at an historic low and a “Demographic Dividend” may be earned.
To analyze the consequences for the economy it is helpful to look at two key points:
a) is the capital:labour ratio changing?
and
b) is dependency changing?
You may recall from the Solow model that capital shallowing is a problem when population is growing. Capital shallowing means that capital per worker is falling. If capital accumulation does not keep pace with population growth, shallowing occurs and labour productivity falls.
When child dependency or age dependency is high, savings are likely to be low. Families and governments must spend on child and elder care. If there are many elderly, they may be liquidating their savings to support their lifestyle.
In the time of demographic dividend, however, savings can be higher. Since savings build up capital, labour productivity can be expected to rise.
In class we shall fill in the following table:
|
|
Y/L Output Per Worker / Labour Productivity |
L/N Fraction of Pop that Works |
Y/N = Y/L * L/N |
|
Young population |
|
|
|
|
Demographic Dividend |
|
|
|
|
Older population |
|
|
|
Young Populations and the Demographic Dividend
Young populations may be that way due to high fertility, high mortality, immigration of young people, or emigration of older people. Usually, young populations are growing populations.
Populations where the share of young is growing experience:
· Higher child dependency
· A growing workforce
· Redistribution of earnings from labour to capital: lower wages, higher prices for housing and other capital goods
· high interest rates due to low supply of savings
· Changing sectoral composition towards goods and services demanded by younger people.
When fertility begins to fall, and aged dependency is still low, a working age cohort will emerge which as few dependents. In that case, a demographic dividend can be earned.
The way the demographic dividend delivers benefits to a nation is that the new cohort of young workers
- is larger compared to previous and subsequent cohorts due to the boom that took place, followed by lower fertility rates
- is larger due to the lower fertility rates, meaning that women are more likely to enter workforce
- is more likely to save because of smaller family size/fewer children
- is more likely to save because of lower aged dependency i.e. fewer parents per worker.
- is willing to adopt new technologies and new ways of doing things due to their youthful attitudes, recent education, and long work horizon
Policies that support the demographic dividend are policies that promote the utilization of this new, large labor force, and policies which keep dependency low so that the labor force can save a large part of its earnings. To successfully absorb a larger labor force, a society must make it easy for businesses to become established, get loans, and hire/fire workers. The labour force should also be healthy and well-educated. Policies that promote the health of dependants, provide flexibility for workers to look after their dependants, and make family planning easier will help reduce dependency.
These policies are also required, and are even more important, before the demographic dividend occurs. When population growth is strong, and there are a large number of child dependents, it is important that business growth is facilitated and loans are available to provide employment and combat capital shallowing.
According to Lee (2003), economically developed nations' dependency ratios have been falling from the mid 60s, and are now set to sneak back up due to aging. Hence our opportunity to collect a demographic dividend is over for the time being. Even the experience we had of our boomers being working age might not have been as large a dividend as we first experienced in Canada a hundred years ago. At that time, elderly survival was lower, and so when fertility fell, during the 20s and 30s for example, there were also fewer aged to care for. Our boomers had relatively few children, but they also had parents to support.
Less developed nations entered their demographic dividend phase around 1970, and it may last until 2020. The least developed nations are also in the dividend phase, having begun later, about 1980.
For the demographic dividend to yield its full benefit, the youth cohort must be healthy and literate and have access to jobs. Jobs may be scarce until the capital stock catches up with the ballooning workforce. Capital shallowing is a problem as the labour force grows, which threatens productivity; on the other hand, the working cohort has more money to save because families are smaller. During the demographic dividend, wages will be competed down by the surge in the number of workers, but wages may also grow if productivity grows. In the meantime, a housing and university boom can be expected, as will be the case whenever populations are becoming younger. Housing and school placements will be in short supply.
With so much competition, young workers face more economic stress. If their expectations are not realized, they may become frustrated. There are more potential recruits for the army, and there are also more young people ripe for radical politics and tempted to act out their frustration.
A recent New York Times article on Middle Eastern youth reported that, because economic opportunities have not grown in pace with population, young adults are having to postpone marriage. Unemployment for those aged 15-29, for example,was 27% in Egypt in 2008, compared to 11% for Canadians 15-24 years old. “I can’t get a job, I have no money, I can’t get married, what can I say?” Mr. Sayyid (Cairo) said one day after becoming so overwhelmed that he refused to go to work, or to go home, and spent the day hiding at a friend’s apartment.” Sayyid’s engagement was called off when he could not pull together $21,530 for his wedding, which budget included $350 for the ceremony, $2100 for the bridal gift, $100 for rings, $,3500 for appliances, $2,500 for furniture, and $12,280 for an apartment. Some governments, like Saudi Arabia and Egypt, offer marriage subsidies to qualifying young couples.
To empower youth to take their place in society and in the workforce, the provision of loans and subsidized education will be important. Creating a positive business environment, where new firms can receive loans and where they are free from too much regulation, fees, and taxes, will assist job creation.
If their talents can be used and their voices heard, young people can bring new energy and ideas to the work force and to public life. They usually have a greater degree of idealism and energy than older citizens. They also more readily adapt to new technologies.
Benefits of an Aging Population
Write Bloom et al. (2003), "An aging population is, fundamentally, a mark of development success." Inasmuch as aging is due to falling mortality, we can all agree that aging is good. Not only are we as individuals likely to live longer, but those we care about, especially our parents and grandparents, are likely to remain with us longer.
A society's elders often help hold families together: they provide love, care, advice, financial support, and a sense of one's place in history. Elders' role as keepers of tradition, masters of craft, and witnesses of history is vital to learning and good government, especially in cultures without writing. Research by Rachel Caspari regarding prehistoric human communities indicates that only the most recent human societies had a high aged dependency ratio, and she speculates that there was a positive feedback loop between the standard of living and the survival of elderly.
Canada is Aging
As seen in a previous lecture, the aged dependency ratio in Canada is rising. Canada’s population structure is aging due to falling mortality and a pervious decrease in fertility.
Life expectancy at birth in Canada has trended upward without interruption since at least 1920. Between 1920 and 1922, life expectancy at birth was 59 for Canadian men : today it is 78.8 . It was 61 years for Canadian women; today it is 84.1 years.
Meanwhile, our TFR and CFR (completed fertility rate) fell steeply between 1960 and 1990, though their decline seems to have ended. Cohorts born during the 70s and 80s were smaller in size than cohorts born in the 40s and 50s.
If present trends continue, Canada in 2017 will look a lot like today’s Kelowna (BC), Victoria (BC), or downtown Kingston (ON), except that it will be more ethnically diverse.
The aged dependency ratio is increasing in much of the world, including Central and Eastern Europe (from Germany to Russia), Japan and South Korea, and the Northern Mediterranean (Italy, Serbia, Greece, Romania). Often, double aging is occurring: the proportion of elderly is increasing, and the average age of the elderly is increasing.
We could also speak of triple aging: not only are the populations of old increasing and getting older on average, but people are retiring from the workforce earlier. In 1910, about half of men aged 74 still worked. In 2000, half of men have finished working at age 63. (Lee, 2003).
Populations where the share of elderly is growing experience:
· Higher aged dependency
· A workforce which is growing less rapidly or shrinking
· Redistribution of earnings from capital to capital: higher wages, lower prices for housing and other capital goods
· high interest rates due to lower supply of savings
· Changing sectoral composition towards goods and services demanded by older people
Types of Pensions
Governments and businesses often offer pensions to workers. Pensions are payments of money which arrive every month or year once a worker is retired. Where do governments and businesses get the money for the pensions? There are two ways.
First, the money for the pensions may come out of current tax revenues (in the case of the government) or current sales revenues (in the case of business). We call this a pay-as-you-go pension. From its beginning in 1964, to 1998, the Canada Pension plan was a pay-as-you-go plan, taking money from workers’ paycheques to give to retired Canadians.
A pay-as-you-go plan works well as long as revenues are increasing every year. When the population is growing and each newborn cohort is larger than the previous, the work force is growing every year and does not have to be taxed very much to provide for the smaller cohort of retirees.
In 1998 the Canadian government realized that the ratio of retirees to workers was growing. Workers would have to be taxed more and more to provide the promised pensions. So Canada began to convert to a fully-funded pension plan. In a fully-funded plan, the workers are taxed and their money is set aside in a fund to earn interest and provide for their own pensions in the future. The success of this plan depends on the interest rate being high enough. In fact, it can be shown that, if the interest rate is higher than the rate of natural increase, the fully-funded plan requires less taxation of earnings than the pay-as-you-go plan, and vice versa.
You cannot switch from a pay-as-you-go plan to a fully-funded plan overnight. The Canadian government increased the amount of money collected from workers, using some of it to pay for retirees’ pensions, and using the rest of it to build a pension fund.
Recall that a shrinking population makes a pay-as-you-go pension plan increasingly expensive. One reason that the US, Canada, and western Europe have been criticized for doing so little saving prior to the current financial crisis is that the West needs some savings in place for pensions and eldercare. We are used to a growing population, where a set tax rate will produce growing revenues every year, just because of population growth. Without strong population growth, we cannot "grow our way out of deficits."
A note on immigration of working-age people
Can immigration of working-age people be used to increase the employment ratio? Canada's Ministry of Finance has estimated that, just having Canada's labour force continue to grow at 1.4% through to 2050 would require immigration to more than quadruple, to almost 900,000 immigrants per year. It would be difficult to support and integrate this many people. Whether the government decides to increase immigration or not, it should design programs to ease transition of immigrants into the workforce and recognize their existing professional certifications.
Aging and health care expenses
We think of the elderly as requiring a great deal of medical intervention. However, many elderly are healthy until their last 6 months of life. And many elderly do not receive costly or aggressive treatment. Morgan and Cunningham (2011) showed that in BC, which has a similar age structure to that of Canada as a whole, inflation-adjusted hospital care, medical care, and prescription drug spending per person grew between 1996 and 2006, but only 1% of this change was attributable to population aging. Most of the increase could be explained by the increased use of specialists and the increased use of diagnostic tests. They also found that improved survival/reduced mortality acted to reduce health care spending.
Other economically-relevant changes in population composition
Besides age composition, two other economically significant aspects of population composition are cultural diversity and family diversity.
Family structures
Not only does family structure affect the economy, family structure is also affected by the economy.
Cultural diversity
Cultural diversity has consequences for the economy. On the one hand, cultural diversity means interesting differences among people from which we can learn and with which we can specialize and become more productive. We discussed the productivity effects of specialization in our discussion of population size. The larger the population, the greater the diversity in talents and interests, ceteris paribus.
On the other hand, cultural diversity may give rise to stresses and strains within the population as misunderstandings or conflicts arise. It may be more difficult to achieve social cohesion. The economy depends on trust and cooperation and a peaceful climate in which to go about one’s business, all of which will be hurt if there is social strife.
The quickest way to change the cultural mix of a population is by migration, with new people coming in and others leaving the country. Migration affects the economy via cultural diversity. Migration itself is usually a consequence of economic pressures.
Changes in Population Composition: Family Structure
The composition of a population in terms of family structure, whether in terms of the proportion of married people in society, or the number of households headed by one parent, or the number of related or non-related people living under one roof, is of interest to demographers and economists. But where does it fit in to economic demography? It fits right at the heart of the micro-economic responses to demography and the micro-demographic responses to the economy. The family is the tiniest population of interest, the tiniest economy. Family structure influences and responds to fertility, mortality, and migration. It influences and responds to economic pressures. An integral part of our culture, family structure is the matrix in which economic and demographic pressures play out.
Family structure is affected by many things, including the three population processes (fertility, mortality, and migration), social norms, the sex-ratio, and economic pressures. In turn, family structure affects the economy through demand for housing and other goods and services, through the dependency ratio, through labour participation rates, and through demand for government social welfare programs.
Figure 42-1. Economics, Demography, and the Family
Fertility Population composition
Mortality Population size
Migration Population rate of growth
Economic pressures
(i.e. prices, wages, incomes)
arising from demand and supply
of various resources including skills and time.
Changes in Family Structure
Over the last 50 years we in the West have seen an increasing tolerance of and incidence of unconventional family structures. Although the number of grandparent-inclusive families is lower, the number of single parent families, step-parent families, blended families , cohabiting adults, and openly homosexual unions has risen.
The greater social tolerance can be attributed to secularization as well as to greater pluralism, education, communication, political freedom to agitate for change, and the willingness of activists to struggle. There has also been an economic connection: a rising standard of living makes people less dependent on family members' support and opinion, and a strong social safety net gives them the courage to try unconventional things.
The economy can affect family structure more directly. A poor economy may force men or women to migrate in search of work, which may break up families or prevent people from getting together. The cost of living may give couples the incentive to stay together during low moments in their relationship, but poverty can also be a strain that drives people apart
As families form or break apart, there may be economic consequences as well as emotional ones. Some innovative family structures provide a strong framework for health and prosperity. Others are weaker and may place family members at greater economic risk. When family structure works well, love, skills and ideas are shared, as well as expenses, care of dependants, and risks.
We now examine changes in family structure that have occurred in the West and which are occurring globally, due mostly to secularization.
Changing role of women
More women work outside the home. This is due to the trends discussed above, particularly feminism. However, economic realities have also played a role. The real wage has stagnated since the 1970s. For those households aspiring to a growing standard of living, it may be necessary for the wife to work.
We have already discussed how an increase in education and in the variety of opportunities available to women tends to decrease fertility. Generally, higher education, and work outside the home, are correlated with fewer children in the family. Women's work affects not only fertility but also, of course, the economy directly. Women working outside the home have greatly expanded the labour force, initially reducing the wage of men in similar occupations. If time worked in the marketplace is more materially productive than time worked at home or in volunteer positions, there is a net material benefit to society. Can we assume that this is the case? Perhaps yes, because women now have the ability to specialize in what they are best at.
Regardless of the material benefit, women appreciate having more choices in life. However, if they are still expected to assume traditional responsibilities while working outside the home, their lives may become more stressful. More and more, men are sharing in childcare and housekeeping, but in 2005 for example, Canadian men aged 25-54 spent 1.1 hours per day on unpaid work, while women the same age spent 1.9 hours.
Gary Becker (A Treatise on the Family, 1981) theorized that the material benefits of specialization (wife to childcare, husband to marketplace) helped keep couples together. The blurring of the expected duties of each partner may stress the relationship. Expectations may have to change and traditions be adapted for the traditional marriage to thrive.
Increased Couple Similarity
With the expanded role of women has come the possibility that women have similar educational levels and similar experiences as their male partners. This has been facilitated also by rising sex ratios. Romantic love and compatibility have become the top criteria for marriage. Couples are taking longer to get to know one another. Goldin and Katz (2002) believe that the contraceptive pill has made longer courtships less costly (in terms of intimacy foregone) and contributed to increased compatibility of married couples. They demonstrate a statistical relationship between access to the pill and higher age at first marriage, lower divorce, and lower marriage rates. They also demonstrate similar, but weaker, effects from the legalization of abortion.
On the other hand, because of the pill, women unwilling to use the pill or have an abortion are facing increased pressure for sex and are no longer able to count on “shot-gun marriages” in the case of a pregnancy. This may explain an increase in out of-wedlock births following the pill and following the legalization of abortion.
Couple similarity may improve marriage viability. It also has consequences for the distribution of income. When only a husband works, and his income is twice as much as his brother’s, the first brother’s household is twice as rich as the second’s. If both brothers have a spouse making a similar amount, then the first household is still twice as rich as the second, but the difference between their incomes is doubled.
Declining Prominence of Marriage
A smaller percentage of westerners are married these days, because of people waiting longer to marry, people choosing not to marry, and people divorcing.
1) Age at Marriage has risen. In 1973 the average Canadian bride and groom getting married for the first time were 22.8 and 25.2 years old respectively , but in 2004 it was 28.3 and 30.3 years old. Economic contributing factors include increased availability of education for women and men, and increased economic opportunities for women. Economic consequences of rising age at marriage include the consequences of delayed fertility and a lower total fertility rate. The rising age of parents may have positive consequence for the viability of marriage, and the parents’ ability to take care of the children.
2) Marriage Rates have declined. In 1950, 80% of Americans aged 21-54 were married. That began to decline in the mid 1960s, with a fairly steep rate of decline over the 70s and 80s. In 2005, it was 60% of the American population married and even less for the Canadian population. Economic factors which have contributed to this include an increase in the standard of living which makes single living more affordable, and increased earnings opportunities for women outside the home which again makes the single life more affordable and, possibly, more attractive.
Again, the rise of couple similarity might stress partnerships in which the traditional specialization described in Becker (1981) has been assumed.
Figure 42-2 shows that marriage rates in Canada are not very much lower than historic levels. Most divorced people seek to marry again.
Figure 42-2. Trends in marital status.
Note: the data point for 1981 includes cohabiting couples
Data source: Statistics Canada series 051-0001, 051-0010, 075-0013, 075-0014.
Figure 42-3. Marriage rates by age and sex, 1981 and 2006, Canada.
Source: Statistics Canada, Report on the Demographic Situation in Canada, 2005 and 2006, Figure 6.1
Figure 42-3 shows both lower and delayed marriage rates for men and women.
To some degree the drop in marriages is made up by an increase in cohabitation, which we discuss next. However there is a net rise in the number of singles. In 1961, 8.6 were singles, but today (2011) it is double that at 17.1%. (Statistics Canada, Fifty years of families in Canada: 1961-2011)
The single life can be satisfying and productive. It is not as likely to produce children, however, so expect a drop in fertility when marriage rates fall.
There are also health consequences for single people, who typically must be economically self-sufficient and responsible for their own health. Married men live longer than unmarried men (for example see Lillard and Panis (1996)). This is likely because of protection conferred by not living alone, and because men who get married have characteristics that make them more likely to live healthy lives. However, Lillard and Panis (1996) found that it is not true that healthier men are more likely to get married; on the contrary, unhealthy men marry earlier than their peers, are less likely to divorce, and are more likely to remarry after being widowed or divorced.
Married women are also healthier than single, divorced, or widowed women – but only if they report a happy marriage. (Gallo et al. (2003)).
In terms of GDP per capita, single people look good for the economy. They work and can save without the diversion of childcare. They are available as community volunteers and activists, as well as supportive relatives.
3) Cohabitation Rates have risen. Cohabitation was relatively rare in the West before 1970, but it has grown in popularity steadily since then as you can see in Figure 42-4 below. This Figure does not include single people. In 2002, the american National Survey of Family Growth found that 50 percent of women aged 15-44 had cohabited at some point, and 9 percent were currently cohabiting. In Canada, most cohabitations do not end in marriage, but most marriages are preceded by cohabitation.
Figure 42-4. Distribution of Census Families by Family Structure, Canada, 1961-2011
Source: Statistics Canada. Fifty years of families in Canada: 1961-2011, Figure 1.
In some times and places, cohabiting couples have financial advantages over married couples, for example being able to file income taxes independently, or being able to receive more in welfare payments. In other respects, cohabitation may mean less entitlement to pension benefits (if a partner dies) or financial settlement (if the relationship breaks up.) Cohabitation may have economic consequences similar to the consequences of divorce (to be discussed later), in that there is some evidence that cohabitation represents more risk of break-up than marriage. Statistics Canada reported in 2006 that the risk of divorce in first marriage is 50% higher for those who lived common-law before marrying. The rate of separation of cohabiting couples exceeds that of married couples.
Economic factors which contribute to cohabitation include the financial cost of divorce, though this has been declining, and government regulations around taxes, welfare, and pensions, if you can collect more money by not marrying.
4) Divorce Rates have risen. In the United States, the divorce rate’s overall trend since 1860 has been upward. The divorce rate increased rapidly 1960-1981, but has fallen somewhat since then. Canada’s experience is similar; our divorce laws were liberalized in the late 1960s. In 2002, Statistics Canada estimated the chance of a couple getting divorced before their 30th anniversary to be 38% for Canadians, ranging from 22% in Nfld to 48% in Quebec. According to the 2001 Census, 25% of Canadian children experienced the separation of their parents before the age of six. The duration-specific divorce rate peaks at 4 years of marriage; after that, the rate of divorce falls steadily. The median length of marriage has been roughly 11 years since 1981.
Non-economic factors contributing to divorce include higher expectations for couple-compatibility, unclear expectations about gender roles, and higher expectations for self-fulfillment. Economic factors contributing to divorce include stresses due to unemployment and poverty, an increase in the average woman’s post-divorce standard of living, and the declining cost of arranging a divorce.
Economic consequences of divorce include increased demand for housing, a reduced standard of living for most spouses and children, and stresses on children which translate into lower economic achievement among other things. According to Stevenson and Wolfers (2007), children from divorced households fare worse “along a range of outcomes”; according to a Canadian government report on the National Longitudinal Study of Children and Youth , children growing up in single-parent families are more likely to repeat grades, have poor language skills, be in poor health, and have behavioural problems, even after accounting for differences in household income. However
-we do not know the counterfactual (how well those children would have done had their parents not divorced.)
-adults who divorce and those who do not may be different in some other respects. That is to say, unobserved factors may explain both divorce and poor child outcomes.
Kay Hymowitz (2006) was one of the first to observe that the rise of single parenthood since the mid 1960s took place disproportionately in poor, less-educated households, specifically, in African American households. Hymowitz says that 92% of US children whose families make over $75,000 a year live with 2 parents; the number is 20% for kids in families making less than $15,000 per year. Higher income children are more likely to have live-in fathers, older mothers, better-educated mothers, and employed mothers. Stevenson and Wolfers (2007) too note a “divorce gap”: U.S. divorce rates are higher, and remarriage rates lower, for those without a college education. This suggests that adverse effects on children fall mostly on children already disadvantaged.
Measuring Marriage and Divorce Rates
Like the crude birth rate and crude death rate, the crude marriage rate is the number of marriages per year, divided by the midyear population, and expressed as a number per 1000. The crude divorce rate could be computed the same way. These rates, however, do not tell us much. The mid-year population includes people who are already married, people who are divorced or widowed, and children too young to marry. Depending on the age structure of the population, the marriage or divorce rate may be very high when it appears to be low.
The rates with the most information have, as their denominators, the population “at risk” of the event in question. Children therefore, who are not “at risk” of getting married, should not be included in the denominator of a more informative marriage rate. For example, the first marriage rate of 21-25 year olds, that is, the number of marriages of 21-25 year olds who are getting married for the first time, divided by the number of 21-25 year olds who have never been married, is a much more informative statistic.
The refined divorce rate is the number of divorces per 1,000 married women.
Divorce is rather like fertility. Just as children can be born in various years, divorce can occur in various years. The most information is found in the various duration-specific divorce rates.
The duration-specific divorce rate, DSDR, is equal to
DSDR = 1000 x
ago
years
n
married
who
people
of
population
midyear
marriage
of
years
n
after
year
this
divorcing
people
The mid-year population of people married n years depends on the number of people who married n years ago, and on how many of them are still alive.
This DSDR is like an age-specific fertility rate (ASFR). We used the ASFRs for different ages of women to compute a Total Fertility Rate. Similarly, we can use the DSDRs for different lengths of marriage to compute a total divorce rate. The total divorce rate is the percentage of marriages that would end in divorce if today's duration-specific divorce rates remained the same throughout a couple's life. It is technically possible for the TDR to be greater than 1, so interpret the TDR with caution.
TDR = ∑ DSDR / 1000,
where the summation is usually over marriage lengths of 1 year to 30 years.
Box 11-1. Western Adolescence. In his recent book The Case Against Adolescence, Robert Epstein argues that western teens are set up to experience frustration and anger. They are forced into a rigid program of education for many years, regardless of ability. They are forced to spend most of their time with other teens rather than adults. Prevented by parents or by law from holding jobs, owning businesses, driving,and getting married, they remain economically dependent on adults regardless of their maturity level.
Epstein contrasts western teens with teens in traditional societies, who take on adult responsibilities and spend a lot of time in the company of adults. He believes that teens who demonstrate an understanding of consequences and an ability to reason should be allowed whatever adult freedoms they desire.
Box 10-2. Canada’s federally-administered pension programs
The CPP or Canada Pension Plan (begun 1964) covers all provinces except Quebec, which administers its own plan. Employers deduct about 5% of your wages/salary above a base amount (like $3,500) and below a ceiling amount (like $41,100). They pay twice that sum to the government. On the basis of how much you have contributed, a lump sum payment is available to your heirs if you die, or a pension will be paid to you upon retirement.
If you have not earned enough in your prime, your CPP payments will be low. If so, you are eligible to receive Old Age Security (origins 1927). OAS is a payment of about $500 a month received by about 93% of people over age 65 who have lived in Canada ten years or more. A further 5% of higher income seniors receive a partial payment. Low seniors may be eligible for an additional cheque called the Guaranteed Income Supplement, or for a spousal allowance (age 60-64). Unlike the CPP or OAS, the GIS is not subject to income tax.
As you can see, OAS and GIS are similar to income-support/welfare programs, while CPP is more of a bona fide pension plan.
All Canada’s public pension payments are indexed to inflation.
Sudden plunge at point of non-recoverability
� EMBED MSGraph.Chart.8 \s ���
� The New York Times, February 17, 2008.
� Source: Statistics Canada, Life expectancy at birth, by sex, by province. Downloaded from � HYPERLINK "http://www.statcan.gc.ca" ��www.statcan.gc.ca� July 27, 2011.
� Source: 2011 estimate from CIA World Factbook, � HYPERLINK "http://www.cia.gov" ��www.cia.gov�, downloaded July 27, 2011.
� David Foot, interviewed on The Agenda (TVO), March 29, 2010.
� assuming constant birth rates. Source: Canada Department of Finance (2005)
� A blended family is one where each spouse brings children from a previous union.
� Marshall (2006)
� Statistics Canada, The Daily, January 17, 2007.
� Statistics Canada, CANSIM, Table 101-1002
� Ambert (2005)
� Statistics Canada,The Daily, May 4, 2004.
� Statitics Canada, Report on the Demographic Situation in Canada, 2005 and 2006, Table A-6.4.
� Ross, Roberts and Scott (1998).
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Econ/background to week 2.docx
Background to lectures 3 and 4
Basic Demographic Calculations
The fundamental equation of population growth is simple:
Population growth over some period of time = births – deaths + immigrants – emigrants.
That is to say,
Population growth = natural increase plus net migration.
About two-thirds of the increase in Canada’s population comes from net migration. However, net migration only accounts for 40% of the new Americans. The US population is able to grow at the same rate as Canada because the US has a higher birth rate.
Birth rate = 1,000 x number of births in the population in question/ midyear size of population in question
To find the birth rate, calculate the number of births in Canada during the year, then divide by the mid-year population[footnoteRef:1]. Multiply by 1000, and you have the birth rate per 1000 people. [1: The mid-year population can be approximated by averaging the population at the beginning and the end of the year.]
Death rates and net migration rates are calculated the same way.
We call these rates “crude” birth, death, and net migration rates because they do not take into account the composition of the population in question. Naturally, a population having a larger proportion of women of child-bearing age will have a higher birth rate than a population with a lower proportion of women of child-bearing age. If we compare only the crude birth rates, we might conclude that the population with more women of child-bearing age has larger families. This may or may not be true.
Fertility rates represent more information than birth rates. The overall fertility rate is the number of births divided by the midyear population of women of childbearing age. This at least adjusts for the number of women of childbearing age. One can also calculate age-specific fertility rates, which are fertility rates specific to a particular age group. For example,
The 15-19 year old fertility rate =
# births to 15-19 year old mothers/ midyear population of 15-19 year olds
Similarly, age and sex-specific mortality rates give us the number of deaths in a group divided by the midyear population of that group. For example,
The mortality rate for 10 year old boys = # deaths of 10 year old boys/ midyear population of 10 year old boys.
Standardizing Rates
It is good to have a whole list of age-and-sex specific mortality rates, but it’s convenient to have just one summary statistic for a nation’s deaths. For this purpose, the crude death rate can be improved by a process called “standardization”. Similarly, the birth rate or any other generic rate can be improved by standardization.
Standardization is only relevant when we want to compare countries. Comparing the crude and death rates of different countries is misleading when the different countries’ populations have different age and sex structures.
To standardize, we choose one country to be the base country. We look at the age, or age and sex structure of the base country and pretend that all the countries have the same structure. So, if Country A has 20% of its population over 65, we’ll assume all countries have the same feature.
Let’s say we have two nations, Algeria and France. We want to standardize the death rates to account for the fact that France has an older population than Algeria. We can use either France or Algeria as the base country. Let’s choose Algeria.
What we have to do next is calculate the death rate for each country using Algeria’s population. Well, we have already done that for Algeria. If Algeria is the base country, Algeria’s standardized death rate = Algeria’s crude death rate.
For France, we multiply its owns age-specific mortality rates (expressed as a decimal) to Algeria’s population.
For example, if the mortality rate in France for newborns is 7 per 1000, then we multiply .007 by the midyear population of newborns in Algeria. This gives us the deaths of newborns that would occur in Algeria if it had France’s mortality rates.
We now have French newborn deaths standardized to Algeria’s population. Next we multiply the mortality rate in France for 1-4 year olds by the midyear population of 1-4 year olds in Algeria. This gives us the deaths of 1-4 year olds that would occur in Algeria if it had France’s mortality rates.
Doing this for all age groups, we then add up all the deaths (for all ages) that would occur in Algeria if it had France’s mortality rates, then divide by the midyear population of Algeria. This gives us France’s death rate standardized by age i.e. standardized to Algeria’s population.
We expect that France, which is a wealthier country, will have a lower death rate than Algeria, once the death rate has been standardized to account for the fact that the Algerians are, on average, younger than the French.
The Sex Ratio
By nature, more boys than girls are born: the “sex ratio” at birth is typically 105 males to 100 females, i.e. 1.05. As the children age, the sex ratio eventually falls below 1 due to lower mortality of females. In Canada, the sex ratio is below 1 by age 15, as shown in Figure 5-1 below.
Figure 5-1: Canadian sex ratios, 2006
Data source: Statistics Canada, Table #830 from the 2006 Census, “Selected demographic, cultural, education, labour force and income characteristics.”
In class we will discuss economic and other factors which explain why the sex ratio in one region may be different from the sex ratio in another region. Migration patterns can be very important in explaining local sex ratios. A very important determinant of the sex ratio after birth is differences in male and female mortality.
Mortality by sex
We can compute the relative mortality of males to females for any age group. For example, in 2007 the mortality rate for Canadian males aged 20-24 was 82.7 per 1000, but the rate for females was 29.8 per 1000. This means that 20-24 year old males had almost three times the mortality rate of their female counterparts. In 2007, only males aged 5-9 had lower mortality rates than their female counterparts. This is shown in Figure 5-3.
Figure 5-3. Relative mortality of Canadian males, 2007.
Source: Statistics Canada Catalogue No. 84F0209x, “Mortality, Summary List of Causes, 2007”.
If you wanted some sense of the number of excess male deaths, you could apply the age-specific female mortality rates to the number of men in each age group, and total. The number of actual male deaths over and above this total will be the excess deaths.
Later in the course we will be discussing the excess female deaths in East Asia. To compute the number of excess deaths we do something a little more complicated than compare female mortality rates to male mortality rates. We compare female deaths not to male deaths but to what female deaths would be if Asian female mortality rates were similar to international female mortality rates.
continued
Calculating life expectancy from the “Life Table”
The life table - formerly called the mortality table - is a statistical construct that has been used for hundreds of years to predict life expectancy.
While the math can be a bit tricky, the data requirements for a life table are minimal. All you need to construct a life table are age-specific mortality rates. The life table does not show how the population grows, shrinks or changes. It merely shows how quickly a cohort - a group of people born during the same time period - decreases in size as the members die.
Life tables can be constructed for men, women, or both together. The age-specific mortality rates used are assumed to be constant. In reality, mortality rates change and life tables must be continuously updated. Recently in Kingston, Ontario, the failure of actuaries to realize that the age specific death rates for Queen’s professors were declining faster than the death rates for other groups resulted in actuaries recommending that Queen’s set aside too little money in the pension plan.
Each life table begins with 100,000 hypothetic newborns. The actual size of the cohort does not matter. In the table below, the newborns are Canadian females born in 2005.
Table 6. Life Table for Canadian females, 2005
|
Age Range |
n |
M |
q |
l |
d |
L |
T |
e |
|
<1 |
1 |
0.00452 |
0.0045017 |
100,000 |
450.17 |
99,594.85 |
8,278,662.15 |
82.79 |
|
1-4 |
4 |
0.00019 |
0.0007597 |
99,550 |
75.63 |
398,048.07 |
8,179,067.30 |
82.16 |
|
5-9 |
5 |
0.00007 |
0.0003499 |
99,474 |
34.81 |
497,283.99 |
7,781,019.2 |
78.22 |
|
10-14 |
5 |
0.0001 |
0.0004999 |
99,439 |
49.71 |
497,072.69 |
7,283,735.25 |
73.25 |
|
15-19 |
5 |
0.00026 |
0.0012992 |
99,390 |
129.12 |
496,625.62 |
6,786,662.56 |
68.28 |
|
20-24 |
5 |
0.00031 |
0.0015488 |
99,261 |
153.74 |
495,918.48 |
6,290,036.94 |
63.37 |
|
25-29 |
5 |
0.00033 |
0.0016486 |
99,107 |
163.39 |
495,125.66 |
5,794,118.46 |
58.46 |
|
30-34 |
5 |
0.00043 |
0.0021477 |
98,943 |
212.50 |
494,185.93 |
5,298,992.80 |
53.56 |
|
35-39 |
5 |
0.00063 |
0.0031450 |
98,731 |
310.51 |
492,878.34 |
4,804,806.87 |
48.67 |
|
40-44 |
5 |
0.00106 |
0.0052860 |
98,420 |
520.25 |
490,801.49 |
4,311,928.47 |
43.81 |
|
45-49 |
5 |
0.00168 |
0.0083649 |
97,900 |
818.92 |
487,453.56 |
3,821,126.98 |
39.03 |
|
50-54 |
5 |
0.00273 |
0.0135575 |
97,081 |
1,316.18 |
482,115.82 |
3,333,673.42 |
34.34 |
|
55-59 |
5 |
0.0041 |
0.0202920 |
95,765 |
1,943.27 |
473,967.21 |
2,851,557.61 |
29.78 |
|
60-64 |
5 |
0.00693 |
0.0340599 |
93,822 |
3,195.56 |
461,120.14 |
2,377,590.40 |
25.34 |
|
65-69 |
5 |
0.01074 |
0.0522959 |
90,626 |
4,739.38 |
441,282.79 |
1,916,470.26 |
21.15 |
|
70-74 |
5 |
0.01727 |
0.0827761 |
85,887 |
7,109.38 |
411,660.89 |
1,475,187.46 |
17.18 |
|
74-79 |
5 |
0.02945 |
0.1371522 |
78,777 |
10,804.50 |
366,876.17 |
1,063,526.57 |
13.50 |
|
80-84 |
5 |
0.05096 |
0.2260067 |
67,973 |
15,362.35 |
301,459.03 |
696,650.40 |
10.25 |
|
85-89 |
5 |
0.08736 |
0.3585030 |
52,611 |
18,861.07 |
215,900.49 |
395,191.37 |
7.51 |
|
90-94 |
5 |
0.14843 |
0.5412906 |
33,750 |
18,268.32 |
123,077.02 |
179,290.89 |
5.31 |
|
95-99 |
5 |
0.24992 |
0.7690793 |
15,481 |
11,906.30 |
47,640.46 |
56,213.86 |
3.63 |
|
100+ |
? |
0.41698 |
1.0000000 |
3,575 |
35,74.94 |
8,573.42 |
8,573.41 |
2.40 |
Source: WHO, Life Tables for WHO Member States.
Have a look at Table 6. The first column shows the age group, and the second column gives us the number of years of life covered by that age group. The third column is the mortality rate expressed as a decimal, M. As you can see in the third column, the infant mortality rate for Canadian females in 2005 was 0.00452 or 4.52 per 1000. Since there are 100,000 hypothetical newborns, does this mean we record 452 deaths for newborns? Notice in column 6, labelled “d” for deaths, we have 450.16871 deaths recorded, not 452.
This discrepancy is due to the fact that the mortality rate is calculated using the mid-year population of newborns. However, the population of newborns is not equal to the mid-year population, except at mid-year, of course. What we really want is not the mortality rate but something slightly different - the probability of dying before the end of the year.
Translating mortality rates expressed as a decimal (M) into probabilities of dying q works as follows:
q = nM/(1+nfM) derivation shown at end of chapter if you are interested
n is the number of years in the age group, and f is the fraction of the year someone who dies that year is dead. For most age groups, f = 0.5. For newborns, f = 0.9, because most newborns who die in their first year of life die soon after birth.
Applying q to column l (small L), of the 100,000 newborns, only 100,000-450.16871, approximately 99,550 survive into the second age group, as you can see in column 5, labelled “l” (small “L”). This is the number of people entering the age group.
The next age group is 1-4 years old. People who survive this age group have spent a full 4 years in it. You can see how important it is to translate the yearly mortality rate for 1-4 year olds into a probability of dying during that age group, q.
Note that the Canadian females were born in 2005. In real life their 1-4 year mortality is governed by the actual death rates for 1-4 year olds applicable during 2006-2009. But this table was calculated as of 2005, and uses the mortality rates applicable to 1-4 years olds at that time. It is unrealistic unless updated.
Note that for the 100+ age group, their mortality rate is 416 deaths per thousand each year. However, each person has a 100% chance of dying within that age group, since there is no higher age group.
We now understand the meaning of the first six columns. But columns 7, 8, and 9 are the really interesting ones.
Column 7, labelled “L”, represents the total years lived by people in that age group. Column 8, labelled “T”, represents the total years lived for that age group from that age on. Column 9, labelled “e”, gives you the life expectancy of people in that row’s age group. Hence “e” in the first row gives you the expectation of life at birth i.e. life expectancy at birth.
Looking at the row that represents 40-44 year olds, we see that total life years remaining (T) for this group is about 4,311,929. They can expect to live 490,802 years in the 40-44 year age bracket, 487,454 years in the 45-49 age bracket, and so on. Dividing 4,311,929 years of life left by the 98,420 people who are 40-44 years old gives us an average of
43.8 years left to live for each person in that age group. These people are truly middle-aged, as their expectation of life is roughly the same as their current age. They are half-way through.
The tricky part of coming up with e, the expectation of life, goes back to computing L, the number of years lived by an age group. Because not everyone survives the age group, you can’t just multiply the number of people in the age group by the number of years in the age bracket. The calculation is this: L = nl- nfd, where l is the number of people entering the age group. f is the fraction of time the average non-survivor is deceased, so multiplying f by n gives you the average number of years the deceased person has missed. d is the number of deaths in the age group. For the last age group, the calculation is slightly different: L = l/M, where M is the mortality rate expressed as a decimal.[footnoteRef:2] [2: To understand why this is, think of deaths = M multiplied by L, so L = deaths/M and also deaths = l (small L), since no one survives the last age group by definition.]
Usually we assume that people who die during an age interval, die half-way through the age interval. This is true on average, except for the newborn age category. Most newborns die early in their first year of life. Hence, when calculating life-years lived by newborns, we use an f = 0.9 rather than f =0.5.
Life Expectancy and Survival
A neat thing that can be done with the Life Table is that we can interpret the l column as a column of survival probabilities, once divided by the original number of newborns. More generally, l(x+t), the number of people alive t years from now, divided by l(x), the number of people alive at age x, is the probability that someone age x survives another t years.
The expected number of life years remaining i.e. the life expectancy of someone aged x is actually:
This equation looks a little strange because there is an infinite number of instantaneous age groups.
We see that life expectancy depends on survival at every age. It is a "long-term process" which begins in utero.[footnoteRef:3] [3: Prof. Alain Gagnon, in an interview for TVO's The Agenda, March 29, 2010.]
Appendix to chapter 16. Converting mortality rates into probabilities of dying.
You will not be tested on this material.
The probability of dying is not the same thing as the mortality rate. The mortality rate is expressed in terms of the underlying number of people in the age group, which changes over time. To get the probability of dying, one needs to adjust the mortality rate for the number of time periods involved and the average amount of time lost by a person who dies.
Define lx as the probability of surviving up to age x. If there were 100 people, lx would be the number of people who live up to age x.
lx - lx+n is the probability that you die between age x and age x+n.
Let f be the fraction of time lived during an age interval, by the people who end up dying during that age interval. Out of 100 people,
lx - lx+n people are living nf years each. These are the people who die between time x and tie x+n.
lx+n people are living the full n years.
Add this up and you get that n/2 multiplied by (lx + lx+n ) is the number of life years enjoyed in this age interval, or the average number of people alive each year multiplied by n years.
Expressed as a fraction of 1, the mortality rate for that age interval is equal to the number of people in that age group who die during the interval, divided by the number of people who are in that age group over the n years.
So the mortality rate M = (lx - lx+n ) / {nf ( lx + lx+n ) }
If you multiply both the numerator and the denominator by lx , and then rearrange, you will get this: lx+n / lx = (1- nfM) / (1 + nfM). Call this Equation A.
We can use this relationship to express the probability of dying in terms of M.
The probability of dying while aged x to x+n is equal to 1 minus the probability of surviving the age period. The probability of surviving the age period is simply
lx+n / lx. So the probability of dying, q, is equal to 1 - (lx+n / lx) . Using Equation A, we can write
q = nM / (1+ nfM)
Sex ratio by age, Canada, 2006
0
0.2
0.4
0.6
0.8
1
1.2
0510152025303540455055606570758085
first year of age group
Male mortality rate relative to female, Canada, 2007
0
0.5
1
1.5
2
2.5
3
0151015202530354045505560657075808590
first year of age interval
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Econ/background to week 3.docx
Interpreting the Life Table
Paradox of the Life Table
When mortality is very high in a particular age group, the next age group may have a higher expected number of life years remaining than the preceding group. For example, in 2009, the expectation of life years remaining for newborns (both sexes together) in Afghanistan was 48.3, but the expectation of life years remaining for 1 year olds was 54.7, and for 5 year olds, 55 years remaining.[footnoteRef:1] In some developing countries today we see a similar Paradox of the Life Table for children under five years old, due to high infant mortality. [1: World Heath Organization, Global Health Observatory Data Repository, apps.who.int/ghodata/?vid=720]
Recall that expected life years remaining at age x, denoted e(x), is equal to T(x)/l(x). If you take the derivative of this expression with respect to x [footnoteRef:2], and then divide by e(x), you will have the percentage change in life expectancy for a 1 percent increase in age. This expression: [2: Use the fact that the derivative of l(x) with respect to x is the number of deaths at age x, i.e. a decrease (negative number d(x)) and the derivative of T(x) with respect to (x) is - L(x). Use the fact that dividing by e(x) is the same as multiplying by l(x) while dividing by T(x).]
is ambiguous in sign. If the first term is larger than the second term, the expectation of life will be higher as age x increases, and we have the paradox of the life table. The first term will be high if the death rate at your age is very high. Your cohort shrinks, so there are fewer people to claim the T(x). The second term shows that your life expectancy goes down because you've used up L(x) of your T(x) life years remaining.
Table 6-2 Life table for Afghan females, 2009. (compare to Table 16-1).
|
Age Range |
n |
M |
q |
l |
d |
L |
T |
e |
|
<1 |
1 |
0.13477 |
0.12316 |
100,000 |
12,316 |
91,379 |
5,024,534 |
50.2 |
|
1-4 |
4 |
0.01955 |
0.0747 |
87,684 |
6,550 |
335,017 |
4,933,155 |
56.3 |
|
5-9 |
5 |
0.00447 |
0.0221 |
81,134 |
1,793 |
401,188 |
4,598,138 |
56.7 |
|
10-14 |
5 |
0.00267 |
0.01327 |
79,341 |
1,053 |
394,072 |
4,196,950 |
52.9 |
|
15-19 |
5 |
0.00385 |
0.01907 |
78,288 |
1,493 |
387,706 |
3,802,878 |
48.6 |
|
20-24 |
5 |
0.0056 |
0.02761 |
76,795 |
2,120 |
378,673 |
3,415,171 |
44.5 |
|
25-29 |
5 |
0.00628 |
0.03093 |
74,675 |
2,310 |
367,598 |
3,036,498 |
40.7 |
|
30-34 |
5 |
0.00691 |
0.03396 |
72,365 |
2,457 |
355,681 |
2,668,900 |
36.9 |
|
35-39 |
5 |
0.00797 |
0.03908 |
69,908 |
2,732 |
342,708 |
2,313,219 |
33.1 |
|
40-44 |
5 |
0.00911 |
0.004452 |
67,176 |
2,990 |
328,403 |
1,970,511 |
29.3 |
|
45-49 |
5 |
0.01086 |
0.05285 |
64,185 |
3,392 |
312,446 |
1,642,107 |
25.6 |
|
50-54 |
5 |
0.01465 |
0.07066 |
60,793 |
4,296 |
293,226 |
1,329,661 |
21.9 |
|
55-59 |
5 |
0.0214 |
0.10158 |
56,497 |
5,739 |
268,139 |
1,036,436 |
18.3 |
|
60-64 |
5 |
0.02809 |
0.13122 |
50,759 |
6,660 |
237,142 |
768,296 |
15.1 |
|
65-69 |
5 |
0.04385 |
0.19759 |
44,098 |
8,713 |
198,708 |
531,155 |
12 |
|
70-74 |
5 |
0.06769 |
0.28946 |
35,385 |
10,243 |
151,318 |
332,447 |
9.4 |
|
74-79 |
5 |
0.10229 |
0.4073 |
25,142 |
10,240 |
100,110 |
181,129 |
7.2 |
|
80-84 |
5 |
0.15261 |
0.55233 |
14,902 |
8,231 |
53,932 |
81,019 |
5.4 |
|
85-89 |
5 |
0.22418 |
0.71832 |
6,671 |
4,792 |
21,376 |
27,086 |
4.1 |
|
90-94 |
5 |
0.30928 |
0.80214 |
1,879 |
1,507 |
4,874 |
5,711 |
3 |
|
95-99 |
5 |
0.42771 |
0.85646 |
372 |
318 |
745 |
837 |
2.3 |
|
100+ |
? |
0.5775 |
1.0000000 |
53 |
53 |
92 |
92 |
1.7 |
Source: WHO, Global Health Observatory Data Repository.
Interpretation of the life table for a stationary population
The Life Table is – hopefully- an accurate depiction of age-specific mortality at any point in time. The age-specific mortality rates are constantly changing, however. But what if they did not change?
Imagine a so-called stationary population – one where the population neither grows nor shrinks. The same number of people are born each year. The same number of people die each year. We shall prove in a later chapter that this happens when mortality rates and fertility rates are constant and consequently, the age structure of the population eventually stabilizes.
A stationary population, which has the same number of people born every year, would have a Life Table that mirrored its population’s age structure, scaled up or down.
“Model” Life Tables
If you do more reading in demography, you will soon come across so-called Model Life Tables. Model Life Tables are fake Life Tables, each of which attempts to generalize the the mortality data of a group of nations. That way, even if you don’t have all the age specific death rates to make a Life Table for your nation, you can use one of these Model Life Tables to predict life expectancy or eventual age structure etc. The procedure is as follows:
1) Choose which Model Life Table to use based on your population’s level of economic development, and how its fertility and mortality rates compare. There are different Model Life Tables for different kinds of countries.
2) Compare some datum from your nation e.g. life expectancy at birth, ASMR for 20-25 year old males etc. to the corresponding datum in the Model Life Table.
3) Scale the Model Life Table up or down until the two data points match.
4) Read the life expectancy or whatever else you are interested in off the scaled Model Life Table.
The Model Life Tables are constructed by using many many real-world life tables to correlate the probability of dying in one age group to the probability of dying in the next age group.
For more information on Model Life Tables, see C.J.L. Murray et al. in the References.
Looking for people missing because of extra-ordinary mortality
We noticed previously that male mortality rates tend to be higher than female mortality rates. There are “extra” male deaths in that sense. But that doesn’t mean there is any foul play. To check whether there is anything suspicious going on, we should recognize that men have different physiologies than women, and we should compare the male deaths in our nation to male deaths in other nations.
Jiang, Feldman, and Jin (2005) estimated the number of Chinese females missing over the last century. To compute this number they use a two-step procedure:
where the first term on the right hand side = expected sex ratio at birth
The subscript “0” refers to brith, “m” refers to male, “f” to female.
# missing females age x = # males age x - actual # females age x
expected sex ratio for age x
using the l columns in the Life Table.
The authors assume that, without human interference, the sex ratio at birth would be 1.06, at the high end of the natural distribution. In parts of China, the sex ratio at birth is much higher due to abortion of female fetuses and infanticide of female infants at the moment of birth.
Jiang et al. conclude that 35 million Chinese females were lost over the course of the twentieth century, about 4.65 percent of all females who were expected to be born. We will discuss this again later.
Crisis vs. Chronic Death Rates
Crisis deaths are those over and above the deaths that can be expected from on-going problems such as endemic disease and malnutrition. Deaths due to usual conditions are known as chronic deaths.
One way of calculating crisis deaths is as follows:
Crisis deaths = actual deaths – average deaths over a twenty-five year period for which the current year is the middle year.
How much of mortality has been due to crises, and how much has been due to chronic poverty and ignorance? Fogel (1992) tackles this question and concludes that chronic conditions were the main determinant of high mortality rates. He has presented two pieces of evidence to support this claim.
First, Fogel examined crisis death calculations by Wrigley and Schofield (1981) covering England during 1541 and 1871. He sums all extra deaths in crisis months and crisis years, and finds that the crisis deaths during the three hundred and thirty year period were a small fraction (<5%) of total deaths. In fact, by 1800, there were almost no crisis deaths in England at all.
The second thing Fogel did was collect data on height – which is a measure of the net intake of nutrition from conception through adolescence – and weight – a measure of current net nutrition. He found that the height and weight of English, French, and Swedish men prior to 1875 implied mortality rates very similar to actual mortality rates. Fogel concluded that most of the mortality 1775-1875, and half the mortality 1875-1975, could be explained by nutrition, at least for the adults age groups he considered.
Kannisto and his team found something similar. Looking at mortality rates during famine (1866-1869) and wars (1789, 1808-9), they concluded that most Finnish deaths during these crises were actually caused by infectious disease spread by armies, veterans, and refugees. In the Finnish case, the basic level of health and disease resistance would have been critical to survival.
Box 26-1. Crisis Mortality Rates. The Food and Agricultural Organization (FAO) and other agencies have developed the following reference table for classifying situations of crisis by mortality rates.
Phase
Food Secure
Border-line
Food Insecure
Acute Food and Livelihood Crisis
Humanitarian Emergency
Famine
Deaths per 100,000 people
per day
<5
5 is equivalent to an annual death rate of 18.25 per 1000, cf. a usual death rate of about 8 per 1000.
<5
5-10 and increasing
10-20 and increasing
>20
Deaths per 100,000 children under age 5 per day
≤10
≤10
10-20
>20
>20
Source: Table 3, IPC Reference Table Technical Guidelines, www.fao.org
Mortality, like so many outcomes in life, depends on nature, nurture, choices, and the inexplicable divine grace or, secularly speaking, dumb luck we encounter.
How does mortality – chronic or crisis – change in response to economic factors like income or wages?
How mortality changes with income
The effect of income on mortality depends very much on whether we are discussing personal income or national income, and whether we are discussing the national trend or the stage of the business cycle (a boom or recession).
Purchasing power or individual income
It makes common sense that the richer you are, the better you are able to afford good nutrition, shelter, and medical care. You are more likely to be literate and educated, which helps you make better informed choices with regards to your health. Indeed, life expectancy rises for individuals with greater income and wealth. As reported by Robert Pear in the New York Times (Gap in Life Expectancy Widens for the Nation, March 23 2008), Americans of higher socioeconomic status gained more in terms of life expectancy than other groups between 1980-2 and 1998-2000. The gap in life expectancy between Americans in the highest decile and the lowest grew from 2.8 years to 4.5 years. Wealth is not the only indicator of inequality. The difference in life expectancy between the poorest black men and the richest white women was more than 14 years. As of 2008, however, the gap between white and black Americans is at its lowest point ever. Non-Hispanic white American male newborns are expected to live 76.2 years, compared with 70.8 years for black newborns.[footnoteRef:3] [3: “Racial Gap in Life Expectancy Hits New Low,” New York Times, June 12, 2012.]
In Canada, life expectancy at birth during 2007-2009 was 79 (men) and 83 (women) nationally, but only 73 (men) and 78 (women) for Yukon, Northwest Territories, and Nunavut taken together.[footnoteRef:4] Differences in personal income may be part of the reason why the life expectancies are so different in different parts of Canada. [4: Statistics Canada, CANSIM table 102-0512.]
National income
Although wealthier people generally live longer, and although life expectancy is higher in countries with higher standards of living, there seems to be a point for nations as a whole at which the benefits from higher income cease and may even reverse. As explained in Bezruchka (2009), a growing body of research indicates that after a country reaches a GNP of $5000 -$10,900 per capita, “few health benefits arise from further economic growth”.
The Business Cycle
Bezruchka goes on to confirm a pattern first observed in 1922[footnoteRef:5]: that for richer nations, mortality follows the business cycle, rising during booms, and falling during recessions. Though suicide rates increase during recessions, and degenerative diseases such as cancer seem unaffected by the business cycle, mortality rates for infants and mortality rates from accident, infection, and other diseases drop during recessions. [5: Ogburn, William F. and Dorothy S. Thomas. 1922. “The Influence of the Business Cycle on Certain Social Conditions,” Journal of the American Statistical Association,18(139): 324-40. ]
When I computed the correlation coefficient between Canada’s unemployment rate and our infant mortality rate (1976-2007, data from OECD.StatExtract), I found a negative correlation, a correlation of -0.11, indicating that infant deaths went down when unemployment went up. (1 or -1 means perfect correlation, zero means no correlation). When I compared infant mortality (1977-2007) to the previous year's unemployment rate, the correlation was a bit stronger, at -0.14.
Dehejia and Lleras-Muney (2004) found that children conceived in times of high unemployment were healthier.
The following table brings some of the relevant issues to light.
Table 7. Income-related determinants of mortality.
|
Poverty |
Needed |
Wealth |
|
cannot afford to meet basic needs |
good diet adequate shelter |
can afford to overindulge |
|
cannot afford healthcare |
healthcare |
can afford |
|
less likely |
positive outlook |
more likely |
|
unemployed and stressed? |
-time for friends, children, rest, exercise -low levels of stress |
overworked and stressed? |
|
rural setting?
urban slum? |
-safety from crime -safety from pandemic disease -sanitation -absence of pollution, congestion |
urbanized
|
Wealth has some unequivocal advantages, in that it helps with mood and makes health care more affordable, but it can also be associated with overindulgence, overwork, and unsafe environments.
Let us now turn to the historical record to see how mortality rates have changed over time.
The Stages of Mortality Transition
The idea that income promotes survival, until you have too much of it, is reflected in the three stages of mortality suggested by Abdel Omran (1971): the Age of Pestilence and Famine, the Age of Receding Pandemics, and the Age of Man-made and Degenerative Disease. The names basically speak for themselves, with the first Age being one of high mortality, the second being one where mortality falls, and the third being an Age where mortality rates creep back up due to poor lifestyle choices.
Happily, Omran’s predicted Age of Man-made and Degenerative Disease has not (yet) come about. Though many individuals do die as a consequence of over-eating and other indulgences, life expectancy at birth has not yet declined because of it.
It might be better to describe the three stages as Pre-transition mortality, Transitioning Mortality, and Delayed Aging. In Canada today we enjoy decreasing mortality rates for all ages and both sexes. Delayed Aging seems to describe our situation well.
In Figure 3 below, we see data collected by Kannisto et al. (1999) for Finland. The figure shows percentage decreases in mortality for different age groups along the horizontal axis. The different coloured lines are different time periods. The top light blue line refers to a time period when mortality was just beginning to decline. The dark blue and red lines refer to a time period of decreasing mortality for kids and youth. Finally, the greenish line in the middle refers to a time when middle aged and senior people’s mortality fell significantly – the period of delayed aging.
Pre-transition mortality
Generally, in pre-industrial times, death rates were particularly high for infants and children. Since so few survived this stage of life, the ratio of children to adults was high. The average life expectancy was between 20 and 40 years. Females had higher mortality rates than males during their adolescent and reproductive years, reflecting the riskiness of childbearing.
Omran (1971) wrote, “The scanty evidence available indicates that frequent and violent fluctuations characterized the mortality patterns of pre-modern societies and that the mortality level was extremely high even in the so-called good years. Caught between the towering peaks of mortality from epidemics and other disasters and the high plateaus of mortality dictated by chronic malnutrition and endemic diseases, life expectancy was short and human misery was assured. ...more than any other single factor, fluctuating but always high mortality offers the most likely explanation of the slow rate of world population growth until 1650 A.D.”
Cippolla (1994) writes, “Mortality was very high indeed in medieval and early modern Europe. A woman who managed to reach the end of her fertile life, let us say at age 45, had normally witnessed the deaths of both her parents, the majority of her brothers and sisters, more than half of their children, and often she was a widow. Death was a familiar theme. And it was a grim business. With no alleviation of pain, the bitterness of death was very real. To make things worse there was the cruelty of people, who had become hardened to the horror of natural death: apart from the give and take of warfare, there was the ferocity of justice, the homicidal intolerance of orthodox religion, and the lack of clemency for the weak and captive.”
During this era, crisis deaths, though fewer in number than chronic deaths, formed a greater fraction of deaths than they would later, because poverty and ignorance kept people vulnerable to crises such as weather, war, and newly introduced or newly evolved contagious diseases.
Falling Mortality
Kannisto et al. describe the years 1880-1945 as the Age of Bacteriology, and the years 1945-1970, the Age of Antibiotics. These stages for Finland are typical of the time when medical advances and a rising standard of living reduce deaths from chronic disease such as diarrhea and tuberculosis. Infants, children, and young adults are the big winners. The Paradox of the Life Table is eliminated. Fewer women die in childbirth, and the female mortality rate drops below the male mortality rate for virtually all ages. Life expectancy at birth rises to 50 for men and women.
Omran attributes this to a reduction in pandemic disease[footnoteRef:6]. However, many of the breakthroughs described by Kannisto et al. are breakthroughs against endemic disease. The battle against both endemic and epidemic disease was undergirded by continuous breakthroughs in farming, engineering, and transportation, which improved the standard of living. [6: A pandemic disease is an epidemic disease which is spreading internationally. An epidemic is a sudden outbreak of a contagious disease that is not constantly present in the population. ]
What brought about the end to high mortality rates? No doubt the science of microbiology reduced infections, and later, sulfa drugs and antibiotics fought infections. An improving standard of living could lead to explosive population growth and terrible competition for scarce resources. There were indeed wars, pandemics, and famines during the nineteenth century. However, by the twentieth century living standards were more than keeping pace with the growing population. As the improvements in technology and achievements in science spiralled ever higher, and as new lands and resources were colonized in America, Australia, and Africa, the West sprung free of the Malthusian trap.
In class we will discuss why some nations have not been able to progress far with mortality transition, so that they are not even close to Delayed Aging.
Delayed Aging
In this stage, people have more than enough resources to meet their basic needs. The standard of living is high and innovation, whether technical or medical, is ongoing. Formerly chronic diseases melt away. Crisis deaths are a tiny fraction of deaths. Life expectancy at birth exceeds 70.
During this stage, most people die of diseases which are degenerative or man-made. Degenerative diseases are those that are a natural result of aging (given the level of medical knowledge). They include cancer, heart disease, stroke, and Alzheimers. Man-made diseases are those that are caused by risky behaviours. They include diseases related to smoking, drinking, over-eating, a fat-rich diet, and lack of exercise.
Deviations from Trend
The stages of mortality transition we have described above imply steady improvement in life expectancy. In reality things may not proceed as smoothly. For example, life expectancy in the Ukraine gyrated wildly in the first half of the twentieth century due to famine (1932-3, 1946-7) and Nazi aggression (1941-1945).
Figure 25-3. Life expectancy at birth, Ukraine, 1927-1959
Source data: Vallin et at. (2002)
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Econ/background to week 4 (3).docx
The general fertility rate is measured differently from the birth rate, with the denominator showing not mid-year population, but the mid-year population of females of childbearing age.
General fertility rate = (# births/midyear population of females aged 15-49) x 1000
Age-specific fertility rates (ASFR) give even more precision as to the age. For example, the (age-specific) fertility rate for females 15-19 years old ≡ number of live births to 15-19 year olds during the year / mid-year population of female 15-19 year olds, all multiplied by 1000.
Though in general, age-specific fertility rates have been dropping in Canada, an exception is the fertility rate for women over 30. Those rates have been rising since the late 70s. In fact, the average age of mother has been rising since the late 70s (see Figure 28-4).
Figure 28-1. Age-Specific Fertility Rates, Canada
Source for data: Statistics Canada, “Fertility rate by age group, Canada, 1926-2008” in Fertility: Overview, 2008, http://www.statcan.gc.ca/pub/91-209-x/2011001/article/11513-eng.htm downloaded October 31, 2013.
Once a woman, or a group of women born the same year, is no longer of child-bearing age, we can record how many children were born to that woman or cohort. We can compute the “completed fertility rate (CFR)” which is children per woman, for that group of women.
CFR = # children born to a group of women/ number of women in the group
For example, for women born in 1946, the completed fertility rate was 2.1, i.e. 2.1 children per woman.
But that is looking into the past. To get an idea of how many children today’s women will have, demographers compute a hypothetical statistic called the total fertility rate (TFR). The total fertility rate is the number of children which would be born to the average woman IF the average woman experiences today’s age-specific fertility rates at each age of her life. This is not completely realistic. In 2010, 25-year old women will behave as predicted by the 2010 fertility rate for 25-year old women. But by 2015, when the women are now 30, we cannot expect their fertility to match the fertility of 30-year-old women in 2010. They will make their own decisions.
TFR = ∑ ASFR over all age groups x 5 / 1000
where ASFR is age-specific fertility rates
“5” represents the 5 years a woman spends in the typcial age group. Age groups are usually 5 years in length e.g. 15-19, 20-24, 25-29 etc.
Why do we divide by 1000? Well, the ASFR gives you the number of children per 1000 women of that age, say 130 children. Now one woman cannot have 130 children. Only 1000 women can. So we divide by 1000 to get the children per woman.
Figure 28-2. Total Fertility Rate, Canada
Source: WDI Online, World Bank Group
As you can see in the Figure above, Canada's TFR was about 1.5 in 2005. It was slightly higher, at 1.58, in 2010.
If we were to count only the female babies in our ASFR, and then compute TFR, we would have the Gross Reproduction Rate, or number of female babies per woman. If we went a step further and multiplied the female baby ASFR by the probability of a female baby living to its mother’s age group, we would have the Net Reproduction Rate. A population is self-sustaining if its NRR is greater than or equal to one.
Instead of using NRR, we usually compute TFR and consider a TFR of 2.1 to be sufficient for a population to be self-sustaining. A TFR=2.1 is considered “the replacement rate” or “replacement fertility”. The last Canadian cohort to achieve a CFR of 2.1 was the women born in 1946. Subsequent cohorts of women have had fewer than 2.1 children per woman.
Tempo-adjusted TFR
Because TFR exaggerates fertility decline when the age of the mother is increasing, demographers have developed a tempo-adjusted TFR.
Adjusted TFR (t) = TFR (t)/ (1-r(t) )
where r(t) measures the influence of postponing fertility.
r(t) =
average age of woman giving birth (t+1) – average age of woman giving birth (t-1)
Demographers refine this calculation by first computing TFR for one kind of child: eldest, second, third, etc. Such a TFR is called a birth-order specific TFR.
Figure 28-3. Fertility trends in the Czech Republic, showing tempo-adjusted TFP.
Source: Philipov and Sobotka (2006)
In Figure 28-3 we see that, when adjusted for the increasing age of mothers, Czech fertility rates are higher than they originally appeared to be.
Figure 28-4. Average age of mother at childbirth, Canada, various years.
Source: Human Resources and Skills Development Canada, 2011.
Determinants of Fertility
Fertility, or how many children per female are born, depends on three things: opportunities for intentional or unintended procreation; intentions; and ability to carry out those intentions.
The decision maker is usually a heterosexual couple relying on their own powers of procreation. In some cultures, the parents of the husband traditionally have influenced a couple’s fertility decisions. Modern western couples have great autonomy in fertility. Greater personal freedom, greater social tolerance of unusual families, and medical technology have united to make it possible for infertile couples, homosexual couples, and singles to become parents.
Opportunities
Procreation, both intentional and unintentional, requires one man and one woman. There is now the possibility of women using sperm banks to conceive, or a couple using a surrogate mother to carry a child to term. Traditional factors governing the union of men and women include the degree of social isolation of men or women; sexual activity rates; the sex ratio; the usual age at marriage or cohabitation; types of marriage (e.g.polygamy vs. monogamy); absence of spouse; likelihood of bereavement, separation, or divorce; and time between unions.
Social and religious norms, income, geography, and political crises influence these things. Generally speaking, prosperity, peace, and secularization mean greater opportunities for coupling and conception.
Intentions
For the decision maker(s), the target number of children depends on personal preferences, social and religious norms, and economic considerations. It also depends on a person's experience of childhood and of raising any previous children. When infant and child mortality is high, extra children may be born in order to achieve the target number.
Extra children are sometimes born to achieve a target number of children with particular characteristics. In the past, one had to “keep trying” until one had the requisite number of boys, girls, healthy children etc. Now genetic testing in utero is making selection easier, and reducing overall fertility. It is ironic that, just when we are treating peoploe with disabilities with dignity,and making it easier for them to take their place in society, we have the means, and often the will, to make sure they are never born.
Even before modern birth control methods were available, when contraception was limited to herbal teas, abstinence, and withdrawal, major declines in fertility took place in industrializing societies as the demographic transition progressed. For example, births per year per married woman in France fell from 0.775 in 1740 to 0.410 in 1891 to 0.273 in 1931 (Wrigley, 1985). Scholars collaborating on the European Fertility History Project in the 1960s produced nine books on the demographic transition in Europe. They concluded that secularization, more than anything else, was associated with falling fertility rates. Thus, fertility fell in European provinces where infant mortality was still high, and where income per person had not yet risen appreciably, if those provinces were integrated with more secularized provinces sharing the same language and culture.
Secularization of a culture occurs as society organizes itself along non-religious lines. The government, the courts, schools, and the like adopt a neutral religious stance. Secularization encourages education, personal development, and decision making without reference to religious authority. It encourages individualism, sometimes at the expense of the community.
Ability to achieve intentions
Although Europeans were able to reduce fertility without modern birth control methods, it is no doubt easier to limit family size today.
Birth control includes contraceptive methods, sterilization of the male or female, and abortion. Abortion continues to arouse serious concern, especially for religious thinkers. The use of abortion to select for boys troubles secular thinkers too. Infanticide, neglect, and abandonment may be forms of delayed birth control.
Some parents, while wishing to reduce family size, reject some or all methods of birth control on moral or medical grounds. Others are ignorant of birth control methods or find them inaccessible. Others simply procrastinate or lack the discipline to use any method of birth control consistently.
The “fertility trap” refers to the phenomenon of delaying child-bearing - perhaps because of a shock such as the collapse of Communism and its parental support programs - until the parents’ fertility has declined or there are simply too few years to give birth to the number of children originally desired. The new, smaller-than-intended families foster new social norms about family size, parental age, and parental career development leading to continuation of the small-family pattern.
Indeed, it is infertility – difficulty conceiving a child – that is perhaps the greatest barrier today to achieving desired family size. Parents must be healthy and physiologically able to conceive a child and carry it to term. Breastfeeding, malnutrition, disease, excessive exercise and stress can interfere with conception and pregnancy. Adoption and fostering are alternative ways to building a family. Adoption and fostering are not part of fertility, but they do contribute to a healthier, more emotionally resilient population.
Economic prosperity makes it easier for people to manage their health and to access birth control. It therefore enhances the ability of parents to achieve a desired family size. However, recent history suggests that intended family size may shrinks with secularization and economic growth.
Economic Influences on Desired Family Size
What benefit and cost considerations affect the number of children a family chooses to have?
Children providing material benefits
First we might ask whether children provide any material benefits to parents. In various times and places children may have been perceived as a net material benefit to parents. Children can work for the family and children can care for their parents when parents are no longer able to work themselves.
In her book on British children brought to Canada, Joy Parr notes that children under the age of 14 could not be boarded out at a profit. Becker (1960) mentioned a finding that male slaves were a net expense to American slave owners until those slaves were about 18 years of age. However, children of about 8 years of age and older have worked in sweatshops and on plantations as long as poverty has existed. Today their tiny fingers weave carpets in Afghanistan and their tiny bodies wriggle through diamond tunnels in Tanzania. At some point they may yield a net profit to their parents.
Whether or not money can be recouped from children before they reach adulthood, adult children can represent a safety net for parents. In societies where healthcare is unsubsidized, insurance is unaffordable, and pensions are inadequate, parents may look to children to meet the needs of their aging. However, in such societies, the capital:labour ratio is likely to be low, and the returns to additional capital greater than the returns to additional labor. If therefore the government could create reliable capital markets, safe vehicles for savings, insurance programs, and pension plans, citizens would dare divert money away from children and toward investments that would provide greater material benefit for themselves and their society.
In this day and age - urban, prosperous, and human rights-oriented - it seems more natural to look at children providing an emotional rather than a financial benefit to their parents.
Children providing psychic benefits to their parents
With children providing “utility” we could use the economic framework of utility maximization within the limits of a budget and a 24 hour day. The decision maker’s constrained utility maximization results in a desired number of children as well as a desired amount of alternative goods and leisure opportunities. The key determinants of the demand for children are income, the cost of children, the cost of substitute goods, and the cost of complementary goods. This is a crass, incomplete, but suggestive approach to understanding the fertility decision.
This approach assumes that children are actually “goods”, i.e., that more children are preferred to fewer. Is this indeed the case?
The following figure uses a large 2007 survey of american heterosexual couples where the female is under 55 years of age.
Figure 30-1. Average number of children, by income rank of families.
A brief glance at Figure 30-1 above suggests that, inasmuch as children are “goods” which enter a parent’s utility function, it is not clear they are normal goods, i.e. goods which are purchased in greater number as income rises. Roughly speaking, lower income families have more children. We also observe that lower income countries have more children than higher income countries.
Willis (1973) developed a detailed model of parental choice. In Willis’ model, each parental unit maximizes utility which depends on the N, the number of children; Q, the level of childhood “quality” for each child which costs time and money; and S, an alternative activity such as skiing. Parents choose between spending on skiing (S) or on child services (N*Q).
Each parental unit also faces constraints. Parents have wage income, and a limited amount of time which for one of the parents – traditionally, the woman - is allocated between work and childcare. Her wage depends on her initial level of skill and her experience in the workforce. Time spent with children means no wage now and a lower wage in the future.
Note that Willis' model is not appropriate for a less-economically-developed nation. Children provide no labour. And there is no consideration of what happens to parents in their old age when they cannot work and when perhaps there is no government support for them.
In Willis' model, if there is an increase in endowment income, and child services is a normal good, the parents will want more child services (NQ). However, we do not know whether more child services means more children, or more money spent on each child. The more they spend on existing children, the more expensive additional children will be, if parents want to treat all children equally. If parents get richer, they might likely choose to increase Q without increasing N. We can thus have increases in income translating into fewer children without children being “inferior goods”.
It is possible that for some people, children are indeed inferior goods, to be foregone or abandoned if more exciting opportunities come along. Another way to explain falling fertility rates for higher income people and nations is that, for them, children are not needed for material benefits, only for psychic ones.
According to Willis’ model, the following things make it likely fewer children will be desired:
-a decrease in the cost of S, where S is a substitute for childservices
-an increase in the time or money cost of NQ
- a high desired Q for each child.
-any decrease in the father’s lifetime earnings.
-if child-rearing is more time-consuming than S, but less expensive than S, an increase in the mother’s wage.
Did you notice the difference between the effects of the father’s and mother's earnings? The father’s earnings were assumed to be independent of the time spent raising the children. Since the father’s time was not the subject of optimal allocation between work and children, it could be treated as manna from heaven, a source of “endowment income” that allows more of everything to be acquired.
The mother’s earnings, however, involve a tradeoff: less time spent at home. They have an opportunity cost: time spent with children.
Substitution and Income Effects
Recall from microeconomic theory that when the price of something changes, there is an income effect and a substitution effect. Consider an example. When the price of apples rises, you switch to cheaper fruits. This is the substitution effect. From the point of view of a consumer, you feel poorer because your purchasing power has fallen. You buy fewer apples and fewer of any goods that are normal. This is the income effect, which, for consumers, works in the same direction as the substitution effect.
For a vendor, however, the substitution and income effects work in opposite directions. A vendor of apples, when snacking, will buy cheaper fruits when the price of apples rises. The substitution effect causes him to buy fewer apples. However, a rising price of apples will make the vendor richer and he or she will buy more apples and more of any other normal goods. The income effect causes a seller of apples to buy more apples, not fewer.
When a potentially care-giving parent is offered a wage increase, there are two effects. The substitution effect tells the parent to work more now that the price (opportunity cost) of her time has risen, and childcare at home is now more expensive. However, the income effect makes her, as a vendor of time, feel richer, and able to afford more time spent with kids. If her partner’s wage rises, again she experiences the income effect telling her she can afford more time with the kids.
At low wages, the income effect is probably less powerful than the substitution effect. So a wage increase leads the parent to work more/spend less time with children. At high wages the income effect may be larger than the substitution effect, so that the parent decides to spend more time at home or have more children.
T. Paul Schulz, a famous development economist, wrote that, “There is an inverse association between income per adult and fertility among countries, and across households this inverse association is also often observed. Many studies find fertility is lower among better educated women [implying that the substitution effect outweighs the income effect] and is often higher among women whose families own more land and assets [a pure income effect].”[footnoteRef:2] [2: Schultz (2005).]
Figure 30-2 shows a declining number of children for wealthier families, apparently contradicting the positive income effect we have postulated.
Figure 30-2. Average number of children by wealth rank of families.
Data source: PSID (2009). All heterosexual couples with a woman less than 55 years of age.
The effect of the wife’s wage on number of children is obscure. A strong substitution effect is not observed.
Figure 30-3. Average number of children for families ranked by size of wife’s wage.
Source: PSID (2009). All heterosexual couples with a woman less than 55 years of age
The Economist (August 8, 2009) describes the research of Myrskyla et al. (2009), which suggests the income effect becomes dominant for countries with high socioeconomic performance. Graphing the total fertility rate against the United Nations’ Human Development Index (HDI)[footnoteRef:3] for 240 countries, the authors observed that fertility fell as HDI increased, but only up to a score of about 0.9. For most countries, Canada and Japan excepted, whose HDIs exceed 0.9,TFR increased as the HDI increased. [3: HDI is an index of life expectancy at birth, income per person, and education levels achieved]
Abeysinghe (1993) studied Canadian fertility and used statistical analysis to correlate wages, income, and the number of children. He concluded that when it comes to female wages, the substitution effect outweighs the income effect of a wage increase, and higher females wages mean fewer children. On the other hand, there is a pure income effect which favours children: men whose incomes compared favourably to their parents had more children.
Although age-specific fertility rates and the total fertility rate fell when female wages rose, the drop in fertility seems to be temporary. That is, higher wages cause women to postpone rather than to avoid childbearing. Abeysinghe found that the female wage rate was not much correlated with the completed fertility rate. Tempo-adjusted TFR would not be as sensitive to female wages as TFR itself.
Not everyone who postpones having kids will find the time or partner, or be fertile enough to have kids later. (Recall the "fertility trap".) However, many of them will be able to have their children later on. Inasmuch as that is the case, TFR underestimates CFR.
Business Cycle Effects
If higher wages are associated with fewer children, at least temporarily, we would expect fewer births during economic boom times, and more children during recessions. However this is not what happens. TFR rises during economic expansions. Mocan (1990) attributes most of this effect to the fact that during economic expansions the age at marriage falls and the divorce rate falls. He believes that fertility itself is slightly countercyclical due to rising wages as predicted by the substitution effect.
In conclusion
When asked how income affects fertility, we must distinguish between three different aspects of income:
Table 30-1. Aspects of income which affect fertility.
|
Wealth |
A pure income effect increases the money and time spent on children. Some studies suggest that the number of children rises.
|
|
Higher wages, better employment possibilities for the caregiving parent(s) |
The substitution effect prevails at lower wages. If wages become high enough, the income effect may prevail leading to greater fertility. However, higher wages are usually associated with fewer children. TFR falls but tempo-adjusted TFR might not fall as much. |
|
Higher wages during economic boom |
The higher wages might lead to fewer children if it were not the case that divorce rates fall and people get married earlier during economic booms. Expect an increase in TFR. |
|
Economic development apart from wealth or higher wages |
· reduced reliance on children for labour · reduced reliance on children for old age security · improved infant and child survival · improved education and awareness of career options, birth control · improved access to birth control and to infertility treatment. · secularization Overall, economic development appears to decrease fertility until high levels of development are reached. |
Canada’s Fertility Rate, 1960-2007
total fertility rate 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 3.8110001087188721 3.753000020980835 3.6809999942779541 3.6070001125335693 3.4560000896453857 3.1150000095367432 2.749000072479248 2.5280001163482666 2.3859999179840088 2.3340001106262207 2.2579998970031738 2.1410000324249268 1.9800000190734863 1.8899999856948853 1.8370000123977661 1.8240000009536743 1.7960000038146973 1.781999945640564 1.7400000095367432 1.7000000476837158 1.690000057220459 1.6799999475479126 1.6499999761581421 1.6699999570846558 1.6799999475479126 1.6799999475479126 1.7699999809265137 1.8300000429153442 1.7000000476837158 1.7100000381469727 1.7000000476837158 1.6390000581741333 1.5920000076293945 1.5499999523162842 1.4900000095367432 1.5199999809265137 1.5299999713897705 1.5299999713897705 1.5399999618530273 1.5900000333786011 1.5900000333786011
Econ/background to week 5 (5).doc
Fertility Policy
Fertility policy is much more complicated, ethically speaking, than mortality policy. Everyone knows that promoting mortality is unethical. Thus mortality policy is concerned only with saving and extending life.
When it comes to fertility policy, values differ. Fertility has been both discouraged and encouraged by governments at different times and places, not usually for its own sake, but to accomplish population growth or shrinkage. For example, Quebec promoted fertility between 1988 and 1997, with the aim of keeping francophone culture alive in North America.
Many people believe that fertility is a deeply personal individual freedom that government has no business tampering with. Many believe that childbearing is a divine imperative that should not be impeded.
We are generally content to allow a government its incentives and advertising regarding fertility, as long as government does not violate our human rights by coercing us, deceiving us, or manipulating us to do something we do not want to do but are too poor to resist doing.
The question of coercion comes up in the abortion debate, where the contested right to life of a fetus/unborn child clashes with the contested right of a woman to abort a fetus/unborn child. The issue of which of these rights are valid and, if both are valid, which right prevails, is an important one. However, at various times and places, abortion legislation has been enacted not to answer this question but to achieve a target level of fertility in the population. The Ceausescu regime in Romania (1965-1989) outlawed abortion to achieve a higher birth rate. Meanwhile, Singapore legalized abortion in 1969 for the express purpose of reducing births. Forced abortion and sterilization have occurred in China since the 1980s for the same reason.
Another example of coercion is the forced sterilization of mentally ill and mentally retarded people in North America and northwestern Europe between the World Wars. A more recent example is the forced sterilization of poor men – particularly Muslim men - in India in the mid 1970s.
Those episodes remind us that many times, fertility policy – like immigration policy – is directed at particular groups of people: ethnic groups, religious groups, or income classes. It is those sub-populations that are targeted for growth or shrinkage. Thus the question of discrimination is another issue complicating fertility policy.
Eugenics
Nazi Germany went furthest in elaborating an ideology of genetic superiority. The fallout – millions killed on the basis of their race, politics, religion, color, intelligence, sexual orientation etc. – served as a wake-up call to the would-be civilized world.
It was not only the Germans, but citizens of many nations who embraced eugenics, including US President Theodore Roosevelt, Planned Parenthood founder Margaret Sanger, and Irving Fisher (celebrated economist). In Canada, the eugenics movement had most influence in Alberta, where a Eugenics Board, with the authority to sterilize people deemed defective, operated between 1928 and 1972.
The damage done by such policies, the horror of Nazi camps, the exploitation, imprisonment and killing of citizens by Communist dictators, and books such as “Brave New World” (Huxley, 1932) have warned us that governments’ social planning can completely override compassion and respect for human rights.
Thus in today’s world, most governments have given up supervising reproductive selection. However, technology – combined with liberal abortion laws – is giving prospective parents the opportunity to themselves screen their offspring for unwanted characteristics.
This is a lot safer than government screening: there is a diversity of parents who will welcome children like themselves, preserving diversity. However, it is not clear that girl children, and children with congenital disabilities, will be as likely to make the cut as boys and healthy children. In the future it may become easier to select for all kinds of apparent abilities and advantages.
Economics cannot be relied upon to dissuade parents from this course of action, especially if children with unwanted characteristics cost more to raise and governments are not willing to share the burden. However, economics can remind us that diversity is a source of strength, providing fresh ideas and approaches as well as opportunities for specialization. Our society's strength, our government's strength, our economy's strength, lies in diversity, cooperation, and competition, rather than in conformity, coercion, and cronyism.
Understanding that we mean no coercion and no discrimination, let us discuss how fertility policy might be implemented successfully.
Five Principles of Policy Design
#1 No discrimination or coercion. As discussed above.
#2 Question the policy. Identify the ultimate goal or the root cause of the problem you are trying to address. Is the proposed policy the most direct way to achieve your goal/fight the problem? For example, if you are embarking on a program to reduce births, there is probably a deeper goal, such as poverty reduction. A policy to encourage births might really be about increasing the labour supply. There may be more direct and faster-acting ways to reduce poverty or increase the labour supply.
#3 Target the binding constraint
A successful policy addresses the most critical bottleneck, the most pressing barrier to achieving the goal or reducing the problem at hand. For example, if the policy is intended to encourage births, you need to know what is really holding people back from deciding to have children or expand their family size. It’s no use offering money to couples to have children, if they are avoiding children for non-financial reasons.
#4 Target the appropriate margin
In microeconomics we learn that people evaluate things at the margin. They decide whether or not to study one more hour, not just whether or not to study at all. They decide whether or not to have kids, but then they decide whether or not to have one more, one at a time. If most people already intend to have one child, you should target people who are at the margin of deciding for another child or not. Similarly, if your target is a limit of two children per family, you can implement a policy that discourages third children.
Poster of Singapore Family Planning and Population Board, 1978.
Another margin that is relevant to fertility is hours worked. Is the parent deciding whether to join the workforce or whether to work a few more hours each day? Is the parent already committed to working full-time no matter what?
#5 Understand who pays the financial cost. Remember that taxes and subsidies always affect both producers and consumers, no matter which of them has the tax or subsidy imposed on them. The least price-sensitive party pays most of the tax. The least price-sensitive party gains most of the subsidy.
This means that subsidies intended to encourage fertility may be ineffective if the supply of houses, childcare spaces, etc. is inelastic. It means that taxes to discourage fertility will not be effective if fertility is price-insensitive; instead, those having children will pay the tax and their ability to look after the children will be compromised.
In class we will evaluate various pro-natalist and anti-natalist policies including cash incentives, subsidized daycare, cash-for-care (Norway), paid parental leave, subsidized birth control, and the general education of girls. We also learn about China’s One Child Policy.
Chinese Population Policy
China’s first official family planning programs were in place in the late 50s in some large cities, encouraging couples to plan the number of children and choose fewer. China’s formal one-child policy, begun in 1979, has been possibly the most focused and wide-ranging birth control program ever. The program was launched with Chairman Deng’s announcement of a zero population growth (ZPG) target for 2000. To this end, births were to be limited to one per couple, with some exceptions.
Program Details
The program stipulates of a maximum number of children permitted, depending on region and ethnicity. Each child requires a birth permit.
Table 34-1. One-Child Policy Details.
Group |
Regulation |
|
urban residents |
one child |
|
most rural residents |
two children if the first child is female or handicapped; or two children four years apart in age |
|
minorities in minority autonomous regions |
two or three children |
|
rural Tibetans |
any number of children |
The program offers economic incentives for compliance, which have included urban one-child families receiving a monthly allowance until the child is 14 years old, plus preferential housing, school admissions, and pensions. Rural one-child families received extra work points until the child was 14 years old, and the same size grain ration and size of plot as 2- child families.
At first, the program was administered centrally, relying on propaganda and yearly “shock drives” –which included forced sterilizations and abortions - to achieve local targets. This led to fierce confrontations. At the same time, market reform was occurring and making peasants less dependent on government subsidies. Peasants stood to gain personally from additional sons to work the land. Consequently, in the mid-80s the targets for rural couples were relaxed. It took until 2001, however, for coercion to be officially prohibited. This came as a result of domestic clashes, international pressure, better demographic data, and positive results from pilot projects which concentrated on providing information and health care, say Zhao and Guo (2007). The new policy also prohibits sex-specific abortion and discrimination against female children. Compliance is imperfect.
Results of the Program for Fertility and Population Growth
Chairman Deng’s original goal, ZPG by 2000, was not achieved. The growth rate in 2000 was 1.07%, not a whole lot less than the 1981 level of 1.4%. By 2009 the population growth rate had fallen even more to 0.61% (Canada had 0.82%). It is estimated that the Chinese population is now significantly smaller that it would have been without Deng's policy, by hundreds of millions of people. To calculate what population would have been without the policy we would need to run a Leslie matrix over the length of time the policy has been in place, using the original fertility rates, but adjusting mortality rates as they changed over time. (However, even without the one-child policy, fertility rates might have dropped with economic development.) Representatives of the Chinese government, which claims that 400 million deaths were averted over 30 years (Lifesitenews.com, 2006), have suggested that China has already made its contribution to fighting climate change.
China's TFR is about 1.9, down from 2.7 in 1980, and well below replacement TFR of 2.1 children per female. This decrease was critical because it helped defuse the population momentum that existed due to a baby boom that took place in the late 60s. The number of people of childbearing age will not decline until 2015.
What would happen if the one child policy were abandoned? In fact the policy is becoming less rigid. Currently, urban Chinese couples are permitted a second child, if each person in the couples was himself or herself the only child in his/her family. As the Chinese population continues to age, and as its people achieve new political freedoms, more children will be permitted. New freedom will also allow the parents to purse new and varied careers. It will be interesting to see to what extent the government’s one-child program has been taken to heart by the Chinese people.
Missing Females
There have been many side effects of the drive to lower fertility.
We have already mentioned that forced abortions and sterilizations have taken place, and we can imagine the scars that are left behind.
Another serious problem linked to the program is girl-specific abortion, infanticide, and neglect. Though most parents in China treasure their girl children, cultural values and economic pressures lead some parents to prefer boys and to do away with girl children in hopes of being able to have a son instead. In some provinces, typically those having large rural non-minority populations, the sex ratio at birth may be as high as 119 compared to 105 in other parts of China or 107 in Tibet.
Selection for boys may not be entirely the fault of the one-child policy. Other nations, such as South Korea, where son preference is declining from its 1990 high, and northewestern India, where it is stronger than ever , also have skewed sex ratios
Table 34-2. Selected Sex Ratios
|
Sex ratios: |
Age 0-4, 1982 |
Age 0-4, 1995 |
Age 0-4, 2005 |
|
|
Beijing, China |
107.3 |
113.5 |
112 |
|
|
Anhui Province, China |
110 |
125.1 |
136.4 |
|
|
Xinjiang Province, China |
103.7 |
101.8 |
1105.5 |
|
|
Sex ratio: |
|
|
Age 0-6, 2001 |
Age 0-6, 2011 |
|
India |
|
|
107.9 |
109.4 |
|
Punjab Province, India |
|
|
125.3 |
118.2 |
|
Dadra and Nagar Haveli Provinces, India |
|
|
102.1 |
108.2 |
|
Sex ratios: |
At birth, 1981 |
At birth, 1989 |
At birth, 1992 |
At birth, 2001 |
|
South Korea |
104 |
112 |
114 |
108 |
Sources: Das Gupta et al. (2009), Census of India (2011), Hesketh and Zhu (2006).
Das Gupta (December 2009) argues that Korea, China, and northwestern India, places where son preference has manifested itself especially strongly, not only have been patrilineal (only men inherit), but moreover have had traditional political systems which are very much organized around male ancestry Ancestor worship helped reinforce notions of loyalty, order, and political hierarchy. In rural areas these values still hold sway and a man’s identity, social status, and access to resources is determined by his position in a clan. For example, the oldest son of an oldest son is in a favoured position. A woman’s identity is determined by her husband. Women born into the clan are required to leave and marry men of other clans. They leave their land and forego any inheritance other than what is given to them as part of the marriage settlement.
Traditionally, Asian women live with their in-laws once married, so it is their brothers who look after their aging parents. In the School of Policy Studies at Queen’s, Wei Li Ding studies rural access to credit in China. She finds that families with sons have an easier time getting loans. One reason is that sons are more likely to be able to earn money and share that money with parents.
Living with in-laws, a women is dependent on them for protection, sustenance, and approval. The husband’s parents are likely to influence her and her husband’s fertility decisions.
In India, the advantage of having a son is heightened by the necessity of paying a dowry to the groom’s family when a daughter gets married. As one advertisement for a fetal-gender test kit put it, "Spend 500 rupees now to save 500,000 rupees later."
Earlier we described the research of Jiang, Feldman, and Jin (2005), who estimated the number of Chinese females missing over the last century. Jiang et al. conclude that 35 million Chinese females were lost over the century, about 4.65 percent of all females who were expected to be born. The number of missing females steadily increased during the years of the One-Child policy. See their Figure 1 on the next page.
The number of missing females may be exaggerated if girls and women are under-reported.
For Asia as a whole, it is estimated that 163 million females that should be present are not. (Hvistendahl, 2011). The Economist predicts that by 2025, China will have only 80.3 million woen in their twenties compared to 96.5 million men in their twenties (a sex ratio of 1.2). One might think that increasing scarcity of females will lead to increasing brideprice (the traditional Chinese norm) at marriage and an increasing appreciation of the role of women, with wives being treated better. Unfortunately, lacking individual rights and freedoms, many women will be at higher risk for being kidnapped, pimped, or forced into monogamous or plural marriage.
There are also negative consequences for men. Many will remain involuntarily single. Single men generally have poorer health and earlier death than married men. They may have to spend more resources or take bigger risks to attract a bride. They may have to migrate to find a partner, or settle for one who is less compatible. For society as a whole, tension and unrest may increase. Fertility will be lower than otherwise because of the absence of so many women.
Following page: Figure 34-2. Females missing from China, as percent of population.
Source: Jiang, Feldman, and Jin (2005)
Regarding Figure 34-2, the following dates are of interest:
1910- slavery abolished
1911- Sun Yat Sen leads revolution against Qing Dynasty
1916+ warlord era
1931-1945 Japanese occupation
1949 Communist Party is established as the government
1957-58 Great Leap Forward and famine
1966-1976 Cultural Revolution
1976 Death of Chairman Mao
1979 One Child Policy instituted
continued
Other consequences of the One Child Policy:
Population composition: Aging population
As birth cohorts fall in size, the population ages. Although the overall dependency ratio in China fell between 1982 and 2000, the aged dependency ratio rose, though at 0.11 it is still lower than Canada’s aged dependency ratio of 0.21. Yet China is experiencing a level of aged dependency usually associated with more economically developed nations.
China’s extensive social welfare system, concentrated in the cities, is being strained. Health care in rural areas will be a challenge.
Population composition: fewer children from urban families. Unless rural areas receive the same educational opportunities as urban, the proportion of the population which is educated may fall if rural families have more children than urban families.
Population composition: little emperors. Some have worried that children with no siblings will be pampered and less socially conscious. On the other hand there may be benefits that come from being raised in an adult-intensive environment and receiving relatively more adult attention. These concerns are beyond the scope of our course!
Population deceleration: reduced rate of capital shallowing. China is currently a low-wage country with a low capital:labour ratio; there is also a housing shortage, an education shortage, and problems of environmental degradation. Yet consider how much worse these problems could have been had fertility not been discouraged. Though the workforce now is smaller than it might have been otherwise, machines, land, and education per person are higher.
� There are some signs of hope at the sub-national level. See Punjab Province in Table 34-2.
� As reported in "Land of the rising son", Globe and Mail, Sept. 12, 2009.
� Some dates to consider: 1911: Revolution against Qing Dynasty begins. 1916: Warlord era begins. 1931-1945: Japanese Occupation. 1949: Communist Party of China takes control. 1957/8: Great Leap Forward leads to mass deaths. 1966-1976: Cultural Revolution. 1976: Deng's economic reforms begin, followed by One Child Policy in 1979.
� “A tale of three islands,” October 22, 2011.
Econ/background to week 6 (5).docx
Demographic History after 1750 AD
After 1750, the demographic and economic history of England, then other nations, have refuted Malthus’ predictions. Populations and the standard of living both grew rapidly. There has also been rapid growth in almost every measurable standard of human development.
This turning point is usually referred to as the Industrial Revolution, as it was marked by key inventions such as those of the steam engine and the cotton jenny.
Much scholarship has been devoted to explaining the causes of the Industrial Revolution. A combination of factors including literacy, social mobility, and cheap coal gelled to create an atmosphere in England that was conducive to research, innovation, and mechanization.
One remarkable thing about the Industrial Revolution is that it raised the standard of living for most people. You might think that labour-replacing machines would be a threat to labourers. You might remember images of eighteenth and nineteenth century London filled with beggars and prostitutes from the writing of Charles Dickens and others. However, the Industrial Revolution lifted millions of people out of abject poverty. Clark (2008) presents data to show that the share of English national income going to unskilled workers actually rose during the Industrial Revolution. How could this be?
The Industrial Revolution replaced unskilled workers with machines, but it also replaced skilled workers with machines. It made machines better and more affordable. It also made land more affordable by replacing horses, oxen, and the food that fueled them with machines and coal. Thus the premium earned by skilled workers, equipment owners, and landowners fell.
The Industrial Revolution was accompanied and facilitated by innovations in central banking and private finance. Loans became more plentiful and affordable, another reason that land, skill, and machinery became more accessible to the poor.
The cost of living fell as land prices and machinery prices fell. The cost of living fell as the price of soap, cotton fabric, and other products new and old fell with mass production and with the importation of raw materials from British colonies around the world. Products produced by slaves, such as sugar and raw cotton, sadly were also important to British economic success.
The Demographic Transition
Seemingly in response to the rising standard of living, death rates began to fall. The English birth rate climbed. The population began to expand until later on, birth rates began to fall like the mortality rates. This pattern of demographic change, with mortality rates falling, and birth rates eventually falling whether or not they initially increase, accompanies economic modernization wherever it occurs and is known as the demographic transition. Figure 4-1 shows the typical pattern.
Figure 4.1 A typical demographic transition.
In France, birth rates and death rates initially at about 40 per 1000 people per year (in 1740) fell pretty much in synch to about 18 per 1000 at the beginning of World War I.
According to the Population Reference Bureau, the world had its first billion people by approximately 1800 AD. Only eighty years later, world population would exceed two billion. The length of time taken to add each extra billion people has shortened; in 2011, twelve years after reaching 6 billion, we reached 7 billion. It is believed that most of the world is now at that stage of the demographic transition where birth rates are approaching death rates, and that population growth is slowing. If current trends continue, it will take thirteen years to reach 8 billion, and the world population will settle at about 10 billion people in 2100 AD.[footnoteRef:1] [1: “World Population Prospects,” United Nations (2010).]
It is believed that, though world population is massive, we are not so many that we exceed the number of people born before our time. In fact, the seven billion of us represent less than 1/10th of the people who have ever lived, as we shall calculate in a later chapter.
Comparing societies before and after industrialization, as we do in Table 4-1, we see that innovation accelerates, mortality falls, and fertility falls. Hence our ability to feed ourselves grows as our population grows, and later possibly grows faster than our decelerating population. However, there is no guarantee that technology can continually improve rapidly. Nor can we assume that people who enjoy a high standard of living will always choose to limit family size. Finally, we cannot assume that mortality will remain low and that new threats to human health and longevity will not develop.
Table 4-1. Comparison of pre- and post-indstrial eras
|
|
Pre modern |
Modern |
|
Technological change |
Rare |
Continuous |
|
Fertility rates |
High. |
Sometimes rise. Eventually fall. |
|
Mortality rates |
High. |
Falling |
|
Standard of living |
Precarious |
A stronger base from which to weather crises and build for the future. |
The more economically-developed nations of our world have mostly passed through the demographic transition, and their rate of population growth has greatly declined. Roughly 37% of the world’s population lives in regions where a woman can be expected to have fewer than 2.1 children during her lifetime.[footnoteRef:2] However, many of the less economically-developed nations are still at the point where fertility rates exceed mortality rates by a large margin. [2: My estimate based on the 2010 World Population Data Sheet published by the Population Reference Bureau.]
Van de Kaa (1987) looked at fertility in Europe and suggested that a “second demographic transition” could be expected, one where the death rate exceeds the birth rate, so that population shrinks in size unless immigration occurs. However, it appears that such a transition may not be inevitable. Today, northern European and western European fertility rates are rising.
In the 1930s, demographers worried about declining birth rates. The baby boom that occurred after World War II put an end to their worries. Thirty or forty years ago academics and the media were worried about exploding population and environmental collapse. In the last ten or twenty years, attention has turned to the aging populations of the West and Japan, and the population of population shrinkage there. In project future trends in population, we would do well to remember that population change, like economic change, depends on the individual decisions of millions of fundamentally unpredictable people who singly or collectively influence and are influenced by the spirit of their times.
Dependency ratios and the Demographic transition
During the demographic transition, the population growth accelerates, then wanes. Meanwhile, the age structure of the population changes. Dependency ratios and population pyramids help us describe the age structure of a population.
The child dependency ratio (CDR) is the number of children per working age person, commonly persons age 0-14 divided by persons age 15-64. The aged dependency ratio (ADR) is the number of older people per working age person, commonly persons age 65 and older divided by persons age 15-64. Counting all youth under 20 years of age as dependants, Canada has a CDR of 0.39 and an ADR of 0.21.[footnoteRef:3] [3: Source: "Dependency Ratio, by age group, Canada, provinces, territories, health regions, and peer groups, 2005," in "Health Indicators – May 2007". Statistics Canada Cat. No. 82-221.]
The total dependency ratio, (DR), {P(0-14) + P (65+)}/ P(15-64) is equal to the child dependency ratio plus the aged dependency ratio. Counting all youth under 20 years of age as dependants, Canada has a DR of 0.60.
Typically, the more economically developed nations have lower child dependency ratios and lower total dependency ratios than the economically less-developed regions. However, many of the world’s developed nations have rising aged and total dependency ratios.
Over time, then, total dependency often first rises and then falls during the first two stages of the Demographic Transition, a hump shape which you can see in Figures 9-1 and 9-4 below.
Figure 9-1. World Dependency Ratios.
Data from United Nations, “World Population Prospects” various years
In the case of Japan we see that, in recent years, the rise in aged dependency exceeds the fall in youth dependency. Total dependency rises. We can consider this the third stage of the Demographic Transition. At this point, population growth falls to zero or even goes negative.
Figure 9-2. Dependency Ratio in Japan
Source: Ibid.
In class we will explore how CDR, ADR, and TDR change over the stages of the Demographic Transition due to changes in youth mortality, senior mortality, fertility, and the population growth rate. Recent data for Canada are presented in Figure 9-3. What stages of the Demographic Transition are suggested in Figure 9-3?
Figure 9-3. Canadian Dependency Ratios, past and projected
Source of Figure: Statistics Canada. http://www.statcan.gc.ca/pub/82-229-x/2009001/demo/dep-eng.htm
The Case of Dependency in sub-Saharan Africa
Figure 9-4 shows us that sub-Saharan Africa was in stage 2 during 1950-2000, and on the descending portion of a hump shape. In Swaziland, for example, the total dependency rate dropped from about 1.22 in 1986 to 0.9 in 2003.[footnoteRef:4] This is surprising because, as you know, AIDS has scoured the region, affecting primarily the working-age population. In Swaziland, almost half of adults age 25-29 were HIV positive by 2002. How is it possible that the number of dependants per working age person continued to drop? [4: S. Drimie (200 ]
Figure 9-4. Dependency Ratio in South Africa
Figure 9-5. HIV Rates in Swaziland, from Drimie (2004). Used by permission.
Source: Drimie (2004). Used by permission.
The answer has to be that the number of children has declined even faster than the number of working-age people. Also, for every working age person who dies, there is one fewer future senior. The falling numbers of children could be due to people choosing to have fewer children, which usually occurs as wages rise due to economic development; it could be because HIV-infected women are less able to conceive and carry to term; it is partly due to rising infant mortality due to complications from HIV infection; and it may be due to increased abstinence and condom use to avoid infection.
Table 9-1. Demographic Indicators for Swaziland
Source: Drimie (2004). Used by permission.
Another factor in the falling dependency ratios is that many working-age adults survive HIV infection for some time. With this in mind, Drimie (2004) estimated an “effective dependency ratio” of the number of dependants (age 0-14 and 65+) to the number of working age people not chronically ill. The effective dependency ratio in 2004 ranged from 0.95 to 1.22, compared to the conventional dependency ratio of 0.92.
Population Pyramids
The detailed age and sex composition of a population can be seen at a glance in a population pyramid. The various age groups ascend the vertical axis, while along the horizontal we see the number of people in each age group: to the left, we see the males; to the right, we see the females.
The five-year age groupings are popular because, in interviews, people tend to round their ages to numbers ending in 5 and 0.
Population Pyramid Shapes
the pyramid – Before the Demographic Transition begins, human societies have high fertility and high mortality, and especially high infant and child mortality. This means that the bottom of the pyramid is wide, and that the width tapers off rapidly. Child dependency is high, aged dependency is low, and overall dependency is high.
Figure 10-1 is an example of the traditional shape.
Figure 10-1. Population Pyramid for Afghanistan, 2005.
This figure and the others in this chapter were generated online at www.census.gov/ipc/www/idb/informationGateway.php with data from the US Census Bureau's International Data Base (IBD)
If fertility increased, child dependency and total dependency would rise as the base layers of the pyramid increased in size relative to the middle layers.
If more children survived, how would the pyramid change? There would be more children, but in a few years, there would be more adults as well. Because more people survive to adulthood, child dependency and even aged dependency could drop. The population would be growing, yes, but dependency could be falling.
As mortality falls, the pyramid’s sides become less concave.
In stage two of the Demographic Transition, fertility falls and the base of the pyramid shrinks. We see this in Figure 10-2, which is roughly spade-shaped.
Figure 10-2. Population Pyramid for Canada, 2005.
This Canadian pyramid shows our Baby Boom Generation becoming middle-aged. No group of newborns born during the same years, i.e no age cohort has been as large since.
The Baby Boomers were born between 1945 and 1964. During that time, Canadian women had an average of 3.7 children per woman. Almost 1/3rd of Canadians are baby boomers!
Because our many baby boomers are aging, Canada is aging. However, we are experiencing a surge in births as well (not show in the pyramid for 2005). While fertility is high by historical standards, the number of births is increasing for two reasons. First, there are relatively many women of child-bearing age, these being the granddaughters of the boomers, or the “Echo of the Echo”. Secondly, many Baby Busters in their thirties and forties, who postponed having children, are having families.
Box 10-1. Prominent Cohorts
1901-1910: Interbellum Generation
1911-1924: Greatest Generation
1925-1945: Silent Generation
1945-1964: Baby Boomers
1965-1980: Baby Busters/ Generation X
1975-1985: Children of Boomers/Echo Generation
1981-1999: Generation Y
1994-2005: Internet Generation
2008+ Canada’s recent baby boom
Some of these cohorts overlap, and different people define the generations differently. Some of the names will change too, depending on events that will take place in the future.
Although we are experiencing a baby boom, our birth rate still falls short of our death rate every year. It is immigration which keeps our population growth rate positive, but even with immigration our population growth rate is less than one percent. (CIA Factbook, 2011 est.)
In the third stage of the Demographic Transition, more adults and elders are surviving, and the population is aging. Aged dependency falls. Child dependency falls too as there are more adults surviving. Total dependency falls.
The population pyramid begins to resemble a muffin as young cohorts are smaller and the older cohorts are persistently large.
Figure 10-3. Population Pyramid for Japan, 2005.
If fertility continues to decline, the muffin may stretch into a kite.
Figure 10-4. Projected Population Pyramid for Japan, 2050
Once fertility rates and mortality rates stabilize, the age structure of the population will eventually stabilize. We discuss this in a future lecture. A stable age structure with low mortality will resemble
the apartment building may result, with cohorts similar in size.
Theory after Malthus
So, after the Industrial Revolution disproved the Malthusian assumption that food production could grow only arithmetically, and could not keep up with population growth, the Demographic Transition disproved the Malthusian assumption that the birth rate would always rise when the standard of living improved.
Since 1750, the western world has enjoyed an increasing standard of living and an increasing population. How do theorists make sense of this?
Paul Ehrlich (author of The Population Bomb, 1968) warned that the prosperity of the West is possible only because we are exploiting natural resources, environmental capital, and other societies in an unsustainable way. At some point we will not be able to do this any longer; confronted by a wasted environment or social upheaval, our civilization will collapse.
Esther Boserup (1965) and Julian Simon (1981) have a rosier view. They note that, as population grows and resources become relative scarce, prices rise. They believe that rising prices motivate people to innovate and develop new technologies.
Clearly that is not happening in ever society. There must be a political and intellectual climate conducive to innovation. Governments help by pursuing peace, upholding civil and commercial law, protecting personal and intellectual property, and funding education and research.
A well-functioning market is also needed to provide innovators with investment funds and inputs, and to help them find customers for their inventions.
Boserup and Simon's model presumes that all relevant resources are marketed. In real life population puts pressures on growth threatens resources such as watersheds and fish stocks, which may not have owners and which may be used without charge. Such "open-access resources" are likely to be overexploited
Gregory Clark (2008) presents a model where, as usual, population growth leads to food scarcity and rising pressures. These tough conditions “select” for those who are literate, numerate, hard-working, and thrifty. Their eventual dominance in the population (especially if they have many children) leads to prosperity. If the literate have more children than the non-literate, population growth leads not only to selection of the literate but also to greater numbers of the literate.
Clark argues that literacy etc. spread through the British population at the time of the Industrial Revolution because people with these skills, whom he identifies as the upper economic classes, had more children than other people. In a sort of "downward mobility", literacy and thrift spread through the population of Britain, enabling it to continue a cycle of growth in numbers and in income.
It is always dangerous to generalize about classes of people. Certainly to call the upper classes of England thrifty and hard-working seems a bit of a stretch. Many of these people were idle landowners whose forebears had invested in slavery-based sugar plantations abroad.
Literacy, numeracy, and other skills can spread through a population by means of institutions such as schools. Clark does not believe that governments were essential to promote education. He believes that governments and other institutions reflect economic conditions rather than shape economic conditions. But surely institutions and the economy are mutually influential? In fact, Clark’s model is similar to the Boserup-Simon model in that it will not result in innovation unless society’s institutions are such that expertise, hard work, thrift and innovativeness are rewarded.
Clark’s position that institutions and beliefs are determined by the economy echoes the views of Marx, who believed that everything boils down to who owns the capital This is ironic since, according to Marx, labour is the only source of material value, and the price of something should reflect only the labour which goes into making it. With a focus on the primacy of labour, early Marxists did not see any disadvantages to population growth. They focused on distributing capital to workers so as to reduce poverty.
Clark’s model reminds us that the composition of population, not just its size or growth rate, can make a difference to the economy.
Jane Jacobs (The Economy of Cities, 1969) wrote eloquently on the importance of cities to economic development. She believed that cities are where all major innovations – even agricultural innovations - have originated, in contrast to the traditional view that cities developed once agriculture was productive enough to feed them. For Jane Jacobs, a rising population can promote innovation if population density and settlement are the result. Population growth leads not only to rising prices but to settlement and cities, and cities lead to innovation and better institutions.
Jared Diamond (Guns, Germs and Steel (1999) believes that, initially, population growth forces societies to adopt more sophisticated legal and governmental structures. This in turn fosters innovation. In tribes, everyone knows each other, and intermediation can happen naturally if conflicts arise. In larger societies, stranger-to-stranger conflicts are more common, and an independent legal system is needed to resolve disputes.
To Diamond, large populations have several advantages over small populations. Not only do they acquire more sophisticated government, not only do they have more military might, but they also have a greater diversity of abilities, aptitudes, and ideas within the population.
Diamond, in contrast to Clark, explains economic development in terms of diversity rather than selection. Regions with more diverse plant and animal life were able to develop richer agriculture. Regions with more diverse trading partners were able to develop richer technology and intellectual life. And regions with larger populations had more ability to attract trading partners, develop new ideas, and develop resistance to contagious disease. Diamond writes about New Guinea and Australia that, “Human populations of only a few hundred people were unable to survive indefinitely in complete isolation. A population of 4,000 (Tasmania) was able to survive for 10,000 years, but with significant cultural losses and significant failures to invent, leaving it with a uniquely simplified material culture.”
Caveat
In considering the ways that population growth or composition can help or hinder economic growth, let us remind ourselves that many other things affect the economy besides population growth or composition. Many other things affect population growth or shrinkage besides the economy.
Jared Diamond puts it this way: “We tend to seek easy, single-factor explanations of success. For most important things, though, success actually requires avoiding many separate causes of failure.”
Allen Kelley (1988) says, “What is clear is that an assessment of the impact of population growth on economic development is highly complex, that problems like unemployment, famine, and malnutrition are caused by many factors (including rapid population growth), and that an emphasis on policies of slowing population growth without simultaneously confronting the other fundamental causes may well lead to disappointing results.”
Econ/background to week 7 (3).docx
Population Growth and Sustainability
As we just learned, two famous thinkers had very different ideas of whether population growth could be compatible with an improving standard of living. Julian Simon, an economist (pictured at left) and author of The Ultimate Resource (1981), believed that human ingenuity will respond to scarcity with new ideas that permit more substitution for natural resources. Prices will signal scarcity and reward innovators. Our standard of living can be sustained and improved.
Paul Ehrlich (at right), a biologist and author of The Population Bomb (1968), believed that innovations buy only temporary respite from scarcity and mask the fact that we will not survive once natural capital is driven below a critical threshold. Our standard of living cannot be sustained, and is jeopardized more and more by population growth.
In 1980, these two scholars made a bet involving mineral prices which we will discuss in class. Simon was so sure that resources would not rise in price over the next decade that he allowed Ehrlich to choose 5 resources that Ehrlich thought would become more expensive. Ehrlich chose 5 different metals, but they all fell in price between 1980 and 1990.
Not to be outdone, Ehrlich proposed a second bet. This time he wanted to wager that in 2004 compared to 1994 there would be less agricultural soil per person, less rice and wheat grown per person, lower sperm cell counts in human males, fewer plant and animal species in existence, a greater gap between the richest and poorest people, etc. This time Ehrlich was focusing on physical counts rather than dollars values.
Simon declined this new bet, saying it measures changes to human welfare only indirectly.
Models of Economic Growth from Economic Theory
Economic models of growth center on the aggregate production function Y = A F(K,L)
Y = aggregate output of the economy
A = multifactor productivity
F(K,L) = the production function
K = physical capital
L = labour
Innovation or technological progress can be modeled by having A grow, either exogenously (automatically) or endogenously (in response to something in the model, such as population growth).
It turns out that, if A is growing for any reason, it becomes trivial mathematically to have output (Y) and consumption grow, even when population is growing.
Enough technological progress solves all our problems. That may have something to do with the fact that this model ignores the existence of exhaustible natural resources. More on that later.
Because technological progress is so handy for achieving sustainability, Robert Solow (1965) decided to formulate a growth model that has no technological progress.
The Solow Model
The Solow model is almost as simple as the Malthusian model. The key difference between Solow’s model and Malthus’ model is the existence of physical capital and the ability of people to save and build up the capital stock.
In the Solow model, Y = A F(K,L) as usual, but A does not change. The production function F(K,L) can be any positive monotonic function of K and L so long as
· Both K and L must be nonzero if F(K,L) is to be nonzero
· F(K,L) demonstrates diminishing marginal returns to K and to L
· constant returns to scale. That means that, if you double the inputs, you double the output. Similarly, if you divide the inputs by some number, you divide the output by that same number. This makes it possible to express the production process in terms of output per worker.
Because of constant returns to scale, Solow can divides everything by the number of workers so that there is one production process which uses capital-per-worker to produce output-per-worker. Capital-per-worker is denoted by little k and is also called the capital:labour ratio.
Figure 18-1. Output per worker and the capital:labour ratio.
Figure 18-2 shows output-per-worker multiplied by a constant savings rate s. s is just some fraction less than one, since you can’t save everything but must eat some of your output.
Figure 18-2. Savings per worker and the capital:labour ratio.
In the Solow model, fraction sY/L of output is not consumed but is invested, that is, used to build up physical capital (K). Every year, K increases by sY/L. It follows (steps not shown here) that choosing to save/invest amount nk
Equation 18-1. sY/L = nk (n is the rate of growth of population).
then the capital:labour ratio will not change, and output per worker will not change. Society can enjoy a steady output-per-worker and consumption-per-worker forever, even if population is growing.
Equation 18-1 is derived in the appendix to this document if you are interested.
According to Equation 18-1, sustainability requires that a nation must save enough to offset something, something to do with population growth. Let’s have a look at Figure 18-3 to learn more.
Figure 18-3. The Solow condition.
Each of the lines in Figure 18-3 is one side of the Solow condition (Equation 18-1). The equation is satisfied when the lines intersect.
The lines intersect at a particular level of k, called the steady state capital:labour ratio.
It happens that, if the blue savings line is higher than the yellow population line, sY/L > nk and capital accumulates. The capital:labour ratio rises and we move along the horizontal axis until we get to the capital:labour ratio that is compatible with the lines intersecting.
If the amount of savings per worker is insufficient[footnoteRef:1], the opposite is true. The capital:labour ratio falls, and we move leftward until once again, the capital:labour ratio is compatible with the lines intersecting. The intersection is therefore an equilibrium. [1: How can the level of savings be insufficient if the savings rate s is constant? The constant savings rate is applied to a variable amount of output per worker. If the capital:labour ratio is too high, diminishing returns means that the extra tools and machines are not very productive. They are not resulting in enough extra output/enough extra savings to be worth the sacrifice. We should choose a lower capital:labour ratio.]
This is exciting: we can achieve an equilibrium level of capital:worker equilibrium level of output:worker equilibrium level of consumption:worker for any savings rate s.
The key is to realize that, because of population growth, the labour force in the Solow model is constantly growing, so capital per worker is constantly falling. The decrease is the capital:labour ratio due to population growth is called capital shallowing. We can prevent capital shallowing by saving and building enough capital to keep pace with the increasing labour force.
In class we will use the Figure 18-3 to find what happens when
-the savings rate increases
-multifactor productivity (A) increases
-the population growth rate rises or falls
In the real world…
In the real world we observe a positive correlation between savings and output per worker in different countries.
In our model, the savings rate is just a parameter, given without explanation. In real life, the savings rate for a nation depends on government’s and people’s savings decisions. It is not clear how those decisions change in response to changes in the rate of population growth. When the rate of population growth is increasing, it is likely that the child dependency ratio is increasing. When dependency ratios are growing, it is likely that savings will fall as parents devote resources to caring for the young. Kelley (1998) calls this the youth dependency effect. It is also likely that investment in various forms of physical and knowledge capital will fall. Instead, investments in the human capital of the young will be made, via spending on education and healthcare. Most of these investments in human capital will not improve the productivity of the current working generation. Kelley calls this the investment-diversion effect.
The youth dependency effect, the investment-diversion effect, and the capital-shallowing effect are listed in Allan Kelley's 1988 review of the population and economic growth literature as reasons to believe that there is an economic benefit from reducing the rate of population growth. However, Kelley concludes that there is no clear empirical relationship between the population growth rate and per capita output. Many other important factors also influence per capita output, factors like the economy's overall size, its civil and political institutions, its educational achievement, and its openness to trade (Bloom (2003)).
Natural and Environmental Capital
The Solow model suggests that consumption could be sustainable in the face of constant population growth if a sufficient amount of savings and capital investment took place. One might ask if consumption could be sustainable in a more realistic model, one that adds nonrenewable resources - like oil - to the production function.
Although the stock of nonrenewable resources is finite, Solow (1974) and Hartwick (1977) showed that IF physical capital could substitute to some degree for nonrenewables, and IF enough physical capital were accumulated to make up for declining nonrenewables, then a constant consumption level could be found. However, the authors set population growth to zero. Instead of looking at capital shallowing due to population, they were looking at natural resource capital shallowing due to depletion.
Hartwick (@Queen’s) derived the formula for the precise amount of savings/physical capital accumulation needed to make up for declining resource stocks. The amount needed is equal to the amount of resources extracted multiplied by profit on the marginal ton. This amount is known as Total Hotelling Rent. This rule became known as "invest resource rents" or "Hartwick's Rule".
Hartwick's Rule tells us that, if there is no population growth or depreciation of physical capital, then investing resource rents in a different kind of capital will allow us to achieve sustainability in the face of exhaustible resources. However, if there is population growth, even more must be invested. The capital stock must not only be maintained, it must grow, to prevent capital shallowing.
In a later paper which included population growth, Hartwick found that sustainability is only possible if population grows at an arithmetic or quasi-arithmetic[footnoteRef:2] rate. It is NOT possible if population grows exponentially. This hearkens back to Malthus’ assumption that food production could never keep up with a population growing exponentially. [2: In quasi-arithmetic growth, N(t) = a + b(t).]
However, food production has indeed kept up with our surging population, which could be said to grow exponentially on a yearly basis. This is because of technical change and efficiency innovations. Neither Malthus nor Solow nor Hartwick include technical change in their models. That is because the introduction of technical change can guarantee (mathematically) sustainability of consumption.
Criticism of Hartwick's Rule
Hartwick's Rule depends on the production function being the kind where the inputs are multiplied together to yield the output. This means that it is always possible to make up for a shrinking amount of one input by using more of another input. In his model, an expanding stock of K made up for a diminishing stock of natural resources R. Herman Daly, one of the founders of Ecological Economics, has pointed out that there may be critical thresholds below which all the physical capital in the world cannot make up for the loss of natural or environmental capital.
Ecological Economics was established as a discipline in 1990 by economists who were concerned that traditional economics does not adequately consider the economy's size and the population's size relative to the carrying capacity of the environment.
On many occasions in human history, the sustainability of human culture and economic activity has been compromised by environmental degradation.
The case of Easter Island is the most famous example of environmental degradation threatening the human population. But this case has recently been re-interpreted, as discussed in Box 20-1.
Box 20-1. The Case of Easter Island
Also known as Rapa Nui, Easter Island is a 71 square km island in the Pacific Ocean which was settled by people of Polynesian ancestry. Initial radiocarbon date excavations indicated settlement between AD 400-800, with the famous statues of heads having been constructed much later.
Dutch navigator Roggeveen was the first European to encounter the island (1722). Several islanders were shot in the encounter. Roggeveen reported the island as being treeless, and the islanders, starving. Later he revised his account and promoted the island as having great agricultural potential. Scholars such as Jared Diamond (2004) concluded that the islanders, who grew to about 15,000 people, deforested Rapa Nui. Their failure to protect the trees, restrict wasteful activities, and solve social problems precipitated declining living standards.
Recently Hunt and Lipo (2006) have suggested that the population of Rapa Nui was never as large as 15,000 because it was not colonized as early as previously thought. Their carbon dating of sites suggests first settlement at AD 1200 or later. They believe that rats brought on boats with the settlers ate too many of the nuts of the slow-growing palm trees, and in this way destroyed the forest. They also think that the settlers managed well despite the deforestation, until European contact brought disease. Europeans slavers took at least 1,000 people from Rapa Nui in the early 1860s.
Compromise
We can take Hartwick's Rule as suggestive rather than definitive. It recommends something that common sense immediately recognizes: do not allow the stock of your capital to diminish. Invest the profits you make from extracting exhaustible resources. Save for the day your resources run out.
Many nations have created "sovereign wealth funds" to invest the tax revenues that government collects from the oil and gas industry. Alberta had such a fund between 1976-1988, but since then it has chosen to share resource profits with citizens by mailing them cheques. Alaska, Kuwait, and Norway do have such sovereign wealth funds. Chile and Venezuela tax resource extraction profits but instead of saving the money, they use the money to help the government balance its budget.
At the point that investments can no longer make up for declining nonrenewable resource stocks, we have to hope that scientific breakthroughs will save the day.
Genuine Savings
Genuine Savings is an estimate of whether a nation's capital stock (including physical, human, natural, and environmental capital) is really growing or not. If genuine savings is positive, then the nation is wisely building up its capital stock. If genuine savings is negative, then the nation is dissipating its capital.
Here is the calculation:
Genuine savings = investment in physical capital
+ current spending on education (i.e. investment in human capital)
minus depreciation of physical capital (due to wear & tear)
minus Total Hotelling Rent (representing depreciation of exhaustible resources)
minus a charge for over-harvesting renewable resources
minus estimated damages from pollution
If the rate of genuine savings is positive, the nation is accumulating capita or “wealth”. However, capital per worker may still be falling if population is growing. The higher the rate of population growth, the higher the rate of capital accumulation must be in order to keep the capital:labour ratio from falling. This time, capital:labour ratio does not mean just physical capital (K) divided by L, it means all forms of capital divided by L.
In Box 20-2 we see estimated Genuine Savings for several countries, computed by the World Bank.
continued
Box 20-2. Genuine Savings and Capital Shallowing for Selected Nations, 2008
|
|
Genuine savings as a % of Gross National Income (GNI) |
Gap between Genuine savings and what is needed to keep the nation's capital stock intact, taking into account population growth, as % of GNI |
|
Ireland |
7.5 |
None |
|
Norway |
16.2 |
None |
|
Denmark |
13.7 |
None |
|
Dominican Republic |
-0.3 |
3.1 |
|
Canada |
7.6 |
None |
|
Kenya |
10.2 |
10.9 |
|
Mexico |
9.0 |
None |
|
USA |
0.9 |
2.0 |
|
Australia |
15.0 |
None |
|
Romania |
13.7 |
None |
|
Bolivia |
-4.7 |
11.9 |
|
Kuwait |
9.7 |
18.9 |
|
Saudi Arabia |
-1.8 |
27.0 |
Source: Tables D.1 and E.1 World Bank (2011): “The Changing Wealth of Nations: measuring development in the new millennium." Washington D.C.
Appendix: Solow Model Math
This is not testable.
Let K(t) be the capital stock at time t. s is the savings rate. d is the rate at which capital breaks down or becomes obsolete: the depreciation rate. We will set d=0 for simplicity. L(t), the labour force at time t, is growing every year at rate n.
The production function is Y(t) = A(t) F(K(t),L(t)). A(t) is efficiency or technology at time t and we just hold it constant.
Y(t)=A F(K(t),L(t)).
Dividing by L(t), we write y(t) = A f (1, k(t)) where y is output per worker and k is capital per worker.
We can ignore the 1 and write y(t)=Af(k(t)).
The following equation shows how the capital stock grows from year to year:
K(t+1) = K (t) + s Y(t) . Translation: capital next year = capital this year + amount saved minus capital lost to decay and obsolescence.
Rearranging, K(t+1) - K(t) = sY(t) = sAF(K(t),L(t))
What we’re going to do now is divide everything by K(t).
{K(t+1)-K(t)}/K(t) = s AF(K(t),L(t))/K(t)
Using the fact that F(K(t),L(t))/K(t) = {F(K(t),L(t))/L(t)} / {K(t)/L(t)} = f(k)/k
the equation becomes {K(t+1)-K(t)}/K(t) = s Af(k)/k
The left-hand side is “percentage change in K”.
Now the percentage change in little k is equal (by definition) to the percentage change in K minus the percentage change in L. The percentage change in L is the population growth rate, since in this model, everyone is in the labour force. So let’s replace the left-hand side of our Solow equation with the percentage change in k plus n, the population growth rate.
{k(t+1)-k(t)}/k(t) + n = s Af(k)/k(t)
{k(t+1)-k(t)}/k(t) = s Af(k)/k(t) - n
Now multiply both sides by k(t) and we have our final version:
k(t+1) - k(t) = s Af(k(t)) – n k(t) Ta da!
Econ/Background to week 8 (4).docx
Ignoring the rate of growth in population, the absolute size that a population has achieved may have implications for the standard of living.
As discussed last week, the absolute size of a population relative to its natural environment may prove a disadvantage if natural resources are strained. However, there are also advantages to having a large population. The advantages of size include external economies of scale, internal economies of scale, bigger markets, thicker markets, possibly higher rates of innovation, and social development.
In class we will discuss external and internal economies of scale at a national level.
Note that the point at which average costs (the red line in Figure 21-1) are lowest is called a firm’s minimum efficient scale.
Figure 21-1. Typical Cost Curves.
Bigger Markets mean that there is a greater variety of human skills and human wants.
Thicker Markets means that it is easier for buyers and sellers to find each other
Improved innovation is possible if a large country has a large research sector, and if innovation is related to the overall amount of stuff being produced.
Other benefits of population size.
In addition to possible learning-by-doing, research, and economies of scale, there are other material benefits of a large population size. Sheer size of population is important, though not conclusive, militarily. Some groups desire population growth to ensure physical safety. Some groups desire a large population in order to preserve their unique culture, language, or beliefs.
There may be threshold sizes necessary for certain forms of government and jurisprudence to emerge. As previously touched on, Jared Diamond (1997) divides societies into bands, tribes, chiefdoms, and states. Tribes typically have a few hundred people, and this seems to be the upper limit for a group where everyone knows each other.
When the local population gets closer to a thousand, a number of factors favour the emergence of centralized authority:
First, people frequently encounter strangers. If conflict arises, there may be no mutual friends or relatives to mediate the conflict. A dispute-resolving institution is needed.
Second, because most people are strangers to each other, sharing of goods is less natural. A central authority may do a better job in redistributing surpluses to those in need. Generally speaking, communal decision making is no longer practical.
Third, the more densely a territory is populated, the more the population will rely on trade to obtain goods and services. Central authority can help smooth relations with trade partners.
Central authority can do both good and ill. In terms of the economy, central authority can 1) protect people and their property from aggression; 2) redistribute goods and services so that marginalized people can participate in the economy; 3) provide public goods; 4) protect open-access resources; 5) tax activities having negative externalities and subsidize activities having positive externalities; and 6) break up firms having monopoly or monopsony power.
The ability of more centralized societies to command soldiers and resources and to motivate the population toward self-sacrifice are reasons Diamond gives for the rise of more complex societies.
Inferring Rates of Population Growth
In real life, population does not grow or shrink at constant rates because fertility, mortality, and migration are affected by and voluntarily respond to ever-changing conditions. Writes Donald Rowland in his 2003 text, “In the twentieth centuries, dire warnings and apocalyptic forecasts for the planet followed from the assumption that a particular pattern of increase…would persist in the future. The twentieth century also brought forth national population decline, or at least a fear of it, as a recurring theme in some more developed countries….Assumptions about constant rates leading to extinction, however, will be as untenable as those about constant rates creating ever burgeoning numbers.”
Despite the unpredictability of nature and of human behaviour, demographers often use the assumption of constant growth to make forecasts. These forecasts are only as good as the assumption that the status quo birth, death, and migration rates will continue.
The three kinds of constant growth in math are arithmetic, geometric, and exponential growth. They are shown in the Figure below.
Figure 8-1. Arithmetic, Geometric, and Exponential Growth
Arithmetic Growth
In the context of height, arithmetic growth means growing a set number of inches per year regardless of how tall you already are. It is like earning a fixed amount of interest each year: the interest does not compound, but is paid only against the initial amount deposited.
Malthus assumed erroneously that agricultural output could only grow arithmetically, for example by clearing a fixed number of additional acres each year. Even he knew that population does not grow arithmetically, but in proportion to the base population. Nevertheless, we sometimes use the assumption of arithmetic population growth, especially for short time periods. Thus, to find the mid-year population, we simply assume that population was growing arithmetically during the year: we sum the population at the beginning of the year with the population at the end of the year, and divide by two.
Often, researchers take a rate of growth for an entire year, and divide it by twelve to get the monthly growth rate. Dividing a growth rate in equal parts to get a sub-period growth rate implicitly assumes arithmetic growth. This assumption is made even when a population is growing exponentially. The assumption is made so that sub-period rates can be calculated easily.
Let it be that:
P(0) is the initial level of immigration
P(1) is the immigration size one period later.
If the immigration grows arithmetically, then P(1) = P(0) + c, where c is some constant unrelated to P(0).
In 1941, 9,239 people immigrated to Canada. In 1971, 121,900 people immigrated to Canada. If we assume that immigration grew arithmetically, then we take the difference between 121,900 and 9,239, and divide by 30 years, to say that immigration grew by 3,755.4 people per year.
To find the total number of people who immigrated between 1941 and 1971, we would do this:
9,239 + (9,239+3,755.5) + (9,239+2(3,755.5)) + … =
which is equal to 31(9,239) + 3,755.4 (30) (31)/2 using the fact that summation of the numbers from 0 to n = n (n+1) / 2
which is equal to 2,032,484 people.
Geometric and Exponential Growth
Geometric growth is like growing a fixed percentage of your initial height at the beginning of each year or month. It is like the growth of your bank account when the interest you earn each period compounds.
r, the rate of growth over the period, is defined as { {P(1)-P(0)}/P(0) }
Equivalently,
P(1) = P(0) (1+r), where r is the rate of growth over the period.
P(2) = P(0) (1+r) (1+r) = P(0) (1+r)2
Generally,
P(n) = P(0) (1+r)n, where n is the number of periods that have gone by.
If we shorten the time between intervals when the “interest” is reckoned, we have continuous compounding i.e. exponential growth. “r" is still the official, annual rate of growth, but a fraction of it is implemented every second.
P(1) = P(0) er
Generally,
P(n) = P(0) er n
Exponential growth occurs when the interval at which growth or interest is compounded shrinks down to almost zero. It is like growing a percentage of your height, every second, with your height being constantly updated. Exponential growth is smooth and continuous, which seems more realistic than geometric growth. However, real-life growth tends to come in spurts and fits, and there is certainly a turnaround time before a new baby can reproduce him or herself. So constant exponential population growth is not all that realistic an assumption.
Incidentally, Rowland (2003) points out that “The world’s population growth rate has never exceeded 2.1 per cent [per year] (doubling time 33 years), and the growth rate has been falling since the mid-1960s.”
A rate such as 2.1 per cent begs the question 2.1 per cent of what? and lets you know that we are talking either about geometric or exponential growth. Usually in demography, we are talking about exponential growth.
Doubling Time
To find doubling time, simply divide the number 70 by the average growth rate per period. For example, if the growth rate is 2.1% per year, then the approximate time it will take for the population to double is 70/2.1 = 33.3 years. This is the “Rule of 70” which comes from the mathematics of exponential growth.
Here is the explanation. We know that P(n) = P(0) er n
or P(n)/P(0) = e r n
We know that the population doubles, so that P(n) = 2 P(0).
Hence
2 = er n
ln (2) = r n
n, the number of periods required for doubling = ln(2)/ r ≈ 0.70/ r, where r is expressed as a decimal. (If using 70 instead of 0.70, r is expressed as a percent as in 70/2.1 = 33.3 years).
Now that you know how to calculate doubling time, have a look at Box 10-2 for another interesting application of the mathematics of exponential growth.
Immigration example revisited
In 1941, 9,239 people immigrated to Canada. In 1971, 121,900 people immigrated to Canada. If we assume that immigration grew geometrically, we can solve for the annual rate of growth this way:
121,900 = 9,239 (1+r)30
13.19 = (1+r)30
(13.19)1/30 = 1+r
1.09 = 1+r
r =0.09 or nine percent.
How many people immigrated during the period? That would be:
9,239 + 9,239(1.09) + 9,239(1.09)2 +9.239 (1.09)3 + … =
If we assume that immigration grew exponentially, we can solve for the rate of growth this way:
121,900 = 9,239 e30r
13.19 = e30r
ln(13.19) = 30 r
2.58 = 30 r so r = 0.086 or 8.6 percent.
How many people immigrated during the period? That would be:
which, unlike our other expressions for the total number of immigrants, is easy to solve using the formula
In this case, the total number of immigrants arriving between 1941 and 1971 is
(1/.086) (9,239) (e.086(30) – e.086(0)) = 1,310,341.4
In reality, the number of immigrants entering the country between 1941 and 1971 was 3,597,689. In reality, the immigration rate was neither smooth nor exponential.
Does it seem funny that our exponential growth assumption resulted in the smallest estimate of total immigrants? Recall that really big gains from exponential growth are not evident for a while. It "takes a while to get started". That is true of geometric growth as well.
In Box 8-1 we use exactly the same math to estimate the number of people who have ever been born.
Box 8-1. The number of people who have ever lived.
Keyfitz and Caswell (2005) explain how to compute the number of people who have ever lived on earth. The calculation is very similar to finding the total number of immigrants over a period. Think of babies as immigrants from heaven.
First, you need estimates of annual births at various time periods. Cook (1962) estimated that there was 1 birth at 600,000 BC, 250,000 annual births by 6,000 BC, 25 million births annual in 1650 AD, and 110 million births annually by 1962 AD.
Next, find the implied growth rate in births between each period. For example, annual births grew from 25 million in 1650 to 110 million by 1962. If r is the constant exponential growth rate in births, then we find r by solving
110 million = 25 million e312r , where 312 is the number of years between 1650 and 1962.
This equation gives us an assumed constant exponential growth rate of 0.475 percent.
Now that we know the growth rate in annual births during the period, we can calculate the number of births during the period using integration.
= {25,000,000 e312(0.00475) – 25,000,000e0(0.00475)}/0.00475
because the integral of eax is (1/a) eax + c
= 17.9 billion people born between 1650 and 1962.
Performing the same calculation for the time periods 600,000 BC - 6,000 BC, and 6000BC – 1650 AD, approximately 70.9 billion people in total were born prior to 1962, so today’s population of less than 7 billion does not even come close to matching the number of people who have lived previously.
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Econ/background to week 9 (2).doc
Forecasting population size and age structure
Earlier in the term we learned that birth rates can be misleading, because they are based on particular populations, which populations have varying proportions of women of childbearing age.
To get a better idea of the reproductive force of a population, we use the total fertility rate (TFR) to predict how many children each woman will have at current age-specific fertility rates.
The birth rate depends on the age specific fertility rates and the proportion of women of different ages in the population.
Similarly, the death rate depends on age-and-sex-specific mortality rates and the share of different age groups of men and women in the population.
Stable and Stationary Populations
In demography we like to predict what the population will look like in the future. Since almost anything can happen to birth, death, and immigration rates, there is no way to know this for sure. We like to assume that “present trends continue.” We can do this by studying a hypothetical “stable population” based on today’s fertility and mortality rates.
A stable population is one where
· There is no immigration or emigration
· age-specific fertility rates do not change
· age-and-sex-specific mortality rates do not change
· enough time has passed for the age structure of the population to stabilize.
When fertility rates are constant, and enough time has passed for the age structure to stabilize, then birth rates will be constant.
But if the age structure changes, birth rates will change, and the overall population growth rate will change.
Consider a population where fertility has recently dropped. The birth rate will not necessarily immediately fall. Fertility may have dropped, but there may be a larger number of women of childbearing age this year than there was last year DUE TO RISING FERTILITY TWENTY YEARS AGO.
Currently Canada is experiencing a baby boom, an uptick in the birth rate. Much of this is due to the fact that, during the late 1940s and the 1950s and the early 1960s, many Canadians were born – our Baby Boom Generation. The grandchildren of these boomers are now reaching child-bearing age. Also, many of the children of the baby boom generation delayed having children and are having them now.
So the birth rate, and, consequently, the population growth rate, is not going to stabilize until the fertility rate has remained constant for some time. Eventually, the age structure of the population will stabilize, and so birth rates will stabilize also given a constant fertility rate.
Later in this unit we will learn how to calculate the age structure of a stable population. We will also learn how to calculate the rate of growth (or shrinkage) of a stable population. The rate of growth of a stable population is called the intrinsic rate of natural increase.
Stationary Populations
A stationary population is a stable population, so the fertility and mortality rates are constant, and there is no migration. Like a stable population, a stationary population achieves a stable age mix eventually, and a stable rate of natural increase called the intrinsic rate. The thing that distinguishes a stationary population from other stable populations is that its intrinsic rate of natural increase is exactly equal to zero. This means that, once the population has stabilized, the same number of people are born as die, each year.
This stationary state is unlikely to persist in real life, but it allows us to pursue an interesting question: If fertility rates drop or mortality rates rise enough that the (eventual) rate of natural increase becomes zero...at what age structure would the population stabilize? And what would the population size become before population growth settles down at zero?
Once the stationary population stabilizes, there is no growth or shrinkage. But this does not happen right away. Though we have the correct fertility rates and mortality rates, the birth and death rates will only come into balance once the age structure has stabilized. The population keeps growing –or shrinking- for a while because the current age structure is different from the ultimate age structure.
Consider the case where the population has been growing, but now fertility rates drop to a level compatible with stationarity. However, the proportion of children in the population is not yet what it will eventually be. The proportion of children is higher than what it eventually will become. These young people will grow into adults; they may have the low stationary fertility rate, but because there are more of them than in the stable state, they will have more children than the stable cohort of parents would have. It will take a while before the number of newborns falls to the stationary level.
Conversely, if we begin with a population that is shrinking, we could ask what would happen if birth rates rose and death rates fell such that the rate of natural increase rose to zero. The stationary population will not shrink, but it will take a number of periods or shrinkage before stationarity is achieved. During the time of adjustment, the number of children is lower because previous generations had lower fertility rates than what they now have. This small band of children may have new, higher fertility rates, but because there are so few of them, it will take a while before the stable number of newborns is achieved.
Population Momentum
The degree to which a population - if its rate of natural increase became zero - would continue to grow or shrink before reaching its stationary size is called population momentum. Population momentum is growth (or decline) that comes only from the maturation of different age groups before the stable age structure is achieved.
There are different ways to measure population momentum. One way is
pm = stationary population size to the current/initial population size.
If the ratio is a number greater than 1, population momentum is positive, with growth occurring before zero population growth (ZPG) is achieved. If the ratio is less than one, population momentum is “negative”, with shrinkage expected before ZPG is achieved.
Sometimes population momentum is approximated using this rough ratio:
momentum factor = crude birth rate multiplied by life expectancy. (UN, World Development Indicators).
Figure 7-1. Population Momentum.
Source: Rowland (1995). Right of use purchased. A score of 60% means the projected stationary population, assuming fertility rates immediately drop to replacement levels, would be 60% larger than the current population.
continued
Using a Matrix to Forecast a Population’s Size and Composition
In this section we will learn how to project a detailed population forward in time, assuming constant fertility and mortality rates.
We will also be able to predict the population’s eventual age structure. I’ll also tell you how the intrinsic rate of natural increase can be found, though I will not attempt this calculation.
The easiest way to show the various age groups using math is to use vectors and matrices.
Let n(t) be a vector with s # rows and 1 column. Each row represents an age group at time t. There are s age groups. The numbers in the row represent the number of gerbils, say, in each age group. Perhaps there are only three age groups, age newborn, age 1 and age 2.
Let there be 10 gerbils in each age group at time t. So n(t) =
10
10
10
To figure out how fast this population will grow, and what the stable age mix is, we need to know how quickly the gerbils reproduce, and what their survival rates are.
Perhaps newborns have a 40% chance of surviving until age 1. Perhaps one year olds have a 20% chance of surviving until age 2. Perhaps two year olds have a 0% chance of surviving until age 3. Perhaps newborns cannot reproduce, but female one year olds have on average 6 live newborns during the year, and female two year olds have on average 6 newborns also. Figure 8-1 illustrates this.
Figure 8-1. Age Group Relationships
In this example, all the age groups are related. For example, not only do one year olds become two year olds, but one year olds generate newborns. Such a set of relationships lends itself well to matrix algebra. A matrix A, with s # rows and s # columns, can summarize this information, and can explain how n(t) becomes n(t+1) a year later. n(t+1) is a vector of the number of gerbils in each age group in the next period, t+1.
n(t+1) = A n(t)
Based on the survival and reproduction data given above, A =
0
2
.
0
0
0
0
4
.
3
3
0
0
We use “3” instead of “6”, because although there are 6 newborns per female, only half the gerbils are female; on average there will be 3 newborns per adult gerbil.
Basically, each column belongs to an age group, with the leftmost column representing the youngest age group. The first row is the fertility row, showing how many babies are contributed per gerbil in each age group. The subsequent rows are survival rows. The second row shows what percentage of gerbils make it to the first age group. It is 0.4,0,0 because 40% of newborns make it to age 1, no 1 year olds turn 1, and no 2 year olds turn 1. The last row shows how many gerbils make it to the last age group. There is no subsequent row because all gerbils in the last age group die (by definition of the "last age group").
To find how many babies there will be next year, we multiply the baby row in A by the age groups in n(t). To find out how many one-year-old there will be next year, we multiply the second row of A by the age groups in n(t). Multiplying the rows in A by the columns in n(t) is the correct way to perform matrix algebra.
The general rule is that, when you multiply matrix A and matrix B, you multiply the ith row of A by the jth column of B to get the ijth element of the resulting matrix C. This means that the number of columns in A needs to equal the number of rows in B, or there won't be enough items in the rows of A to multiply with the number of items in the columns of B.
Since n is just a single column, we will be multiplying each row of A by n(t) to get our new column n(t+1).
Recall that we start out with 10 gerbils in each age group. n(t) =
10
10
10
To get the first row of n(t+1), i.e. the number of newborns next period, we multiply the first row of A by n(t) like this: 0*10 + 3*10 + 3*10 = 60 newborns. Our calculation shows us that newborns do not give birth to any newborns, but the 10 one-year-olds (male or female) give birth to an average of 3 babies each, as do the 10 two year olds.
To get the second row of n(t+1), we perform 0.4*10 + 0*10 + 0*10 = 4 to show that there will only be 4 one-year-olds next year, since only 40% of today’s ten newborns will survive, and today’s one-year-olds and two-year-olds cannot become tomorrow’s one-year-olds.
Finally, to find out how many two-year-olds there will be next period, we must multiply the third row of A by n(t) to find that there will be 2 two-year-olds next year.
Our vector n(t+1) becomes
2
4
60
and the population, just one year later, is now composed of 60 newborns plus 4 one-year-olds, plus 2 two-year-olds, for a total of 66 gerbils.
Figure 8-2. Initial Population Age Structure
0246810
number of gerbils
0
2
4+
age group
Gerbil Age Structure - Year 1
Figure 8-3. Age Structure One Year Later
0204060
0
2
4+
age group
Gerbil Age Structure - Year 2
What a difference! The magic in the math is that eventually, – usually in less than 70 periods - the age distribution will stabilize. Because the age distribution stabilizes, the population’s growth rate – and the growth rate of every single age group - stabilizes too.
The point of writing the population’s dynamics in matrix form is that, once it is in matrix form, it is very “easy” to see what will happen to the population in the distant future.
To find what the population will look like in 70 years, “simply” compute
n(t + 70) = A70 n(t)
A computer can do this easily.
One can also find, using a computer or matrix algebra, the eigenvalues of A. An eigenvalue is a number, λ, that, together with some non-zero vector v(t), can "take the place of" matrix A in the equation:
A v(t) = λ v(t)
The largest, positive, real eigenvalue happens to be related to the intrinsic rate of population growth! Take the natural logarithm of this eigenvalue and you have the intrinsic rate of natural increase/decrease. I do not expect you to perform this calculation.
One can also use algebra to calculate the intrinsic rate of natural increase using the survival and reproduction rates, but this calculation is very complicated. For the gerbils above, the intrinsic rate of natural increase is approximately 0.185 or 18 and a half percent. We found this by running simulations of the gerbil population, one year at a time, using a computer spreadsheet. The growth rate stabilized after 14 years.
Calculating the stable age structure
Once we have the intrinsic rate of growth, we can predict the stable age distribution. We do this in Table 8-2. For each age group, the number of people in the i-th age group is related to the number of newborns i years ago by the exponential growth factor eir and the survival rates.
For example, how many one year olds will there be compared to the number of newborns? Call the number of newborns NN. Since the population (and all its age groups) are growing steadily at 18.5%, there must have been about 16 percent fewer newborns last year. 40% of these would have survived, meaning that there are 0.3324 NN one-year-olds now.
Table 8-2. Calculating Population Age Composition Using the Intrinsic Rate of Natural Increase
|
|
Chance of surviving to next age |
Number in this age group should be… |
Which equals what? when r = .185 |
Number as a fraction of the total population |
|
Newborns |
40 % |
Call this NN |
NN |
NN/1.3877 NN = 0.72 |
|
One year olds |
20% |
.40 NN e-r |
0.3324 NN |
0.3324 NN/ 1.3877 NN = 0.24 |
|
Two year olds |
0% |
(.20) (.40) NN e-2r |
0.0553 NN |
0.0553 NN/ 1.3877 NN= 0.04 |
|
Total population |
|
|
NN(1+0.3324+0.0553) = 1.3877 NN |
1.3877 NN/ 1.3877 NN = 1 |
We see that the age distribution eventually becomes 72% newborns, 24% one-year-olds, and 4% two-year-olds. We started with 33% newborns, 33% one-year-olds, and 33% two-year-olds, but once the reproductive and survival rates start working, the population rapidly converged to the stable age distribution and to the intrinsic rate of natural increase. Using a spreadsheet you can confirm that, after only 14 periods, the gerbil population is up to 439 individuals, with an age distribution of 74:21:4, very close to 72:24:4. The stable distribution 72:24:4 is achieved by the end of year 26 and lasts as long as the fertility and survival rates do not change.
Figure 8-4. Population Age Structure after 13 Years
050100150200250300
number of gerbils
0
1
2
3
4+
age group
Gerbil Age Structure - Year 14
By the 40th year or 40th period we have 36,692 gerbils, up 18.5% from the year before. The age distribution is still the same, with each age group also up 18.5 % from the year before.
Figure 8-5. Population Age Structure 39 Years Later
050001000015000200002500030000
number of gerbils
0
1
2
3
4+
age group
Gerbil Age Structure - Year 40
An example of population projection
Vallin et al. (2002) (see Figure 25-3 in previous chapter) investigate crisis deaths in the Ukraine in the 1930s and 1940s. The problem is, no death statistics were published between 1931 and 1954. They must estimate both the number of total deaths and the number of crisis deaths. Their solution is to begin with a 1926 census and predict how many people should be alive in 1939 (when there is another census). To predict how many people there are expected to be in the later census, they need to apply –perhaps using a Leslie matrix - some estimate of mortality rates and fertility rates to the population alive in the earlier census. The difference between how many people should be alive and how many are alive gives us the number of unexpectedly missing –though not necessarily dead - people (more detail to follow). They do the same thing with the 1939 and 1959 censuses.
There are three reasons that the actual population in the 1939 census would be smaller than the 1939 population which has been estimated by using the 1926 census and projecting it forward, three reasons why people would be missing.
The first reason is that some people left the country. The second reason is that fertility was actually lower than what was assumed when making the projection. And the third reason is that mortality was actually higher than was assumed when making the projection. The idea is that the crises in Ukraine caused extra deaths, extra emigration, and lower fertility.
Vallin et al. assume that, without the famines and conflicts that occurred, mortality rates would have fallen steadily over the period in question, as in other nations. He uses other countries’ mortality rates to make his projection. It is not clear what fertility would have done in the absence of those events. Fertility had been falling in the 1920s, as in other countries, but surged after the famine of the early 1930s ended. The surge could be a consequence of the recovery and/or a consequence of Soviet policy aimed at increasing fertility. Vallin et al. make a conservative (i.e. low) estimate of what fertility would have been without the crises, which if anything will underestimate the births foregone due to the crisis.
Vallin et al.'s approach can be summarized as follows:
For each age-sex group:
projected population in year X on the basis of a previous year's census, using estimates of non-crisis age-specific mortality and non-crisis fertility rates i.e. what it would have been without the crises
minus actual population in year X
= total population loss (due to crisis deaths, births foregone due to the crisis, and net emigration)
projected population in year X on the basis of a previous year's census, using estimates of non-crisis age-specific mortality rates and actual fertility rates
minus actual population in year X
= population loss due to crisis deaths and net emigration
minus estimates of net emigration
=population loss due to crisis deaths
Vallin et al. conclude that between 1926 and 1939, Ukraine experienced a total population loss of 4.6 million people out of 29 million (1926). That’s about 16% of the initial population. However, births continued and the population did grow, nearing 31 million in 1939. Vallin et al. estimate that 0.9 million people left the country, voluntarily or, often, involuntarily; 1 million people were not born because of the crisis; and 2.6 million people died because of the crisis.
� The intrinsic rate of natural increase can be calculated as (ln R)/ (R1/R – 0.7 ln R), where R is the net reproduction rate, and R1 is the mean length of a generation. The net reproduction rate and the mean length of a generation have to be computed from fertility and survival rates.