as the population increases the value of life decreases essay

Essay on Population Growth for Students and Children

500+ words essay on population growth.

There are currently 7.7 billion people on our planet. India itself has a population of 1.3 billion people. And the population of the world is rising steadily year on year. This increase in the population, i.e. the number of people inhabiting our planet is what we call population growth. In this essay on population growth, we will see the reasons and the effects of this phenomenon on our planet and our societies.

One important feature of population growth is that over the last century it has shown exponential growth. When the pattern of increase is by a fixed quantity, we call this linear growth, for example, 3, 5, 7, 9 and so on. Exponential growth shows an increase by a fixed percentage, for example, 2, 4, 8, 16, 32 and so on. This exponential growth is the reason our population has seen such an immense increase over the past century and a half.

Causes of Population Growth

To fully understand the phenomenon, in this essay on population growth we will discuss some of its causes. Understanding the reasons for such exponential growth will help us better understand how to plan for the future. So let us begin with one of the main causes, which is the decline in the mortality rate.

Over the last century, we have made some very significant and notable advancements in medicine, science, and technology. We have invented vaccines, found new treatments and even almost completely eradicated some life-threatening diseases. This means that people now have a much higher life expectancy than their ancestors.

Along with the decrease in mortality rate, these advancements in medicine and science have also boosted the birth rates. We now have ways to help those with infertility and reproductive problems. Hence, birth rates around the world have also seen massive improvements. This coupled with slowing mortality rates has caused overpopulation.

Often the lack of proper education is also stated as the culprit of rampant overpopulation. People around the world need to be made aware of the ill-effects of global overpopulation. Values of family planning and sustainable growth needs to be instilled not only in children but adults also. The lack of this awareness and education is one of the reasons for this growth in population.

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Effects of Population Growth

This exponential population growth that our planet has experienced over the last 150 years has had some severe negative effects. The most obvious and common impact is that overpopulation has put a great strain on the natural resources of the earth. As we know, some of the resources available to us come in limited quantities, for example, fossil fuels. When the population explosion happened, these resources are becoming rarer and will one day run out completely.

The increased population had also lead to increased pollution and industrialization . This has adversely affected our natural environment leading to more health problems in the majority of the population. And as the population keeps growing, the poorer countries are running out of food and other resources causing famines and various such disasters.

And as we are currently noticing in India, overpopulation also leads to massive unemployment. Overall the economic and financial condition of densely populated regions deteriorates due to the population explosion.

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Understanding Global Change

Discover why the climate and environment changes, your place in the Earth system, and paths to a resilient future.

Population growth

Population growth is the increase in the number of humans on Earth. For most of human history our population size was relatively stable. But with innovation and industrialization, energy, food , water , and medical care became more available and reliable. Consequently, global human population rapidly increased, and continues to do so, with dramatic impacts on global climate and ecosystems. We will need technological and social innovation to help us support the world’s population as we adapt to and mitigate climate and environmental changes.

World human population growth from 10,000 BC to 2019 AD. Data from: The United Nations

Human population growth impacts the Earth system in a variety of ways, including:

• Increasing the extraction of resources from the environment. These resources include fossil fuels (oil, gas, and coal), minerals, trees , water , and wildlife , especially in the oceans. The process of removing resources, in turn, often releases pollutants and waste that reduce air and water quality , and harm the health of humans and other species.
• Increasing the burning of fossil fuels for energy to generate electricity, and to power transportation (for example, cars and planes) and industrial processes.
• Increase in freshwater use for drinking, agriculture , recreation, and industrial processes. Freshwater is extracted from lakes, rivers, the ground, and man-made reservoirs.
• Increasing ecological impacts on environments. Forests and other habitats are disturbed or destroyed to construct urban areas including the construction of homes, businesses, and roads to accommodate growing populations. Additionally, as populations increase, more land is used for agricultural activities to grow crops and support livestock. This, in turn, can decrease species populations , geographic ranges , biodiversity , and alter interactions among organisms.
• Increasing fishing and hunting , which reduces species populations of the exploited species. Fishing and hunting can also indirectly increase numbers of species that are not fished or hunted if more resources become available for the species that remain in the ecosystem.
• Increasing the transport of invasive species , either intentionally or by accident, as people travel and import and export supplies. Urbanization also creates disturbed environments where invasive species often thrive and outcompete native species. For example, many invasive plant species thrive along strips of land next to roads and highways.
• The transmission of diseases . Humans living in densely populated areas can rapidly spread diseases within and among populations. Additionally, because transportation has become easier and more frequent, diseases can spread quickly to new regions.

Can you think of additional cause and effect relationships between human population growth and other parts of the Earth system?

Visit the burning of fossil fuels , agricultural activities , and urbanization pages to learn more about how processes and phenomena related to the size and distribution of human populations affect global climate and ecosystems.

Investigate

Learn more in these real-world examples, and challenge yourself to  construct a model  that explains the Earth system relationships.

• The Ecology of Human Populations: Thomas Malthus
• A Pleistocene Puzzle: Extinction in South America

Links to Learn More

• United Nations World Population Maps
• Scientific American: Does Population Growth Impact Climate Change?

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

19.2 Population Growth and Decline

Learning objectives.

• Understand demographic transition theory and how it compares with the views of Thomas Malthus.
• Explain why there is less concern about population growth now than there was a generation ago.
• Explain what pronatalism means.

Now that you are familiar with some basic demographic concepts, we can discuss population growth and decline in more detail. Three of the factors just discussed determine changes in population size: fertility (crude birth rate), mortality (crude death rate), and net migration. The natural growth rate is simply the difference between the crude birth rate and the crude death rate. The U.S. natural growth rate is about 0.6% (or 6 per 1,000 people) per year (Rosenberg, 2009). When immigration is also taken into account, the total population growth rate has been almost 1.0% per year (Jacobsen & Mather, 2010).

Figure 19.6 “International Annual Population Growth Rates (%), 2005–2010” depicts the annual population growth rate (including both natural growth and net migration) of all the nations in the world. Note that many African nations are growing by at least 3% per year or more, while most European nations are growing by much less than 1% or are even losing population, as discussed earlier. Overall, the world population is growing by about 80 million people annually.

Figure 19.6 International Annual Population Growth Rates (%), 2005–2010

Source: Adapted from http://en.wikipedia.org/wiki/File:Population_growth_rate_world_2005-2010_UN.PNG .

To determine how long it takes for a nation to double its population size, divide the number 70 by its population growth rate. For example, if a nation has an annual growth rate of 3%, it takes about 23.3 years (70 ÷ 3) for that nation’s population size to double. As you can see from the map in Figure 19.6 “International Annual Population Growth Rates (%), 2005–2010” , several nations will see their population size double in this time span if their annual growth continues at its present rate. For these nations, population growth will be a serious problem if food and other resources are not adequately distributed.

Demographers use their knowledge of fertility, mortality, and migration trends to make projections about population growth and decline several decades into the future. Coupled with our knowledge of past population sizes, these projections allow us to understand population trends over many generations. One clear pattern emerges from the study of population growth. When a society is small, population growth is slow because there are relatively few adults to procreate. But as the number of people grows over time, so does the number of adults. More and more procreation thus occurs every single generation, and population growth then soars in a virtual explosion.

We saw evidence of this pattern when we looked at world population growth. When agricultural societies developed some 12,000 years ago, only about 8 million people occupied the planet. This number had reached about 300 million about 2,100 years ago, and by the 15th century it was still only about 500 million. It finally reached 1 billion by about 1850 and by 1950, only a century later, had doubled to 2 billion. Just 50 years later, it tripled to more than 6.8 billion, and it is projected to reach more than 9 billion by 2050 (U.S. Census Bureau, 2010) (see Figure 19.7 “Total World Population, 1950–2050” ).

Figure 19.7 Total World Population, 1950–2050

Source: Data from U.S. Census Bureau. (2010). Statistical abstract of the United States: 2010 . Washington, DC: U.S. Government Printing Office. Retrieved from http://www.census.gov/compendia/statab .

Eventually, however, population growth begins to level off after exploding, as explained by demographic transition theory , discussed later. We see this in the bottom half of Figure 19.7 “Total World Population, 1950–2050” , which shows the average annual growth rate for the world’s population. This rate has declined over the last few decades and is projected to further decline over the next four decades. This means that while the world’s population will continue to grow during the foreseeable future, it will grow by a smaller rate as time goes by. As Figure 19.6 “International Annual Population Growth Rates (%), 2005–2010” suggested, the growth that does occur will be concentrated in the poor nations in Africa and some other parts of the world. Still, even there the average number of children a woman has in her lifetime dropped from six a generation ago to about three today.

Past and projected sizes of the U.S. population appear in Figure 19.8 “Past and Projected Size of the U.S. Population, 1950–2050 (in Millions)” . The U.S. population is expected to number about 440 million people by 2050.

Figure 19.8 Past and Projected Size of the U.S. Population, 1950–2050 (in Millions)

Views of Population Growth

Thomas Malthus, an English economist who lived about 200 years ago, wrote that population increases geometrically while food production increases only arithmetically. These understandings led him to predict mass starvation.

Wikimedia Commons – public domain.

The numbers just discussed show that the size of the United States and world populations has increased tremendously in just a few centuries. Not surprisingly, people have worried about population growth and specifically overpopulation at least since the 18th century. One of the first to warn about population growth was Thomas Malthus (1766–1834), an English economist, who said that population increases geometrically (2, 4, 8, 16, 32, 64, 128, 256, 512, 1024…). If you expand this list of numbers, you will see that they soon become overwhelmingly large in just a few more “generations.” Malthus (1798/1926) said that food production increases only arithmetically (1, 2, 3, 4, 5, 6…) and thus could not hope to keep up with the population increase, and he predicted that mass starvation would be the dire result.

During the 1970s, population growth became a major issue in the United States and some other nations. Zero population growth , or ZPG, was a slogan often heard. There was much concern over the rapidly growing population in the United States and, especially, around the world, and there was fear that our “small planet” could not support massive increases in the number of people (Ehrlich, 1969). Some of the most dire predictions of the time warned of serious food shortages by the end of the century.

Fortunately, Malthus and ZPG advocates were wrong to some degree. Although population levels have certainly soared, the projections in Figure 19.7 “Total World Population, 1950–2050” show that the rate of increase is slowing. Among other factors, the development of more effective contraception, especially the birth control pill, has limited population growth in the industrial world and, increasingly, in poorer nations. Food production has also increased by a much greater amount than Malthus and ZPG advocates predicted. Concern about overpopulation growth has weakened, as the world’s resources seem to be standing up to population growth. Widespread hunger in Africa and other regions does exist, with hundreds of millions of people suffering from hunger and malnutrition, but many experts attribute this problem not to overpopulation and lack of food but rather to problems in distributing the sufficient amount of food that exists. The “Sociology Making a Difference” box discusses these problems.

Calls during the 1970s for zero population growth (ZPG) population control stemmed from concern that the planet was becoming overpopulated and that food and other resources would soon be too meager to support the world’s population.

James Cridland – Crowd – CC BY 2.0.

Another factor might have played a role in weakening advocacy for ZPG: criticism by people of color that ZPG was directed largely at their ranks and smacked of racism. The call for population control, they said, was a disguised call for controlling the growth of their own populations and thus reducing their influence (Kuumba, 1993). Although the merits of this criticism have been debated, it may have still served to mute ZPG advocacy.

Sociology Making a Difference

World Hunger and the Scarcity Fallacy

A popular belief is that world hunger exists because there is too little food to feed too many people in poor nations in Africa, Asia, and elsewhere. Sociologists Stephen J. Scanlan, J. Craig Jenkins, and Lindsey Peterson (2010) call this belief the “scarcity fallacy.” According to these authors, “The conventional wisdom is that world hunger exists primarily because of natural disasters, population pressure, and shortfalls in food production” (p. 35). However, this conventional wisdom is mistaken, as world hunger stems not from a shortage of food but from the inability to deliver what is actually a sufficient amount of food to the world’s poor. As Scanlan and colleagues note,

This sociological view has important implications for how the world should try to reduce global hunger, say these authors. International organizations such as the World Bank and several United Nations agencies have long believed that hunger is due to food scarcity, and this belief underlies the typical approaches to reducing world hunger that focus on increasing food supplies with new technologies and developing more efficient methods of delivering food. But if food scarcity is not a problem, then other approaches are necessary.

Scanlan and colleagues argue that food scarcity is, in fact, not the problem that international agencies and most people believe it to be:

If the problem is not a lack of food, then what is the problem? Scanlan and colleagues argue that the real problem is a lack of access to food and a lack of equitable distribution of food: “Rather than food scarcity, then, we should focus our attention on the persistent inequalities that often accompany the growth in food supply” (p. 36).

What are these inequalities? Recognizing that hunger is especially concentrated in the poorest nations, the authors note that these nations lack the funds to import the abundant food that does exist. These nations’ poverty, then, is one inequality that leads to world hunger, but gender and ethnic inequalities are also responsible. For example, women around the world are more likely than men to suffer from hunger, and hunger is more common in nations with greater rates of gender inequality (as measured by gender differences in education and income, among other criteria). Hunger is also more common among ethnic minorities not only in poor nations but also in wealthier nations. In findings from their own research, these sociologists add, hunger lessens when nations democratize, when political rights are protected, and when gender and ethnic inequality is reduced.

If inequality underlies world hunger, they add, then efforts to reduce world hunger will succeed only to the extent that they recognize the importance of inequality in this regard: “To get at inequality, policy must give attention to democratic governance and human rights, fixing the politics of food aid, and tending to the challenges posed by the global economy” (p. 38). For this to happen, they say, food must be upheld as a “fundamental human right.” More generally, world hunger cannot be effectively reduced unless and until ethnic and gender inequality is reduced. Scanlan and colleagues conclude,

In calling attention to the myth of food scarcity and the inequalities that contribute to world hunger, Scanlan and colleagues point to better strategies for addressing this significant international problem. Once again, sociology is making a difference.

Demographic Transition Theory

Other dynamics also explain why population growth did not rise at the geometric rate that Malthus had predicted and is even slowing. The view explaining these dynamics is called demographic transition theory (Weeks, 2012), mentioned earlier. This theory links population growth to the level of technological development across three stages of social evolution. In the first stage, coinciding with preindustrial societies, the birth rate and death rate are both high. The birth rate is high because of the lack of contraception and the several other reasons cited earlier for high fertility rates, and the death rate is high because of disease, poor nutrition, lack of modern medicine, and other problems. These two high rates cancel each other out, and little population growth occurs.

In the second stage, coinciding with the development of industrial societies, the birth rate remains fairly high, owing to the lack of contraception and a continuing belief in the value of large families, but the death rate drops because of several factors, including increased food production, better sanitation, and improved medicine. Because the birth rate remains high but the death rate drops, population growth takes off dramatically.

In the third stage, the death rate remains low, but the birth rate finally drops as families begin to realize that large numbers of children in an industrial economy are more of a burden than an asset. Another reason for the drop is the availability of effective contraception. As a result, population growth slows, and, as we saw earlier, it has become quite low or even gone into a decline in several industrial nations.

Demographic transition theory, then, gives us more reason to be cautiously optimistic regarding the threat of overpopulation: as poor nations continue to modernize—much as industrial nations did 200 years ago—their population growth rates should start to decline. Still, population growth rates in poor nations continue to be high, and, as the “Sociology Making a Difference” box discussed, inequalities in food distribution allow rampant hunger to persist. Hundreds of thousands of women die in poor nations each year during pregnancy and childbirth. Reduced fertility would save their lives, in part because their bodies would be healthier if their pregnancies were spaced farther apart (Schultz, 2008). Although world population growth is slowing, then, it is still growing too rapidly in much of the developing and least developed worlds. To reduce it further, more extensive family-planning programs are needed, as is economic development in general.

Population Decline and Pronatalism

Still another reason for the reduced concern over population growth is that birth rates in many industrial nations have slowed considerably. Some nations are even experiencing population declines, while several more are projected to have population declines by 2050 (Goldstein, Sobotka, & Jasilioniene, 2009). For a country to maintain its population, the average woman needs to have 2.1 children, the replacement level for population stability. But several industrial nations, not including the United States, are far below this level. Increased birth control is one reason for their lower fertility rates but so are decisions by women to stay in school longer, to go to work right after their schooling ends, and to not have their first child until somewhat later.

Spain is one of several European nations that have been experiencing a population decline because of lower birth rates. Like some other nations, Spain has adopted pronatalist policies to encourage people to have more children; it provides 2,500 euros, about $3,400, for each child.

Wikimedia Commons – CC BY-SA 3.0.

Ironically, these nations’ population declines have begun to concern demographers and policymakers (Shorto, 2008). Because people in many industrial nations are living longer while the birth rate drops, these nations are increasingly having a greater proportion of older people and a smaller proportion of younger people. In several European nations, there are more people 61 or older than 19 or younger. As this trend continues, it will become increasingly difficult to take care of the health and income needs of so many older persons, and there may be too few younger people to fill the many jobs and provide the many services that an industrial society demands. The smaller labor force may also mean that governments will have fewer income tax dollars to provide these services.

To deal with these problems, several governments have initiated pronatalist policies aimed at encouraging women to have more children. In particular, they provide generous child-care subsidies, tax incentives, and flexible work schedules designed to make it easier to bear and raise children, and some even provide couples outright cash payments when they have an additional child. Russia in some cases provides the equivalent of about $9,000 for each child beyond the first, while Spain provides 2,500 euros (equivalent to about $3,400) for each child (Haub, 2009).

Key Takeaways

• Concern over population growth has declined for at least three reasons. First, there is increasing recognition that the world has an adequate supply of food. Second, people of color have charged that attempts to limit population growth were aimed at their own populations. Third, several European countries have actually experienced population decline.
• Demographic transition theory links population growth to the level of technological development across three stages of social evolution. In preindustrial societies, there is little population growth; in industrial societies, population growth is high; and in later stages of industrial societies, population growth slows.

For Your Review

• Before you read this chapter, did you think that food scarcity was the major reason for world hunger today? Why do you think a belief in food scarcity is so common among Americans?
• Do you think nations with low birth rates should provide incentives for women to have more babies? Why or why not?

Ehrlich, P. R. (1969). The population bomb . San Francisco, CA: Sierra Club.

Goldstein, J. R., Sobotka, T., & Jasilioniene, A. (2009). The end of “lowest-low” fertility? Population & Development Review, 35 (4), 663–699. doi:10.1111/j.1728–4457.2009.00304.x.

Haub, C. (2009). Birth rates rising in some low birth-rate countries . Washington, DC: Population Reference Bureau. Retrieved from http://www.prb.org/Articles/2009/fallingbirthrates.aspx .

Jacobsen, L. A., & Mather, M. (2010). U.S. economic and social trends since 2000. Population Bulletin, 65 (1), 1–20.

Kuumba, M. B. (1993). Perpetuating neo-colonialism through population control: South Africa and the United States. Africa Today, 40 (3), 79–85.

Malthus, T. R. (1926). First essay on population . London, England: Macmillan. (Original work published 1798).

Rosenberg, M. (2009). Population growth rates. Retrieved from http://geography.about.com/od/populationgeography/a/populationgrow.htm .

Scanlan, S. J., Jenkins, J. C., & Peterson, L. (2010). The scarcity fallacy. Contexts, 9 (1), 34–39.

Schultz, T. P. (2008). Population policies, fertility, women’s human capital, and child quality. In T. P. Schultz & J. Strauss (Eds.), Handbook of development economics (Vol. 4, pp. 3249–3303). Amsterdam, Netherlands: North-Holland, Elsevier.

Shorto, R. (2008, June 2). No babies? The New York Times Magazine . Retrieved from http://www.nytimes.com/2008/06/29/magazine/29Birth-t.html?scp=1&sq=&st=nyt .

U.S. Census Bureau. (2010). Statistical abstract of the United States: 2010 . Washington, DC: U.S. Government Printing Office. Retrieved from http://www.census.gov/compendia/statab .

Weeks, J. R. (2012). Population: An introduction to concepts and issues (11th ed.). Belmont, CA: Wadsworth.

Sociology Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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• Population Growth Essay

Essay on Population Growth

One of the major problems the world is facing is the problem of the exponential growth of the population. This problem is the greatest one. Most countries in the world are showing a steep rise in population figures. The world’s resources are limited and so they cannot support a population beyond a certain limit. There has been news about the scarcity of food grains and the paucity of jobs mounting across the world. The number of human beings is multiplying at a steady rate. The world population has already crossed the six billion mark and it is expected to double in the next three or four decades. 

If the population continues to grow at this rate then the economy of the overpopulated countries will be unable to cope up with the growth of the population. Every attempt to bring peace, comfort and welfare to everybody’s door will be thwarted and misery will become prominent if the population is not kept within proper limits. Except for a few countries, all countries are facing a population boom. Currently, the largest populated country in the world is China and India is the second-largest populated country. India represents 17% of the world’s population. Other countries like Bangladesh, Japan, Indonesia and some countries of Europe are threatened to be burst into the seams by population explosion.

Causes of Population Growth

The major cause of population growth is the decrease in death rate and rise in the life span of the average individual. Earlier, there was a balance between the birth and death rate due to limited medical facilities, people dying in wars, and other calamities. The rapid spread of education has made people health conscious. People have become aware of the basic causes of diseases and simple remedies for them.

Illiteracy is another cause of an increase in population. Low literacy rate leads to traditional, superstitious, and ignorant people. Educated people are well aware of birth control methods. 

Family planning, welfare programs, and policies have not fetched the desired result. The increase in population is putting tremendous pressure on the limited infrastructure and negating the progress of any country.

The superstitious people mainly from rural places think that having a male child would give them prosperity and so there is considerable pressure on the parents to produce children till a male child is born. This leads to population growth in underdeveloped countries like India, Bangladesh. 

Poverty is another main reason for this. Poor people believe that the more people in the family, the more will be the number of persons to earn bread. Hence it contributes to the increase in population. 

Continuous illegal migration of people from neighbouring countries leads to a rise in the population density in the countries. 

Religion sentiment is another cause of the population explosion. Some orthodox communities believe that any mandate or statutory method of prohibition is sacrilegious. 

Impact Due to Population 

The growth of the population has a major impact on the living standards of people. Overpopulation across the world may create more demand for freshwater supply and this has become a major issue because Earth has only 3% of freshwater. 

The natural resources of Earth are getting depleted because of the exponential growth of the population. These resources cannot be replenished so easily. If there is no check on the growth of population then there will be a day in the next few years when these natural resources will run out completely. 

There is a huge impact on the climatic conditions because of the growth of the population. Human activities are responsible for changing global temperature. 

Impact of Overpopulation on Earth’s Environment

The Earth's current population is almost 7.6 billion people, and it is expanding. It is expected to surpass 8 billion people by 2025, 9 billion by 2040, and 11 billion by 2100. The population is quickly increasing, far surpassing our planet's ability to maintain it, given existing habits.

Overpopulation is linked to a variety of detrimental environmental and economic consequences, including over-farming, deforestation, and water pollution, as well as eutrophication and global warming. Although many incredible things are being done to increase human sustainability on our planet, the problem of too many people has made long-term solutions more difficult to come across.

Overpopulation is mostly due to trends that began with a rise in birth rates in the mid-twentieth century. Migration can also result in overcrowding in certain areas. Surprisingly, an area's overcrowding may arise without a net increase in population. It can happen when a population with an export-oriented economy outgrows its carrying capacity and migratory patterns remain stable. "Demographic entrapment" has been coined to describe this situation.

Some Major Effects of the High Population are as Follows

The rapid growth of the population has caused major effects on our planet. 

The rapidly growing population in the world has led to the problem of food scarcity and heavy pressure on land resources. 

Generating employment opportunities in vastly populated countries is very difficult. 

The development of infrastructural facilities is not able to cope up with the pace of a growing population. So facilities like transportation, communication, housing, education, and healthcare are becoming inadequate to provide provision to the people. 

The increasing population leads to unequal distribution of income and inequalities among the people widened.

There will be a large proportion of unproductive consumers due to overpopulation. 

Economic development is bound to be slower in developing countries in which the population is growing at a very fast rate. This also leads to low capital formation. Overpopulation makes it difficult to implement policies. 

When there is rapid growth in a country then the government of that country is required to provide the minimum facilities for the people for their comfortable living. Hence, it has to increase housing, education, public health, communication and other facilities that will increase the cost of the social overheads.

Rapid population growth is also an indication of the wastage of natural resources. 

Preventive Measures

To tackle this problem, the government of developing countries needs to take corrective measures. The entire development of the country depends on how effectively the population explosion is stemmed. 

The government and various NGOs should raise awareness about family planning and welfare. Awareness about the use of contraceptive pills and family planning methods should be generated. 

The health care centres in developing and under-developed countries should help the poor people with the free distribution of contraceptives and encourage the control of the number of children. 

The governments of developing countries should come forward to empower women and improve the status of women and girls. People in rural places should be educated and modern amenities should be provided for recreation. 

Education plays a major role in controlling the population. People from developing countries should be educated so that they understand the implications of overpopulation.

Short Summarised Points On Population Growth

Based on the number of deaths and births, population growth might be positive or negative. 

If a country's birth rate outnumbers its death rate, the population grows, whereas more ends result in a drop.

There are 7.7 billion people on the earth, and India, with 1.3 billion people, is the second-most populous country after China.

Mumbai, the Bollywood capital, is India's most populous city, with a population of 12 billion people. Delhi, India's most populous city, comes in second with 11 billion inhabitants.

The advancement of knowledge in science, medicine, and technology has resulted in lower mortality and higher fertility, resulting in population rise.

Factors contributing to India's population expansion, such as mortality and fertility rates, child marriage, a lack of family planning, polygamy marriage, and so on, have wreaked havoc on the ecosystem.

Industrialization, deforestation, urbanisation, and unemployment have all been exacerbated by population expansion. These causes degrade our environment and contribute to societal health issues.

Pollution, global warming, climate change, natural catastrophes, and, most importantly, unemployment are all caused by the population.

To keep population increase under control, individuals must have access to education and be aware of the dangers of overpopulation.

The government must raise public awareness about illiteracy and educate individuals about the need for birth control and family planning.

Overpopulation may lead to many issues like depletion of natural resources, environmental pollution and degradation and loss of surroundings.  All countries must take immediate steps to control and manage human population growth.

FAQs on Population Growth Essay

1. What Do You Mean By Population Growth and How is it a Threat to the World?

Population growth refers to the rapid increase in the number of people in an area. It is a threat to the world because the world’s resources are limited and it cannot support a population beyond a certain limit.

2. What are the factors of Population Exponential Growth?

The factors for the exponential growth of the population are illegal migration from other countries, illiteracy, lack of awareness of contraceptive methods, poverty, lack of basic amenities, religious sentiments and superstitions. 

3. What steps should India take to reign in population growth?

Family planning and welfare must be made more widely known by the Indian government. Women and girls should be given more power. Free contraceptives should be distributed and people should be educated at health care centres. In schools and colleges, sex education should be required. Some more points to ponder are given below:

1. Social Actions

The minimum age for marriage is 18 years old.

Increasing women's status

Adoption of Social Security and the Spread of Education

2. Economic Interventions

Increased job opportunities

Providing financial incentives

3. Additional Measures

Medical Services

Legislative Initiatives

Recreational Resources

Increasing public awareness

4. What Impact Does Overpopulation Have on Our Planet?

Overpopulation is linked to a variety of detrimental environmental and economic consequences, including over-farming, deforestation, and water pollution, as well as eutrophication and global warming. Although many incredible things are being done to increase human sustainability on our planet, the problem of too many people has made long-term solutions more difficult to come across. Because of the exponential rise of the human population, the Earth's natural resources are depleting. Overpopulation has a significant impact on climatic conditions. The fluctuating global temperature is due to human activity.

5. What are the impacts on the population?

The influence of population expansion on people's living conditions is significant. Overpopulation around the world may increase demand for freshwater, which has become a big issue given that the Earth only possesses 3% freshwater. Because of the exponential rise of the human population, the Earth's natural resources are depleting. These materials are not easily replenished. If population growth is not slowed, these natural resources will run out altogether in the next several years. The population explosion has had a significant impact on climatic conditions. The fluctuating global temperature is due to global warming and needs to be regulated immediately as glaciers have already started melting and global temperature is rising at an alarming rate.

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Peer-reviewed

Research Article

The Importance of Population Growth and Regulation in Human Life History Evolution

* E-mail: [email protected]

Affiliation Department of Anthropology. Stanford University, Stanford, CA 94305

• Ryan Baldini

• Published: April 1, 2015
• https://doi.org/10.1371/journal.pone.0119789
• See the preprint
• Reader Comments

Explaining the evolution of human life history traits remains an important challenge for evolutionary anthropologists. Progress is hindered by a poor appreciation of how demographic factors affect the action of natural selection. I review life history theory showing that the quantity maximized by selection depends on whether and how population growth is regulated. I show that the common use of R , a strategy’s expected lifetime number of offspring, as a fitness maximand is only appropriate under a strict set of conditions, which are apparently unappreciated by anthropologists. To concretely show how demography-free life history theory can lead to errors, I reanalyze an influential model of human life history evolution, which investigated the coevolution of a long lifespan and late age of maturity. I show that the model’s conclusions do not hold under simple changes to the implicitly assumed mechanism of density dependence, even when stated assumptions remain unchanged. This analysis suggests that progress in human life history theory requires better understanding of the demography of our ancestors.

Citation: Baldini R (2015) The Importance of Population Growth and Regulation in Human Life History Evolution. PLoS ONE 10(4): e0119789. https://doi.org/10.1371/journal.pone.0119789

Academic Editor: Stephen Shennan, University College London, UNITED KINGDOM

Received: July 20, 2014; Accepted: February 3, 2015; Published: April 1, 2015

Copyright: © 2015 Ryan Baldini. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Data Availability: All relevant data are within the paper.

Funding: The author received no specific funding for this work.

Competing interests: The author has declared that no competing interests exist.

Introduction

The unusual life history characteristics of humans provide a unique challenge to evolutionary anthropologists. Humans have a distinctive life history even among our closest living relatives: compared to other primates, we endure a long juvenile period of intensive growth, learning, and extreme dependency; we mature and reproduce late; we have long reproductive careers with short interbirth intervals; and we enjoy a long post-reproductive lifespan [ 1 , 2 ]. This pronounced life course has attracted the attention of many theorists, and consequently some novel, human-specific theories have been proposed [ 1 , 3 , 4 , 5 ] alongside more species-general life history theory [ 2 , 6 , 7 ].

Theorists often use optimization methods to understand how selection acts on life histories. The general method is to maximize a fitness function with respect to some physiological tradeoff. For example, we might assume that energy devoted to immune function cannot be devoted to gamete production (or any other biological function). A life history theorist might ask: which proportion of energy allocation to immune function will serve to maximize fitness? The maximization method is widely used in introductory life history textbooks on which empirical researchers strongly rely (e.g., [ 8 , 9 , 10 ]).

One of the major difficulties with optimization methods arises in the first step: that of specifying the fitness quantity to be maximized. As I demonstrate here, this problem is usually solved by specifying a complete model of demography and inheritance, from which one can derive a quantity which natural selection maximizes. Unfortunately, traditional life history theory often does not begin with the construction of complete population models, but rather with the theorist simply choosing a common fitness quantity. The chosen maximand is usually only valid under particular demographic conditions [ 11 , 12 ], but, without full justification from a population model, most readers never know these conditions.

This paper aims to clarify the role of demography in life history theory, with a focus on how demographic assumptions determine the correct fitness maximand. First, I review two general models of selection on age-structured populations, showing which quantities are maximized under density-independent and density-dependent population growth. I then show that one common maximand, a strategy’s expected lifetime number of offspring (often denoted by R ), is valid under only a limited set of conditions. These conditions do not appear to be widely appreciated among anthropologists. In particular, zero population growth alone is not sufficient to justify R as a fitness maximand. Then, to concretely show how demographically vague models can lead to premature conclusions, I reanalyze the model in an influential paper on the evolution of human life histories: Kaplan et al.’s [ 1 ] “A theory of human life history: diet, intelligence, and longevity.” I show that Kaplan et al.’s conclusions, which address the coevolution of a long lifespan and late age of maturity, do not hold under simple changes in the action of density-dependence, even while their stated assumptions remain intact. This sensitivity to the precise form of population regulation implies that we need to better understand the demographic history and prehistory of our species if our models are to provide specific, realistic predictions.

What does selection maximize?

Here I review how different forms of population regulation lead to different maximization procedures. There are an infinite number of possible demographic scenarios one could assume, but much can be learned from studying the two broad categories of density-independent or -dependent growth. The latter usually implies that population growth rates decrease as the population becomes more dense, via increased competition for resources. This section borrows heavily from Charlesworth’s classic book, Evolution in Age-Structured Populations [ 13 ]. To simplify matters, I assume asexual, haploid genetic inheritance and no frequency-dependent selection, as is often done in fitness maximization models. The extension to sexual reproduction is usually straightforward [ 13 ]. The goal, for each case, is to find the quantity that natural selection maximizes, and to briefly explain how a theorist can apply the results to specific problems.

Maximization under density-independent growth

It follows from this result that selection does not necessarily maximize the expected lifetime number of offspring, R , under density-independent growth. This fact is not immediately obvious, so I provide a simple demonstration. Imagine two asexual life history strategies, A and B . All individuals survive for exactly two seasons and produce two offspring, but A and B differ in their timing of reproduction. Individuals of strategy A produce one offspring in both their first and second seasons, while individuals of strategy B produce both offspring in their second season only.

Table 1 shows the result of selection, beginning with a population composed of one newborn individual of each strategy. Strategy A grows faster than B and eventually approaches frequency 1 in the population. The reason is that A reproduces much earlier than B , and thus has a shorter generation length and ultimately a higher r .

• PPT PowerPoint slide
• PNG larger image
• TIFF original image

p A is the frequency of strategy A among the total population. The frequency of p fluctuates as it approaches 1 because strategy B does not converge a unique age distribution and growth rate.

https://doi.org/10.1371/journal.pone.0119789.t001

Overall, these results readily imply a maximization methodology: we simply write down l and m as a function of some set of tradeoffs, find r by solving Equation (1) , and then maximize r with respect to the tradeoff. In practice, this can be challenging, as the integral in Equation (1) often cannot be solved in elementary terms. In these cases, numerical approximations can be used.

Maximization under density-dependent growth

The general procedure, then, is to specify some tradeoffs in l and m , use Equation (3) to solve for N ^ , and then maximize N ^ . In practice, there is no limit to how complex the functions l and m can be with respect to population size, so this procedure can be very difficult.

When is R an appropriate maximand?

The expected lifetime number of offspring, commonly denoted by R , is often used as a maximand in life history theory. Hawkes et al.’s model [ 3 ], for example, relies heavily on the theory developed by Charnov (e.g. [ 17 ]), which is based on R as a maximand. Kaplan et al.’s model [ 1 ], which I reanalyze below, uses R to develop a general theory of human life history evolution. R is commonly used outside of anthropology; many examples can be found in [ 8 , 9 ] and [ 10 ]. An important problem, then, is to determine the conditions under which R can be used in optimality models. I show here that the conditions are more limiting than some authors appear to appreciate.

It is frequently claimed that R is a correct fitness measure under zero population growth. This is true in the sense that it determines the rate of gene frequency change over a short period when r = 0 [ 13 ]. As such, R is an appropriate dynamical measure of fitness under such conditions. In particular, R is a useful dynamical measure of fitness in density-dependent populations because, over evolutionary time, the population will usually be near carrying capacity at which r = 0 (assuming no cyclic or chaotic dynamics). Maximization methods, however, treat long-term evolutionary questions: they assume that enough time has passed for all possible strategies to invade, and for selection to bring the optimal strategy to high frequency (see [ 18 ] for a discussion of timescale in models of natural selection). As a fitness maximand , R generally fails, even in density-dependent populations with zero growth. The reason is that, under density dependence, a strategy does not have a single number R . Rather, R becomes a function of population size. Without a single number by which to compare different strategies, one cannot use a maximization procedure. One could choose an arbitrary N at which to evaluate R , but this has no justification in general—especially because the ordering of R across strategies may vary with N . In fact, the theory of the previous section shows that the single number of interest is N ^ , a strategy’s carrying capacity.

• Density dependence only affects expected fertility via the same multiplier for all strategies, independently of age. Survival is not density-dependent.
• Density dependence only affects the probability of survival to reproductive ages via the same multiplier for all strategies. Fertility is not density-dependent.
• Density dependence affects both fertility and survival via the mechanisms in (1) and (2) , only.

The three conditions noted above do not appear to be well appreciated, especially among anthropologists. There is no mention of these strict conditions by Kaplan et al. [ 1 ], for example. This is probably because life history theorists have not always been clear about demographic assumptions in the classic models. For example, Hawkes et al. [ 3 ] rely on Charnov’s R -based models, including a paper in which Charnov claims that R is “a Darwinian fitness measure appropriate for a nongrowing population,” and uses it as a maximand [ 19 ]. We have seen that this is incorrect in general. Fortunately, Charnov’s models frequently assume the second density-dependence case listed above (see, e.g., [ 20 , 17 ]), for which R is appropriate. Unfortunately, this form of density dependence is not mentioned in the articles cited by [ 3 ]; it is not surprising, then, that they do not state restrictions themselves. The three conditions are also not noted influential life history textbooks [ 8 , 10 , 9 ].

The broad conclusion here is that one cannot study the evolution of a density-dependent population in general by maximizing a density- independent function of R . Further, the assumption of zero population growth alone does not justify R as a maximand. R is only appropriate under the specific forms of density dependence listed above. Whether these conditions are accurate for human populations is largely unknown; certainly they have not been justified by anthropologists.

The coevolution of age at maturity and investment in survival

I now shift attention to the model of Kaplan et al. [ 1 ]. I review the assumptions and claims of the model, and then reanalyze it under various forms of population regulation. My goal is not to discredit Kaplan et al.’s hypothesis (which I think is promising), but to demonstrate that the results they derive fail under many forms of population regulation.

The model in Kaplan et al. ([ 1 ], p. 165) treats the coevolution of two life history characteristics: age at maturity and investment in survival. Individuals experience two life stages: a juvenile, pre-reproductive stage, and an adult, reproductive stage, which begins at age t . In both stages, individuals invest some proportion λ of available energy to mortality reduction. Among juveniles, the remaining energy is devoted to the development of embodied capital (growth and learning). Among adults, the remaining energy is devoted to reproduction. Only t and λ evolve in this model.

The instantaneous death rate, μ , is constant across ages for any given strategy. Since λ measures investment in mortality reduction, μ is a decreasing function of λ : strategies with high λ live longer. To allow for external effects on mortality, the parameter θ is introduced to quantify the extrinsic mortality risk. μ is an increasing function of θ .

Kaplan et al. do not provide fertility functions, but they do provide a term that represents the energy invested in fertility. I simply let this equal fertility outright, so that an m function is recovered. Thus, fertility at age t is equal to the embodied capital produced up to that point, multiplied by 1− λ (as the rest of the energy continues to be invested in survival). Let the embodied capital at age t be denoted by P ( t , λ , ε ). P is an increasing function of t : more time in maturity allows for more embodied capital. It is a decreasing function of λ , as this energy is lost to survival investment. ε is an ecological parameter that measures the ease of the environment with respect to fertility: all other things being equal, greater ε implies higher fertility. Finally, Kaplan et al. assume that energy production grows at an exponential rate g after maturity due to skills and knowledge acquired from experience during the reproductive stage. I translate this energy production directly to fertility.

The claimed results

Inequalities (10) say that, all other things being equal, niches more hospitable to reproduction favor later maturity and greater investment in mortality reduction. Inequalities (11) say that as extrinsic mortality increases, selection favors earlier maturity and lesser investment in mortality reduction. Inequalities (12) say that a greater growth rate of energy production (and therefore fertility) after maturity selects for later maturity and greater investment in mortality reduction.

Kaplan et al. emphasize not only the directional effects of the ecological parameters, but also the positive coevolutionary relationship between age at maturity and investment in survival. For each parameter change, they found that the age at maturity and the investment in survival always increased or decreased together (i.e., for each line, the derivatives have the same sign).

Forms of population regulation.

The main problem with the original analysis in Kaplan et al. is a failure to specify the form of population regulation, precluding identification of the proper maximand. Instead, they claim zero population growth without specifying precisely how this occurs, and then assume that selection maximizes a density-independent R . To reanalyze the model properly, one must first specify forms of population regulation; I choose three simple cases here (although two produce identical outcomes, as seen just below). I generalize by allowing one case of nonzero population growth, as well as two forms of density dependence.

• Density-independent (exponential) growth
• Density-dependent fertility
• Density-dependent mortality

In case 1, all fertility and mortality rates are fixed quantities, independent of population density. Selection maximizes r here, whereas it maximizes N ^ for all other cases. This would be reasonable if, over the evolutionary timescale of interest, human populations were largely regulated by density-independent factors.

In case 2, fertility across all ages and strategies depends on population size via the same multiplier. This is precisely the condition under which R happens to be maximized, as discussed above (see equations (5) and (6) ). As shown there, I assume that m ( x , N ) = e − DN m 0 ( x ), where m 0 is the fertility under zero population density and D quantifies the extent to which fertility is adversely affected by population density. Survival rates are independent of density.

In case 3, the same form of density dependence applies to mortality for each age, rather than fertility. That is, l ( x , N ) = e − DNx l 0 ( x ). Fertility is independent of density. This form, too, was mentioned in the previous section (equations (8) and (9) ), but selection does not maximize R here.

Note that in both density-dependent cases, the D parameters are assumed to be fixed. That is, all strategies are affected by density equally. I assume this only for simplicity, as different strategies could realistically vary in their susceptibility to crowding. Fortunately, this assumption also leads to a useful simplification: cases 1 and 3 favor the exact same strategy for l and m . This follows because r and D N ^ , which are respectively maximized in cases 1 and 3, take the same functional form in the Euler-Lotka equation, as is seen by comparing the integral of Equation (1) to those of (9) . This simplification implies that we need only consider two cases: cases 1 and 3 together, and case 2. These simple differences in population regulation lead to very different optimal life history strategies.

Cases 1 and 3.

The analogous equations for the case of density-dependent mortality are found by replacing r in the above equations with D N ^ , subject to the constraint that N ^ implies 0 population growth as in Equation (3) . These two models favor the same strategy at equilibrium, so all further results apply to both.

Equations (19) and (20) can be substituted into Equations (17) and (18) , which can then be solved numerically. While this procedure cannot prove general results, contradictions to most of Kaplan et al.’s claims readily arise (see Figs. 1 and 2 ). Under all parameter values numerically investigated (see supporting text), I find that, contrary to inequalities (10) , t ^ and λ ^ both decrease as ε increases; niches more hospitable to reproduction prompt earlier maturity and lesser investment in survival. Contrary to inequalities (11) , t ^ and λ ^ both increase with θ ; niches with greater extrinsic mortality risk favor later maturity and greater investment in survival. Finally, while λ ^ does increase with g as Kaplan et al. predicted, t ^ decreases; niches in which production continues to grow in adulthood favor earlier maturity. This latter finding also shows that λ and t may not evolve in the same direction.

α = 0.1, β = 0.2, μ 0 = 1, γ = 5, ε = 0, g = 0.

https://doi.org/10.1371/journal.pone.0119789.g001

The solid line depicts t ^ , while the dashed line depicts λ ^ . α = 0.1, β = 0.2, μ 0 = 1, γ = 5, ε = 0, θ = 0.

https://doi.org/10.1371/journal.pone.0119789.g002

Curiously, some of Kaplan et al.’s results do not hold in this case, suggesting that the authors made assumptions that were not printed in the paper. Again assuming functions (19) and (20) , I first find that ε drops out entirely; the extrinsic costs of fertility have no effect on the equilibria. Second, numerical calculations show that λ evolves upward with θ , which is opposite to t . Finally, both t and λ evolve upward with g , as Kaplan et al. predict.

What can we conclude?

Despite the small set of demographic conditions investigated here, my analysis quickly found contradictions to the general claims of Kaplan et al. [ 1 ]. More complicated forms of population regulation would probably produce still more widely varying outcomes. Thus any strong claims like inequalities (10) , (11) , and (12) seem unlikely to hold in general; there is probably some form of density-dependence for which almost any conclusion does not hold.

Still, to avoid leaving the reader with the unsatisfying message that “anything can happen,” I conducted a systematic search for general parameter effects (the supporting text describes the methods). I found two consistent effects: first, increasing α , the initial rate at which embodied capital grows, always favors earlier maturity and lesser investment in survival. Second, increasing g , the rate at which production (and, hence, fertility) grows after maturity, always favors greater investment in survival. Fortunately, these conclusions are compatible with Kaplan et al.’s general argument: if the transition to the intensive human foraging niche caused slower initial rates of growth and learning (due to the difficulty of acquiring complex skills), and allowed for greater production growth during adulthood, then this may well have contributed to the evolution of the human extended life history. Other ecological effects, unfortunately, remain ambiguous. For example, if the niche transition also implied higher extrinsic mortality due to the difficulty of acquiring resources, then this could have selected for either shorter or longer life histories, depending on the form of population regulation ( Fig. 1 ).

Directions for future research

Even my extended analysis of Kaplan et al.’s [ 1 ] model remains limited. I did not allow the strength of density dependence to vary across ages or strategies, effectively assuming that all individuals are equally affected by population density. The functional forms I chose for numerical evaluation were only one of an infinite number of possibilities. I ignored the potential problems of cyclic or chaotic population dynamics, as well as all of the difficulties introduced by frequency-dependence, separate sexes, realistic genetic structures, and environmental change. Theory exists for all these details, but it is doubtful that broad generalizations like (10) , (11) , and (12) would hold even under a limited range of realistic model assumptions.

The difficulty of finding such broad generalizations suggests that we need to shift our focus away from broad-scope evolutionary models and toward understanding how human populations have been regulated throughout our evolutionary history. Knowledge of these details would allow theorists to constrain model space to only the most realistic cases, leading to more pointed predictions. Studies of density-dependent effects in human populations may be necessary, but are surprisingly rare. I know only of the study by Wood and Smouse [ 21 ], which found evidence of density-dependent mortality among the very youngest and oldest age classes in a New Guinea population. Studies among large, nonhuman mammals also find that juvenile mortality is more sensitive to environmental stress than is adult mortality ([ 22 , 23 ]; but see [ 24 ] for a case where adult mortality is driven strongly by predation). Adult fertility among nonhuman mammals also appears to be sensitive, although this is sometimes confounded with yearling survival, and may depend on the mother’s age [ 25 ]. That the effects on fertility and mortality depend on age suggest that the age-independent models treated in this paper cannot be taken too seriously. On the other hand, if it is true that density dependence acts mostly on fertility and infant survival, then case 2 may turn out to be the closest to reality. In any case, it is clear that both theoretical and empirical work is needed to advance our understanding of human life history evolution.

Supporting Information

S1 file. methods for exploring parameter space..

https://doi.org/10.1371/journal.pone.0119789.s001

Author Contributions

Conceived and designed the experiments: RB. Performed the experiments: RB. Analyzed the data: RB. Contributed reagents/materials/analysis tools: RB. Wrote the paper: RB.

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• v.117(10); 2020 Mar 10

Dynamics of life expectancy and life span equality

José manuel aburto.

a Interdisciplinary Centre on Population Dynamics, University of Southern Denmark, 5000 Odense, Denmark;

b Lifespan Inequalities Research Group, Max Planck Institute for Demographic Research, 18057 Rostock, Germany;

Francisco Villavicencio

c Department of International Health, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, 21205;

Ugofilippo Basellini

d Laboratory of Digital and Computational Demography, Max Planck Institute for Demographic Research, 18057 Rostock, Germany;

e Mortality, Health and Epidemiology Unit, Institut National d’Études Démographiques (INED), 93322 Aubervilliers, France;

Søren Kjærgaard

f Center for Research in Econometric Analysis of Time Series (CREATES), Aarhus University, 8000 Aarhus, Denmark;

James W. Vaupel

g Duke University Population Research Institute, Duke University, Durham, NC, 27708;

h Emeritus Research Group, Max Planck Institute for Demographic Research, 18057 Rostock, Germany

Author contributions: J.M.A. and J.W.V. designed research; J.M.A., F.V., U.B., and S.K. performed research; J.M.A., F.V., U.B., and S.K. contributed new reagents/analytic tools; J.M.A., U.B., and S.K. analyzed data; and J.M.A., F.V., U.B., and J.W.V. wrote the paper.

Reviewers: C.M., University of Oxford; M.M., London School of Economics; and C.R., University of Oxford.

Associated Data

Description to access the data and the code to reproduce results are in a permanent repository, accessible via the following link: https://zenodo.org/record/3571095 . All data are publicly available.

Significance

Why life expectancy and life span equality have increased together is a question of scientific interest. Both measures are calculated for a calendar year and might not describe a cohort’s actual life course. Nonetheless, life expectancy provides a useful measure of average life spans, and life span equality gives insights into uncertainty about age at death. We show how patterns of change in life expectancy and life span equality are described by trajectories of mortality improvements over age and time. The strength of the relationship between life expectancy and life span equality is not coincidental but rather a result of progress in saving lives at specific ages: the more lives saved at the youngest ages, the stronger the relationship is.

As people live longer, ages at death are becoming more similar. This dual advance over the last two centuries, a central aim of public health policies, is a major achievement of modern civilization. Some recent exceptions to the joint rise of life expectancy and life span equality, however, make it difficult to determine the underlying causes of this relationship. Here, we develop a unifying framework to study life expectancy and life span equality over time, relying on concepts about the pace and shape of aging. We study the dynamic relationship between life expectancy and life span equality with reliable data from the Human Mortality Database for 49 countries and regions with emphasis on the long time series from Sweden. Our results demonstrate that both changes in life expectancy and life span equality are weighted totals of rates of progress in reducing mortality. This finding holds for three different measures of the variability of life spans. The weights evolve over time and indicate the ages at which reductions in mortality increase life expectancy and life span equality: the more progress at the youngest ages, the tighter the relationship. The link between life expectancy and life span equality is especially strong when life expectancy is less than 70 y. In recent decades, life expectancy and life span equality have occasionally moved in opposite directions due to larger improvements in mortality at older ages or a slowdown in declines in midlife mortality. Saving lives at ages below life expectancy is the key to increasing both life expectancy and life span equality.

The rise in human life expectancy over the past two centuries is a remarkable accomplishment of modern civilization ( 1 , 2 ). This progress was achieved during the demographic transition of societies from regimes of high mortality and fertility to regimes of low mortality and fertility ( 3 , 4 ). At present, among the world’s nations, Japanese women have the highest life expectancy at birth, above 87 y. In 1840, the record was held by Swedish women, with an average life span of 46 y ( 5 ). This advance has been accompanied by an increase in life span equality: In low mortality populations today, most individuals survive to similar ages ( 6 – 11 ).

Life span equality matters because it captures a fundamental type of inequality: variation in length of life. This variation is not revealed by life expectancy and other measures of average mortality levels ( 12 ). Two populations that share the same level of life expectancy could experience substantial differences in the timing of death, e.g., deaths could be more evenly spread over age in one population than another. Although life expectancy is monitored in every country in the world, few countries have begun to monitor and acknowledge the importance of disparities in age at death.

For values of life expectancy at birth from under 20 to above 85 y, life span equality rises linearly ( Fig. 1 ). This relationship between life expectancy and life span equality has been found to hold in a life span continuum over millions of years of primate evolution, in many countries and among subgroups in a population ( 6 – 11 , 13 – 15 ). The dual advance, however, might be coincidental rather than causal. Even though both life expectancy and life span equality are computed from the same information, namely age-specific death rates, doubt about a common causal link is sown by messier and sometimes negative relationships between them in various datasets and using alternative indicators of life span equality ( 16 ). The United States, for example, has relatively low equality in life spans in comparison with other countries that have similar levels of life expectancy ( 17 ). Scotland reached similar levels of life expectancy with 10% higher life span inequality than England and Wales since 1980 ( 18 ). Finnish females from lower educational levels experienced increases in life expectancy, while life span equality decreased at age 30 since the 1970s ( 12 ). In Denmark, life span equality decreased among the lowest income subgroup over the period of 1986 to 2014 despite the increase in life expectancy ( 19 ). In some countries in Eastern Europe and Latin America, life expectancy and life span equality moved independently over periods of slow improvements in life expectancy ( 20 – 22 ). Indeed, in many countries and subgroups within a country in recent decades, life span equality declined, although the average life span rose or vice versa (as indicated by the points in the second and fourth quadrants of Fig. 2 A and B ). In addition, causes of death that contributed to increasing life expectancy somewhat differ from those that increased equality in life spans in developed countries after 1970 ( 23 , 24 ). Nonetheless, despite these exceptions and discrepancies, life expectancy and life span equality generally move in the same direction ( 11 ).

Association between life expectancy at birth e o and life span equality h .

( A ) Association between changes in life expectancy at birth e o and life span equality h . ( B ) Association between changes over 10-y rolling periods.

In this article, we develop a mathematical framework to explore how life expectancy at birth and life span equality relate to each other and evolve over time. We rely on two dimensions of aging: the average length of life (pace) and the relative variation in length of life (shape) ( 25 ). The former refers to how fast aging occurs, while the latter describes how sharply populations age. The shape of mortality pertains to the distribution of life spans. Statisticians and demographers, based on both theoretical and practical considerations, have developed different indicators to summarize the distribution of life spans ( 26 , 27 ). Here, we measure average length of life by life expectancy, and we analyze the distribution of life spans with three different indicators of life span equality. These indicators are variants of 1) the life table entropy, 2) the Gini coefficient, and 3) the coefficient of variation of the age-at-death distribution ( 28 , 29 ). Other indicators of absolute dispersion in life spans exist, such as the variance of the age-at-death distribution, its SD, or life years lost due to death ( 30 , 31 ). However, these are pace indicators measured in units of time and do not capture the dimensionless shape of aging ( 26 ).

We focus on how age-specific mortality improvements change life span equality and life expectancy at birth. We analyze changes over time in these two longevity measures for Swedish females since the 18th century, and 48 additional populations from the Human Mortality Database with reliable data, in many cases since the beginning of the 20th century, for females and males separately ( 5 ). Mortality risks implied by a period life table generally differ from the risks individuals will experience over their lifetimes. Nonetheless, life table information on life expectancy and life span equality may provide information individuals use to make life course decisions, and information policymakers use to assess population health and well-being ( 32 – 34 ).

Trends in Life Expectancy and Life Span Equality

Life expectancy at birth for both men and women increased throughout the 20th century ( 5 , 35 ). Paralleling the rise of life expectancy, all countries included in our study became more equal in life spans ( Fig. 1 ). This is a significant advance in giving people more equitable opportunities. Furthermore, the rise in life span equality has influenced the decisions individuals make over their life course, such as when to have children, study, work, or retire, and how much to save for retirement, because such decisions are based not only on expected lifetime but also on uncertainty about age at death ( 14 ). Analysis of the relationship between life expectancy at birth e o and life span equality, as measured by h , a log-transformation of life table entropy H ¯ ( Materials and Methods and Box 1 ), indicates a strong correlation (Pearson coefficient of 0.985 for the data in Fig. 1 ). We also analyzed the relationship between average life span and two other measures of life span equality based on the Gini coefficient and the coefficient of variation, and found similarly high correlations, 0.981 and 0.975, respectively ( SI Appendix , Fig. S1 ). Although life expectancy and life span equality have been positively correlated, it is apparent that the relationship is less strong and often reversed in recent decades, resulting in negative correlations in some countries in yearly and 10-y changes ( Fig. 2 ).

Box 1. The Threshold Age and the Life Expectancy at Birth

Life span equality measured by h refers to an indicator closely related to the life table entropy, which was first developed by Leser ( 29 ) and further explored by Demetrius ( 62 ), Keyfitz ( 42 ), and Keyfitz and Golini ( 63 ). The life table entropy is a dimensionless indicator of the relative variation in the length of life compared to life expectancy at birth, and can be expressed as follows:

Function ℓ ( x ) denotes the probability of surviving from birth to age x , whereas e † refers to life disparity—the average remaining life expectancy at ages of death ( 31 , 45 , 46 )—and e o is the life expectancy at birth.

Life span equality measured by h = − ln H ¯ has previously been used as an indicator of life span equality ( 11 ). If mortality improvements over time occur at all ages, there exists a unique threshold age that separates positive from negative contributions to H ¯ as a result of those improvements ( 52 ). Because h is a logarithmic transformation of H ¯ , it has the same threshold age, which we denote by a h (vertical dashed lines in Fig. 3 ). This threshold is reached when

Weights for the changes in life expectancy w ( x ) ( A and B ) and life span equality w ( x ) W h ( x ) ( C and D ). Each line refers to a given period and represents how life expectancy and life span equality react to age-specific mortality improvements for Swedish women in selected periods.

where H ( a h ) is the cumulative hazard to age a h and H ¯ ( a h ) is the life table entropy conditional on surviving to age a h ( 52 ).

Box 1, Fig. 1 shows the evolution of life expectancy at birth e o , the threshold age a h , and the most common age at death after infancy, M , for Swedish females since 1900 ( A ). The figure highlights how the three measures move together. The threshold age in A is the age that separates “early” from “late” deaths in terms of the effect on life span equality. Averting deaths before a h increases equality, while averting deaths after this age has the opposite effect. It is a population-specific measure that depends on the observed mortality pattern. The threshold age and the life expectancy at birth move in the same direction, either increasing or decreasing together; note that they are very close in recent decades. The modal age at death M was fairly constant before 1950 and rose in tandem with e o and a h thereafter. More than 40% of deaths occur below e o and a h , whereas more than 60% of deaths occur below M ( B ). C and D show that mortality improvements below e o and a h were responsible for around 80% of gains in life expectancy at birth and life span equality in the beginning of the 20th century, while they are responsible for around 60% in contemporary Sweden.

Box 1, Fig. 1. ( A ) Life expectancy at birth e o , threshold age a h , and modal age at death M . ( B ) Proportion of deaths below life expectancy at birth e o , threshold age a h , and modal age at death M . ( C ) Percentage of changes in life span equality due to changes in death rates below life expectancy at birth e o , threshold age a h , and modal age at death M . ( D ) Percentage of changes in life expectancy at birth due to changes in death rates below life expectancy at birth e o , threshold age a h , and modal age at death M .

How Strong Is the Relationship Between Life Expectancy and Life Span Equality over Time?

To study how strongly life expectancy and life span equality are related over time and whether they respond in the same direction to age-specific mortality changes, we complement demographic analysis with time series analysis (see SI Appendix , section A for details). This framework is designed to integrate the stochastic properties of dynamics over time ( 8 , 9 ). Focusing on changes over time improves our analysis by avoiding misleading inferences from correlations, such as confounding due to unobserved or unmeasured variables ( 36 ). Econometric time series theory indicates that life expectancy and life span equality have a long-run relationship if there exists a single process that drives both indicators toward a long-term equilibrium, even if temporary departures from it occur (as observed more often in recent decades). If this equilibrium exists, changes over time in life span equality are proportional to changes in life expectancy in the long term. In other words, while life expectancy and life span equality increase over time, a linear combination of both leads to a residual time series consistent with stationarity (i.e., with stable mean and variance), referred to as cointegration in time series analysis ( SI Appendix , section A.2 ).

The results reveal that, in most populations, life expectancy and life span equality are linked by a long-run relationship for both sexes ( SI Appendix , Fig. S2 ). In 91% of the populations we investigated (males and females from 45 countries and regions by sex), this relationship holds under the same model specifications ( SI Appendix , section A.2 ); similar results are exhibited for all three indicators of life span equality ( SI Appendix , Fig. S2 ). At the 5% significance level, negative results are expected for 5% of the cases due to random variations. We got negative results in 9% cases. So, the importance of negative results in specific populations should not be overly emphasized ( SI Appendix , section A.3 ). These results hold for countries that have experienced substantially different mortality patterns, including women in Japan; men in the United States with life expectancy of about 77 y and relatively high life span inequality ( 17 ); and men in Russia and Ukraine with the lowest levels in life expectancy in this study (about 65 and 66 y in 2013, respectively) and high inequality ( 21 ). Importantly, for every population in our study, females’ lives tend to be longer and more equal compared to males’ lives in a given year, consistent with previous research ( 11 , 37 ). This underscores the advantage of females over males not only in average life span but also in lower uncertainty about age at death.

Age-Specific Dynamics of Mortality.

The field of demography has long been known within the social sciences for its innovations in decomposition analysis ( 38 ). Decomposition analysis is based on the principle of separating demographic measures, e.g., life expectancy or life span equality, into components that contribute to their dynamics, such as age-specific mortality. Several methods to analyze change in life expectancy over time have been developed. Pollard ( 39 ), Arriaga ( 40 ), and Andreev et al. ( 41 ), among others, focused on discrete differences in life expectancy, while other authors considered continuous change ( 42 – 46 ). Some of these methods have been extensively used in population health studies to disentangle age- and cause-specific effects because they are easy to implement ( 40 , 47 , 48 ). Here, we relate changes in both life expectancy and life span equality to the average pace of improvement of mortality and the average number of years lost at death ( 31 ). We are able to describe specific properties of both indicators.

Changes in life expectancy and in life span equality over time are weighted averages of rates of progress in reducing age-specific mortality, ρ ( x ) , albeit with different weights ( Materials and Methods ). These weights— w ( x ) for life expectancy at birth and the product w ( x ) W h ( x ) for life span equality—evolve over time and vary by age. They indicate the potential gain (loss) in life expectancy and life span equality if lives are saved at a specific age and in a given period. Fig. 3 A and B shows the weights for life expectancy at birth and from age 5 for Swedish women. From the 18th to the first part of 20th century, the largest potential increases in life expectancy were concentrated in infancy. The effect on life expectancy improvements due to saving lives in midlife was higher than at older ages. This changed dramatically after 1950, when the effect of infant mortality decreased significantly. By 2010, the effect of reducing mortality by 1% at birth was the same as reducing mortality by 1% at age 71. In the 21st century, saving lives between ages 5 and 40 y had a negligible effect on life expectancy, as opposed to the relatively high impact of these ages before 1900. A shift over time toward the importance of older ages is clear. This ongoing wave toward older ages is in line with recent evidence documenting an advancing front of old-age survival that has driven recent increases in average life span ( 49 ). Indeed, the postponement of old-age mortality is an ongoing process that started more than 50 y ago ( 50 , 51 ). Fig. 3 A and B shows that whenever mortality improvements occur life expectancy increases. The size of the increase depends on the ages at which lives are saved. These improvements ρ ( x ) and the weights w ( x ) are the drivers of life expectancy at birth over time ( 31 ). Fig. 3 C and D shows the weights w ( x ) W h ( x ) for life span equality h . As in A and B , each value represents the effect on life span equality of reducing mortality at a given age. Saving lives at very young ages had the largest effect on increasing equality of life spans throughout the 18th, 19th, and first half of the 20th centuries. In contemporary Sweden, the impact of reducing mortality at birth on life span equality is the same as saving lives at all ages between 76 and 80 y.

As with life expectancy, there is an ongoing shift toward older ages, but with an important difference. At older ages, there is a threshold age above which saving lives decreases life span equality ( Box 1 ). This age is depicted with the dashed lines colored according to the respective period: An increase of this age over time clearly appears in the graphs. The threshold age gives valuable information for understanding of the relationship between life expectancy at birth and life span equality: To the extent that improvements at ages below the threshold age outpace those above it, life expectancy will move in the same direction as life span equality ( 52 ). The shift from positive to negative effects has previously been explored using other indicators ( 53 , 54 ). The three life span equality indicators that we analyze behave similarly ( SI Appendix , Fig. S3 ); their sensitivity to changes in age-specific mortality resembles that of other indices of life span variation ( 27 ).

Fig. 4 A shows the contributions, in years, of mortality fluctuations below the threshold age (early component), and Fig. 4 B shows contributions above the threshold age (late component) to changes in life expectancy and life span equality in 10-y rolling periods for all countries included in our study. The points in the first and third quadrants in Fig. 4 A and the second and fourth quadrants in Fig. 4 B reflect a mix of reductions in death rates at some ages below and above the threshold and increases at other ages. Because the weights for specific ages differ for life expectancy and life span equality, the aggregate effect of such a mix of mortality changes can be positive (negative) for life expectancy and negative (positive) for life span equality. The sum of the early and late components gives the total change in each indicator ( Fig. 2 A ). We report similar results for the two other indicators of life span equality in SI Appendix , Fig. S4 . There is a strong positive association between changes in life expectancy and life span equality below the threshold age, while the relationship is negative above that threshold. Since the two effects oppose each other, as shown by the regression lines, the relationship is driven by the component that makes the larger contribution. Reductions in death rates below the threshold age were significantly larger than reductions above it before 1960, resulting in a strong positive association between life expectancy and life span equality. Since 1960, mortality reductions above the threshold age have become more comparable in magnitude to the early-life component, with more increases in life expectancy coinciding with decreases in life span equality. Until now, the absolute change in both indicators per decade is mainly driven by mortality changes below the threshold age (83.7% and 82.0% on average per decade for life span equality and life expectancy, respectively [ Fig. 4 and Box 1, Fig. 1 B and C ]).

( A ) Association between 10-y changes in life expectancy at birth e o and life span equality h because of mortality changes below the threshold age. ( B ) Association between 10-y changes in e o and h because of mortality changes above the threshold age. The dotted lines show the directions of the relationship below and above the threshold age.

As life expectancy increases, the threshold age also increases ( Box 1 and SI Appendix , Fig. S5 ). There is then more scope to save early lives below the threshold age and maintain the positive relationship between life expectancy and life span equality. This is an essential characteristic of the long-run equilibrium. Progress, however, after the threshold age has been increasing. For example, in Sweden the most common age at death at older ages was stagnant up until the 1950s when it started rising with life expectancy ( Box 1, Fig. 1 A ), and contributions to changes in life expectancy and life span equality increased above the threshold age ( Box 1, Fig. 1 C ). These results underscore the effect of mortality improvements at advanced ages (i.e., above the threshold age) in recent years and shed light on recent interruptions in the relationship between changes in life expectancy and life span equality. This process follows a redistribution of mortality over age and causes of death ( 23 , 55 , 56 ). In the past, deaths were concentrated at young and working ages, mainly due to infectious diseases and to some extent wars and famines that resulted in high inequality of life spans ( 57 ). In recent decades, because of major improvements in health services and medical treatment, living standards, sanitation, and various social determinants of health ( 58 – 61 ), lifesaving is concentrated at older ages, sometimes above the threshold age.

The dynamics of life expectancy and of life span equality are driven by changes in age-specific death rates. The impact of the change at some age differs somewhat for the two measures. At younger ages, the impacts are similar. After a threshold age late in life, a reduction in age-specific death rates increases life expectancy but decreases life span equality. Because of progress in recent decades in reducing death rates above the threshold age, rises in life expectancy more often coincide with declines in life span equality. For the populations we analyzed, in the period 1900 to 1950 less than 16% of the annual changes in average life span coincided with opposite changes in life span equality. In the 1960s, this discrepancy rose to 47%; and thereafter the average has been around 32%. These trends were driven by Eastern and Central European countries and by Nordic countries, which experienced divergent patterns in mortality at different ages ( 21 , 24 ). Since 1960, life span inequality was high and fluctuated strongly in Central and Eastern Europe. A recent study shows that in the decades 1960 to 1980, life expectancy and life span equality changed in opposite directions in half the years and populations analyzed, largely because trends in age-specific death rates were positive at some ages and negative at other ages ( 21 ). This is consistent with our findings. Previous evidence suggests that alcohol-related and cardiovascular diseases might have been important in driving the observed trends in Central and Eastern Europe ( 21 , 64 – 66 ). Danish males experienced deterioration caused by smoking-related and cardiovascular mortality between ages 35 and 80, while negative trends in Norway and Sweden were mostly caused by an increase in cardiovascular mortality ( 24 ).

Are there paths other than the joint, linear rise in Fig. 1 that might have been followed if social conditions and public policies had been different? This is an intriguing question that can be examined in our framework. Fig. 5 shows the relationship between life expectancy and life span equality for Swedish women from 1751 to 2017 under three different scenarios. Blue points refer to observed life expectancy from values below 20 y in 1773 to 84.1 y in 2017. The process of increasing life expectancy with greater equality in individual life spans has been referred to as the compression of mortality or the rectangularization of survivorship, and has been studied from various perspectives over the last couple of decades ( 7 – 11 , 21 , 67 ). Understanding the dynamics of the compression of mortality is important for forecasting heterogeneity in future age patterns of population health as well as for assessments of the timing of individual mortality ( 12 ).

Life expectancy at birth e o and life span equality h for three different scenarios: 1) observed points: Swedish females, 1751 to 2017; 2) youngest equality: life span equality derived by matching observed life expectancy levels by reducing the youngest age; and 3) constant change over age: death rates in each year at all ages are reduced at the rate ρ to achieve the observed change in life expectancy at birth.

Consider the difference of life expectancy and life span equality between two consecutive years. The regression line in Fig. 5 indicates that the average change in life expectancy is about 25.4 times the life span equality change, a value close to the 27 reported elsewhere ( 11 ). Here, we demonstrate that each of these first differences, as an approximation to the time derivative ( Materials and Methods ), is a weighted total of mortality improvements in a given year ( Fig. 3 ). Our main motivation lies on the remarkably tight relationship between life expectancy and life span equality through time illustrated by the regression line (slope, 0.04; P < 0.001). For example, in 1773 Sweden underwent the last major famine that caused starvation across the country ( 68 ). Approximately 50% of excess deaths were due to dysentery, and most deaths (20%) were concentrated in infancy ( 57 ). Even under periods of such mortality stress, observed life expectancy and life span equality fall on the linear trend that holds in more favorable years. Is this tight connection coincidental or a result of fundamental social and physiological forces? We have shown that the connection is largely due to change in death rates at younger ages. Can more be said?

The observed path (blue points, Fig. 5 ) is a combination of age-specific mortality improvements and the weights shown in Fig. 3 . Improvements in mortality are uneven across ages ( 31 ). Hence, we explored an alternative scenario in which the same rate of mortality reduction (or increase) occurred at all ages, the “constant scenario,” with the rate chosen to be consistent with observed levels of life expectancy over time. The red rhombuses in Fig. 5 illustrate the resulting trajectory for Sweden. When the average life span rises above 40 y, levels of life span equality start to diverge and become lower than the observed ones. The relationship between life expectancy becomes nonlinear and levels off at around a life expectancy at birth of 70 y.

Another hypothetical scenario is represented by the purple squares labeled “youngest equality.” This curve refers to the case when all progress in reducing death rates is concentrated at the youngest ages. For example, to get the 1752 life expectancy level from 1751, only deaths at age zero are reduced. Then when deaths at birth are zero, deaths are reduced at age 1, then age 2, and so on, to match the observed life expectancy in the following years. That is, all lifesaving is concentrated at the youngest age(s) at which deaths still occur. Results yield a steeper slope (0.051; P < 0.001), which translates into larger equality in individual life spans at levels of life expectancy after age 50.

Consider now another scenario, the “potential scenario.” From the level of life expectancy in 1950 to contemporary Sweden, age-specific rates of improvement are chosen such that 1) life expectancy increases continuously match the observed levels every decade, and 2) life span equality increases optimally. That is, when life expectancy increases, progress is concentrated at the ages when change in death rates most increases life span equality. Also consider the “constant scenario” in which the life expectancy improvement every decade was achieved by reducing mortality at the same rate for every age. Table 1 shows life span equality under these scenarios for Swedish females from 1960 as well as the actual observed trajectory of life span equality. The potential scenario leads to the highest attained life span equality, while the constant scenario shows the lowest equality in life spans. Interestingly, what was observed in Sweden is close to 50% on average of the difference between the potential and constant scenarios. Hence, the observed trajectory might be called the “semioptimal scenario.” These alternative scenarios show that the narrow passageway that describes the relationship between life expectancy at birth and life span equality is not a coincidence. The transition from low levels of average life span and high variation in length of life to longer and more equal life spans is a result of saving lives at ages that matter—but semioptimally. The tight link between life expectancy and life span equality has been shaped by improvements in mortality at the most important ages for life expectancy and for life span equality: early ages in the 18th century and adult ages today.

Life expectancy at birth e o and life span equality h for three different scenarios

The three different scenarios are as follows: 1) observed points: Swedish females, 1960 to 2017; 2) potential equality: life span equality derived by matching observed life expectancy levels by reducing death rates that increase life span equality the most; and 3) constant change in mortality improvements ρ ( x ) over age matching observed life expectancy levels every decade.

In recent years, more instances of a temporary reversal of the relationship between life expectancy and life span equality have been observed in several countries and subgroups of populations ( 12 , 20 – 22 ). Often these cases were due to midlife mortality deterioration or to major improvements in old-age mortality above the threshold age. In Sweden, death rates among octogenarians and nonagenarians have fallen since 1950 ( 69 ). For other developed countries, the pattern has been similar ( 70 ). If improvements at advanced ages continue and if they outpace those made at younger ages, the pattern of the relationship between life expectancy and life span equality could reverse in the future. It is, however, unlikely that rates of improvement above the threshold age will outpace progress at younger ages in the long term. Furthermore, as life expectancy increases, the threshold age will increase.

Across primate species, there is a rough association of life expectancy and life span equality. Several instances, however, where a relationship between the pace and shape of aging is not found have been documented in other species. Across the tree of life, 46 diverse species did not show a strong correlation between life expectancy and life span equality ( 71 ), and among plants a nonlinear, but weak, positive association has been reported ( 72 ). These findings compare different species, whereas our results are for a single species in a changing environment. Two studies, one of the nematode worm Caenorhabditis elegans and the other of Drosophila melanogaster , of individuals held under different conditions, found that life span equality appeared to be independent of life expectancy ( 73 , 74 ).

For humans, a sharp worsening of conditions tends to lead to substantial increases in infant and child mortality ( 57 ), and in some cases mortality at young adult ages, e.g., as experienced in the former Soviet Union after the end of the anti-alcohol campaign and the dissolution of the USSR ( 21 ), lowering both life expectancy and life span equality. On the other hand, improvements in standards of living, nutrition, education, public health, and other environmental conditions tend, at least when life expectancy is less than 70, to predominately affect life expectancy—and life span equality—through reductions in death rates at young ages ( 2 ).

A key question is whether changes in environmental conditions have their biggest effects on mortality in infancy and childhood because of human agency or because of human physiology. Do societies act to focus mortality improvements at the ages that matter the most, or is human mortality for physiological reasons most sensitive at younger ages to environmental changes? Study of the impact of environmental change on life expectancy and life span equality in nonhuman primate species, being undertaken by Fernando Colchero, Susan Alberts, and colleagues, could shed light on the role of agency versus physiology. More generally, our findings—coupled with the mathematical relationships we derived to analyze how changes in age-specific death rates affect life expectancy and life span equality—suggest that a link may be found for species in which environmental change affects life expectancy largely because of changes in death rates at young ages.

Materials and Methods

We used death rates by age and sex from the Human Mortality Database ( 5 ) for 49 countries and regions by single age and year, with data available from the beginning of the 20th century for some of the countries and regions and later in the 20th century for others and with data up to the most recent year available (see SI Appendix , Table S1 for detailed information). We constructed life tables following standard demographic procedures (7,717 life tables) ( 75 ). For each population, we investigated life expectancy at birth and life span equality by sex. The analysis is restricted to countries with data available for consecutive years (without gaps in the information over time) in order to study age-specific mortality patterns on a yearly basis. We decided not to analyze dispersion at death conditional on survival to any older age because of major improvements made in early ages during the 20th century ( 76 ). In addition, we did not include Chile, South Korea, and Croatia in the cointegration analysis due to limited data availability, spanning less than 20 y. All of the analyses were carried out with R software ( 77 ) and are fully reproducible, including data handling, from the public repository at https://zenodo.org/record/3571095 .

Contributions to Mathematical Demography.

Changes over time in life expectancy..

Changes over time in life expectancy at birth are a weighted average of rates of progress in reducing mortality ( 31 ). Letting ℓ ( x , t ) be the period life table probability at time t of surviving from birth to age x , life expectancy at birth can be expressed as follows:

Because ℓ ( x , t ) = exp [ − ∫ 0 x μ ( a , t ) d a ] , where μ ( a , t ) is the force of mortality (hazard rate) at age a at time t , changes over time in e o ( t ) are given by the following:

A dot over a function denotes its partial derivative with respect to time. For simplicity, variable t will be omitted as an argument in the following. We define the following:

as the age-specific rates of mortality improvement over time and the remaining life expectancy at age x , respectively. Then, Eq. 1 can be expressed in terms of these two functions as follows:

This last result shows that changes over time in life expectancy at birth are a weighted total of rates of progress in reducing mortality, with weights given by the function w ( x ) = μ ( x ) ℓ ( x ) e ( x ) , as shown by Vaupel and Canudas-Romo ( 31 ).

Measures of life span equality and their change over time.

Several indicators have been proposed to measure variation in age at death ( 27 , 78 , 79 ). Selecting the best measure when comparing aging patterns among populations that differ in length of life is of great importance, since indicators vary in their sensitivity to mortality fluctuations and in their mathematical interpretation ( 27 ). In this study, we use three indicators based on the pace and shape of aging framework ( 25 ), which suggests a set of properties that indicators should satisfy ( 26 , 80 ).

A variant of the life table entropy: h .

A measure of life span inequality is the life table entropy H ¯ ( 29 , 62 , 63 ), which can be defined as follows:

where c ( x ) = ℓ ( x ) / ∫ x ∞ ℓ ( a ) d a is the life table age composition, and H ( x ) = ∫ 0 x μ ( a ) d a is the cumulative hazard to age x . Hence, H ¯ can be interpreted as an average value of the cumulative hazard. It can also be expressed as follows:

where e † = − ∫ 0 ∞ ℓ ( x ) ln ⁡ ℓ ( x ) d x accounts for “life disparity,” the average number of life-years lost as a result of death or the average remaining life expectancy at ages of death ( 9 ). For instance, an individual dying at age 50 in a population with remaining life expectancy at age 50 of 20 y would have lost those 20 y of life.

This definition of entropy provides a dimensionless indicator of relative variation in the length of life compared to life expectancy at birth, permitting comparison of populations with different age-at-death distributions ( 26 ). An alternative measure to H ¯ is the following:

which has previously been used to study life span equality across different primate populations, including humans ( 11 ). Note that H ¯ can be interpreted as an indicator of “life span inequality,” given that higher values represent more variation in life spans, whereas h (the logarithm of the inverse) is a measure of “life span equality.” From Eq. 3 , the variation over time in h is given by the following:

An equivalent expression to Eq. 4 was previously derived using calculus of variation by Fernandez and Beltrán-Sánchez ( 81 ), who found that

This shows that changes over time in h are equal to minus the relative change in the life table entropy H ¯ . Similarly to life expectancy at birth, Aburto et al. ( 52 ) proved that

where w ( x ) = μ ( x ) ℓ ( x ) e ( x ) are the same weights for changes over time in e o defined in Eq. 2 , and

Function H ¯ ( x ) = e † ( x ) / e ( x ) is the entropy conditional on surviving to age x , where e † ( x ) refers to life disparity above age x , and e ( x ) is the remaining life expectancy at age x ( 52 ). Because h ˙ = − H ¯ ˙ / H ¯ , it follows that

with W h ( x ) = − W ( x ) . This result shows that changes in life span equality over time are weighted totals of rates of progress in reducing mortality ρ ( x ) , with weights given by the product w ( x ) W h ( x ) .

A variant of the Gini coefficient: g .

The Gini coefficient is a popular index in social science used to measure distributions of positive variables, such as income ( 82 ). It has also been used to describe inequality in life spans as a measure of population health and in survival analysis as an indicator of concentration in survival times ( 26 , 28 , 64 , 83 , 84 ). In life table notation, the Gini coefficient G is given by the following:

Function ϑ = ∫ 0 ∞ ℓ ( x ) 2 d x relates to perturbation theory as it measures life expectancy from doubling the risk of death at all ages. From Eq. 6 , G can also be expressed in terms of the life table age distribution,

Note that ℓ ¯ = ϑ / e o = ∫ 0 ∞ c ( x ) ℓ ( x ) d x is a dimensionless indicator of life span equality, bounded between 0 and 1. If life spans are completely concentrated, all individuals die at the same age, the indicator equals 1; if they are equally spread the indicator tends to 0. In addition, if two babies are born at the same time in a population, then ℓ ¯ measures their shared life span as a proportion of life expectancy ( 85 ). An alternative indicator to the Gini coefficient is the logarithm of its inverse:

which is also a measure of equality rather than inequality.

Note that the derivative of ℓ ¯ with respect to time is as follows:

Hence, changes over time in g are given by the following:

Similar to h , the time derivative of g can be reexpressed as follows:

where w ( x ) = μ ( x ) ℓ ( x ) e ( x ) are the same weights for changes over time in e o , and

Function ℓ ¯ ( x ) is defined as follows:

and can be interpreted as life span equality above age x . A detailed proof of Eq. 9 can be found in SI Appendix , section B . This result shows that changes in life span equality over time, measured by g , are a weighted total of the rates of progress in reducing mortality ρ ( x ) , with weights given by the product w ( x ) W g ( x ) .

A variant of the coefficient of variation: v .

The coefficient of variation of the age-at-death distribution is the quotient of its SD σ and the life expectancy at birth:

This indicator has been previously used to measure life span inequality ( 24 , 26 ). Here, we define a measure of life span equality as the logarithm of the inverse of the coefficient of variation,

Similar to life table entropy and the Gini coefficient, changes over time in v are given by the following:

which can be reexpressed as follows:

As before, w ( x ) are the weights for e o , whereas W v ( x ) are weights defined as follows:

Note that C V ( x ) is a weighted average of deviations from life expectancy at age x , which can be expressed as the difference between the average age of the population above age x ( a ¯ x ) and the life expectancy at birth. A detailed proof of Eq. 12 can be found in SI Appendix , section C . This result shows that changes over time in the alternative measure v of the coefficient of variation are a weighted total of the rates of progress in reducing mortality ρ ( x ) , with weights given by the product w ( x ) W v ( x ) .

Demographic Methods to Calculate Threshold Ages and Age-Specific Contributions.

From life tables, we calculated for each of the three indicators the threshold age below which averting deaths increases life span equality, and above which equality decreases. Eqs. 5 , 9 , and 12 indicate that the age-specific contribution to changes over time in life span equality can be expressed as the product ρ ( x ) w ( x ) W k ( x ) , for k ∈ { h , g , v } . Note that w ( x ) is a strictly positive function, whereas the indicator-specific weights W k ( x ) are strictly decreasing. Hence, under the assumption that death rates remain constant or decline at all ages [i.e., ρ ( x ) ≥ 0 for all x ] or remain constant or increase at all ages [i.e., ρ ( x ) ≤ 0 for all x ], for each indicator there is unique threshold age that we denote by a h , a g , and a v , respectively. These threshold ages are reached when the corresponding weights equal 0; that is, when W h ( x ) = 0 , W g ( x ) = 0 or W v ( x ) = 0 . The assumption that death rates need to decline (or increase) at all ages is necessary to have a unique threshold age. If death rates increase for some ages and decline for others, there may be several threshold ages that separate positive from negative contributions to life span equality, since the product ρ ( x ) w ( x ) W k ( x ) may switch from positive to negative several times across ages. For instance, whenever ρ ( x ) and W ( x ) are both positive (or both negative), contributions will be positive; on the contrary, whenever W ( x ) > 0 and ρ ( x ) < 0 , or W ( x ) < 0 and ρ ( x ) > 0 , contributions will be negative. We quantified age-specific contributions to yearly changes in life expectancy and life span equality for all of the data available and estimated contributions above and below those thresholds. We used a model defined on a continuous framework that assumes gradual change in mortality over time ( 86 ) used in previous studies of life span inequality ( 13 , 20 , 21 , 24 ).

Stochastic Properties of Life Expectancy and Life Span Equality.

We analyzed the stochastic properties of e o and life span equality over time to determine whether they are stationary processes (for further details, see SI Appendix , section A ). In case of nonstationarity, we also find the order of integration. We performed the Kwiatkowski–Phillips–Schmidt–Shin test ( 87 ) for e o and the three measures of life span equality, and the augmented Dickey–Fuller test ( 88 ) in their levels and first differences, respectively (we also perform tests against higher orders of integration but could not reject the hypothesis that the variables were integrated at a lower level). Using the 95% critical values, the null hypothesis of stationarity can be rejected in 94.9% of the cases for life expectancy and 93.9% for life span equality h . Moreover, at the same level, the null hypothesis of a unit root in their first differences is rejected in 97% of the cases for e o and h . These analyses suggest that the variables are nonstationary processes and achieve stationarity after differencing once for both females and males. In the statistical analysis, we treat both variables as integrated of order one. The concept of cointegration was developed to avoid misleading interpretations regarding the relationship between two integrated variables ( 89 ). It refers to the case of a model that can adjust for stochastic trends to produce stationary residuals, and it permits detection of stable long-run relationships among integrated variables. Formally, two cointegrated variables can be expressed using a two-dimensional vector autoregressive model in its error correction form, defined as follows:

Operator Δ denotes the first differences; z t is a 2 × 1 vector of stochastic variables ( e o and life span equality in our case) at time t ; Γ contains the cumulative long-run impacts; α and β are two 2 × 1 vectors of full rank; μ is a vector of constants; and ε t is a vector of normally, independently, and identically distributed errors with zero means and constant variances ( 90 ). We specify the model with an unrestricted constant in the cointegration space and dummy variables in contexts where life expectancy experienced historical shocks, such as world wars and epidemics (see SI Appendix , Table S2 and section A , for additional details and sensitivity analyses).

Data Availability.

Supplementary material, supplementary file, acknowledgments.

The research was funded by the Max Planck Society and the University of Southern Denmark. J.M.A. was partially supported by the Lifespan Inequalities research group at the Max Planck Institute for Demographic Research (European Research Council Grant 716323). J.M.A., U.B., and S.K. acknowledge support from the European Doctoral School of Demography when it was hosted at Sapienza University of Rome. Researchers at the Interdisciplinary Centre on Population Dynamics, University of Southern Denmark, and Alyson van Raalte provided helpful input.

The authors declare no competing interest.

Database deposition: A description to access the data and the code to reproduce results have been deposited on Zenodo ( https://zenodo.org/record/3571095 ).

This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1915884117/-/DCSupplemental .

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The value of life and the value of population

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Increasing longevity and life satisfaction: is there a catch to living longer?

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Human longevity is rising rapidly all over the world, but are longer lives more satisfied lives? This study suggests that the answer might be no. Despite a substantial increase in months of satisfying life, people’s overall life satisfaction declined between 1985 and 2011 in West Germany due to substantial losses of life satisfaction in old age. When compared to 1985, in 2011, elderly West Germans were, on average, much less satisfied throughout their last five years of life. Moreover, they spent a larger proportion of their remaining lifetime in states of dissatisfaction, on average. Two important mechanisms that contributed to this satisfaction decline were health and social isolation. Using a broad variety of sensitivity tests, I show that these results are robust to a large set of alternative explanations.

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1 Introduction

Over the last four decades, human life expectancy has, on average, increased by one year every four years in OECD countries (OECD 2016 ). The rise in life expectancy holds true for both men and women, at various ages, and across countries, although recently life expectancy has plateaued, if not fallen, in the UK and the USA (e.g., Case and Deaton 2015 ; Chetty et al. 2016 ; Marmot et al. 2020 ). But are longer lives more satisfied lives? This question is vital for individuals and public policymakers because longer lives might come at the price of lower quality and life satisfaction in old age. Longer lives will be less valuable to people if the additional life years are spent in dissatisfaction and this causes overall life satisfaction (i.e., life satisfaction totaled over the life course minus a death value) to decrease. Both issues are pivotal in the context of private and public decision-making, where decision makers may face the tradeoff between lengthening human life and enhancing the quality of life.

Despite its importance for public policy and individuals, little is known about how life satisfaction in old age has changed with improved longevity over time. The previous literature has almost exclusively focused on health-related measures (e.g., Crimmins and Beltrán-Sánchez 2011 ; Jagger and Robine 2011 ; and Chatterji et al. 2015 for recent reviews), although health is only one determinant of life satisfaction (Easterlin 2002 , 2003 ) and people partially adapt to poor states of health (Oswald and Powdthavee 2008 ; McNamee and Mendolia 2014 ). Evidence on life satisfaction and related concepts of well-being is limited to studies that investigate time trends of average and cumulative life satisfaction (e.g., Perenboom et al. 2004 ; Yang 2008 ; Realo and Dobewall 2011 ), or that analyze patterns of life satisfaction across a person’s lifecycle (e.g., Blanchflower and Oswald 2004 , 2008 ; Baird et al. 2010 ). However, these studies fail to control for time to death (Gerstorf et al. 2010 ) and reveal little about changes in terminal life satisfaction over time. Moreover, due to their reliance on cross-sectional data, studies are often unable to separate age, cohort, and period effects (Schilling 2005 ).

In this study, I combine two approaches to investigate how life satisfaction in old age has changed with improved longevity in West Germany between 1985 and 2011. The time-to-death approach estimates time trends of average life satisfaction by time to death. This approach focuses on the last five years of life because, unlike earlier life years in old age, these years are characterized by a sharp satisfaction decline (Gerstorf et al. 2008a , 2008b , 2010 ). Due to its distinction by time to death, this approach can uncover varying end-of-life satisfaction patterns in aging societies across time, such as a shift in the onset or a change in the slope of terminal decline. Hence, this approach is particularly useful for informing end-of-life decision-making in modern societies. The life-expectancy approach estimates time trends of satisfied life expectancy at age 60. Satisfied life expectancy at age 60 is a summary measure that collapses age-specific mortality and satisfaction prevalence rates observed in a given year into a single number. It provides information on the number of satisfied life years that a member of a 60-year-old life table cohort can expect to live given age-specific mortality and satisfaction prevalence rates as of that year. This approach adds to the time-to-death approach by accumulating satisfied life years beyond the age of 60 (analysis in absolute terms) and relating them to total remaining lifetime (analysis in relative terms) for the average individual. In doing so, it weighs increases in (satisfied) lifetime against possible satisfaction losses at the end of life and, thus, informs policymakers about the overall value of longer lives. Footnote 1

To overcome the major shortcomings of previous studies, I use data from the longest running household panel with continuous information on overall life satisfaction, the German Socio-Economic Panel (GSOEP). This data set is unique in that it allows researchers to closely follow a respondent’s life satisfaction over the life course until death for more than 30 years now. Due to its longitudinal structure and a large set of controls, this data set allows me to rule out many alternative explanations for the observed life satisfaction changes over time, including, for example, compositional, cohort, period, and time-in-panel effects.

This study contributes to the existing literature in four important ways. First, it is the first study to analyze how life satisfaction in the final period of life has changed with improved longevity over time. It provides evidence that the terminal decline in life satisfaction holds over time but has increased in length and magnitude of decline, thereby adding to the small but growing literature on end-of-life satisfaction (e.g., Gerstorf et al. 2008a , 2008b , 2010 ; Palgi et al. 2010 ; Berg et al. 2011 ). Second, this study challenges the conclusions that were drawn about life satisfaction in aging societies based on the age-satisfaction curve (e.g., Steptoe et al. 2015 ). By introducing a novel framework, this study highlights the importance of the final period of life, as opposed to age, when drawing conclusions about satisfaction patterns in aging societies across time. Third, contrary to most related studies that exploit variation in longevity over time to study well-being in aging societies (e.g., Perenboom et al. 2004 ; Yang 2008 ), this study carefully explores the role of explanations other than improved longevity. Therefore, it can exclude a large set of alternative explanations for the satisfaction decline in West Germany over time. Fourth, this study furthers our understanding of successful aging by shedding light on two important mechanisms: health and social isolation. Although these mechanisms are not new to the literature (see Oswald and Powdthavee 2008 for the former and Helliwell 2003 , 2006 for the latter), this study is the first to show that health and social isolation also play an important role in aging societies over time.

This paper proceeds as follows. Section  2 provides some background information and gives an overview of related studies. Section  3 discusses the framework that motivates the two empirical approaches of this paper. Section  4 describes the data. Section  5 presents the time-to-death approach and its results. Section  6 presents the life-expectancy approach and its results. Section  7 discusses two potential mechanisms (health and social isolation) and provides some evidence for these mechanisms. Section  8 concludes and provides some policy implications.

2 Background

Life satisfaction is an important contributor to the general construct of subjective well-being. It indicates the extent to which people positively evaluate the overall quality of their life as-a-whole (Veenhoven 1996b ). That is, in contrast to hedonic (e.g., feelings of happiness, sadness, stress) or eudemonic measures of well-being (e.g., sense of meaning and purpose in life), it provides a global assessment of the people’s quality and goodness of life (Steptoe et al. 2015 ). Life satisfaction is commonly assessed by single direct questions in surveys, with assessment scales ranging from very satisfying to very dissatisfying. Footnote 2

Empirical research on life satisfaction has grown exponentially since its start in the 1970s (Veenhoven 2015 ). This growth is likely explained by three matters: First, single-item direct questions on life satisfaction were integrated in many national and international surveys (see Dolan et al. 2008 for an overview). Second, previous research in psychology, sociology, and economics has shown that life satisfaction correlates well with a large set of outcomes and major life events (e.g., Di Tella et al. 2001 ; Frijters et al. 2004b ; Deaton 2008 ; Clark et al. 2008 ), and predicts relevant future behavior (e.g., Koivumaa-Honkanen et al. 2001 for suicide). Overall, the reliability, validity, and sensitivity of life satisfaction measures is fairly high. Footnote 3 Third, life satisfaction is coming to the forefront of the public policy discourse, in which the improvement of population satisfaction is emerging as a key societal aspiration (Steptoe et al. 2015 ). Footnote 4

Facing the challenges of population aging, an important field of research on life satisfaction has investigated the association between age and satisfaction (see Steptoe et al. 2015 for an excellent review). Using data from large-scale national and international surveys, studies in this field often, but not always, find that the association between age and life satisfaction is U-shaped with a strong dip in life satisfaction in middle age, and possibly another downturn in old age (e.g., Blanchflower and Oswald 2004 , 2008 , 2019 ; Wunder et al. 2013 ; Graham and Ruiz Pozuelo 2017 ; Blanchflower 2021 ). However, the downturn in old age almost vanishes upon controlling for time to death (e.g., Gerstorf et al. 2008a , 2010 ). This suggests that life satisfaction in old age is a function of time to death rather than age. Nevertheless, patterns of terminal life satisfaction decline may depend on age. Exploring interindividual differences in terminal satisfaction decline, Gerstorf et al. ( 2008b ), for example, show that individuals dying at older ages spend more time in the period of terminal satisfaction decline than individuals dying at earlier ages. However, it is yet unknown how such cross-sectional results translate to changes in overall life satisfaction in aging societies over time.

A second strand of research has analyzed changes in life expectancy in well-being within a country across time. Most studies in this field estimate healthy life expectancy and—depending on the health indicator and country of investigation—report mixed results (see Jagger and Robine 2011 for a review). Only two studies use concepts of well-being that are more closely related to satisfaction. Perenboom et al. ( 2004 ) estimate life expectancy in hedonic well-being at the ages 16 and 65 and show that it significantly increased for men and women between 1989 and 1998 in the Netherlands. Yang ( 2008 ) computes happy life expectancy for both men and women at various ages in the United States. He finds that happy life expectancy at all ages rose in both absolute (number of years) and relative terms (proportion of life) between 1970 and 2000. Thus, both studies suggest that increases in longevity came with improvements in well-being. However, it is yet unknown whether these results also generalize to other countries and later time periods.

In what follows, I present a simple framework that furthers our understanding of the age-satisfaction association within the context of an aging society.

3 A framework

To evaluate the impact of improved longevity, it is necessary to compare the overall quality of two representative lives that differ with respect to their length. In economics, the quality of life is measured by lifetime utility. Lifetime utility captures the idea that people attach value to both length and quality of life, thus accounting for the fact that the value of a longer life strongly depends on its quality. As life satisfaction is a good proxy for utility (Benjamin et al. 2012 , 2014 ; Fleurbaey and Schwandt 2015 ), a measure of overall life satisfaction is obtained by replacing contemporaneous utility scores in the lifetime utility function with their corresponding reported life satisfaction scores. Assuming that people attach equal weight to each year of life (i.e., there is no discounting), overall life satisfaction of the representative agent is then given by

where \(A \in \mathbb {R_{+}}\) is the age in the last year of life, \(LS_{a} \in \left [\underline {LS}, \overline {LS}\right ]\) is the life satisfaction score at age a , and \(LS_{d} \in \left [\underline {LS}, \overline {LS}\right ]\) is the life satisfaction score that is attached to death. The normalization by L S d accounts for the fact that there are states of life that are considered not worth living (e.g., Ditto et al. 1996 ; Rubin et al. 2016 ). In this framework, an increase in longevity from A to \(A^{\prime }\) is considered to be welfare improving if \(TLS^{\prime } > TLS\) , i.e., if overall life satisfaction of the representative agent increases.

One major drawback of this framework is its reliance on the cardinality assumption. This is because life satisfaction in surveys is typically measured on an ordinal scale. To remain as close as possible to the notion of overall life satisfaction without having to rely on cardinality, I use a combination of two approaches: the time-to-death approach and the life-expectancy approach. The former, new to the satisfaction literature, rests on a minimum set of assumptions and can be sufficient to conclude that past increases in lifetime were welfare improving. The life-expectancy approach complements it for the cases where increases in (satisfied) lifetime have to be weighed against losses in end-of-life satisfaction. This latter approach requires some additional assumptions, most importantly, the choice of a cutoff value to distinguish between states of satisfaction and dissatisfaction. Footnote 5

In the following, the underlying idea of the approaches will be presented. For the time-to-death approach, it is useful to observe two important facts about the evolution of life satisfaction in old age:

Stability-despite-loss paradox: For years more distant from death, life satisfaction is relatively stable in old age despite aging-related losses (Diener et al. 1999 ; Kunzmann et al. 2000 ; Schilling 2006 ).

Terminal decline: For years close to death, life satisfaction strongly declines with proximity to death. This decline is linear, possibly with a more pronounced drop in the last year of life, and it starts, on average, roughly three to five years before death (e.g., Gerstorf et al. 2008a , 2008b , 2010 ; Palgi et al. 2010 ; Berg et al. 2011 ).

This suggests that it is crucial to investigate changes in terminal life satisfaction over time to understand whether overall life satisfaction has increased with improved longevity in aging societies.

Characteristics of the terminal life satisfaction decline might change with improved longevity. It is, for example, possible that the terminal decline extends, leading to much lower life satisfaction scores immediately before death. Alternatively, there might be a shift in the onset of terminal decline to an older age, or a change in the slope of terminal decline. Figure  1 illustrates some of these possible changes for the representative agent (graphs on the left). How these changing terminal life satisfaction patterns over time can be uncovered by analyzing time trends of average life satisfaction by time to death is illustrated in Fig.  1 on the right. Footnote 6 If, for example, a downward sloping time trend of average life satisfaction for the last year of life is observed, this is consistent with an extension of the terminal decline (see panels a and d). A change in the slope of terminal decline over time is reflected by narrowing (see panel c) or widening (see panel d) gaps between the average life satisfaction trends over time.

Illustration of the time-to-death approach. This figure illustrates how possible changes of terminal life satisfaction patterns for the representative agent over time (graphs on the left) can be uncovered by focusing on the last five years of life and analyzing time trends of average life satisfaction by time to death (graphs on the right). Each panel (a to d) shows a different change in terminal life satisfaction patterns. Source: Author’s representation

A clear indication for a welfare improvement in terms of overall life satisfaction is the pattern of average life satisfaction trends that are upward sloping or flat over time. This is easily seen for the limiting case, which is depicted in panel b of Fig.  1 . If the shift in the onset of terminal decline exactly corresponds to the shift in the age at death, the additional lifetime is exclusively spent in satisfaction. Further, considering that life satisfaction scores in the terminal decline phase are identical, it must be that overall life satisfaction of the representative agent increases. This holds even in the absence of the cardinality assumption. Footnote 7 In contrast, if average life satisfaction trends are downward sloping, this is a necessary but not sufficient condition for a welfare loss in terms of overall life satisfaction. The reason is that downward sloping time trends indicate a deterioration of the final period of life that can be compensated by an increase in satisfied lifetime. That is, overall life satisfaction may increase or decrease, depending on how losses in terminal life satisfaction are valued relative to gains in satisfied lifetime. Hence, in this case a summary measure is required to obtain clear predictions.

As this summary measure, I use satisfied life expectancy at age 60. It does not rely on the cardinality assumption, but requires weighting increases in satisfied lifetime against increases in dissatisfied lifetime to allow for welfare comparisons across time. To do so, I compare the proportion of expected satisfied lifetime to expected total lifetime at the age of 60 across time. Under the assumption that at the age of 60, people prefer a high proportion of satisfied lifetime over a higher number of satisfied life years, successful aging requires this proportion to be non-decreasing over time. This implies, however, that people are willing to accept an extension of the dissatisfied lifetime at the end of their life, provided that it is not too long compared to the extension in satisfied lifetime. This is one important feature that also finds empirical support in discrete choice experiments on the willingness-to-pay for life extensions (Pennington et al. 2015 ; Ahlert et al. 2016 ; Fischer et al. 2018 ).

Overall, this section argues that we need to observe an increase in the proportion of satisfied lifetime at the age of 60 to conclude that overall life satisfaction has increased with improved longevity. This is clearly the case if average life satisfaction trends by time to death are upward sloping or flat. However, it may also be the case if we observe a deterioration of the final period of life (downward sloping trends) because a possible increase in satisfying lifetime may compensate for a worse final period of life.

This study uses data from the German Socio-Economic Panel. The GSOEP is a nationally representative longitudinal study of households in Germany. It was launched in 1984. Initially, it included West German households only. After the German reunification, a representative sample of East German households was added. Currently, more than 20000 adult residents are interviewed on an annual basis. The survey content includes rich information on demographics, household composition, health, attitudes, and values. Footnote 8

Information on overall life satisfaction has been gathered annually since 1984. It is collected using the question “How satisfied are you with your life currently, all things considered?” The answer is measured on an 11-point Likert scale, ranging from 0 (very dissatisfied) to 10 (very satisfied). Information on mortality and the year of death is obtained either directly at the yearly interviews from remaining household members, relatives, and neighbors, or indirectly from official registries, which were contacted throughout dropout studies. Time to death is calculated by subtracting the survey year from the year of death. Lacking information on the month of death, I refer to people as being one year, two or three years, and four or five years before death in what follows.

Beyond the GSOEP data, two additional data sources are used. I use data from the official German Death Statistics (GBE 2016 ) to adjust the estimates throughout the time-to-death approach. This adjustment was necessary because women are underrepresented among older GSOEP participants. Scale weights were constructed based on gender, five-year age-at-death intervals, German nationality, and time to death. They were merged to the GSOEP by year of death and group characteristics (i.e., gender, age, and German nationality), implicitly assuming that the composition of the population in West Germany was constant in the five years before death. To compute satisfied life expectancy at age 60, I use gender-specific period life tables for West Germany. They have been provided by the German Statistical Office on an annual basis since the late 1950s (German Federal Statistical Office 2012a , 2012b ).

The two main samples were obtained as follows: I used data from the GSOEP samples A to F. Footnote 9 The elderly in East Germany were excluded because their life satisfaction levels were strongly affected by the institutional and ideological changes in East Germany following German reunification (e.g., Frijters et al. 2004a ; Vogel et al. 2017 ). This renders their data less appropriate for longitudinal comparisons. Furthermore, I excluded migrants because the composition and the share of migrants changed over time. These changes are likely problematic because reported satisfaction levels vary with nationality (Steptoe et al. 2015 ). Finally, I restricted the analysis to the elderly, i.e., I focused on respondents who died at age 60 or older and were within five years of death (time-to-death sample) or respondents who were aged 60 plus at the time of the survey interview irrespective of their remaining lifetime (life-expectancy sample). The age threshold of 60 was chosen because in the last three decades the vast majority of age-related deaths in West Germany occurred at the age of 60 or older. Footnote 10

Figure  2 shows the distribution of life satisfaction scores for the time-to-death and life-expectancy samples. It illustrates for both samples that the life satisfaction distribution is highly left-skewed. For the life-expectancy sample, almost 50% of the responses are concentrated on the categories seven and eight, and only 7.7% of the respondents report a life satisfaction score below five (the midpoint of the scale). The distribution of the time-to-death sample is less skewed than the distribution of the life-expectancy sample. The stronger concentration of responses at lower life satisfaction scores for the time-to-death sample is consistent with the terminal decline in life satisfaction.

Distribution of life satisfaction scores by sample. N = 9371 (time-to-death sample) and N = 26870 (life-expectancy sample). Life satisfaction is measured on an 11-point Likert scale, ranging from 0 (very dissatisfied) to 10 (very satisfied). Source: Author’s calculations based on SOEPv30 (1984–2013)

5 Time-to-death approach

This section analyzes how terminal life satisfaction changed with improved longevity across time. Before presenting the results, additional details on the estimation are provided.

5.1 Empirical strategy

Time trends of average life satisfaction were estimated based on 2446 West German respondents who were within five years of death between 1985 and 2011 (unbalanced sample). Satisfaction trends are shown separately by time to death to allow us to uncover changes in both slope and onset of terminal satisfaction decline. I estimated three-year moving averages in order to smooth the satisfaction trends slightly. Estimates in a given year rely on roughly 200 to 400 observations. Weighted estimates are reported throughout using the scale weights that were described in Section  4 .

A meaningful interpretation of these estimates relies on the assumption that changes in terminal life satisfaction over time can only be attributed to increased longevity. This requires ruling out a large variety of time-varying factors that may also contribute to changes in terminal life satisfaction over time. Therefore, following the results, a broad set of sensitivity checks shows that the time-to-death results cannot be explained by compositional, cohort, or time-in-panel effects, general macroeconomic trends or aging-unrelated period effects, an endogenous onset of disease and terminal life satisfaction decline, an increasingly negatively selected sample due to the age restriction, or increasing attrition among the elderly across time.

5.2 Results

Figure  3 depicts the time trends of average life satisfaction and average age at death for elderly West Germans without a migration background who were one year (solid line in dark gray), two or three years (dashed-dotted line in black), and four or five years (dashed line in light gray) prior to death. Footnote 11 This figure clearly suggests that the last five years of life, on average, deteriorated with improved longevity over time. The graph on the left indicates that average life satisfaction prior to death strongly declined over time, irrespective of the time to death. Between 1985 and 2011, average life satisfaction decreased by almost one Likert point, which corresponds to about half a standard deviation of life satisfaction. Footnote 12 The decline in life satisfaction reaches statistical significance, and it is large, when compared to the change in life satisfaction that is caused by a change in alternative respondents’ characteristics such as education or employment status (e.g., Oreopoulos 2007 for education and Clark and Oswald 1994 , Winkelmann and Winkelmann 1995 , and Kassenboehmer and Haisken-DeNew 2009 for unemployment and job loss). The graph on the right demonstrates that the decline in life satisfaction went along with an increase in the average age at death. Footnote 13 Time series correlation coefficients for the satisfaction and age at death trends range between − 0.58 and − 0.78.

Average life satisfaction and average age at death for elderly West Germans within five years of death, 1985–2011, by time to death. Estimated based on the time-to-death sample. Estimates in a given year represent three-year averages. Life satisfaction is measured on an 11-point Likert scale, ranging from 0 (very dissatisfied) to 10 (very satisfied). Age at death is measured in years. Source: Author’s calculations based on GBE ( 2016 ) and SOEPv30 (1984–2013)

Linking the results in Fig.  3 to the stylized profiles in Fig.  1 , Fig.  3 offers some additional insights. First of all, it shows that the terminal life satisfaction decline also holds in aging societies across time. In each given year, life satisfaction declines, on average, with proximity to death. However, patterns of the terminal satisfaction decline have changed with improved longevity over time. Until 2000 average satisfaction trends fell in parallel. This is consistent with an extension of the terminal decline and, thus, substantially lower life satisfaction scores in the last five years of life (cf. panel a in Fig.  1 ). After 2000, average life satisfaction continued to decrease for the elderly who were more than one year prior to death, but stayed relatively constant for those in the last year of life. This narrowing gap between the average life satisfaction trends is consistent with a flattening slope of terminal decline over time (cf. panel c in Fig.  1 ). Finally, as average life satisfaction four to five years prior to death did not stay constant but decreased over time, the possible shift in the onset of terminal decline was smaller than the shift in the age at death (cf. limiting case in panel b in Fig.  1 ). That is, the duration of the terminal decline phase extended. This extension came with satisfaction losses in old age that go beyond the last five years of life.

5.3 Sensitivity tests

This section discusses the results of a large battery of sensitivity checks. Supporting figures and tables are provided in Appendix 1 .

To assess the role of compositional effects, cohort effects, and time-in-panel effects, I estimated weighted individual-level life satisfaction regressions by time to death. Footnote 14 Using the pooled three-year average data set, I regressed life satisfaction on a set of year dummies, subsequently adding distinct sets of controls to the regressions: To account for compositional effects, I added a dummy for males, years of education, net household income, dummies for the interview month, and dummies for the state of residence; to account for cohort effects, I added five-year cohort dummies; and to account for time-in-panel effects, I added a linear term for time-in-panel duration. Footnote 15 Figure  7 in Appendix 1 graphically depicts the year dummy coefficient estimates of these regressions relative to the year 1985. It demonstrates that the decline in terminal life satisfaction across time persists, even after controlling for compositional, cohort, and time-in-panel effects, although there is some evidence that time-in-panel effects contributed to the decline of end-of-life satisfaction over time. Footnote 16

To investigate whether the decline in terminal life satisfaction over time is driven by macroeconomic effects (e.g., German reunification) or simply represents a general aging-unrelated time trend, I used a difference-in-difference type of approach. Footnote 17 More specifically, I estimated time trends of average life satisfaction for three control groups of West German respondents that were formed based on age. In order to rule out the possibility that macroeconomic events or a general time trend contributed to the terminal life satisfaction decline over time, life satisfaction trends for the control groups should be upward sloping or flat. Figure  8 in Appendix 1 shows that there is at most a small decline in average life satisfaction over time for all three control groups.

Previous literature suggests that more satisfied people tend to live longer (see Veenhoven 2008 for a review). Here, reverse causality is problematic for two reasons. First, the age restriction for the time-to-death sample may lead to an increasingly negatively selected sample over time. Second, at the individual level, onset of disease, onset of terminal life satisfaction decline, and age at death are endogenous. To address the concern of increasing sample selectivity, I dropped the age restriction, i.e., I added 383 people who died before age 60 to the sample. Figure  9 in Appendix 1 shows that average life satisfaction trends exhibit the same slopes of decline, thereby ruling out this potential explanation. To address the concern of endogeneity at the individual level, I re-estimated average life satisfaction trends using objective death probabilities instead of actual distance to death. Objective death probabilities were retrieved from period life tables (German Federal Statistical Office 2012a , b ) and indicate a person’s probability of dying before her next birthday. If population aging rather than endogenous shifts in the onset of terminal life satisfaction decline led to the decline in terminal life satisfaction over time, average life satisfaction trends should be downward sloping. Figure  10 in Appendix 1 shows that for West Germans aged 60 and older, this was indeed the case.

Finally, to investigate whether differential attrition patterns over time contributed to the downward slope of average life satisfaction trends, I estimated a linear probability model for study dropout using the unbalanced time-to-death sample. Table  2 in Appendix 1 reports the regression results. It shows for the last five years of life that less satisfied elderly West Germans are more likely to drop out of the GSOEP, but that the attrition pattern with respect to life satisfaction did not change over time.

6 Life-expectancy approach

This section investigates whether increases in satisfied lifetime compensated for the worse final period of life such that people became better off in terms of overall life satisfaction (i.e., the proportion of expected satisfied lifetime after age 60) with improved longevity. Again, details on the estimation are provided first.

6.1 Empirical strategy

Time trends of satisfied life expectancy at age 60 were estimated based on Sullivan’s method (Sullivan 1971 ). Footnote 18 The idea of this method is quite simple. It divides total life expectancy at age 60 into satisfied and dissatisfied life expectancy at age 60 by combining data from two different sources. While the person-years lived in each age interval are obtained from period life tables, satisfaction prevalence rates for the corresponding age intervals are estimated based on survey data and then used to weight the person-years lived in each age interval. After weighting, the computation of satisfied life expectancy is equivalent to that of standard life expectancy. That is, satisfied life expectancy at age 60 is computed by summing up the weighted person-years lived after age 60 and then dividing it by the number of 60-year-old survivors. Formally, Sullivan’s estimator is defined as

where A 60 represents the set of starting ages x such that x ≥ 60, \(\hat {h}_{x, n_{x}}^{s}\) denotes the sample fraction of satisfied survey respondents in the age interval [ x , x + n x ), \(L_{x, n_{x}}\) indicates the person-years lived in the age interval [ x , x + n x ), and l 60 gives the number of 60-year-old survivors. Footnote 19 Dissatisfied life expectancy at age 60 is estimated either by replacing \(\hat {h}_{x, n_{x}}^{s}\) with the sample fraction of dissatisfied survey respondents, \(\hat {h}_{x, n_{x}}^{ds} = 1 - \hat {h}_{x, n_{x}}^{s}\) , in ( 2 ) or by directly subtracting satisfied life expectancy at age 60 from total life expectancy at age 60.

I used five-year age intervals, i.e., n x = n = 5 for all but the last age interval, which ranged from 85 to the oldest observed age. Gender-age-specific satisfaction prevalence rates were estimated by the gender-age-specific sample fractions of GSOEP respondents in any of the three states: dissatisfied (life satisfaction of 0 to 6), moderately satisfied (life satisfaction of 7 or 8), and very satisfied (life satisfaction of 9 or 10). The threshold values correspond to the first and third quartiles of the pooled life satisfaction distribution in the life-expectancy sample. Consistent with the data from period life tables, I estimated the satisfaction prevalence rates using three-year averages. Footnote 20 Estimates were weighted using cross-sectional survey weights in order to account for the sampling structure of the GSOEP.

To allow for comparisons of satisfied life expectancy at age 60 across time, estimates are reported for the years 1985, 1990, 2000, and 2010 in both absolute (number of years) and relative (proportion of life) terms. For testing purposes, standard errors were derived based on the delta method (see Appendix 2 ). They differ from those that are usually employed in the literature, because I use longitudinal data and pool the data of three years when estimating the satisfaction prevalence rates for a given year. While testing, I implicitly assume that the covariance between two life expectancy estimates can be ignored because I independently computed the standard errors of satisfied life expectancy across the different years. Since this assumption is most plausible for the largest time difference, I only report test results for the difference between 1985 and 2010. For this difference, less than 5% of the observations stem from respondents who took part in the survey in both years (including the surrounding years).

6.2 Results

Table  1 presents the estimates of satisfied life expectancy at age 60 for West Germans without migration backgrounds by gender and year and contrasts them with the increase in total life expectancy at age 60. Between 1985 and 2010, total life expectancy for a 60-year-old man continuously grew from 17.1 years in 1985 to 21.4 years in 2010. In 2010, he was expected to spend about 15 years of his life in states of satisfaction, which made up for 70% of his remaining lifetime. More than half of the additional lifetime was, on average, spent in states of satisfaction, despite the steady decline in very satisfied lifetime after 1985. For a 60-year-old woman, the pattern across time was very similar, but the increase in average satisfied lifetime of 1.4 years was substantially lower than that for a 60-year-old man. It only accounted for 40% of the overall increase in a 60-year-old woman’s lifetime. Nevertheless, in 2010, women at the age of 60 were also expected to spend a fairly high fraction (about two-thirds) of their remaining lifetime in states of satisfaction.

However, there also was a flip side to the coin. The extension of the terminal decline period as well as the larger fraction of dissatisfied West German elderly people within five years of death (cf. results in Section  5.2 ) were reflected in a significant rise of expected dissatisfied lifetime. The rise in expected dissatisfied lifetime outweighed the rise in expected satisfied lifetime such that the proportion of satisfied lifetime to total lifetime fell after 1985. Footnote 21 In 2010, the decline in the proportion of satisfied lifetime equaled 3 to 4 percentage points. This corresponds to a 5% reduction in the proportion of satisfied lifetime or a 12% increase in the proportion of dissatisfied lifetime, on average. The decline in the proportion of satisfied lifetime is statistically significant for both men and women, albeit for men only at the 10% level in a one-sided test. Thus, if we rely on the assumption that at the age of 60, people prefer a high proportion of satisfied lifetime over a higher number of satisfied life years (cf. Section  3 ), the life-expectancy results suggest that the overall quality of life deteriorated with improved longevity in West Germany between 1985 and 2010. Footnote 22

To better understand what contributed to the changes in satisfied life expectancy at age 60 over time, I estimated counterfactual satisfied life expectancy at age 60, keeping age-specific mortality rates constant as of 1985. This allows me to distinguish between changes that result directly from declines in mortality and changes that result both indirectly from declines in mortality and from changes in satisfaction prevalence. Footnote 23 Figure  4 presents the estimates of counterfactual life expectancy at age 60 by gender and year and contrasts them with the estimates of actual life expectancy at age 60 that were presented in Table  1 . At each point in time, total life expectancy — as indicated by the full length of a bar — is divided into the number of years that a 60-year-old survivor can expect to live in the very satisfied, moderately satisfied, and dissatisfied states. Changes in satisfied life expectancy that result from changes in satisfaction prevalence and the indirect mortality effect are shown within the bar charts for counterfactual life expectancy. In contrast, changes that result solely from declines in mortality (direct mortality effect) are assessed by comparing changes of actual and counterfactual satisfied life expectancy across the bar charts for men or for women.

Actual and counterfactual satisfied life expectancy at age 60 by gender and year, West Germany (1985–2010). LE, life expectancy. This figure shows the evolution of total and satisfied life expectancy at age 60 in West Germany by gender (actual LE, cf. Table  1 ) and contrasts it with the evolution that would result if mortality rates were kept constant as of 1985 (counterfactual LE). In each year, total life expectancy is divided into the expected number of very satisfied (life satisfaction of 9 or 10), moderately satisfied (life satisfaction of 7 or 8), and dissatisfied (life satisfaction of 0 to 6) life years. Changes in satisfied life expectancy that only result from reduced mortality (direct mortality effect) are assessed by comparing changes of satisfied life expectancy across actual and counterfactual bar charts for men and for women. Changes that result from changes in satisfaction prevalence but also include an indirect mortality effect (due to possible shifts in the onset of satisfaction decline) are assessed by comparing satisfied life expectancy within the counterfactual bar charts for men or for women across time. Source: Author’s calculations based on German Federal Statistical Office ( 2012a , 2012b ) and SOEPv30 (1984–2011)

A comparison of counterfactual estimates within the bar charts for men and women suggests that the observed decrease in very satisfied life expectancy between 1985 and 2010 was fully attributable to a decline in satisfaction prevalence over time, as reflected by the strong decrease in counterfactual very satisfied life expectancy over time. Footnote 24 The direct effect of declining mortality did not contribute to the decline in very satisfied life expectancy, as the comparison of actual and counterfactual estimates shows. The opposite holds true for the changes in dissatisfied life expectancy. Almost the full increase in dissatisfied life expectancy at age 60 between 1985 and 2010 is explained by direct declines in mortality. Changes in satisfaction prevalence over time contributed, if at all, only very little to the increase in dissatisfied life expectancy over time. This result is crucial because it suggests that explanations other than improved longevity, including period, cohort, and time-in-panel effects, are unlikely to explain the increase in dissatisfied life expectancy.

6.3 Sensitivity tests

The life satisfaction scale in the GSOEP does not indicate where on the scale “dissatisfied” stops and “satisfied” starts. This challenges the interpretation of scores. To explore the sensitivity of the life-expectancy results, I used two alternative classification schemes. First, I used the midpoint of the Likert scale to distinguish between dissatisfied and moderately satisfied states and kept the threshold value for the very satisfied state constant. Second, I used an equal point split classification. That is, I classified respondents as dissatisfied (moderately satisfied, very satisfied) if they reported a life satisfaction score between 0 and 4 (5 and 7, 8 and 10).

Figure  11 in Appendix 1 depicts the results. Under the midpoint split classification (left panel), I continue to find qualitatively the same results. That is, between 1985 and 2010, there was again a strong increase in dissatisfied life expectancy at age 60 in both absolute and relative terms. However, the change in relative terms was no longer statistically significant. Under the equal point split classification (right panel), a different picture emerges. Here, expected satisfied lifetime at age 60 increased between 1985 and 2010, as did expected dissatisfied lifetime, but the increase in the former was, on average, more than 10 times larger than in the latter. Therefore, with a threshold value of four for dissatisfied states, the proportion of expected satisfied lifetime to expected total lifetime at age 60 no longer decreased, but stayed at a constant level of about 91 to 92%, which corresponded to a total of about 20 expected satisfied life years across sexes in 2010.

6.4 Discussion

The life-expectancy results differ from those reported in Perenboom et al. ( 2004 ) and Yang ( 2008 ). This discrepancy in findings may be explained by three crucial differences across studies. First, the other two studies rely on different measures of well-being. While Perenboom et al. ( 2004 ) measure hedonic well-being based on the negative items of the Bradburn Affect Balance Scale, Footnote 25 Yang ( 2008 ) uses happiness — a concept that is more closely related to life satisfaction. However, in his study, happiness is only measured on a 3-point scale. This may hide important data patterns, in particular, if states of satisfaction and dissatisfaction are pooled in the intermediate category. In fact, I can replicate his findings when pooling states of satisfaction and dissatisfaction in the intermediate category under the equal point split classification. Second, the other two studies focus on earlier time periods. Since in earlier time periods life expectancy levels were lower, the differences in results may also be explained by a level effect. In all three studies, the observed gender differences would be consistent with such a level effect. Third, the other two studies focus on different countries. Veenhoven ( 1996a ) showed that happy life expectancy strongly differs across countries, and that contextual factors such as affluence, freedom, and tolerance explain 70% of the statistical variance in happy life expectancy. In line with his findings, I find that the results for West Germany are worse than for the Netherlands and the United States.

7 Mechanisms

This section discusses two important mechanisms for the decline in terminal life satisfaction over time: health and social isolation.

Health gradually declines with age (DePinho 2000 ; Rosenthal and Kavic 2004 ) and poor health is negatively related to life satisfaction (e.g., Oswald and Powdthavee 2008 ). Thus, one obvious channel through which increased longevity can affect life satisfaction is health.

Figure  5 shows time trends of the main health indicators in the GSOEP by time to death. It suggests that a deterioration of health is likely an important mechanism. Three out of the four objective health indicators show a sharp rise with increased longevity (top and middle graphs). The share of elderly people within five years of death who had a severe disability more than doubled between 1985 and 2011. Footnote 26 In 2011, more than every second elderly person exhibited a health impairment immediately before death. Subjective health measures (bottom graphs) also indicate a significant decline in health for all but the last year of life, however, the size of the decline is small. One likely explanation for this difference between objective and subjective health measures is interpersonal comparison (Steffel and Oppenheimer 2009 ). Footnote 27

Average health indicators for elderly West Germans within five years of death, 1985–2011, by time to death. Estimates in a given year represent three-year averages. Having a severe health impairment is measured by legally attested disability status. Doctor visits refer to the last three months. Hospital stays refer to the last year. Health satisfaction is measured on an 11-point Likert scale, ranging from 0 (very dissatisfied) to 10 (very satisfied). Self-assessed health status is measured on a 5-point scale, ranging from 1 (bad) to 5 (very good). Due to missing information (information not collected in 1990 and 1993) and item non-response estimates were obtained from a smaller sample than in Fig.  3 for all but the health satisfaction indicator. s1, s23, and s45 indicate the slope estimates for fitted linear trend lines (not shown in graphs). ‡ p < .10; * p < .05; ** p < .01; *** p < .001. Source: Author’s calculations based on GBE ( 2016 ) and SOEPv30 (1984–2013)

Figure  12 in Appendix 1 provides further evidence for the health mechanism. It demonstrates that the decline in terminal life satisfaction over time becomes much smaller after controlling for health indicators in individual-level life satisfaction regressions. Health satisfaction explains roughly one-third of the decline in life satisfaction of respondents who were two or three years before death, while the disability status fully explains the decline in life satisfaction of respondents who were four or five years before death. Overall, these results support the expansion of morbidity hypothesis (Gruenberg 1977 ; Olshansky et al. 1991 ).

7.2 Social isolation

Social isolation and inactivity are negatively associated with life satisfaction (e.g., Chappell and Badger 1989 ; Pinquart and Sörensen 2000 ; Powdthavee 2008 ), also prior to death (Gerstorf et al. 2016 ). Among various measures of social isolation, disconnectedness with social peers and a low number of friends have the most detrimental impact on life satisfaction (Chappell and Badger 1989 ; Pinquart and Sörensen 2000 ). Due to a reduction of multigenerational households (German Federal Statistical Office 2016 ) and increased geographical distance between adult children and elderly parents in Germany (e.g., Mahne and Huxhold 2017 ), fewer personal contacts with family members likely contributed to the decline in terminal life satisfaction over time. Moreover, given the increased variation in longevity at age 60 in industrialized countries (Engelman et al. 2010 ), it is possible that elderly West Germans became more likely to experience a friend’s death early in life, reducing the frequency of personal contacts with friends over time. In addition, fewer personal contacts with family and friends might have resulted from reduced mobility because mobility strongly declines with age among the elderly people (Ferrucci et al. 2016 ), likely due to impoverished health.

Figure  6 shows that the frequency of mutual visits with family and friends strongly decreased over time for the West German elderly who were within their last five years of life. Footnote 28 Between 1990 and 2008, the shares of the elderly with less than monthly mutual visits (only for mutual visits with friends) and without any visits (for both types of mutual visits) each increased by more than five percentage points. I investigated three additional indicators of social isolation: single household status, partnership status, and widowhood. I find that these indicators contributed to the decline in terminal life satisfaction over time as well, also after controlling for health. Footnote 29 Overall, these results suggest that increased social isolation was an additional explanation for the steady decline in terminal life satisfaction over time.

Share of elderly West Germans within five years of death that had mutual visits with family and friends, 1990–2008, by frequency of visits. Due to missing information (information only available for five years) and item non-response estimates were obtained from a smaller sample than in Fig.  3 . A distinction by time to death (cf. Figs.  3 and  5 ) was not meaningful because of small sample sizes. Shares do not add to 100% as the category “weekly visits” is not shown. Source: Author’s calculations based on GBE ( 2016 ) and SOEPv30 (1984–2013)

8 Conclusion

Given the rapid increase in human life expectancy throughout the last decades, this study asks: Are longer lives more satisfied lives? Using data from the German Socio-Economic Panel, this study suggests that the answer might be no. Although expected satisfied lifetime increased for West Germans at the age of 60 by two years between 1985 and 2010, this increase likely did not compensate for the substantial losses of life satisfaction that occurred at the end of people’s lives. In 2010, average life satisfaction scores in the last five years of life were roughly one-third to half a standard deviation lower than in 1985. Moreover, the period of terminal satisfaction decline was substantially longer. With, on average, slightly more than two additional dissatisfied life years, 60-year-old survivors in 2010 were expected to spend 10% more of their remaining lifetime in states of dissatisfaction, which suggests a drop in this study’s measure of overall quality of life. Nevertheless, in 2010, the proportion of expected satisfied lifetime to expected total lifetime at age 60 was still relatively high, with an average level of about 65% to 70%.

To better understand what contributed to the decline in terminal life satisfaction in West Germany, I explored the role of two potential mechanisms: health and social isolation. Several health indicators (e.g., severe disability, number of hospitalizations) indicated a deterioration of the end-of-life health status over time and, thus, provided support for the expansion of morbidity hypothesis (Gruenberg 1977 ; Olshansky et al. 1991 ). Among all health indicators, the increase in legally attested disability had the most detrimental impact on terminal life satisfaction. All measures of social isolation contributed to the decline in terminal satisfaction over time, but individual-level life satisfaction regressions indicated that increased isolation mainly worked through the health channel. These results are in line with studies that show that the onset of disability relates to a lasting well-being decline (Lucas 2007 ; Oswald and Powdthavee 2008 ), and that a socially active life is associated with higher late-life well-being, less pronounced late-life decline, and a later onset of terminal satisfaction decline (Gerstorf et al. 2016 ).

One likely explanation for the findings of this study is the decline in sudden death. Over the last three decades, age-standardized mortality from ischaemic heart disease has fallen by more than half in high income countries (Finegold et al. 2013 ; Hartley et al. 2016 ). So while in earlier times, when smoking was still very common, quite healthy and satisfied people suddenly dropped dead, nowadays new medical technologies (e.g., drug-eluting stents) allow the medical profession to extend people’s lives even with disease. As a consequence, people are much more likely to experience novel types of diseases as well as an increased burden and complexity of multimorbidity (WHO 2010 ). Moreover, thinking of slowly progressing diseases such as Alzheimer’s disease or dementia that come with a progressive decline in memory and cognitive function and eventually lead to severe disability (Alzheimer’s Association 2016 ), it is very plausible that people are much less satisfied throughout their final period of life nowadays. Overall, higher dissatisfaction levels may result from the burden associated with disease, including increased social isolation, as well as the fact that people know that there is no cure or modifying treatment for a disease (Daviglus et al. 2010 ).

The final conclusion that the overall quality of life decreased with improved longevity between 1985 and 2011 rests on a very strong assumption, namely that at the age of 60, people value a high proportion of satisfied to total lifetime more strongly than the actual number of satisfied life years. Although consistent with the literature (Pennington et al. 2015 ; Ahlert et al. 2016 ; Fischer et al. 2018 ), this assumption may not hold. Another related issue is that of acceptable satisfaction levels. Many people would argue that satisfaction levels above the neutral (i.e., 5 on the 0 to 10 scale) are still quite satisfying and, thus, the elderly in our sample, though more dissatisfied in the final period of life, were still quite satisfied in 2011. However, there is a well-documented issue of over-reporting satisfaction scores in surveys with face-to-face interviews (see Diener et al. 2013 for review). Even satisfaction scores of about four (on the 0 to 10 scale) may be predictive of suicide (Koivumaa-Honkanen et al. 2001 ). If people nevertheless believe that life is still satisfying at very low satisfaction scores (i.e., three and lower), then the final conclusion of this study will no longer hold.

Should people and policymakers further invest in life extensions? This study shows that it is important to complement investments that extend the length of human life with investments that improve the quality of life in old age. Under-investments in the latter result in declining satisfaction levels at the end of people’s lives. Quality-of-life-improving policies may have a more positive effect on increasing overall life satisfaction. This is because they would increase satisfaction during a person’s lifetime, and furthermore, may also extend the length of life itself since more satisfied people tend to live longer (Veenhoven 2008 ; Steptoe et al. 2015 ).

Which quality-of-life-improving policies should be targeted? As suggested by the analysis of potential mechanisms, potential candidates would be policies that aim to prevent noncommunicable diseases (e.g., via reduced tobacco use, healthy diets, or physical activity) and policies that aim to achieve a better integration of the elderly in today’s societies (e.g., via better provision of public transportation in remote areas). Further research on these and other potential mechanisms is required to decide upon the policies that are most promising. Moreover, future research needs to explore potential heterogeneity in order to better target policies to groups of recipients.

In what follows, the term final period of life refers to the last five years of life (time-to-death approach) or the period of terminal satisfaction decline, which may comprise more or less than five years, depending of the country and the reference year. The term remaining period of life refers to all life years after age 60 (life-expectancy approach).

However, multi-item measures such as the satisfaction with life scale also exist (Diener et al. 1985 ).

There is, however, an ongoing debate about whether or not multi-item measures outperform single-item measures in terms of such outcomes (Veenhoven 1996a ; Diener et al. 2013 ).

The recent issue “On Happiness Being the Goal of Government” from Behavioural Public Policy provides an excellent overview on whether happiness research using, e.g., subjective well-being measures should inform public policy. In Frijters et al. ( 2020 ), the authors provide a strong argument for the use of life satisfaction as the goal of government, but also discuss current barriers to its adoption.

The life satisfaction scale of the GSOEP, for instance, does not specify where “dissatisfied” stops and “satisfied” starts.

As usual, I compute averages to get from individuals to the representative agent of a society. Interestingly, time trends of the proportion of elderly people in each state of satisfaction would lead to the same conclusion as average life satisfaction trends. This implies that, despite averaging, the results do not rest on the cardinality assumption.

However, in the absence of the cardinality assumption, the magnitude of the welfare gain cannot be quantified. Under the cardinality assumption (and in continuous time), in panel B overall life satisfaction for 1985 or 2010 would correspond to the area between the respective age-satisfaction curve and the horizontal line at L S d . The welfare gain would correspond to the difference between the two areas for 2010 and 1985, i.e., the area between the black and the red age-satisfaction curves, and the horizontal line at L S d .

For further information on content and sampling structure of the GSOEP, see Wagner et al. ( 2007 ).

The samples A and B represent the original samples of West German households. The samples C to F were added at later stages to include East German households and to compensate for attrition.

According to the official German Death Statistics (Gesundheitsberichterstattung des Bundes (GBE) 2016 ), in West Germany less than 8% of the people with German nationality died before age 60 in 1985. In 2010, this share was even lower at 4.6%.

Each trend line stops at a different point in time as a GSOEP respondent’s death is only observed until the mid of 2013. Respondents who died in 2013 were one year prior to death in 2012, three years prior to death in 2010, and five years prior to death in 2008. To avoid compositional changes in the study population across years when computing three-year averages, the corresponding trend lines end in 2011, 2009, and 2007.

For more distant years before death trend lines stop earlier. Hence, the observed satisfaction decline is smaller. With 0.64 and 0.89 Likert points it corresponds to about one-third and two-fifths of a standard deviation.

In a balanced panel (i.e., in the absence of attrition and sample refreshment), time trends of the average age at death should be identical in shape. They would simply be shifted to the right with increasing proximity to death because people who were, for example, four or five years prior to death in 1985 correspond to those who were two or three years prior to death in 1987. The fact that I find time trends of the average age at death that are parallel to each other (also pre-weighting) suggests for the GSOEP that attrition with respect to age is neither increasing nor decreasing in the final period of life over time, despite improved longevity.

Cohort effects may arise because of Germany’s unique history during and after World War II. For example, because of their war experience earlier born cohorts may more positively assess their current life than later born cohorts when making intrapersonal comparisons, though empirical evidence in this regard is mixed (Baird et al. 2010 ; Gwozdz and Sousa-Poza 2010 )). Time-in-panel effects can appear because reported life satisfaction is negatively related to the duration spent in a panel (e.g., Kassenboehmer and Haisken-DeNew 2012 ; Baetschmann 2014 ).

The classical identification problem between age, year, and cohort does not arise because age is not included in these regressions. The coefficient on time-in-panel duration is identified due to sample refreshment and non-response. Household income is deflated and need-weighted, i.e., it adjusts for purchasing power, and household size using modified OECD equivalence weights.

This result also holds if I control for relative as opposed to absolute income (e.g., poverty indicators, distance to median income). Moreover, I find that an urban-rural drift in the place of living is unlikely to account for the decline in terminal life satisfaction over time. Since information on community size only became available in 1995, I did not control for it in the regressions presented here.

A general aging-unrelated time trend may result from (unobserved) time-varying factors such as, for example, technological progress that is unrelated to aging, change in nutritional habits, or improvements in access to health care.

This method differs from the multistate life table method in that it uses stock rather than flow data. Despite this difference, both methods produce similar results if changes over time are smooth and occur regularly (Mathers and Robine 1997 ).

To understand ( 2 ), consider the following example. Suppose that in a population 100 people at age 60 are still alive. Half of them suddenly drop dead on their 61st birthday (i.e., they live another year), the other half on their 63rd birthday (i.e., they live another three years). During their remaining lifetime, half of the people are satisfied, while the other half is not. In this case, total life expectancy at age 60 equals two years (= (100 + 50 + 50)/100), whereof one year is spent in satisfaction, on average. That is, satisfied life expectancy at age 60 equals one (= (100 ⋅ 0.5 + 50 ⋅ 0.5 + 50 ⋅ 0.5)/100).

Sample sizes used to estimate the gender-age-specific satisfaction prevalence rates in a given year range from 120 to 1546 observations. Two exceptions represent the estimates for men aged 85 and older in 1985 and 1990.

This holds because the proportion of expected satisfied lifetime was over 50% in 1985.

Again, the life-expectancy results are slightly more pessimistic for women. This might be explained by a level effect. With increasing life expectancy, over time it might get harder to ensure a high quality of life towards the end of people’s lives.

If I were to vary only the mortality rates, I would clearly capture the effect of population aging. However, I would neglect the effect that declining mortality may have on satisfaction due to a shift in the onset of terminal decline, possibly overestimating the negative effect of population aging.

Further analysis revealed that time-in-panel effects strongly contributed to the decline in satisfaction prevalence over time.

The Bradburn Affect Balance Scale gathers information on feelings. It consists of 10 items: five positive and five negative (Bradburn 1969 ).

The decline in the share of severely disabled elderly people between 1996 and 2000 resulted from a revision of the assessment criteria for legally attested disability status in 1996.

Interpersonal comparisons do not equally apply to life satisfaction as well (Junghaenel et al. 2018 ). One possible explanation for this observation is that interpersonal comparisons are more difficult to make when rating life satisfaction because life satisfaction is affected by many domains of life.

Information on these indicators was only collected in five years between 1985 and 2011. Therefore, in this figure, I pool the data of two years together (if applicable) and do not distinguish by time to death.

The magnitude of effect was similar to the one observed for the other two social isolation indicators, but it did not work as much through the health channel (results available upon request).

In practice, this is a suitable approach, which under the stated conditions produces almost the same standard errors as if the first term was not ignored (Jagger et al. 2014 ).

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Acknowledgements

I thank the editor, Alessandro Cigno, the associate editor, Andrew Clark, and two anonymous referees for many helpful comments and suggestions. The paper benefited from discussions with Pieter Bakx, Pietro Biroli, Paul Frijters, Kristina Hess, Wanda Mimra, Andrew Oswald, Rainer Winkelmann, and Christian Waibel. I also acknowledge helpful comments from audiences at various conferences, seminars, and workshops.

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Appendix 1: Supplementary tables and figures

Role of compositional, cohort, and time-in-panel effects: Year dummy coefficient estimates from terminal life satisfaction regressions, by time to death and regression specification. This figure shows the change of year dummy coefficient estimates after sequentially adding controls for compositional effects (add controls), cohort effects (add cohort effects), and time-in-panel effects (add time-in-panel effects) to weighted individual-level life satisfaction regressions that linearly regress terminal life satisfaction on a set of year dummies (baseline specification). Separate regressions were estimated by time to death and results are shown in distinct graphs (with increasing time to death from the left to the right). Coefficient estimates are relative to the year 1985. Trends for the baseline specification correspond to those in Fig.  3 . Upward tilting trends indicate a contribution of the added set of controls to the decline of terminal life satisfaction over time. Source: Author’s calculations based on GBE ( 2016 ) and SOEPv30 (1984–2013)

Average life satisfaction for West German adults, 1985–2011, by (age based) control group. Estimates in a given year represent three-year averages. Estimates were adjusted for time-in-panel effects. Like in Fig.  3 , estimates refer to West Germans without a migration background. Non-declining time trends suggest that macroeconomic effects or a general time trend did not contribute to the decline of terminal life satisfaction over time. Source: Author’s calculations based on GBE ( 2016 ) and SOEPv30 (1984–2013)

Average life satisfaction and average age at death for West German adults within five years of death, 1985–2011, by time to death. Estimates in a given year represent three-year averages. The sample corresponds to that in Fig.  3 , except that it also includes respondents who died at the ages 18 to 54. Time trends that are similar to those in Fig.  3 suggest that the age restriction does not come with an increasingly negatively selected sample over time, and hence, does not explain the decline of terminal life satisfaction over time. Source: Author’s calculations based on GBE ( 2016 ) and SOEPv30 (1984–2013)

Average life satisfaction and average age for elderly West Germans, 1985–2011, by objective death probability (ODP). ODPs indicate a person’s period life table probability of dying before her next birthday. Estimates in a given year represent three-year averages. The sample corresponds to that in Fig.  3 , except that it also includes non-deceased respondents. Downward sloping time trends suggest that the decline of terminal satisfaction over time was not driven by endogenous shifts in the onset of disease, the onset of terminal satisfaction decline, and age at death. Source: Author’s calculations based on German Federal Statistical Office ( 2012a , 2012b ) and SOEPv30 (1984–2013)

Total and satisfied life expectancy at age 60 by gender, year, and classification scheme, West Germany (1985–2010). LE, life expectancy. This figure shows the sensitivity of the life-expectancy results (cf. Tab  1 and Fig.  4 ) to alternative classification schemes. Under the midpoint split classification (equal point split classification), respondents are classified as dissatisfied if their life satisfaction lies between 0 and 5 (0 and 4), as moderately satisfied if their life satisfaction lies between 6 and 8 (5 and 7), and as very satisfied if their life satisfaction lies between 9 and 10 (8 and 10). Source: Author’s calculations based on German Federal Statistical Office( 2012a , 2012b ) and SOEPv30 (1984–2011)

Role of health: Year dummy coefficient estimates from terminal life satisfaction regressions, by time to death and regression specification. This figure shows the change of year dummy coefficient estimates after adding a linear term for health satisfaction (add health satisfaction) or indicators for the disability status (add disability status) to the weighted individual-level life satisfaction regressions of the final specification in Fig.  7 (now called adjusted baseline). Indicators for the disability status were constructed based on the disability degree: not disabled (0), low (1 to 49), medium (50 to 79), high (80 to 99), and fully disabled (100). Again, separate regressions were estimated by time to death and results are shown in distinct graphs (with increasing time to death from the left to the right). Coefficient estimates are again relative to the year 1985. Upward tilting trends indicate a contribution of the added health indicator to the decline of terminal life satisfaction over time. Source: Author’s calculations based on GBE ( 2016 ) and SOEPv30 (1984–2013)

Appendix 2: Standard error of satisfied life expectancy at age 60

In this appendix, I derive the standard error of satisfied life expectancy at age 60, which is used to test for significant differences across time. Using Chiang’s (1984) result, I first rewrite the formula of satisfied life expectancy in terms of survival probabilities, \(p_{x,n_{x}}\) . Then, I use the delta method to obtain the standard errors for this non-linear function of random variables.

Chiang ( 1984 ) showed that the person-years lived in the age interval [ x , x + n x ), \(L_{x, n_{x}}\) , are a linear function of the cumulative survival probability up to age x , which itself is a product of the probabilities of surviving from each starting age x to age x + n x , \(p_{x,n_{x}}\) :

where B x = { i ∈ B : x > i } and a x the average proportion lived by people who die in the age interval [ x , x + n x ). Inserting ( 3 ) and ( 4 ) in the formula of satisfied life expectancy at age 60 (see ( 2 ) for its empirical counterpart), I obtain

That is, satisfied life expectancy at age 60 is a nonlinear function of the age-specific survival probabilities, \(p_{x,n_{x}}\) , and the satisfaction prevalence rates, \({h}_{x, n_{x}}^{s}\) , all of which are random variables.

Next, the delta method is applied to this non-linear function of random variables. As the age-specific satisfaction prevalence rates are estimated based on a different data source than the age-specific survival probabilities, they can be considered independent of the age-specific survival probabilities, and the covariance terms between these variables can be ignored (Mathers 1991 ). Moreover, given that the survival probabilities for two non-overlapping age intervals are estimated based on two distinct groups of people, the estimated survival probabilities are uncorrelated across age intervals (Chiang 1960 ). This argument also holds for German period life tables, which rely on repeated cross-sectional data and pool the data of three years to obtain the life table estimates for a given year.

A similar argument would apply to the age-specific sample fractions of satisfied survey respondents, if pooled data of repeated cross-sections were used. In my case, however, this argument does not apply because I use longitudinal data and compute three-year averages. Taking into account that I use five-year age intervals, the sample fractions of satisfied GSOEP respondents at a given point in time are correlated across two adjacent age intervals, while they continue to be uncorrelated across the other non-overlapping age intervals. Thus, the delta method yields the following variance of satisfied life expectancy at age 60:

where w is the starting age for the oldest age interval. The first term describes the variation in survival (or mortality), while the second and third terms describe the variation in satisfaction prevalence.

According to Newman ( 1988 ), the variation resulting from mortality rates will be negligible if the sample size of the survey population relative to the sample size of the population on which the mortality data are based is small. Therefore, I ignore the first term in ( 6 ). Footnote 30 After explicitly writing down the derivatives, the standard error of satisfied life expectancy at age 60 is then given by

where n is the sample size of the survey population which is used to estimate the satisfaction prevalence rates, \({h}_{x, n_{x}}^{s}\) . The estimator is obtained by using the information from period life tables and replacing the population variances and covariances in the final equation with their sample counterparts. Unlike in studies that use repeated cross-sectional data, I compute clustered variances and covariances for the satisfaction prevalence rates in a given year to account for serial correlation across observations of the same respondent within age intervals and across two adjacent age intervals.

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Nemitz, J. Increasing longevity and life satisfaction: is there a catch to living longer?. J Popul Econ 35 , 557–589 (2022). https://doi.org/10.1007/s00148-021-00836-3

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Declining population and GDP growth

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• Development studies

Businesspeople and politicians seem to be afraid that population reduction will be accompanied by economic recession. In this paper we examine the experience of some countries of various sizes in which population has been declining and observe how GDP, GDP per capita, unemployment rate, and labour force participation rate are evolving during the period that population is declining. Using the pooled mean group (PMG) estimation method, we find that population decline can go hand in hand with growing GDP and increasing per capita GDP, and at the same time the labour participation rate may increase and unemployment may fall.

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Introduction.

Population is an important variable in the economy and its changing size has always been a source of concern among economists and other scientists. As far back as the fourth century B.C., Plato ( Laws ) and Aristotle ( Politics ) were concerned about overpopulation and suggested a constant land-population ratio (Plato 1926 ; Aristotle 1932 ). In the early 16 th century, Thomas More wrote his Utopia , where every city has a constant number of six thousand families (More 1551 ). At the end of the 18 th century, Malthus published anonymously his Essay on the Principle of Population and five years later, in 1803, an enlarged version appeared with his name on it, where he suggests ways for population reduction in order to avoid poverty (Malthus 1803 ).

More recently, Alvin Hansen, in his presidential address to the American Economic Association in 1938, expresses fears that the decline of population growth will lead to a reduction of investment. If population declines, an important outlet for investment will be closed. Thus, the idea of secular stagnation was introduced (Hansen 1939 ). A year earlier Keynes ( 1937 ) was arguing for population stability when he was saying that, with no major wars and no important increases in population, the economic problem might be solved within a hundred years. The first reaction to Hansen’s fears came from Schumpeter ( 1942 , chapter X) who argued that population ageing and population decline do not need to restrict output neither from the demand side nor from the supply side Footnote 1 .

In the years following the end of the Second World War, when the world population was rapidly growing, the interesting question was not how the low rates of population growth might affect total output but exactly the opposite, i.e. how the very high growth rates might affect output. During the 1920–1930 and the 1930–1940 decades the world population grew by 9.2 and 10.6%, respectively, whereas in the next two decades the growth rates were 9.1 and 20.8% (Gapminder 2022 ). Simon Kuznets, in a 1967 paper, examined the question “to what extent does a high rate of population growth impede the growth of product per capita” (Kuznets 1967 ). A year later the publication of Paul Ehrlich’s “The Population Bomb” made the population explosion a world issue (Ehrlich 1968 ).

In recent decades, the world population continues to increase but at lower rates (1.35% in 2000 and 1.01% in 2020). The same is true for most countries but at lower rates. For the period 2000–2020, the annual population growth rates declined from 1.13 to 0.96% in the USA, from 0.69 to 0.27% in France, from 0.05 to −0.49% in Italy, from 0.79 to 0.24% in China, from 1.82% to 0.96 in India, etc. (World Bank 2023 ). Declining rates of growth lead to an aging population, although the total population may be growing. The fast-growing world population has motivated a large number of studies on the effects of population growth on the economy and the environment and the optimal population size Footnote 2 . A different line of research is motivated by the aging of population due to the reduced, but still positive, rates of population growth. These studies examine the effects of population aging on GDP per capita and on other macroeconomics variables. Footnote 3 At present, there are some countries which experience not just reduced rates of population growth but declining or stable population. After 1990 and the dissolution of the USSR some countries which were members of the USSR experienced a significant reduction of their populations. The same is true for some countries which were under the domination of the USSR. In recent years Japan, Italy, and Portugal are also experiencing population decline. Footnote 4

The effect of declining population on growth and per capita income is also examined in the context of modern growth theory. Elgin and Tumen ( 2012 ) have constructed a model of fertility and growth in advanced economies and come to the conclusion that negative population growth and positive change in per capita consumption can coexist. Jones ( 2022 ) examines fully endogenous and semi-endogenous growth with declining population and concludes in both cases that GDP per person will increase asymptotically to a certain level while population declines. He calls this “the Empty Planet result”. Strulik ( 2022 ) also arrives at the result that declining population does not need to lead to a pessimistic outlook as his model predicts continuing economic growth with declining population. Similar results are obtained by Sasaki and Hoshida ( 2017 ) who find that with a declining population the long-run rate of technological change becomes zero, total output declines, but per capita output increases. The main factor for these results is human capital in some form.

In these models and in the relevant literature (see e.g. Tamura 2006 ; Tamura and Simon 2017 ) population change is the result of family decisions whereas in the countries we examine, with the exception of Japan, Portugal, and Italy, population decline is the result of major political changes that have resulted in very significant migration flows.

In this paper we examine data from nineteen countries with declining population in recent years and increasing GDP and, therefore, increasing per capita GDP. Of course, we are not implying that population decline directly causes GDP growth, but only that population decline may bring about changes in other variables that positively affect GDP and a fortiori raise per capita GDP.

Possible effects of population decline

Population decline is expected to have effects on the supply side of the economy as well as on the demand side. Generally speaking, on the supply side, a decline in population implies a reduction of labour supply (because population is the source of labour) and a fall of the labour input in production; and on the demand side, a reduction in the demand of consumption goods and services and of housing because these goods are demanded by people, and by extension a reduction in the demand for investment. The effect of these changes is expected to be, sooner or later, a fall in gross domestic product. Also, a reduction of population means an increase in the dependency ratio which involves risks for the viability of the pension systems. These are reasons that cause concern about the future of economies with declining population.

On the other side, it is argued that population growth inevitably means growth of production and therefore increasing environmental problems in numbers and in intensity. The detrimental effects of economic growth on the environment are well documented (Meadows et al. 1974 , 2004 ; Schade and Pimentel 2010 ; Díaz et al. 2019 ; Bradshaw and Brook 2014 ; Bradshaw et al. 2021 ; O’Neil et al. 2010 ; Daily et al. 1994 ). Climate change, loss of biodiversity, deforestation, pollution, degradation of land for production are some of the often mentioned effects of human activity on the environment, which undermines future growth and well-being (Wackernagel et al. 2019 ; Crist et al. 2022 ; Ripple et al. 2022 ; Lianos and Pseiridis 2021 ).

In this paper we examine how some economic variables have changed in nineteen countries with declining population. The decline of population may cause an increase in the labour participation rate particularly if population reduction is accompanied by higher wages and more opportunities for employment. Also, unemployed people may find jobs easily and therefore the unemployment rate may fall. It is also reasonable to expect that as labour becomes scarcer and wages increase, labour saving technologies may be introduced in the production process leading to higher per capita product, more efficient use of labour, and reorganization of business.

It was said earlier that on the demand side, population decline may lead to lower consumption and lower investment in capital that is needed for the production of consumption goods. But it may also lead to a change in the pattern of consumption. The part of income that was intended for the care of the second or third child may be spent for better care of the first two (better education, healthcare, etc.). Also, the propensity to consume may increase as low income families earn higher incomes (because of higher wages and higher participation in the labour market) and therefore feel less uncertain about their economic situation.

Other changes of economic significance may also take place as a result of less population. For example, the fall in population density, particularly in big cities, may reduce commuting time and increase leisure time and the demand for goods used at leisure time. Also, a smaller population in high population density cities may reduce crime rates and the costs associated with citizens’ protection and thus money may become available for other uses. Agricultural land per capita will increase, farm fragmentation may be reduced and thus productivity in the agricultural sector may increase. Smaller families will mean increased bequeaths per individual and therefore more wealth per family and higher propensity to consume, etc. Footnote 5

To the factors mentioned above some additional ones can be mentioned which are relevant for the countries we examine. The dataset we use in this paper covers short periods in the recent economic history of nineteen countries sixteen of which (with the exemption of Japan, Italy and Portugal) were members of the Soviet Union or of the Soviet block or their political regime was not democratic. Therefore, the fall of the Soviet Union in 1992 brought drastic changes to their political system and to the economy. Six of them are relevant to our examination of the effects of population reduction. First, all of these countries experienced flows of emigration mainly to European countries. Second, emigration also meant loss of young and educated labour force. Third, migrant remittances increased disposable incomes and consumption of their families in the country of origin. Fourth, the reorganization of firms according to the free market system may have introduced technological innovations in the production methods. Fifth, significant capital flows may have been invested in these countries. Sixth, the political liberties that allow freedom of choice may raise productivity because young people can choose professions in which they have an inclination or a talent and thus become more productive. The last three factors, i.e. reorganization of firms, foreign investment, and political liberties, are expected to have resulted in significant increases in labour productivity. These three factors have introduced embodied and disembodied technological changes as a result of a major institutional change.

It should be noted that the effects of population decline may be different in the short run and in the long run. For example, the structure of demand may change immediately as the age structure of population changes. Consumer taste changes and new technologies may take longer.

In this paper we examine the relationship between the declining population and GDP, GDP per capita, labour force participation rate, and unemployment rate in nineteen countries. Some of these countries were members of the USSR, some were members of the Soviet Block, some were part of Yugoslavia, and some were independent. For most of these countries the decline of population is mainly the result of substantial out-migration flows after the fall of the communist regimes in 1991 and the breaking up of Yugoslavia.

The population decline rates differ substantially between countries, as shown in Table 1 . The rate of population decline ranged from 28 and 25% in Latvia and Bosnia-Herzegovina, to 6 and 2.5% in Hungary and Russia. For Portugal, Italy, and Japan population increased between 2.5 and 5.5% during 1990–2019. However, population in these three countries declined during more recent years: in Japan it declined by 1% in 9 years (2011–2019), in Italy by 1.5% in 5 years (2015–2019), and in Portugal by 2.5% in 8 years (2011–2018). The rates of change of our variables of interest for the years 2000-2020 are provided in Table 2 .

The data sources used in our study are shown in Table 3 .

Estimating methodology

A cointegration analysis has been used to examine the long-run relationship between (i) the per capita GDP and population, (ii) per capita GDP and labour participation rate, and (iii) total GDP and unemployment rate with panel data. By checking for the existence of a cointegrated combination of two or more series, cointegration analysis is used to determine whether there is a statistically significant relationship between two or more variables. Two or more time series can be referred to as cointegrated, and have an equilibrium relationship if their combination has a low order of integration. In this case, cointegration analysis must be utilised instead of conventional linear regression methods because the latter will yield false (spurious) results when used in non-stationary time series.

We estimate three empirical models that examine the three long-term relationships. The general models used are:

where i denotes country i ; t denotes time (annual data is used); GDP i,t is per capita GDP of country i at time t in PPP (in constant 2017 USD); POP i,t is the population of country i at time t ; LABOR i,t is the labour participation rate (ILO data) in country i at time t ; TOT_GDP i,t is the total GDP of country i at time t in constant 2015 USD; and U_ILO i,t is the unemployment rate (ILO data) in country i at time t .

Finding the long-term relationship is particularly important if the econometric model is used for policy planning in the long-run. The long-term effects of regressands and the independent variables of the three models are examined using datasets from 19 countries. The method used is the pooled mean group (PMG) method which can be characterised as a panel error correction model (ECM), where the long-run effects are estimated from an autoregressive distributed lags (ARDL) model (Pesaran and Shin 1999 ).

The typical methods to estimating panel data models fall into two categories: mean-group methods, which involve estimating separate regressions for each country and averaging the country-specific coefficients, and dynamic fixed effects models (with control for country-specific effects) which impose homogeneity on all slope coefficients while only allowing the intercepts to vary across countries (see, for example, Arellano and Bond 1991 ; Arellano and Bover 1995 ). Pesaran and Smith ( 1995 ) criticise the former class of models, claiming that when there is slope heterogeneity, heterogeneity bias affects the estimates of convergence. Because outlier countries may have a significant impact on the averages of the country coefficients in the latter type of models, the estimator may be ineffective. The PMG method offers a middle ground between dynamic fixed effects methods, which impose homogeneity on all slope coefficients, and the mean group method, which does not impose any kind of homogeneity on slope coefficients. The PMG method imposes homogeneity on the long-run coefficients but permits variation among countries in the short-run coefficients, adjustment speed, and error correction variances. Consequently, it is more effective in comparison to the mean group method and less constrained than the dynamic fixed effects method (Pesaran and Shin 1999 ). The PMG method’s long-run homogeneity hypothesis enables the direct identification of the parameters of variables that have an impact on the dependent variable’s “steady-state” trajectory.

Consequently, we decided to utilise the PMG method as an error correction method in the panel data models since it offers two benefits over the dynamic fixed effects alternatives: averaging might conceal the dynamic relationship between the regressand and the regressor(s), particularly when countries have different macroeconomic characteristics, and especially when the population effect and labour participation effects on the per capita GDP and unemployment effects on total GDP might be different across countries. This is because (a) averaging results in a loss of information that can be used to more accurately estimate the coefficients of interest while (b) allowing for parameter heterogeneity across countries.

Additionally, asymmetric changes in population were introduced by the POP + and POP − variables, the hypothesis being that large changes in these two variables do not affect with the same intensity the per capita GDP as low changes. These variables for the introduction of asymmetries in the POP variable were constructed following Shin et al. ( 2014 ) and (Greenwood-Nimmo et al. 2012 , 2013 ) with the difference that for the decomposition of the variable into POP + and POP − the mean threshold has been used instead of the zero threshold Footnote 6 . This was to avoid having a low number of effective observations in one regime (Greenwood-Nimmo et al. 2012 , 2013 ). Consequently, \(POP_{i,t}^ + = \mathop {\sum}\nolimits_{j = 1}^t {{{{\mathrm{max}}}}( {{{{\mathrm{{\Delta}}}}}POP_{{{{\mathrm{i,}}}}j},\,\overline {POP_{{{\mathrm{i}}}}} })}\) , \(POP_{i,t}^ - = \mathop {\sum}\nolimits_{{{{\mathrm{j}}}} = 1}^{{{\mathrm{t}}}} {min} ( {{{{\mathrm{{\Delta}}}}}POP_{{{{\mathrm{i,}}}}j},\,\overline {POP_{{{\mathrm{i}}}}} })\) , where the bar indicates the average of the variable, and t and i denote time (measured in years) and country, respectively. Note that the mean of the variable is different for each cross-section (country).

The PMG method also has the benefit of generating consistent estimates of the parameters in the long-run relationship between integrated and stationary variables. This allows the model to be estimated when both I(0) and I(1) Footnote 7 variables are present, whereas other methods only allow I(0) or I(1) variables.

However, the PMG method demands that the variables not be I(2) since this would lead to false findings. In order to confirm that the co-integrating variables are I(0) or I(1) and not I(2), we analyse the order of integration of the variables examined before moving further with the estimation of the model. The Im, Pesaran, and Shin panel unit root test has been used for this.

The values of the panel unit root test are presented in Table 4 for the variables used in all three estimated models. The null hypothesis (H 0 ) of a unit root (non-stationarity) in some panels (countries in this case) is tested against the alternative. H 0 was rejected at the 1% level of statistical significance for U_ILO i,t (unemployment rate) at the 5% level of statistical significance. The remaining variables used as determinants in the three models and the regressand were found to be non-stationary at their level for all panels while they were found to be stationary at their first difference. Therefore, it is concluded that the variable U_ILO i,t is I(0) while GDP i,t (per capita GDP), GDP_TOT i,t (total GDP), LABOR i,t (labour participation rate), and both the asymmetries variables \(POP_{i,t}^ +\) , \(POP_{i,t}^ -\) are I(1).

The null hypothesis is the existence of a unit root. For stationarity, the null hypothesis has to be rejected at at least 5% level of statistical significance.

Since all three equations contain I(0) and I(1) variables but not I(2), the PMG modelling can be applied. The responsiveness of cointegrated variables to any deviation from long-run equilibrium is one of their key characteristics. In order to estimate the rate of adjustment to the long-run relationship while allowing for unconstrained cross-section heterogeneity in the adjustment dynamics and fixed effects, the PMG method is used to an ECM.

Following Pesaran and Shin ( 1999 ), the PMG restricted version of (1), (2), and (3) is estimated on pooled cross-country time-series data as:

where i  = 1,…,19 and denotes countries; t  = 1,…,32 and denotes time; Δ is the first-difference operator; Y i,t is the regressand of each of the three models in (1) to (3); μ  = 2 for (1) while μ  = 1 for (2) and (3) and is the number of determinants; G  = ( \(POP_{i,t}^ +\) , \(POP_{i,t}^ -\) ) for (1), G  = ( LABOR i,t ) for (2) and G  = ( U_ILO i,t ) for (3) is the vector with the explanatory variables Footnote 9 . The parameter φ i is the error-correcting speed of adjustment to the long-run relationship. This parameter is of particular importance because it shows the existence (or not) of cointegration among the variables. Cointegration exist if φ i is found to be negative and statistically significant. Furthermore, the estimated coefficients of the determinants ϑ k,i s show the long-run relationship between the variables while the β k,i s are their short-run coefficients. v i is the country-specific fixed-effect, ε is a time-varying disturbance term, and p and q are the number of lags.

The following stages provide a basic explanation of the PMG method. First, the model described by (4) must have its ARDL order identified. The value of p for the dependent variable and q for each regressor must therefore be determined. The lag order of the ARDL was established using the Akaike Information Criterion (AIC) Footnote 10 lag selection criterion, and Eq. ( 4 ) was estimated for each cross-section (country) separately for (1), (2) and (3). For the determination of the lag order of the ARDL model for each country, a maximum number of four lags in Eq. ( 4 ) was considered. Then, using the most common lag order for each variable across all cross-sections, the final form of (4) for the estimation of (1), (2), and (3) was as follows:

Second, using a maximum likelihood estimator, the long-run coefficients ϑ k,i s, are jointly estimated across countries. Last but not least, using the maximum likelihood method and the estimates of the long-run coefficients that were obtained in the previous step, the short-run coefficients, λ ij s and β k,i,j s, the speed of adjustment φ i , the country-specific intercepts v i , and the country-specific error variances are estimated on a country-by-country basis.

The following specification requirements need to be verified against the PMG estimates: The model is first evaluated for dynamic stability (existence of a long-run relationship). The coefficient of the error correction term must be negative and not less than −2 for our model to be dynamically stable (i.e., within the unit circle) Footnote 11 . For (5), φ i has a value of −0.293, and is less than 1% statistically significant. The same applies for (6) and (7) where the φ i has a value of −0.076 and −0.125, respectively. As a result, the prerequisite for dynamic stability has been met. Testing for co-integration between the dependent and explanatory variables is a further requirement.

A co-integration, indicated by a negative and statistically significant coefficient on the error correction term φ i , is necessary. This coefficient’s value displays the percentage change in any disequilibrium between the explanatory and dependent variables that is resolved within a given time frame (one year, in our case). Its value denotes how quickly the long-run equilibrium is being adjusted. In our situation, for (5) the value of φ i is −0.293, indicating the existence of a long-term link between the variables and the correction of 29.3% of any short-term disequilibrium between the dependent and explanatory variables in one time period. A slower adjustment to long-run equilibrium is found for (6) and (7) since a correction of 7.6 and 12.5%, respectively, of any short-term disequilibrium between the dependent and explanatory variable is made in one time period.

Thirdly, the PMG estimator requires that the long-run coefficients be equal across all cross-sections, as was previously mentioned. When the applied limitations are valid, that is, when the long-run coefficients are the same across countries, this pooling across cross-sections produces accurate and reliable estimates. The PMG results are inconsistent if the true model is heterogenous in the slope parameters across cross-sections. Using a Hausman-type test, this homogeneity hypothesis is examined. The comparison of the PMG and mean group (MG) estimators forms the basis of this test. The level of statistical significance ( p ) for the Hausman test statistic was 0.508 and its value was \(\chi _2^2 = 1.35\) for (5), while p  = 0.282 and \(\chi _1^2 = 1.16\) for (6) and p  = 0.240 and \(\chi _1^2 = 0.62\) for (7). Therefore, it is concluded that all three models are homogenous in the slope parameters across countries, and the null hypothesis that the variation in coefficients is not systematic cannot be rejected.

The estimation results are presented in Tables 5 – 7 .

From Table 5 we see that population changes affect very little the change in the per capita GDP in the long-run: the value of the \(POP_{i,t}^ +\) coefficient is 0.018 and of the \(POP_{i,t}^ -\) 0.009. However, there is an asymmetric effect of the population change on the per capita GDP because by using a Wald test of equality of the two coefficients the null hypothesis of equality is rejected at a high level of statistical significance ( \(\chi _1^2 = 76.57\) , p  < 0.001). The latter means that a reduction in population reduces per capita GDP less than the effect that an increase in population has on the increase of the per capita GDP; both effects though are very small.

From Table 5 we see also the value and the statistical significance of the short-run coefficients of both regimes of population changes for up to five years’ time-lag. We see that population changes, either increases or decreases, do not affect the per capita GDP as all short-run coefficients of both regimes are statistically insignificant at the 1% level of statistical significance.

Table 6 and Table 7 present the estimation results of (6) and (7), i.e. the effects of labour participation on per capita GDP and the effects of unemployment on total GDP, respectively. The long-run coefficients are statistically significant at the 1‰ level of statistical significance and are of the expected sign as the coefficient of the labour participation rate is positive (the higher the labour participation rate the higher is the per capita GDP) and the coefficient of the unemployment rate is negative (the higher the unemployment rate the less is the total GDP). Again, their value is small; it is 0.017 for the labour participation rate and –0.019 for the unemployment rate.

The short-run coefficients of previous periods are statistically insignificant except for the current period for both (6) and (7) and their sign and value are the same as that of the long-run period.

Therefore, we conclude that, in countries which experienced a decline in their population size, population changes up to five years back do not affect the changes in per capita GDP; additionally, the long-run effects of increases and decreases of the population on per capita GDP are very small, with the latter affecting considerably less the change in total GDP than the former, as described above. Furthermore, there are no short-run effects found of the labour force participation on per capita GDP and the unemployment rate on total GDP. Long-run effects do exist and show that the labour force participation rate positively affects per capita GDP and that the unemployment rate negatively affects total GDP. However, in both estimations, the coefficient’s value is very small.

Comments and conclusions

There seems to be an impression among the general public, businesspeople, and some professionals that population decline is harmful to the economy. Businesspeople in particular are concerned about profits, as wages may increase and demand may stagnate as a result of population decline. Footnote 12

The results of our regressions provide evidence that population decline may not be a danger for the economy. In a sense, our results may be viewed as an empirical confirmation of the results obtained by the growth models mentioned in the introduction. Population decline can go hand in hand with growing GDP and increasing per capita GDP, and at the same time the labour participation rate may increase and unemployment may fall. At least this much is supported by the data from the nineteen countries we examined. One may assume that the introduction of labour-saving technology is also one major factor that prevented GDP from falling when population declined in the countries we examined. From the results found in our study for the effects of population changes on the per capita GDP we can see that population reduction does not need to be disastrous economically. Hence the fears that economic stagnation will follow population decline may be unfounded.

It should be noted that population decline is very different from a declining rate of population growth that leads to population increase and therefore our findings are not strictly comparable with those of studies examining the effects of declining population growth rates. Also, the channels through which population decline and population aging each affect GDP and GDP per capita may be different. For instance, Maestas et al. ( 2023 ) who examined the relationship between GDP per capita and population aging, have found that two thirds of the reduction in GDP per capita was due to a reduction in labour productivity whereas it can be seen that, during the period we examine, labour productivity as expressed in real wages was increasing (see Table 8 in the Appendix ). Also, a reduction in growth of employment per capita reduces GDP per capita whereas in the countries we examined employment per capita has increased as evidenced by the increasing labour force participation rate.

The total population of the nineteen countries examined here was 9 and 6% of the world population in 1990 and 2019, respectively. Would changes like those presented above take place in case the decline in population were a global phenomenon? In such a case, the flows of migration, the volume of international trade, and the demand for resources might decline, and there is no obvious reason to expect that the long run changes would be different from those described above. This could be an idea for further work.

Data availability

The datasets generated during and/or analysed during the current study are available in the Harvard Dataverse repository, https://doi.org/10.7910/DVN/FILTWF .

In a footnote on p. 115 Schumpeter makes fun of the economists’ attempt to forecast future populations. He refers to Malthus, Keynes, and H. Wright and ends the footnote with “Will economics never come of age?”.

See the many works by Daly on the steady state economy model (Daly 1968 , 1972 , 1991 , 2008 , 2019 ; (Ehrlich and Holdren 1971 ; Daily et al. 1994 ; Pimentel et al. 1994 ; Cohen 1996 , 2017 ; Pimentel et al. 2010 ; Schade and Pimentel 2010 ; Lianos 2013 , 2018 , 2021 ; Lianos and Pseiridis 2016 ; Díaz et al. 2019 ; Bradshaw et al. 2021 ; Dasgupta et al. 2021 ).

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See Clark et al. ( 2010 ) for a discussion of Japan’s case.

Additional consequences of population decline are discussed in Coleman and Rowthorn ( 2011 ).

For robustness other thresholds (median and zero) have also been used. The lag order of equation (5) was found to be the same and the values of the estimated long-run coefficients and their statistical significance were found to be approximately the same. Furthermore, all the estimated short-run coefficients were also found to be statistically insignificant. Results are available upon request from the authors.

I(d) denotes the order of the integration of a time series, i.e. it shows the minimum number of differences required to obtain a covariance stationary series.

The full description of the data used is provided in section 3 (Data), above.

The AIC is a measure of the relative quality of a statistical model for a given set of data and, therefore, it provides a means for model selection.

See Agiomirgianakis et al. ( 2017 ) and Tsounis et al. ( 2022 ) for further analysis.

Real GDP has increased in all countries except Italy during the two last decades (see Table 2 ). Real wages have increased in all countries during the 2000-2019 period with the exception of Italy, Japan, and Portugal where they are practically constant (see Table 8 in the Appendix ).

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Department of Economics, Athens University of Economics and Business, Athens, Greece

Theodore P. Lianos

Institute of Urban Environment & Human Resources, Department of Economics and Regional Development, Panteion University, Athens, Greece

Anastasia Pseiridis

Laboratory of Applied Economics, Department of Economics, University of Western Macedonia, Kastoria, Greece

Nicholas Tsounis

School of Social Sciences, Hellenic Open University, Patras, Greece

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TPL: Conceptualization (lead); methodology; writing – original draft (equal); review and editing (equal). AP: Conceptualization (supporting); data curation; writing-original draft (equal); investigation; formal analysis; visualization; writing–review and editing (equal). NT: Formal analysis; methodology; writing-original draft (equal).

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Lianos, T.P., Pseiridis, A. & Tsounis, N. Declining population and GDP growth. Humanit Soc Sci Commun 10 , 725 (2023). https://doi.org/10.1057/s41599-023-02223-7

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DOI : https://doi.org/10.1057/s41599-023-02223-7

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The population increases the value of life decreases?

The effect of growing population will be an increased demand for resources and space. Both of which we are running out of. The Earth just can't keep up with us and our habit of wastage is not helping.

I would argue the opposite side of that. It’s like saying as the number of telephones increases, the value of each phone decreases.

The value of a human life is defined by connections. One person alone in the universe can’t accomplish much, and there would be no one to care or remember if she did. Two people can value each other, and maybe do a bit more. A larger population can accomplish much more per person, and have more people to value the results, and endure through time.

But I wouldn’t limit it to humans. It is possible there are non-human entities with which humans could form mutually valuable connections.

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