U.S. Demographic Trends
Six main demographic trends in the U.S. are the following:
Worldwide Demographic Trends
(Lutz, W. PopNet Nr. 25, Summer 1994)
World Population Projections to 2150
(from Population Division, Dept. of Economic and Social Affairs, United Nations Secretariat, New York, NY 10017; Feb. 1, 1998)
The long-range population projections presented here prepared by the United Nations Population Division, cover the period from 1950 to 2150. A total of seven projections for each of the eight major areas of the world are considered in this report. The variants are distinguished by their assumptions regarding future scenarios in total fertility rates. The range of potential demographic outcomes underscores the difficulty in focusing on any particular scenario and also highlights the critical importance of current policies and actions for the long-range future of the world population.
The seven main conclusions from these long-range population projections are:
Elementary Characteristics of Populations
Information on populations is obtained either through a census or through a survey, the distinction of which is far from clear-cut. A complete convass of an area is typically thought of as a census where the intent is to enumerate every individual in the population by direct counting and further, to cross-classify by age (stage), sex and so forth. The intent of a survey is to estimate population characteristics on a sample basis.
Population Size. In concept, the notion of population size is extremely simple since it means the total number of individuals in the population.
Distribution. There are two broad spatial measures that characterize a particular distribution. These are: i. Number by spatial subdivision--statistics in this case can be given as i): percentage of the total by subdivision; or ii) a rank order from the subdivision with the highest count to the spatial unit with the lowest. Depending upon which method is used, comparisons of two census times will reveal the change in percent or the change in rank by spatial location. ii. Measures of central location--the center of a population or the mean point of the population distributed over an area is defined as the center of population gravity or of population mass. The formula for the coordinates of the population center is given by:
Structure. The structure of a population is the relative frequency of any enumerable or measurable characteristic, quality, trait, attribute or variable observed for individuals. These items could include age, sex, genetic constitution, weight, length, shape, color, biotype, birth origin and spatial distribution. Only age and sex will be covered here since they are the most common traits by which individuals in populations are decomposed. Sex ratio (SR) is the principle measure of sex composition and is usually defined as the number of males per female or:
where nm and nf represents the number of males and the number of females, respectively. The simplest kind of analysis of age or stage data is the frequency distribution of the total population by age or:
where fx is the frequency of individuals aged x, nx is the number in the population at age x and Nt is the total number in the population.
An age pyramid is often used to illustrate the age-by-sex distribution of a population. An age pyramid gives number or percentages of population in various age groups. If wide base then large proportion of births and thus rapidly growing population. If narrower base then moderately growing population. If rectangular shape then zero or negative population growth.
Population Change (in size)
If a population numbers Nt and Nt+1 at times t and t+1, respectively, then the amount of change equals
Nt+1 - Nt = Amount of Change
which is simply the difference in the population number at the two time periods. However, the rate of change is given by
Total Rate of Change
which gives the factor by which the population changed over one time period relative to the number at time t and
Fractional Rate of Change
which give the fraction by which the population changes over one time period relative to the number at time t.
Population Change (in space)
Population change occurs when migrants move from one area to another. Every move is an out-migration with respect to the area of origin and an in-migration with respect to area of destination. The balance between in-migration and out-migration is termed net migration. The sum total of migrants moving one direction or the other is termed gross in-migration or gross out-migration. The sum total of both in and out migration is termed turn over. A group of migrants having a common origin and destination is termed a migration stream. The difference between a stream and its counterstream is the net stream or net interchange between two areas. The sum of the stream and the counterstream is called the gross interchange between the two areas.
Rate of Change
All models concerned with population dynamics are concerned with population rate of change. This notion is different in an important respect from the rate of speed of a physical object like an automobile. If an insect population is 100 at the beginning of a week, and at 120 at the end of the week then by analogy with the automobile its rate would be 20 insects per week. To become a population rate this has to be divided by the population at the start of the week. Therefore the population is growing at a rate of 20/100 or .20 per week. This means every individual is increasing its number 20% or 1.2-fold per week.
The two kinds of rates are distinguished in symbols. The analogue of the physical rate x' in terms of population at times t and t + 1, Nt and Nt+1 is:
x' = Nt+1 - Nt (= amount of change)
Nt+1 = Nt + x'
while the demographic rate is
x = (Nt+1 - Nt)/Nt (= fraction or x-fold change)
Nt+1 = Nt(1-x)
Both of these relations can be expressed in terms of a short time period.
The rates x' and x yield different results if projected into the future. A population of 100 growing by 20 persons per year would have grown by 40 at the end of 2 years and by 60 at the end of 3 years. However, a population growing at a rate of 20% per year will have grown by 44 at the end of 2 years and by 73 at the end of 3 years. This last rate is called geometric increase and the former is called arithmetic increase. The distinction between these is that an arithmetic series will have a common difference while a geometric series will have a common ratio. For example, the series 1, 4, 7, 10, 13 is arithmetic with the difference being 3 (i.e. 4- 1 = 3; 7 - 4 = 3, etc). The series 1, 3, 9, 27, 81 is geometric with a common ratio of 3 (i.e. 81/27 = 3; 27/9 = 3; etc.).
The Balancing Equation
The crude rate model is the simplest of all population models. It is based on the Balancing Equation which relates the total population this year (or month, week, day, etc.) to the total population last year. Suppose last year was the initial population at time 0 (i.e. t=0; Pop0) then this equation is given as:
Pop1 = Pop0
This model partials out the relative contribution of birth, death and migration. Migration is not typically considered for purposes of simplification (closed population). Since births and deaths represent totals, these terms can be re-expressed as:
births = Pop0(b)
deaths = Pop0(d)
where b and d denote per capita birth and death rates, respectively. Substituting these terms into the equation yields (excluding migration terms):
Pop1 = Pop0 + Pop0(b) - Pop0(d)
= Pop0(1 + b - d)
Note that if b - d = 0 the population at time t will equal the population at time t+1, if b > d the population will increase and if b < d the population will decrease. The population at time t=2 (i.e. Pop2) is determined as follows:
Pop2 = Pop1 (1 + b - d)
= Pop0 (1 + b - d) (1 + b - d)
= Pop0 (1 + b - d)2
The relationship for t number of time units is:
Popt = Pop0 (1 + b - d)t
The Crude Rate Model has three assumptions: 1)Homogeneity assumption (no age structure); 2)Birth and death rates remain fixed; 3)closed population. The only major conceptual difference between the crude rate model and the models covered later is that of homogeneity. Age structure adds a more realistic and interesting dimension but does not change the notion of geometric population growth. As an example projection using the Balancing Equation use birth rate b=.03 births/person/year and death rate d=.01 deaths/person/year. Also let Pop1989=5 billion. Then
Pop1990 = Pop1989(1+b-d)
= 5 (1+.03-.01)
= 5.1 billion
Pop1991 = Pop1990 (1.02)
= 5.202 billion
Projecting to the year 2000 yields:
For perspective in the year 2000 there will be: 1. 122 million new people added that year; 2. 334,247 new people added each day; 3. 13,927 new people added per hour; 4. 232 new people added per minute; 5. 4 people added per second.
Stable Population Theory
Stable population theory provides the foundation for our understanding of age structured population growth. It is based on three basic assumptions:
The main conclusions are: i)a closed population subject to the basic assumptions of fixed birth and death rates and no migration will eventually attain a constant rate of increase (intrinsic rate of increase) and a constant fraction of the total population in each age class (stable age distribution); and ii)this rate of increase and the stable age distribution are independent of initial conditions.
The age structure of a population is determined by three factors: i)population growth rate; ii)mortality rates; and iii)transient effects (eg. baby boom). Consider the following hypothetical population with no mortality and the birth rate is 10-fold greater with each time step:
Note here that this growing population contains a total of 111 individuals at time step #3 (i.e. 100+10+1) with 90.1% in age class #1, 9.0% in age class #2 and .9% in age class #3. Now note the situation where the population experiences a 10-fold decrease in births each time step:
Note here that this decreasing population contains a total of 111 individuals at time step #3 (i.e. 1+10+100) with 90.1% in age class #3, 9.0% in age class #2 and .9% in age class #1. The point here is that growth rate alone determined the age distribution in these two hypothetical populations.
Pick one time frame in which at most one event can happen between two states. Suppose we divide a population into five marital states: single (S), married (M), divorced (Dv), widowed (W) and dead (D). Designate these states by circles and connect them via various pathways. We organize the various pathways and transition probabilities using what is called a "transition matrix". For example, we determine: i)the proportion of individuals that make the transition from the single state to the married state; or ii)the proportion of individuals that make the transition from the married state to the widowed state.
|The comple matrix is given as|
The significance of this is that we can now bring matrix algebra to bear on the problem of population projection.
A matrix formulation of the Lotka model is known as the Leslie Matrix. It is useful for illustrating and studying the transient properties of populations as they converge to the stable state and provides a technique of cohort-component projection. The Leslie Matrix is given as:
where the top row are the birth elements Fx, the subdiagonals px are the period survival elements and the vectors Nx,t and Nx,t+1 denote the numbers at age x at times t and t+1, respectively. A population is projected through time by first entering an initial number of individuals into one or more age classes and multiplying the Leslie Matrix by the age vector, Nx,t. The resulting age vector, Nx,t+1, is then substituted for the age vector Nx,t and the process repeated. This is referred to as matrix iteration. As an example, consider a population with three age classes starting with N0,t = N1,t = N2,t = 1 and with Leslie matrix elements of F0 = 0, F1 = 5, F2 = 2, p0 = 0.8 and p1 = 0.5. Two iterations be computed as follows:
|3-age class Leslie Matrix|
The results for selected time periods between 0 and 10 days are presented in Table 1. Shows: i)change in numbers, age structure and growth rate with time. Note that the growth rate of the population, , becomes damped with time as it converges to a stable state (constant).
Table 1. Results of Leslie Matrix projection of hypothetical population (=2.091)
Demographic Transition Theory
Demographic transition theory describes the changes that take place in birth and death rates as a population passes from traditional to urban/industrialized. It is based on two observation:
There are three states:
Fundamental Properties of Populations
CURRENT ISSUES IN POPULATION
The Overpopulation Crisis
Malthus (London economist) originated concept that food supply increases in arithmetic progression while population increases geometrically. Published "Population: The First Essay" in 1798.What brings end to growth? Only two things--fertility and mortality. Little progress toward fertility control and no thought of increasing mortality. But mortality is increased through misery and starvation. Thus get dismal theorem:
Crucial principle is that there must be some limit to the number of mankind and that growth of population, at no matter how slow a rate, must eventually bring the number to this limit. If present population were to grow at 2% per year then in 750 years the whole surface of the earth sould be covered with a solid mass of people and in 8,000 years the whole known universe 2,000 light years in radius would be solid humanity. Same argument that if start with single pair of breeding house flies in March would cover earth to depth of 12 feet by September.
Population Policy in the Developing World (from Bongaarts, J. 1994 Science 263, 771)
We are currently adding around one billion people to the globe per decade or 100 million per year. This is equivalent to adding all of the people in California, New York Texas and Florida combined. The vast majority of the growth is in the developing world, particularly in Africa, Asia and Latin America. It is impossible to understand the world today without understanding demographics--poverty, welfare, pollution, military and so forth all involve age structure, growth rate and migration.
The concerns were expressed by Malthus 200 yrs ago when he stated in his famous "First Essay" (1798) that "...the power of population is indefinately greater than the power in the earth to produce subsistence for man."
Three broad policy options for slowing population expansion:
How Many People Can Live on Earth?
(From Joel Cohen, May 7, 1994; PAA Meetings in Miami, FL)
Questions about how many people:
Table 1. Demographic traits of major regions of the world--1984 and 2000.
Note that the developed regions (North America and Europe) constituted 15.8% of world population in 1984 but will constitute only 13.2% in the year 2000. There are currently 1.2 billion people in China and 800 million in India. Thus around one out of three people in the world are either East Indian or Chinese. In the year 2000 nearly 60% of the world population will be in East and South Asia and nearly 87% of the population will in developing countries.
|"Longevity is not an end in itself. We need a reason to get up each morning." (Helen Caro quoted in NY Times Magazine3/3/96)|
The elderly as a concept is an inadequate generalization that obscures the heterogeneous nature of a population group that spans more than 40 years of life. The elderly are at least as diverse as younger age groups in terms of personal and social resources, health, living arrangements and intergration into social life.
Aging trends in U.S. population (from Rice and Feldman 1983):
Retirement and Social Security
Social security was set up in 1935 was a trust fund. Fifty years ago there were 42 workers for every beneficiary wheras now there are only 3.2 workers for every beneficiary and in 2010 there will be only 2.9. Furthermore, the government has increased payoffs. A worker who retired in 1980 got back his contribution in less than three years. "Social Security paid off nicely for the generation that set it up" (like the originators of a chain letter). Government officials say they have enough money today to meet Social Security's commitments until 2036. There are several steps that could be taken to sustain Social Security (Atlantic Monthly, June, 1995, p53): i)starting in 10 years the minimum age for receiving Social Security payments should be raised to 70. The 10-year delay would give future retirees time to plan. When Social Security was enacted, life expectancy in the U.S. was 61.7 years; now expectancy has increased to 76.3 years and it is time for the law to reflect this demographic change. Of the 43 million people who received monthly Social Security benefits in December 1993, 27% were under age 65 and 58% were women; ii)the rate of growth of Social Security payments should be gently slowed. It is the rate of increase that has helped to put the Social Security trust fund on the road to insolvency; and iii)a 2 percent increase in the contribution rate would probably make the Social Security program (old age and survivors benefits) solvent for the period lasting through 2070.
According to researchers, the average retiree lives on five income streams (from Worth Magazine, December/January 1995):
|Percent of Population 65 and over|
Fig. 1. The world's 20 oldest countries in 1992
Bongaarts, J. 1994. Population policy options in the developing world. Science 263:771-776.
Cohen, J. E. 1995. Population growth and earth's human carrying capacity. Science 269:341-346.
Connelly, M. and P. Kennedy. 1994. Must it be the rest against the West? Atlantic Monthly, December, 61-91.
Fogel, R. W. 1994. Economic growth, population theory, and physiology: the bearing of long-term processes on the making of economic policy. American Economic Review 84:369-395.
Graubard, S. R. 1986. The Aging Society. Daedalus 115:1-400.
Keyfitz, Nathan. 1984. The population of China. Scientific American 250(2):38-47.
Keyfitz, Nathan. 1989. The growing human population. Scientific American Sept. 1989.
Malthus, Thomas Robert. 1798. Population: The First Essay. Reprinted by Ann Arbor Paperbacks, The University of Michigan Press.
Table 1. Demographic indicators by country or area in the world, major areas and regions (from United Nations, 1984. The World Population Situation in 1983 (Department of International Economic and Social Affairs, Population Studies, No. 85).
|Annual Growth Rate||Age Distribution||Crude Rates|
|Country or Area||1984||2000||1950-55||1980-85||1995-2000||0-14||15-64||65+||Births||Deaths||1980-85||1980-85||1980|
|More developed regions||1,165,789||1,272,194||1.3||0.6||0.5||23.0||65.6||11.4||15.5||9.5||0.96||73.1||71.0|
|Less developed regions||3,597,297||4,851,083||2.1||2.0||1.8||40.0||56.2||3.8||31.2||11.0||2.00||56.6||30.6|
|United Republic of Tanania||21,710||39,129||2.2||3.5||3.7||48.4||49.3||2.3||50.4||15.3||3.50||51.0||11.2|
|Central African Republic||2,508||3,736||1.2||2.3||2.6||41.5||54.6||3.9||44.7||21.8||2.90||43.0||40.9|
|United Republic of Cameroon||9,371||14,045||1.9||2.4||2.6||41.9||54.3||3.8||43.6||19.2||2.85||46.0||34.3|
|Libyan Arab Jamahiriya||3,471||6,072||1.8||3.8||3.3||46.7||51.1||2.2||45.6||10.9||3.50||57.9||52.5|
|B.||Latin America||397 138||549 971||2.7||2.3||1.9||39.4||56.3||4.3||31.8||8.2||2.01||64.1||65.5|
|Trinidad and Tobago||1,105||1,321||2.5||0.9||1.0||34.2||60.8||4.9||24.6||6.2||1.40||70.1||23.5|
|United States of America||235,764||268,443||1.7||0.9||0.7||22.5||66.2||111.3||16.0||9.2||0.90||74.2||75.5|
|13.||Other East Asia||67,597||86,697||0.6||1.8||1.4||34.9||61.1||4.0||23.8||6.6||1.42||66.7||59.5|
|Korea, Democratic People's Republic of||19,630||27,256||-1.4||2.3||1.8||40.0||56.3||3.7||30.5||7.4||1.95||64.6||59.7|
|Korea, Republic of||40,309||49,485||1.0||1.4||1.1||33.4||62.7||3.9||21.0||6.3||1.20||67.5||55.3|
|Lao People's Democratic Republic||4,315||6,213||2.1||2.5||2.1||43.4||53.7||2.9||40.6||15.5||2.85||49.7||12.8|
|Iran, Islamic Republic of||43,799||65,549||3.7||3.0||2.2||44.2||52.4||3.4||40.5||10.4||2.75||60.2||49.1|
|Western South Asia||109,651||168,2998||2.7||2.9||2.5||41.6||54.4||4.0||37.8||10.1||2.67||60.6||54.0|
|Syrian Arab Republic||10,189||18,102||2.5||3.7||3.3||47.5||49.3||3.2||46.5||7.2||3.50||67.0||51.3|
|United Arab Emirates||1,255||1,916||2.5||5.8||1.9||29.0||69.0||2.0||27.0||4.0||2.90||70.6||53.3|
|German Democratic Republics||16,647||16,459||-0.5||-0.1||-0.0||19.5||64.2||16.3||12.5||13.9||0.80||72.4||77.3|
|Germany, Republic of||61,212||59,456||0.9||-0.2||-0.2||18.6||66.3||15.0||10.2||12.0||0.69||73.3||83.7|
|Papua New Guinea||3,601||5,292||1.6||2.7||2.2||42.4||54.3||3.2||40.4||13.6||2.92||53.3||27.3|
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