Throughout the course we will refer to a number of key demographic concepts and measures. Before we begin the substantive course material, I want to go over some of these.
Fertility
crude birth rate: The crude birth rate (cbr or b) in a population during a given year is defined as the total number of births (B) divided by the midyear population (P). It is normally expressed per thousand population, so we have
age-specific fertility rate: The age-specific fertility rate (asfr) for women of age group i in a population during a given year is defined as the total number of births to women age i during the year (Bi) divided by the total (midyear) number of women age i (Wi). Expressed per thousand, we have
total fertility rate: Mathematically, the total fertility rate (TFR) equals the sum of age-specific fertility rates from the minimum to the maximum age at which childbearing occurs, multiplied by the number of years in each age group and divided by 1000. Thus, for example, if age groups are for five-year intervals (15-19, 20-24, etc.), we have
The total fertility rate just described would be a period TFR, and it would tell us the average number of children a group of women would have if, throughout their reproductive lives, they were to bear children at the rates given by the asfrs. Alternatively, we can also think about a cohort TFR. In demography, a cohort refers to a group of people all born at the same time (e.g., in a single year, like the birth cohort of 1970, or during a longer period, like the birth cohort from 1980-84). A cohort total fertility rate, then, would reflect the asfrs actually realized by a given cohort of women. (Matrix to be presented in class will highlight the difference between the period TFR and the cohort TFR.)
The preceding discussion provides a nice lead-in to the notion of age, period, and cohort effects. In brief, we can think of age effects as those specific to a particular age or age range. These may consist of biological processes related to aging, such as the onset of puberty, or social processes such as beginning schooling at age 6.
Period effects pertain to events transpiring during a specific period (e.g., the high fertility manifested during the Baby Boom following WWII up to the mid-1960s), while cohort effects refer to phenomena particular to specific cohorts (e.g., the birth cohorts of women from the 1920s and the 1930s had relatively high TFRs). Note that these three kinds of effects are intertwined, in that there are only two degrees of freedom.
A final useful fertility concept is the notion of replacement fertility, which can be defined as the level of fertility at which a population just replaces itself. In a world with no mortality, replacement fertility would exist with a TFR of 2.0. The low level of mortality in the U.S. and other industrialized countries means that our replacement TFR is about 2.1, while in countries with higher mortality the replacement TFR will be correspondingly higher (e.g., in much of sub-Saharan Africa the replacement TFR is about 2.7).
Mortality
crude death rate: The crude death rate (cdr or d) in a population during a given year is defined as the total number of deaths (D) divided by the midyear population (P). It is normally expressed per thousand population, so we have
age-specific death rate: The age-specific death rate (asdr) for individuals age i in a population during a given year is defined as the total number of deaths to people age i during the year (Di) divided by the total (midyear) population age i (Pi). Expressed per thousand, we have
Note that the crude death rate is simply a weighted average of age-specific death rates, with the weights equal to the proportion of the total population represented by those age i. That is,
This formulation highlights the importance of age composition as a factor influencing the crude death rate (cf., State College vs. St. Petersburg, FL).
life expectancy at birth: Life expectancy at birth (e0) measures the average number of years that a newborn baby can expect to live. We can think of cohort life expectancy at birth, which would be the average age at death of a cohort of individuals (equal to the total number of person-years lived by the cohort divided by the size of the initial cohort).
More common is a period measure of life expectancy at birth. Like the period TFR, this is a synthetic measure, showing the hypothetical experience of a cohort passing through life subject to the relevant age-specific rates from a given period. Hence, if life expectancy at birth for 1996 were, say, 75 years, this would mean that a cohort of individuals experiencing the age-specific death rates that prevailed in 1996 would live for an average of 75 years.
A more general aspect of life expectancy is the notion of remaining life expectancy as of age x (ex). This simply shows the average number of years of life remaining for individuals who reach age x and then experience a given set of age-specific death rates.
Migration
Migrants are people who change their place of residence. In-migrants (I) move into a place, while out-migrants (O) leave that place. Gross migration flows measure movement in both directions, while net migration reflects the difference between two opposing gross migration flows. Thus, for example, if during a particular period 300,000 people moved from New York to California and 100,000 moved from California to New York, we'd characterize the situation as one with a net migration of 200,000 from New York to California.
When migration entails crossing an internation border, then we speak of immigration or emigration, depending on whether the place we're focused on is the one migrants are moving into or out of, respectively.
Age and Sex Composition
The age and sex composition of a population is reflected by an age pyramid. These diagrams are drawn with age (ascending) on a central vertical axis, horizontal bars showing the number or proportion of males on the left, and bars showing the number or proportion of females on the right. They are an extremely useful means of depicting the age and sex composition of a population, and typically will provide a good deal of information about the past history of fertility and perhaps also mortality and migration in a population.
Population Growth
The change in population from one year to the next equals the excess of births over deaths plus the amount of net in-migration:
The first portion of the right hand side of the equation (B-D) equals the natural increase in the population. Note that the rate of natural increase in the population equals the difference between the crude birth rate and the crude death rate. The overall rate of population growth equals the rate of natural increase plus the rate of net immigration.
Further, note that because of the effects of age composition, it is possible for a population to manifest below-replacement fertility and yet still experience natural increase (in the demographic short and medium run). This has been the case for most of the past two decades and more in the U.S.
A useful thing to know in considering population growth is how to estimate the time required for a population to double. If r is the annual rate of population growth in percent, then the doubling time of the population (T2) may be approximated by
Demographic Transition
The notion of the demographic transition refers to the long-term process of transition from a demographic regime of high birth and death rates to one of low birth and death rates. Every industrialized country has undergone this transition, and developing countries may be seen as being in various stages of the transition.
© 1997 David Shapiro
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For questions, comments, and suggestions, write to: dshapiro@psu.edu.