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Lecture: Net reproduction rate of the population. Net population replacement rate Gross population replacement rate example

Lecture: Net reproduction rate of the population. Net population replacement rate Gross population replacement rate example

22.01.2022

What the Net Reproduction Rate Says and Doesn't Say

Except for the very illiterate ones, those who talk about the demographic situation on the basis of general birth and death rates, then most people who are more or less seriously interested in demography know that in order to correctly judge what is happening, one must use more subtle meters. . These include, in particular, the total fertility rate, life expectancy and other functions of mortality tables, as well as gross and net reproduction rates.

An analysis of these indicators and their dynamics makes it possible to judge the changing reproductive situation, comprehend the various components of this situation, and makes it possible to compare the conditions for the reproduction of the population of countries or regions in time and space.
At the center of such an analysis is an indicator well known to demographers - the net coefficient (net coefficient) of the reproduction of the female population. It is equal to the number of girls born in a given period (usually one year, but another period can be chosen, for example, a five-year period, as is done in Table 1) and who have a chance to survive - at the age-related mortality levels of this period - to the average age of motherhood, calculated for the same period, per woman. The components of the calculation of the net coefficient for five-year periods, starting from the last five years of the 19th century and ending with the last five years of the 20th century, are given in Table. 1, changes in the net coefficient itself are also shown in fig. 1. The red line in the figure is the line of simple reproduction, the boundary that separates expanded reproduction from narrowed reproduction.

The last column of the table contains the so-called "true" coefficient of natural increase, i.e. the coefficient of natural increase of a stable population corresponding to the age functions of fertility and mortality in each period. It shows with what annual coefficients the population can increase (decrease) due to natural growth, if an unchanged birth and death regime is maintained indefinitely for the calculation period indicated in the first column of the table.

Table 1. Components of the net reproduction rate of the female population and the "true" rate of natural increase in Russia over 100 years

Period	Average number of children per woman	including girls	Average age of mother, years	Probability of surviving to maternal middle age*	Net reproduction rate (2x4)	True coefficient of natural increase, ‰

At the end of the 19th - in the first decade of the 20th century, at best, only half of the girls born reached the average age of motherhood, however, with a birth rate of 7 or more children per woman, expanded reproduction of the population was steadily ensured in Russia - each new generation of girls was about 1.5 times more than the maternal generation (the net reproduction rate fluctuated in the range of 1.5-1.6). As a result, the population could increase annually by 1.4 - 1.6% (the true coefficient of natural increase was 14.0 -15.5 ppm). The slow decline in the birth rate at that time was compensated by a gradual improvement in the survival of children's generations, so that the integral indicators of reproduction changed little.

Figure 1. Net reproduction rate of the Russian population during the 20th century

The smooth change in indicators is interrupted by the First World War and the Civil War and the accompanying famine and epidemics. The fall in the birth rate and a sharp deterioration in the situation with mortality caused a short-term demographic crisis. With a long-term preservation of the indicators of the reproduction regime recorded in 1915-1919, the population of Russia would decrease by 0.4% per year. Compensatory growth in the birth rate and noticeable successes in reducing mortality in the 1920s again restored the previous characteristics of population reproduction. The value of the net reproduction rate calculated for 1925-1929 is even higher than at the end of the 19th century - 1.7, which was almost a record value in the entire history of Russia.

In the 1930s, the trend towards a decrease in generation replacement rates, caused by a decrease in the birth rate (the situation with mortality practically did not improve), becomes predominant against the background of fluctuations caused by the forced "building of socialism" and famine. The Second World War, in turn, intensifies the fluctuations and causes another demographic crisis. The probability of surviving to the average age of motherhood again drops to 37%, and the birth rate - about 3 children per woman - turns out to be clearly insufficient to simply replace generations (the maternal generation was replaced by a generation 44% smaller in number - net reproduction rate population in the first half of the 1940s, according to our estimate, was 0.56). It is clear that if such a regime of reproduction is maintained, the population in the future would begin to decline rapidly - at a rate of at least 1.8% per year.

In the post-war years, the birth rate, after a short-term and inconspicuous compensatory growth, restored its downward trend. At the same time, the two post-war decades were marked by a sharp decline in infant mortality - the chances for a girl to become a mother increased rapidly to 90-95% by the early 1960s. Due to such a decrease in mortality, the reproduction regime in the 1950s - the first half of the 1960s still ensured a simple replacement of generations (each new generation reproduced the parent with an excess of 10-20 percent). However, even then the prospect of a transition to narrowed reproduction, when each new generation would be smaller in number than the parent, became more and more obvious.

Since the mid-1960s, the effect of reducing mortality has become insignificant. An increase in the probability of a newborn girl surviving to the average age of motherhood from 0.96 to 0.98 was not able to seriously affect the integral characteristics of population reproduction. The decisive factor in the change in reproduction rates in the last third of the 20th century and for the entire subsequent historical perspective is the birth rate. And it only for a short time, in the second half of the 1980s, rose to the level of 2.1 children per woman (the border of simple reproduction at the current level of mortality). Therefore, it is not surprising that since the mid-1960s, a reproduction regime has been established in Russia that does not even ensure a simple replacement of generations ("narrowed" reproduction). The fall in the birth rate in the 1990s further increased the degree of "underreproduction" (each new generation of children today is 30-40% less than the parent).

Since the population of Russia has not been reproduced for four decades, the prospects for its growth due to natural increase in the next two decades are negligible. In the absence of additional migration support and maintaining the birth rate of the second half of the 1990s, the population may decline at an annual rate of up to 1% per year, and, in the limit, up to 2% per year, as indicated by the natural growth rate. stable population (20.3 per 1000 population), shown in Table 1.

With all the analytical value given in Table. 1 and in fig. 1 indicators, they are also not perfect. These indicators refer to the so-called "conditional" generations and are, in essence, nothing more than an assessment of the actual demographic conditions for the reproduction of the population in a given calendar year (and not a description of the actual course of the reproduction process, as is often thought).

The quantitative characteristics of the real reproduction of the population would correspond to these indicators only if these conditions remained unchanged for a sufficiently long time. But in reality, they constantly fluctuate, and during the period of demographic transition they are subject to long-term and significant directed changes.

The popularity of indicators for conditional generations ("transverse" or transversal) is explained by the relative simplicity of their calculation. But to get a complete and deep understanding of what is actually happening with the reproduction of the population is possible only when it is possible to use indicators for real generations, or cohorts ("longitudinal", or longitudinal). It is these indicators, this time really describing the real course of the reproduction process, that are considered in the subsequent sections of this article.

However, if each of the women of reproductive age gives birth on average R daughters, this does not mean that the number of generations of daughters will be R times more or less than the number of generations of mothers. After all, not all of these daughters will live to the age at which their mothers were at the time of birth. And not all daughters will make it to the end of their reproductive years. This is especially true in countries with high mortality, where up to half of newborn girls may not survive until the start of the reproductive period, as was the case, for example, in Russia before the First World War 2 . In our time, of course, this is no longer the case (in 1997, almost 98% of newborn girls survived to the start of the reproductive period, but in any case), an indicator is needed that also takes into account mortality. Given the assumption of zero mortality until the end of the reproductive period, the gross reproduction rate of the population has hardly been published or used recently.

An indicator that also takes into account mortality is net reproduction rate of the population, or otherwise Beck-Kucinsky coefficient . Otherwise, it is called the net reproduction rate of the population. It is equal to the average number of girls born in a woman's lifetime and surviving to the end of the reproductive period, given birth and death rates. The net reproduction rate of the population is calculated using the following approximate formula (for data on five-year age groups):

where all designations are the same as in the formula for the gross coefficient, a 5 L x f And l 0 - respectively, the number of people living in the age interval (x+5) years from the female mortality table. The formula for calculating the net reproduction rate of the population uses the number of people living in the age interval (x+n) years from the female mortality table, and not a function of survival, i.e., not the number of those surviving to its beginning (lx), because it is an approximate formula. In rigorous demostatistical analysis and mathematical applications of demography, it is the survival function that is used 1(x).

Despite the somewhat “threatening” look, this formula is quite simple and allows, without much difficulty, especially using the appropriate software, for example, Excel spreadsheets, to calculate the value of the net reproduction rate of the population. In addition, many programs have been developed that make it possible to reduce the calculation of the net coefficient to a simple input of initial data. For example, the International Program Center of the US Bureau of Census (IPC of the U.S. Bureau of the Census) has developed a PAS (Population Spreadsheets Analysis) spreadsheet system, one of which (SP) is based on data on the values of age-specific fertility rates and the number of people living in the age interval (x+n) years calculates gross and net reproduction rates, as well as the true rate of natural increase and generation length, which will be discussed below 3 .

In table. 7.1 shows an example of calculating the age-specific fertility rate, gross and net reproduction rates of the population, in which the above software is not used. Using this example, as well as a similar example given in V.A. Borisov 4, one can easily learn how to calculate all the main indicators of population reproduction. But, of course, it is desirable to have at least some computer equipment, it is best, of course, to use the Excel program.

The calculation was carried out according to the following step-by-step procedure:

Step 1. In column 2 we enter the values of the age-specific fertility rates (5 ASFR X , taken in this case from the Demographic Yearbook of the Russian Federation for 1999 (p. 155**).

Step 2 Calculate the total fertility rate (TFR). For this number in the lines of column 2, we divide by 1000 to express the age-specific fertility rates in relative shares of 1 (in other words, we bring these values to 1 woman of the conditional generation). We enter the received private numbers in column 3. The sum of these numbers, multiplied by 5, gives us the value of the total birth rate equal to 1.2415 (highlighted bold italics). This, up to the third decimal place, coincides with the official data of the State Statistics Committee of the Russian Federation (1.242. FROM. 90).

Step 3 We calculate the gross reproduction rate (TO), or the number of daughters a woman has in her lifetime. To do this, we multiply the data in column 3 line by line by the proportion of girls among newborns (D). In this case, its average value for the period 1960-1998 was taken equal to 0.487172971301046. The sum of the numbers in column 4, multiplied by 5, gives the value of the gross reproduction rate equal to 0.6048. The same result can be obtained by simply multiplying the total fertility rate by the proportion of girls among newborns (1.2415 0.487 ... = 0.6048).

Step 4 In column 5 we enter the values \u200b\u200bof the numbers living in each age interval (x + 5 years (x = 15, 20,..., 45) from the mortality table for the female population of Russia for 1998. In column 6, these numbers are reduced to relative fractions of a unit by dividing them by the root of the mortality table (in this case, by 10,000). An alternative way is to average two adjacent values of the numbers of those surviving to the beginning of each age interval from 15 to 50 years from the mortality table for the female population for 1998 (p. 188). Multiplying the obtained averages by 5, we determine the number of people living in each age interval necessary for calculating.

Step 5. We calculate the net reproduction rate. To do this, we multiply the data in column 4 line by line by the numbers in column 6. Summing up column 7, we obtain the value of the net reproduction rate equal to 0.583. This value differs only by 0.002 from the officially published Goskomstat of the Russian Federation (0.585, p. 114 of the 1999 Demographic Yearbook).

The net reproduction rate is calculated for a conditional generation. As a measure of the replacement of the maternal generation by the generation of daughters, it is valid only for the so-called stable population, in which the mode of reproduction does not change, i.e. birth rate and death rate. The size of such a population changes (i.e. increases or decreases) in R0 once in a while T, called the average generation length.

Calculation of indicators of reproduction of the population of Russia for 1998 5

Table 7.1

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Medkov V. M
M 42 Demography: Textbook. Series "Textbooks and teaching aids". - Rostov-on-Don: "Phoenix", 2002. - 448 p. The textbook summarizes the experience of teaching demography to sociology students

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Basic principles for conducting population censuses
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Current record of vital events
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Population lists and registers
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Primary demographic information, secondary demographic information, population data sources, census, current record, lists, registers, surveys, qualifications, audits, population categories

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Demographic Balance Equation
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Average population
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Relative indicators of population dynamics
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Growth and growth rates for the period
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Average annual growth and growth rates
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Population doubling period
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Population structures
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Gender as a scientific category
In general terms, sex is a combination of genetic, morphological and physiological characteristics of the body that provide sexual reproduction. Applied to the person gender considered

Gender structure of the population
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Age as a universal independent variable
Age is the second most important demographic characteristic. Age is the period from the birth of a person to one or another moment of his life. Age is measured in years, months (

Age structure of the population
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Age accumulation
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Population aging
Population aging, or demographic aging, is understood as an increase in the proportion of elderly and old people in the population. Population aging is the result of long demographic

Age-sex pyramid
For a visual and joint representation of the age and sex structures of the population, the so-called. age-sex pyramids. The age-sex pyramid is a two-sided ruler

Marital status and marital structure
Under the marital status (status) understand the position of the individual in relation to the institution of marriage, determined in accordance with the customs or legal norms of a particular country31.

Review questions
1. Demographic balance equation and its components. 2. The concept of natural increase (loss) of the population. 3. Relative indicators of population dynamics - types, def.

Marriage as a sociological and demographic category
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Marriage
If the concept of marriage refers to a social institution, and the concept of marriage characterizes an individual act of forming a marriage union between a man and a woman, then the term br

Absolute number of marriages
In demography, marriage is measured by a whole system of indicators that characterize the trends in its formation and change from different angles. The starting point is the absolute number of marriages,

Marriage rates
Marriage refers to the number of processes that are formed by repeated events. In modern conditions, you can enter into marriage several times throughout your life. Another thing is that in the first

Average age of marriage
An important indicator of the marriage process is the age of marriage. It is calculated as the time elapsed between the date of birth and the date of marriage. Age of Entry Data Source

Marriage potential
The marriage rates considered above, in addition to the general coefficient, characterize the marriage rate separately for men and women. And although a separate analysis of nuptiality for each sex is important,

Unregistered marriages or cohabitations
Although, as mentioned at the beginning of the chapter, the demographer is interested not so much in the legal form of marriage as in its reality and effectiveness, nevertheless, unregistered marriage occupies a significant place.

Divorce and divorce
Divorce is the dissolution of a marriage during the lifetime of both spouses in the civil registry offices or, in cases specifically provided for by law, by a court decision. Divorce is made according to

Divorce rates
Divorce is measured by a system of indicators, the first of which is the absolute number of divorces for a period, usually a year. The dependence of this indicator on the population makes it necessary

Divorce Factors
The question of the causes of divorce and, accordingly, the factors of divorce is still not fully investigated. Divorce as a social phenomenon is studied by the sociology of the family, that section of it, which is called

Demographic concept of fertility
Birth rate is a mass statistical process of childbearing in the totality of people that make up a generation, or in the totality of generations - the population. Demographic usage of the word

Fertility and fertility
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Birth rates
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Fertility rates for the conditional generation (fertility rates for the period)
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Coefficient (index) of children
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Absolute number of births
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total fertility rate
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Special birth rate
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Partial fertility rates
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Age-Specific Fertility Rates
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total fertility rate
Age-specific fertility rates make it possible to analyze the level and dynamics of the net intensity of fertility in a conditional generation, free from the influence of the age structure as a population as a whole.

Birth calendar indicators of the conditional generation
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Real generation birth rates (cohort birth rates)
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Cumulative birth rates at a given age
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Indicators of the calendar of births of real generations
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Extrapolation for 2-5 years
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The concept of reproductive behavior
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Two approaches
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Regulatory Approach
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Fertility indices E. Cole
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Empirical approach
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Keywords
Fertility, natural fertility, fecundity, I infertility, childlessness, infertility, sterility, I fertility index, total fertility rate, special fertility rate, n

Review questions
1. How are the concepts of birth, fertility, fertility, natural fertility related? 2. Which of the following is superfluous: agamia, childlessness, infertility

Demographic concept of mortality
Mortality is the second most important demographic process after birth. The study of mortality has as its object the influence that death has on the population, on its size and structure.

Mortality rates
A system of indicators is used to measure mortality. The first and simplest of these is the absolute number of deaths. Statistical authorities collect and publish data on the number of deaths

Standardization of death rates
The value of crude mortality rates, being free from the influence of the absolute population, nevertheless depends on structural factors, i.e. from the ratio of the numbers of male and female

Standardization methods
With direct standardization**, the age-specific mortality rates of the real population are reweighted according to the age structure of the standard. Thus, the number cm is obtained

Mortality tables
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Building a complete mortality table
The construction of mortality tables is, in principle, a simple, but rather time-consuming computational procedure. It includes several stages3: calculation of the values of the initial

Construction of a summary table of mortality
The idea and method of constructing a summary mortality table are similar to those just discussed for complete mortality tables. The difference is only in the length of the age interval. The length of a typical i-th inte

Dynamics of life expectancy in Russia in the 1990s
The dynamics of the average life expectancy in our country over the past century is characterized by strong heterogeneity, the change of periods of growth of this indicator by periods of its rather sharp increase.

Mortality by cause
Quantitative indicators of the level of mortality and its dynamics are an important tool for analyzing the demographic situation in the country. However, quantitative indicators alone, even if the limit

epidemiological transition
The dynamics of mortality by causes described above characterizes the situation in one particular country and in a specific period of time (in this case, in Russia in the last third of the last century). She expresses

Review questions
1. Demographic concept of mortality. 2. What are the specifics of calculating the infant mortality rate? 3. What do the coefficients a and p express in the denominator of the Rats formula? 4.

Gross reproduction rate
As for the frequency of the birth of girls in women of different ages, then, generally speaking, it is different. However, it will not be a big error to assume that the proportion of girls among births is the same for all

Generation length
Generation length is the average time interval separating generations. It is equal to the average age of the mother at the birth of daughters who live at least to the age in which their mothers were.

Review questions
1. What is the relationship between the concepts of natural increase (decrease) of the population and reproduction of the population? 2. Can we assume that positive natural population growth is guaranteed to mean

By the length of the forecast horizon
The first criterion for classifying demographic forecasts is the length of the forecast horizon, or the length of the forecast period. Usually there are short-term (5-10 years), medium-term (25-30

Analytical forecast
The purpose of the analytical forecast is to study current trends in population reproduction by assessing their possible impact on the future size and composition of the population, as well as on social

Forecast-caution
A variation of the analytical forecast is a warning forecast. The purpose of the warning forecast is to show the possible adverse or dangerous consequences of the current demographic

Normative forecast
The main purpose of the normative forecast is to develop specific recommendations for achieving some desired state of demographic processes. With normative forecasting

Functional forecast
The purpose of functional forecasting is to obtain predictive information about the population, which is necessary for making decisions in the economic, social, political and other areas of activity.

Methods based on the application of mathematical functions
The main area of application of methods of this class is the forecasting of the population of small territories (for example, regions of a country), especially those for which there is no

extrapolation method
The extrapolation method is based on the direct use of linear and exponential functions, i.e. data on average annual absolute changes in population for a period or on average annual

Analytical method
As can be seen, the calculation by the exponential function gave a larger number for the Novosibirsk region as of January 1, 2000 than the calculation by the linear function. This reflects the greater rate of change in the case

Component method, or age shift method
The component method opens up more opportunities for demographic forecast developers. Unlike extrapolation and analytical, it allows you to get not only the total number

Mortality prediction
The most methodologically developed is the forecasting of mortality. Therefore, let us briefly consider the main methodological methods for predicting the levels of demographic processes, namely

Fertility forecasting
The most complex and creatively interesting stage of fertility forecasting is forecasting either the general level of fertility (usually in terms of its total coefficient), or its

Functions of the value of the total coefficient
fertility. Taiwan, 1958-198729 for target

Population projections for the world and Russia
Currently, practical work on the development of demographic forecasts is carried out by international organizations, government agencies and scientific institutions. The most ambitious work

Chart 8.2
Ideal and desired number of children according to surveys of women (VTsIOM), 1991-199951

Spiegelman M. Op. cit. P. 408.
10 Ibidden. "See: Population. Encyclopedic Dictionary. M., 1994. S. 209. 12 See: Arriaga E. Population Analysis w

H WPP-2000. R. 9.
41 Antonov A.I., Sorokin S.A. The fate of the family in Russia in the 21st century. M., 2000. P.49. 42WPP-I,P. 8-9. 4

General works
Andreev E.M., Tsarsky L.E., Kharkova T.L. Demographic history of Russia: 1927-1959. M., 1998. Antonov A.I. Sociology of fertility. M., 1980.

Reference books
Demographic Yearbooks of the Russian Federation. M., Goskomstat RF, 1993-2001. Demographic encyclopedic dictionary. M., 1985.

Glossary of demographic terms
Abortion is a spontaneous (spontaneous abortion) or artificial (induced abortion) termination of pregnancy in the first 22 weeks, when the fetus is not yet viable. actuary

The concept of population reproduction

Topic 11. Population reproduction

The main feature of the population is that, despite the constant changes in its size and structure, it remains as a population, i.e. as a self-reproducing collection of people . It can even be said that the population is self-preserving, remaining itself precisely and exclusively thanks to these incessant changes.

This process of self-preservation of the population in the course of its continuous changes is called the reproduction of the population, and it is precisely this process that forms the subject of demography as a science.

population reproduction- this is a constant renewal of the size and structure of the population in the process of changing generations of people, through births and deaths. The set of parameters that determine this process is called mode of population reproduction.

The parameters that determine the reproduction of the population are the birth rate and death rate, presented in the form of their meters, as well as the number of arrivals and the number of departures1.

Usually, the reproduction of the population is considered not as a whole, but in relation to any one sex, most often female. The choice of the female population is due to the following factors:

The reproductive period in women is shorter than in men;

· The main parameters of female reproduction (the number of children born to a woman, her age at birth, etc.) are much more accessible than similar characteristics for men, especially with regard to out-of-wedlock births.

The role of age as a universal independent variable in demographic analysis and its constant change (every person inevitably either dies or gets older, i.e., more strictly speaking, moves to another age group) determine that much attention is paid to age in the analysis of population reproduction , the study of this process in the context of age groups.

Population reproduction indicators refer to a real or hypothetical cohort (generation), i.e. are essentially cohort.

If certain birth and death rates differentiated by sex and age are given, as well as a secondary sex ratio, which is a universal biological constant and equals approximately 105-106 live births of boys per 100 live births of girls, then this completely determines the reproduction of the population and its age and sex structure. The totality of precisely these parameters is what is meant when speaking about the mode of population reproduction.

Since the reproduction of the female population is usually studied, the whole question comes down to considering the age-specific mortality of women and the frequency of the birth of girls in women of different ages.

Mortality is usually measured using the survival-to-age function X years, i.e. using the function . In practice, they use the values of the numbers surviving to the age X years from the complete tables of mortality of the female population. A generalizing characteristic of female mortality is the average life expectancy of a newborn, i.e. .

Gross reproduction rate is the number of girls that each woman will give birth to on average during the entire reproductive period. When calculating the gross coefficient, it is assumed that there is no mortality of women until the end of the reproductive age.

The gross replacement rate of the population is equal to the total fertility rate multiplied by this proportion of girls among newborns:

where R- gross reproduction rate; TVR - total fertility rate; ASBR x - age-specific fertility rates; -proportion of girls among newborns.

In Russia, the average proportion of girls among newborns over the past 40 years was about 0.487.

As can be seen from the calculation formula, the gross reproduction rate of the population is the total birth rate adjusted for the secondary sex ratio.

The gross reproduction rate of the population can be interpreted in various ways:

as an age-standardized birth rate;

as the average number of daughters that a group of women who started life at the same time could give birth to, if all of them lived to the end of the childbearing period;

· as the ratio between the number of women of one generation, for example, at the age of 15, to the number of their daughters at the same age, provided that there is no mortality within the childbearing period;

· as the ratio between female births in two successive generations, assuming that no one dies between the beginning and end of the reproductive period.

The last three definitions are usually used when talking about real cohorts.

The calculation was carried out according to the following step-by-step procedure:

Step 1. In column 2 we enter the values of the age-specific fertility rates (5 ASFR X , taken in this case from the Demographic Yearbook of the Russian Federation for 1999 (p. 155**).

Calculation of indicators of reproduction of the population of Russia for 1998 5

Table 7.1

Generation length

Generation length is the average time interval separating generations. It is equal to the average age of the mother at the birth of daughters who survive at least to the age in which their mothers were at the time of their birth.

To calculate the generation length, you can use an approximate formula, which is given in many demography textbooks 6:

where all designations are the same as in the previous formula. As can be seen from the formula, the desired generation length is obtained as the arithmetic mean of the ages of mothers at the birth of daughters (in this case, the middle of the corresponding age interval is used.), Weighted by the number (share) of the latter, surviving at least to the age at which their mothers were in the moment of their birth. Note that calculating the length of a generation is exactly the same as calculating the average age at birth of a child, which we did in the chapter on fertility. The only difference is in the weights used (when calculating the average age at the birth of a child, as you remember, age-specific birth rates were used as weights) and in the fact that in this case we are not talking about all children born, but only about daughters, and only those of them who live to at least their mother's age at their birth.

Let's return now again to tab. 7.1 and do the last, sixth step.

Step 6 We calculate the length of the generation, or the average age of the mother at the birth of daughters who live at least to the age at which their mothers were at the time of their birth. For this, the numbers in the lines of column 7 are multiplied by the middle of each age interval (column 8) and entered in column 9. The resulting products are the number of person-years lived by all daughters born to 1 woman of the conditional generation in this age interval and surviving at least to the age of their mother at the time of their birth. Summing these products, we get the numerator of the above formula for calculating the generation length, approximately equal to 14.8709. This number is the number of person-years lived by all daughters born to 1 woman of the conditional generation throughout her life and surviving at least to the age of the mother at the time of their birth. Dividing this last value by the number of all such daughters, i.e., by the net reproduction rate of the population (0.5859), we obtain the required length of the female generation in Russia in 1998. For the data we have chosen, it is equal to 25.38232512 years, or rounded 25 ,38 years old.

True Rate of Natural Increase As mentioned above, the net reproduction rate of the population (R0) shows that the size of a stable population, corresponding to the real one with given general birth and death rates, which are assumed to be unchanged, changes (i.e. increases or decreases) in R 0 times per time T, i.e., for the length of a generation. Taking this into account and accepting the hypothesis of exponential growth (decline) of the population, we can obtain the following relationship linking the net coefficient and the generation length. This ratio is derived from the following equation: P T \u003d P () R 0 \u003d P 0 - e g T (remember chapter 3, that section of it that talks about population growth and growth rates):

In the theory of a stable population, r in these expressions is called the true coefficient of natural population growth (or A. Lotka's coefficient). This coefficient is the root of the so-called integral equation of population reproduction, or Lotka's equation 7 . It is widely used in mathematical applications of demography, in particular in the theory of a stable population. However, we do not consider this equation here, since this topic is beyond the scope of our manual. Those interested are referred to the Demography Course, ed. AND I. Boyarsky (M, 1985. S. 90-91 and 103-118), as well as to the corresponding articles of the Demographic Encyclopedic Dictionary (M., 1985) and the Encyclopedic Dictionary "Population" (M, 1994). For a very close approximate solution of the Lotka equation with respect to the true coefficient and generation length, as well as a computational procedure, see: Shryock H.S., Sigel J.S. The Methods and Materials of Demography / Condensed Edition by E.G. stockwell. N.Y., San Francisco, London, 1969. P. 316-31.8.

Lotka Alfred James (1880-1949), American biologist and demographer. [...] President of the American Population Association (1938-1939), the American Statistical Association (1942) ... In 1907, he showed that a population that grows at a constant rate and maintains an unchanged order of extinction tends to a certain age composition and is constant / and birth and death rates. ... For the first time, he proposed a mathematical expression for the natural growth rate of a closed population with a constant order of extinction and childbearing, the algebraic expression of which was given in the work "On the true coefficient of natural population growth" (1925), showing the relationship of this coefficient with the net reproduction rate of the population. .. Lotka studied the process of generational change, gave a modern analytical expression for the length of a generation ...

Population. Encyclopedic Dictionary. M., 1994. S. 210.

The last formula, proposed by the American demographer E. Cole, already familiar to you from the chapter on fertility, in his article "Calculation of approximate true coefficients" 8 , can be used to estimate the true coefficient of natural population growth, given that, as mentioned above, the length of a generation is the average the age of the mother at the birth of daughters surviving at least to the age of their mothers at the time of their birth. In modern conditions, the length of a generation does not differ too markedly from the average age of a mother at the birth of a child *. Therefore, the evaluation of the last parameter by any method allows one to approximately establish both the sign and the value of the true rate of natural increase.

If we now use E. Cole's formula and divide the just calculated length of the female generation by the natural logarithm of the net reproduction rate (lnO.5859 \u003d -0.534644249954392), then we get the true rate of natural increase of the population of Russia for the conditions of 1998. This value is -0.0210636435922121, or =-2.1%.

The real value of the coefficient of natural increase of the population of Russia in 1998 was equal to -0.48%, or almost 4.4 times less in absolute value. This difference is due to the relatively high proportion of women of reproductive age in the Russian population, which, in turn, is associated with a certain increase in the birth rate in the first half of the 1980s. of the last century and with the influence of previous demographic waves. The real age structure of our country is younger than the age structure of a stable population corresponding to modern parameters of fertility and mortality. The population has accumulated some growth potential, or, more precisely, the potential for a slowdown in population decline, whereby our country's population is not declining as rapidly as it would otherwise.

But this situation will end very soon. Generations born during the period of the birth rate decline that began in the second half of the 1980s will begin to enter reproductive age. last century and continues to this day**. And then the potential for demographic “growth” will be exhausted, and the natural decline in the population of our country, if no measures are taken, will be even faster (in 4 -5 times faster than now). And no replacement migration, which some demographers rely on, will not save our country from the horrors of depopulation.

For example, in the same 1998, the average age of a mother at the birth of a child, according to S.V. Zakharov, was 25.34 years. See: Population of Russia 1999. Seventh Annual Demographic Report / Ed. ed. A.G. Vishnevsky. M., 2000. P. 55. The State Statistics Committee of the Russian Federation gives a value of 25.3 years (see: Demographic Yearbook of the Russian Federation 1999. P. 170).

The increase in the number of births in the last two years is nothing more than an artifact.

Although, strictly speaking, the net reproduction rate is a measure of the replacement of the maternal generation by the generation of daughters, it is usually interpreted as a characteristic of the replacement of generations in the entire population (not just women). At the same time, the nature of the replacement of generations (reproduction of the population) is assessed in accordance with the following rule:

The clarification "after a time equal to the length of a generation" is very significant. If R0< 1, this does not yet mean that in the year for which the net reproduction rate is calculated, there is a decrease in the population, absolute numbers of births and the total birth rate. The population can grow for quite a long time, despite the fact that the value of the net coefficient is less than or equal to 1. This has been the case, for example, in Russia since the late 1960s. until 1992, the net coefficient in our country was less than 1 all these years, respectively, the true rate of natural increase was negative, and the population increased due to the potential for demographic growth accumulated in a relatively young age structure. Only when this potential turned out to be exhausted (and this happened just in 1992), the birth rate became less than the death rate, and the population began to decline in numbers.

We can say that the depopulation in Russia has changed from latent, latent to overt and open. And this did not depend at all on the specific political and socio-economic situation of the 1990s. of the last century, no matter what the so-called "nationally concerned scientists" and self-styled "patriots" of any color, from the ultra-left to the ultra-right, may say. The beginning of depopulation in our country was predetermined by the processes that took place in the population throughout the 20th century, especially in the post-war period, when there was a sharp drop in the need for children, which caused a rapid and deep drop in the birth rate. This is exactly what happens in all developed countries. Approximately a third of the world's countries have a birth rate that is less than what is necessary for simple reproduction of the population. In other words, in these countries, as in Russia, there is a hidden or obvious depopulation. And most of these countries are those in which the standard of living of the population is much higher than in our country.

In the previous paragraph, it was said about the birth rate necessary to ensure simple reproduction of the population. In this regard, the question arises of how to determine this level of fertility. Various methods are used to answer it.

One of them was proposed by V.N. Arkhangelsk 9 . The method is based on a simple comparison of the actual total fertility rate with its conditional value equal to the total mortality rate. The ratio of the second to the first shows (in fact, this is the reciprocal of the vitality index, which was discussed at the beginning of the chapter), how many times more the value of the total birth rate must be in order to ensure zero natural population growth with a given mortality rate and the current age structure:

where TFR h , TFR a , GMR, GBR- respectively, the hypothetical total birth rate necessary to ensure simple reproduction, the current total birth rate, the total death rate and the total birth rate.

Gross and net ratios make it possible to answer this question differently, but it is also quite simple. To do this, either the ratio of the net coefficient to the gross coefficient, or the inverse ratio, is used.

The first ratio, i.e. the ratio of the net coefficient to the gross coefficient (R0 / R), shows what the level of potential reproduction of the population is, or otherwise, how many women in each next generation replace women of the previous generation per one born girl 10 .

Inverse ratio, i.e. the ratio of the gross coefficient to the net coefficient (R/R 0), shows how many girls a woman of a conditional generation needs to give birth to ensure that simple reproduction of the population is guaranteed. It is usually denoted by the Greek letter r:

In particular, for our example (see Table 7.1):

From here it is easy to obtain the value of the total birth rate required to ensure simple reproduction of the population. To do this, you just need to divide this expression by the proportion of girls among newborns, that is, by the secondary sex ratio:

Calculation by the method of V.N. Arkhangelsky gives the value of the total fertility rate required to ensure simple reproduction, approximately equal to 2.04, which is much less. Apparently, this difference is affected by the fact that the method associated with the use of gross and net coefficients gives the ratio of births and deaths in its pure form, and in the method of V.N. Arkhangelsky, the role of the age structure is also taken into account. It is interesting to compare the dynamics of the hypothetical total fertility rate (TFR h), calculated by these two methods, for 1996-1998.

If we use the calculations of V.A. Borisov, it turns out that the value of the hypothetical total fertility rate (TFR h), calculated by the method of V.N. Arkhangelsky, in 1996 was equal to approximately 2.05, i.e. we have a decrease by 0.01 over two years. The calculation by the alternative method gives for 1996 the value TFR h , equal to 2.12, which, on the contrary, is 0.01 more than 11. As you can see, the dynamics of the hypothetical total fertility rate, calculated by various methods, turned out to be the opposite. Under the conditions of decreasing mortality at that time, this difference can be explained both by a certain rejuvenation of the age structure of the reproductive contingent, and by an increase in the gap in the dynamics of fertility and mortality (the birth rate continued to fall even faster than before, and the death rate also decreased somewhat, but not in the same proportion ).

In Russian literature, r is sometimes called at the cost of simple reproduction. It is believed that its value characterizes the so-called. "economical" reproduction of the population, or the ratio of demographic "costs" And "results"."Costs" are respectively measured by the gross coefficient, and "results" - by the net coefficient. Moreover, the lower the value of p and the closer it is to 1, the more "economical" is the reproduction of the population 12 . The application of allegedly "economic" terminology to the reproduction of the population seems somewhat strange (it is not clear what to do with ethics). In addition, it seems that the name of this indicator ("price of simple reproduction"), and its interpretations in the mouths of many of our demographers are needed only to prove to ourselves and readers that the situation with reproduction in our country is far from one that could cause alarm. What, in fact, to worry about, if the value of p in our country is practically the same as in advanced countries of the West. We, so to speak, if not ahead of the planet then at least in the front ranks progressive humanity.

Being involved in progress is, of course, impressive. But the question arises whether this is progress. Can the inexorable and rapid fall into the abyss of depopulation be called progress? Unfortunately, many demographers either ignore these damned questions, or relate to the negative demographic dynamics in our country, at best, conciliatory, and at worst, even believing current demographic trends (especially the situation with the birth rate) to be something quite normal.

All the indicators of population reproduction described above refer to the female population. However, in principle, similar indicators (gross and net reproduction rates, true rate of natural increase, length of the male generation, etc.) can be calculated for the male population, as well as for the entire population. Analysis of the reproduction of the male population in recent years has become increasingly widespread in demography. We have already discussed one of the successful examples of this kind of analysis done by V.N. Arkhangelsk. However, their consideration is beyond the scope of our book.

Keywords

Population reproduction, replacement of generations, reproduction mode, vitality index, gross coefficient, net coefficient, stable population, true natural increase coefficient, Lotka coefficient, generation length, simple reproduction, narrowed reproduction, expanded reproduction, price of simple reproduction.

Review questions

1. What is the relationship between the concepts of natural increase (decrease) of the population and reproduction of the population?

3. What is the difference between gross and net reproduction rates?

4. What is the Lotka ratio and what exactly does it mean?

5. How is the "price of simple reproduction" calculated? What is the methodological role of this indicator?

Otherwise, the net reproduction rate of the population is called the net reproduction rate of the population. It is equal to the average number of girls born in a woman's lifetime and surviving to the end of the reproductive period at given birth and death rates.

The net reproduction rate of the population is calculated using the following approximate formula (for data on 5-year age groups):

All designations are the same as in the formula for the gross coefficient and - respectively, the number of people living in the age interval (x + 5) years from the table of female mortality, and - its root. The factor 1000 in the denominator of the fraction is added in order to calculate the net rate per woman.

6 Question. What is the essence of the concept of conditional and real generation.

Generations can be real and conditional (hypothetical). Characterizing the difference between one and the other, we can say that the formation of a real generation occurs in one relatively small age period, and the demographic processes in it occur throughout the subsequent life of the generation (for example, births during the entire childbearing period in women born in 1950-1954. ). In the conditional (hypothetical) generation, the situation is reversed. It is formed from people born in completely different years, but living at the same time, in which demographic events occur, the frequency of which is measured for this generation (for example, those born in 2000 to women of all years of birth).

The real generation is a set of people born in the same time period. They are called peers. The advantage of demographic analysis by real generations lies mainly in the fact that in this case it is possible to track changes in demographic processes more accurately, to more correctly identify their determinants when comparing data for different generations. Analysis of demographic information for real generations has its drawbacks. The final number of births in a real generation can only be determined when all women in it complete the process of childbearing (until then, we can only talk about the number of children born by a particular age). In this case, one can reliably know only the birth rate that was in the past (albeit not so long ago). But the analysis of demographic processes presupposes their current assessment and characterization. In this case, data on conditional (hypothetical) generations are used.

A conditional or hypothetical generation is a collection of people of different ages, but living at the same time. They are called contemporaries. Data on conditional generations are used in the description of demographic processes by the method of cross-sectional analysis. The conditionality here lies in the fact that such a generation does not really exist, but in demographic calculations it is assumed that throughout the life of the totality of contemporaries, the intensity of various demographic processes at each age is the same as that which takes place in the analyzed calendar period. People of different ages living at the same time are considered to belong to the same generation.