As for the frequency of births of girls among women of different ages, then, generally speaking, it is different. However, it would not be a big mistake to assume that the proportion of girls among births is the same for all ages and is approximately 0.487-0.488. From here we can obtain a summary characteristic of the female population, which is gross factor vospopulation production-number of girls, which on averageEvery woman lives during her entire reproductive period. When calculating the gross coefficient, it is assumed that there is no mortality among women until the end of their reproductive years.
The gross population reproduction rate is equal to the total fertility rate multiplied by this proportion of girls among newborns:
Where R - gross reproduction rate, TFR - total fertility rate, ASFR X - age-specific birth rates, Δ - the proportion of girls among newborns.
In our country, the average value of the proportion of girls among newborns over the past 40 years was approximately 0.487 (the minimum value for these years was approximately 0.485 and the maximum was 0.489. See also Chapter 3). If the calculation is carried out at five-year intervals, and data of this kind are usually available, then the formula for calculating the gross reproduction rate is as follows:
As you can see, the gross population reproduction rate is the total fertility rate adjusted for the secondary sex ratio.
In 1999, the gross coefficient in our country was only 0.570, which means it decreased more than twofold over the period from 1960 to 1999.
The gross population reproduction rate...can be interpreted in various ways: firstly, as an age-standardized fertility rate...; secondly, as the average number of daughters that a group of women who began life at the same time could give birth to if they all lived to the end of their childbearing period; thirdly, as the ratio between the number of women of one generation, for example, at the age of 15 years, to the number of their daughters at the same age, provided that there is no mortality within the childbearing period; fourthly, 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, but any of these interpretations can be used regardless of whether the gross reproduction rate is calculated for a hypothetical generation or for a real one. Shryock H.S., Sigel J.S. The Methods and Materials of Demography. N.Y., San Francisco, London, 1973. P. 3/5.
Net population reproduction rate
However, if each of the women of reproductive age gives birth on average R daughters, this does not mean that the number of daughters’ generation will be in R times more or less than the size of the mothers' generation. After all, not all of these daughters will live to reach the age their mothers were at the time of birth. And not all daughters will survive to the end of their reproductive period. This is especially true for countries with high mortality, where up to half of newborn girls may not survive to the beginning of the reproductive period, as was the case, for example, in Russia before the First World War 2 . Nowadays, of course, this no longer exists (in 1997, almost 98% of newborn girls survived to the beginning 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 population reproduction rate has recently been practically not published or used.
An indicator that also takes into account mortality is No then is the population reproduction rate, or otherwise, coefficient Physician Beck-Kuczynski . Otherwise it is called the net population replacement rate. It is equal to the average number of girls born to a woman in her lifetime and surviving to the end of her reproductive period, given the birth and death rates. The net population reproduction rate is calculated using the following approximate formula (for data for five-year age groups):
where all the notations 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 at the age interval (x+n) years from the female mortality table, and not a function of survival, i.e., not the number of people surviving until it begins (l x ), because this is an approximate formula. In strict demostatistical analysis and mathematical applications of demography, it is the survival function that is used 1(x).
Despite its somewhat “threatening” appearance, this formula is quite simple and allows you to calculate the net reproduction rate without much difficulty, especially using appropriate software, such as Excel spreadsheets. In addition, many programs have been developed that allow the calculation of the net coefficient to be reduced to simple input of initial data. For example, the International Program Center of the US Bureau of Census (IPC of U.S. Bureau of the Census) has developed a system of spreadsheets PAS (Population Spreadsheets Analysis), one of which (SP) 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 birth rate, gross and net population reproduction rates, in which the above software is not used. Using this example, as well as a similar example given in the textbook by V.A. Borisov 4, you can easily learn to calculate all the main indicators of population reproduction. But, of course, it is advisable to have at least some computer equipment; it is best, of course, to use Excel.
The calculation was carried out according to the following step-by-step procedure:
Step 1. In column 2 we enter the values of age-specific birth rates ( 5 ASFR X , taken in this case from the Demographic Yearbook of the Russian Federation for 1999 (p. 155**).
Step 2. We calculate the total fertility rate (TFR). For this number in the lines of column 2, we divide by 1000 in order to express age-specific fertility rates in relative fractions of 1 (in other words, we reduce these values to 1 woman of a conditional generation). We enter the resulting quotients in column 3. The sum of these numbers, multiplied by 5, gives us the value of the total fertility rate equal to 1.2415 (highlighted bold italic). This, up to the third decimal place, coincides with the official data of the State Statistics Committee of the Russian Federation (1.242. WITH. 90).
Step 3. We calculate the gross reproduction rate (TO), or the number of daughters born to a woman during her lifetime. To do this, we multiply the data in column 3 line by line by the share of girls among newbornsIn 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 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 of the numbers living at 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 given as relative fractions of a unit by dividing them by the root of the mortality table (in this case, per 10,000). An alternative way is to average two adjacent values of the numbers 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 resulting averages by 5, we determine the number of people living at each age interval necessary for the calculation.
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 a net reproduction rate equal to 0.583. This value differs only by 0.002 from that officially published by the State Statistics Committee of the Russian Federation (0.585, p. 114 of the Demographic Yearbook for 1999).
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 reproduction regime does not change, i.e. birth rate and death rate. The size of such a population changes (i.e. increases or decreases) in R 0 once in a while T, called average generation length.
Calculation of indicators of population reproduction in Russia for 1998 5
Table 7.1
CHAPTER 8
POPULATION REPRODUCTION
8.1. The concept of population reproduction and its indicators
The process of population reproduction is a continuous change of generations of people. As a result of fertility and mortality, parental generations are constantly replaced by generations of their children. If generations of parents are replaced by more numerous generations of children, then they speak of expanded reproduction. If the generations of children are small relative to the parental generations, then in this case reproduction is narrowed. Where the numbers of parental and child generations coincide, we are talking about simple reproduction.
Sometimes population reproduction is identified with population growth. But demographic dynamics depend not only on population reproduction, but also on migration processes. Only in the case of a closed population, if there is no external migration, as was practically the case in the Soviet Union, is demographic growth entirely determined by reproductive processes. An ideal example of a closed population is the population of the entire globe.
The category “population reproduction” entered scientific circulation at the beginning of the twentieth century. Already at the turn of the 20-30s. it was actively used by Soviet scientists. But almost immediately, specific features emerged in the interpretation of population reproduction in domestic science, which have survived to this day. Unlike foreign researchers, domestic demographers placed greater emphasis on the “socio-historical” conditionality of the process of generational replacement. In addition, in the 1960-80s. Broader interpretations of this term have been proposed. Population reproduction was presented as a combination of three forms of movement: natural (fertility and mortality), spatial (migration) and social (changes in social structures, social and professional mobility, etc.). Some demographers include migration as a reproductive process in addition to fertility and mortality. However, it is unlikely we can talk about the replacement of parental generations with generations of their children, since migrants for the most part represent the population of another territory. It is an independent source of demographic dynamics.
The definition of population reproduction as a process of generational replacement suggests that its measures should be some special “generational” indicators. The most common quantitative characteristics of reproduction, due to their simplicity and availability of statistical information, are natural increase and the coefficient of natural increase.
Another simple indicator of population reproduction is the vitality index. The vitality index I V, in contrast to natural increase, is not a difference, but a ratio of the number of births B to the number of deaths D, multiplied by one hundred for ease of interpretation:
I V= B/ D* 100
Russian historian M.N. Pokrovsky used the vitality index to characterize reproductive processes in the Russian Empire over an almost hundred-year period, starting from the end of the 10th century. VIII century. Therefore, in our country this indicator is also called the Pokrovsky index.
Recently, another indicator has begun to be used, the so-called depopulation coefficient. It represents the ratio of the number of deaths to the number of births. If this coefficient exceeds one, it means that depopulation is occurring in the country, like in present-day Russia.
Both indicators of natural increase and the vitality index measure the rate of “natural movement” of the population and are general characteristics of the replacement of generations. If over a certain period of time the number of births exceeds the number of deaths, then it can be assumed that older generations are being replaced by larger generations of children and grandchildren. Otherwise, older generations probably do not reproduce themselves quantitatively.
The natural growth rate, like other general demographic indicators, is influenced by numerous structural factors, the main one of which is the age composition of the population. Thus, the young population will have a higher natural increase compared to a population in which the same age-specific characteristics of mortality and fertility are observed, but the proportion of older age groups is higher.
The most adequate quantitative characteristics of reproduction are indicators that most directly reflect the process of generational change and do not depend on the age structure of the population. The most obvious way to measure the rate of generational replacement is a direct comparison of the number of generations of mothers and their daughters, fathers and sons, parents and their children at an age that is approximately equal to the average age of the parents (father, mother) at the birth of their children. Typically, population reproduction rates are calculated not for real, but for hypothetical (conditional) generations. In the latter case, to calculate reproduction rates, it is enough to collect data on age-specific levels of fertility and mortality for a calendar period, for example, one year. To estimate the replacement rate of real generations, it is necessary to have appropriate information for a period covering the life of generations over 50 years - from the time of their birth until the moment when all representatives of each generation leave reproductive age.
There are two more indicators of generation replacement: gross and net reproduction rates. They were introduced into scientific circulation by the German demographer R. Kuchinsky. The net reproduction rate was developed by Kuczynski's teacher, the famous German statistician R. Beck in 1884. However, contemporaries were unable to assess the significance of this indicator. Demography owes Robert Kuczynski the appearance in 1907 at the Fourteenth International Congress on Social Hygiene and Demography (Berlin) of the total fertility rate and, somewhat later, the gross reproduction rate. However, a complete mathematical justification for these indicators was given by A. Lotka within the framework of the theory of a stable population.
Gross population reproduction rate (accepted designationsR or GRR) can be considered as a special case of the total fertility rate. Calculations of the gross coefficient are performed using the approximate formula:
Where:
d - the proportion of girls among newborns. As a rule, it is taken equal to» 0.488 and the same for all ages of women. Thus, if the total fertility rate in Russia in 2000 was 1.214, then the gross reproduction rate was equal toR » 0,488 ´ 1.214 = 0.592. Let us recall that the total fertility rate is equal to the sum of the age-specific rates.
However, there is a significant difference in the interpretation of these two indicators. The total fertility rate is the number of births of children of both sexes that a woman can have while maintaining the observed levels of age-specific fertility. The gross reproduction rate for a conditional generation is the average number of girls that one woman can give birth to, provided she survives to the end of the reproductive period and maintains current levels of fertility at each age throughout it. As an indicator of generation replacement, the gross coefficient has one significant drawback. In fact, when calculating it, the assumption is made that all daughters survive to the end of the reproductive period. Thus, the gross rate represents an extreme case of generational replacement. This shortcoming is eliminated in the net reproduction rate.
In terms of generational replacement net population reproduction rate (accepted designations R0 or NRR ) is the average number of girls born to one woman in her lifetime who survive to the end of her reproductive period at given birth and death rates. If appropriate information is available, net and gross coefficients can also be estimated for the male population. In fact, the net coefficient measures the rate of replacement of the mother generation by the daughter generation. CalculationsR0are performed according to the formula:
, Where
Fx – age-specific birth rate at age X,
L x- average number of living women aged X according to the mortality table;
l 0 =100000 – radix of the mortality table.
In table 8.1. An algorithm for calculating the net coefficient is presented using the example of the female population of Russia for 2000.
Table 8.1.
Calculation of population reproduction rates in Russia for 2000.
|
Age groups |
Age-specific fertility rates Fx |
Fx = d*Fx |
L x/ l 0 |
d * Fx* L x / l 0 |
|
0,0137 |
||||
|
0,0465 |
||||
|
0,0335 |
||||
|
0,0360 |
0,0176 |
|||
|
0,0120 |
0,0059 |
|||
|
0,0012 |
||||
|
0,0000 |
||||
|
Amount |
0,2426 |
0,1184 |
R0 = 0.5 73 |
|
|
Amount*5 |
F sum =1.213 |
R= 0.59 2 |
Since the net coefficient includes a combination of fertility and mortality levels, it is used as an integral general characteristic of population reproduction. However, one often encounters incorrect interpretation of this indicator. The net reproduction rate calculated for a hypothetical generation as a measure of the replacement of the maternal generation by the daughter generation makes sense only within the framework of a stable population model. The size of such a population increases (or decreases) inR 0 once in a while T, equal to the average generation length. Below the average generation length T, as noted earlier, understand the average time interval separating generations of parents and their children (mothers and daughters, fathers and sons). For a rough estimate T in practice, the average age of the mother at birth is used.Thus, in 2000, the net reproduction rate in the Russian Federation was equal to 0.57. This does not mean that the country's population will decrease by 43% in 25-30 years (the approximate length of a generation in Russia). Such a statement is true only for a stable population, which the population of Russia is not.
The dynamics of the gross reproduction rate fully corresponds to the dynamics of the total fertility rate. The value of the net coefficient before the start of the demographic transition was subject to significant fluctuations, reflecting catastrophic changes in the mortality rate caused by epidemics, wars, famines, and natural disasters. The average level around which these fluctuations occurred over a long historical period remained quite stable and was slightly above the level of simple reproduction. With the onset of the demographic transition, the net coefficient increased, which was due to a significant decrease in mortality. Even at the end of the twentieth century. in some developing countries, mainly Arab, (Saudi Arabia, Oman, Jordan, Yemen, etc.) its value exceeds 2.5. As the demographic transition completes, the net coefficient tends to approach 1. In almost all European countries, including Russia, its value is less than one.
In Figure 8.1. presents changes in gross and net replacement rates for the female population in a hypothetical country over a period of almost 120 years. According to its historical characteristics, this country is closer to the states of Western Europe. The total fertility rate in the first stages of the demographic transition increased from 5.5 to 6.3, and then decreased to 2. Age-specific mortality characteristics correspond to the “West” family of standard mortality tables. At the same time, life expectancy gradually increased from 25 to 80 years. The dynamics of the gross coefficient repeats the changes in the total fertility rate, adjusted for the share of girls among newborns. It increased from 2.6 to 3.1 and then decreased to 0.98 female births per woman. The net reproduction rate at the first stage of the demographic transition increases from 1.06 to 1.73, and then decreases to 0.97.
Fig. 8.1 Model estimates of gross and net reproduction rates during the demographic transition.
In a similar direction, taking into account all the fluctuations caused by the terrible cataclysms of the twentieth century, there was a change in the gross and net coefficients in Russia (see Table 8.2). The net coefficient reached its maximum values in the mid-20s. last century. Then its level began to decrease. Already from the mid-1960s. the net reproduction rate was less than 1, while the values of the natural increase rate were positive. This means that the demographic reproduction regime established in Russia four decades ago did not ensure the quantitative replacement of generations.
Table 8.2.
Coefficients and price of simple reproduction of the population of the Russian Federation.
|
Years |
Gross reproduction rate |
Net reproduction rate |
The price of "simple" Reproduction |
|
1894-1903 |
3,244 |
1,636 |
1,98 |
|
1927 |
3,282 |
1,681 |
1,95 |
|
1939 |
2,394 |
1,367 |
1,75 |
|
1958-1959 |
1,276 |
1,186 |
1,08 |
|
1964-1965 |
1,044 |
0,971 |
1,08 |
|
1969-1970 |
0,972 |
0,934 |
1,04 |
|
1974-1975 |
0,973 |
0,932 |
1,04 |
|
1979-1980 |
0,911 |
0,874 |
1,04 |
|
1986-1987 |
1,071 |
1,038 |
1,03 |
|
1989 |
0,983 |
0,953 |
1,03 |
|
1995 |
0,656 |
0,633 |
1,04 |
|
2000 |
0,592 |
0,571 |
1,04 |
A temporary increase in the birth rate as a result of the demographic policy of the 80s led to a slight increase in the net reproduction rate, the value of which in 1987-1988. exceeded 1. However, in the subsequent period its value fell to a level below 0.6.
Positive population growth lasted until the early 90s, thanks to migration and the growth potential accumulated in the age structure. In a population with a significant proportion of people of reproductive age, even at a birth rate that does not ensure simple reproduction, the number of births at a certain stage will exceed the number of deaths. However, the growth potential inherent in the young age structure is soon exhausted. In conditions of low birth rate and the progressive aging process, positive values of natural increase are gradually replaced by negative values.
Gross and net coefficients calculated for hypothetical generations have all the shortcomings inherent in all indicators of cross-sectional analysis. They can distort the real course of demographic development, their dynamics are influenced by market factors. As is known, these shortcomings are overcome using longitudinal analysis methods. Therefore, back in the 40s. French demographer P. Depois proposed estimating reproduction rates for real generations. He was the first to perform similar calculations for the population of France for the entire X I X century.
There are several methods for estimating the net reproduction rate of real generations. The most obvious one is to use the formula
Only now it must use birth and death rates for real generations. Complete and reliable estimates of cohort mortality rates have been made only in a few developed countries, where adequate recording of population mortality has long been established.
French demographer J.-P. Sardon, based on corresponding estimates of mortality and birth rates of cohorts, calculated net reproduction rates for real generations in Western European countries. The results he obtained are amazing. In Belgium, Sweden, Switzerland, Germany, Italy, Greece, not a single generation born in 1901-1955. has not reproduced itself quantitatively. Only in Iceland and Ireland did the net coefficients of these generations exceed one. In Austria, Great Britain, Denmark, France, the Netherlands, Portugal and Spain, only certain generations born between the First and Second World Wars had fertility levels that ensured expanded population replacement.
Available calculations show that the net reproduction rate of cohorts born in X I X century, was at the level of 1.4 - 1.5, i.e. each generation gave birth to 1.4 - 1.5 times more children than the generation of its parents. Cohorts 1880-1900 births reproduced themselves with an increase of 10-20% (NRR = 1.1 – 1.2), but compared with previous generations their contribution to population growth decreased sharply. The reproductive activity of these cohorts occurred during the First World War and subsequent crisis years. Generations born at the beginning of the twentieth century. demonstrate a sharp drop in the net reproduction rate, reaching a level of 0.65 - 0.7 for generations born in 1915-1920. A similar result of reproductive activity is noted for the generations of the 1920s and 1930s. birth. Only a few generations born after the war showed slightly expanded reproduction.
| | |
There are several such indicators, two of them are gross and net population reproduction rates. Unlike the rate of natural increase, these indicators characterize the change in population not over a year, but over a period of time during which the parent generation is replaced by the generation of their children. Since generation replacement is characterized by the ratio of fertility and mortality levels, and the latter differs significantly between males and females, population reproduction rates are calculated separately for each sex, more often for females. Usually, external migration of the population is not taken into account, i.e. the so-called closed population is considered.
The gross population reproduction rate is calculated in the same way as the total fertility rate, but unlike the latter, only girls are taken into account in the calculation. In the form of a formula, the calculation can be represented as follows: R1=SKR*d
where r 1 is the gross population reproduction rate; TFR - total fertility rate; d is the proportion of girls among newborns.
Thus, the gross population reproduction rate shows the number of girls that an average woman gives birth to in her entire life. It is assumed that none of the women and their daughters die until the end of the reproductive period of life (conditionally - up to 50 years). Obviously, the assumption of no mortality is too unrealistic for the gross rate to be of any usefulness for use in analytical work. Indeed, in recent years this indicator has not actually been used. If we take into account the influence of mortality on the degree of population reproduction, then we move on to the net population coefficient. It is calculated using the following formula:
where R 0 is the net population reproduction rate; F x - age-specific birth rates; F L x - the number of living women from mortality tables, which serve as an adjustment for mortality (or for survival to a certain age, which in this case is the same thing); l 0 - the “root” of the mortality table, equal to 100,000 or 10,000, depending on its digit; d is the proportion of girls among newborns; n is the length of the age interval (usually either 1 or 5).
Traditionally, the coefficient is calculated on average per woman, so the formula contains a multiplier of 0.001. But it is possible to calculate on average per 1000 women. This, again, as in the case of the names of population reproduction indicators, is a matter of arbitrary choice by the user.
The net replacement rate of the population characterizes the replacement of the generation of mothers with the generation of their daughters, but is often interpreted as an indicator of the replacement of generations in the entire population (both sexes together). If this coefficient is equal to 1.0, this means that the ratio of fertility and mortality levels ensures simple reproduction of the population over periods of time equal to the average age of mothers at the birth of daughters. This average age varies slightly in direct proportion to the height of the birth rate, ranging between 25 and 30 years. If the net coefficient is more or less than 1.0, this means, respectively, expanded population reproduction (the generation of children is numerically larger than the parent’s) or narrowed (the generation of children, taking into account their survival to the average age of their parents, is numerically smaller than the parent’s).
The average age of mothers at the birth of daughters (more precisely, at the birth of daughters, who, in turn, live at least to the age of their mothers at the time of their birth, but this condition is pronounced at such a long time that almost everyone, even the most strict specialists, omitted), also called the length of the female generation, is approximately calculated by the formula:
where T is the length of the female generation (the average age of mothers at the birth of daughters); F x - age-specific birth rates; F L x - number of living women from mortality tables; d is the proportion of girls among newborns; x is the age at the beginning of the age interval; n is the length of the age interval in years.
Since in the above formula the indicators of the length of the age interval (n) and the proportion of girls among newborns (d) are included in both the numerator and the denominator of the fraction, they could obviously be reduced. But in practice, it turns out, there is no need to do this (the number of columns in the calculation table increases unnecessarily).
It is easy to notice that the denominator of the above formula contains the expression of the net reproduction rate of the population, and in general the formula expresses the arithmetic mean of the average ages for each five-year age interval, weighted by the proportion of newborn girls surviving to the age of their mothers at the time of their birth.
Let's consider the calculation algorithm in its stages:
1) age-specific birth rates are written out from the Demographic Yearbook of Russia (M., 1997, p. 215) in column 1 of Table 7.1, and they are converted from ppm to fractions of a unit (by dividing each by 1000);
2) multiplying each of the age-specific birth rates by the share of girls among newborns (assuming it to be the same in all age groups of mothers), we obtain age-specific birth rates for girls, which are recorded in column 2;
3) according to the mortality tables of the population of Russia for 1996 (See Demographic Yearbook of Russia. M., 1997. P. 250), the numbers of people living in each age group are determined as the arithmetic mean of two adjacent numbers of those living, i.e.:
where F L x is the number of living women, calculated from mortality tables; l x and l x+5 are the numbers of people surviving to ages x and x+5 from the same mortality tables.
The numbers of living people obtained in this way are divided by the root of the mortality table l 0 (in this case it is equal to 100,000) and are entered in column 3 of table 7.1;
5) age-specific birth rates for girls from column 2 are multiplied line by line by the number of living women from column 3 (i.e., in this way an adjustment is made for their survival to the age of the mothers at which they gave birth to these daughters). The multiplication results are recorded in column 4;
6) indicators in columns 1, 2, and 4 are summed vertically, and the sums are multiplied by 5 (by the length of age intervals). As a result, in column 1 we get the total fertility rate TFR = 1.2805, or rounded 1.281; in column 2 the gross population reproduction rate is equal to 0.625, and in column 4 - the net population reproduction rate R 0 = 0.60535, or rounded 0.605.
Naturally, it is interesting to compare the results obtained with official publications of the State Statistics Committee of Russia, which are calculated in the most accurate manner based on one-year age coefficients. It turned out that the total fertility rate we calculated for Russia for 1996 exactly coincided in value with that calculated by the State Statistics Committee of Russia - 1.281. The value of the net coefficient differed from Goskomstat calculations by only 0.002. This discrepancy can be considered insignificant.
Let's return to Table 7.1 and now determine the average age of mothers at the birth of daughters - the length of the female generation. To do this you need:
7) multiply the data in column 4 line by line by the age indicators in the middle of each five-year age interval (in column 5), and write the results of this multiplication in column 6. After summing the resulting products and multiplying the sum by 5, we obtain the numerator of the fraction (15.1237), dividing which by the net population reproduction rate (0.60535), we obtain an indicator of the length of the female generation in Russia in 1996 equal to 24.98 years (or rounded - 25 years).
The net population reproduction rate makes it possible to assess the state of the population reproduction regime actually existing at any given moment in time (the ratio of birth and death rates in their abstraction from the impact of the age-sex structure of the population) from the standpoint of its probable further development. It characterizes not the current demographic situation, but its ultimate state in some future if the given reproduction regime remains unchanged. In other words, the net coefficient is a tool for assessing the situation and forecasting its future trends.
NET REPLACEMENT RATE
(net reproduction rate) The number of female children in a population divided by the number of adult women in the previous generation. The figure thus obtained is a good guide to future population trends, which will increase if the stated ratio exceeds one.
Finance. Dictionary. 2nd ed. - M.: "INFRA-M", Publishing House "Ves Mir". Brian Butler, Brian Johnson, Graham Sidwell and others. General editor: Ph.D. Osadchaya I.M.. 2000 .
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To obtain a real idea of the nature of population reproduction, indicators are needed that do not depend on the age-sex structure. In the early 1930s. German demographer, economist, statistician R. Kuchinsky (1876--1947) and domestic scientist, demographer, health care organizer G.A. Batkis (1895-1960) used indicators that give a clear picture of the state of the numbers of the new and old generations in the years adjacent to the years of population censuses, helping to determine the extent to which the living population has prepared for its replacement:
total fertility rate;
gross reproduction rate;
net reproduction rate.
The total fertility rate shows the number of children born on average to one woman during the entire fertile period of her life (i.e. from 15 to 49 years inclusive). It is calculated like this:
where n x is the age-specific birth rate for women aged x years.
The calculation can also be performed for five-year intervals:
and for 10 year olds:
An example of calculating the total fertility rate is given in table. 1.
Table 1. Calculation of the total fertility rate for the rural population of the Novosibirsk region, 1999
As follows from the table. 1, over the entire fertile period, each 1000 rural women in the Novosibirsk region will give birth to 1404 (1403.5) children, i.e. 1.414 on average per woman or rounded 140 children per 100 women.
The total fertility rate as an indicator of population reproduction is not without its shortcomings. Thus, he does not take into account: firstly, that the reproduction of a new generation can be characterized by the number of girls that each woman leaves behind; secondly, that some children die before reaching the age of the mother at the time of their birth, leaving no offspring or leaving a smaller number of children compared to their peers who successfully survived to the end of their childbearing period.
The first drawback can be eliminated using the gross reproduction rate R b, calculated by the formula
where d is the proportion of girls among births.
For the example given in table. 1, and at d - 0.488
R b =1.4035 0.488 = 0.6849.
Consequently, every 1000 women leaves behind 685 girls (684.9), i.e. In the rural population of the region, even simple reproduction is not carried out.
The advantage of the gross coefficient is that its value is not affected by the composition of the population by gender and that it takes into account the age composition of women of fertile age. However, it does not take into account the mortality of women of fertile age.
For the most accurate characterization of population reproduction, the net coefficient is used. In the statistical literature it is called pure or purified. It shows the number of girls that each woman leaves behind on average, taking into account the fact that some of them will not live to reach the age of their mother at the time of their birth.
However, if each of the women of reproductive age gives birth to R daughters on average, this does not mean that the size of the daughters’ generation will be R times greater or less than the size of the mothers’ generation. After all, not all of these daughters will live to reach the age their mothers were at the time of birth. And not all daughters will survive to the end of their reproductive period. This is especially true for countries with high mortality, where up to half of newborn girls may not survive to the beginning of the reproductive period, as was the case, for example, in Russia before the First World War. Nowadays, of course, this is no longer the case (in 2004, more than 98% of newborn girls survived to the beginning 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 population reproduction rate has recently been practically not published or used. An indicator that also takes into account mortality is the net population reproduction rate, or otherwise the Böck-Kuczynski coefficient, proposed by the German statistician and demographer G.F.R. Byök. Otherwise it is called the net population replacement rate. It is equal to the average number of girls born to a woman in her entire life and surviving to the end of the reproductive period, at given levels of fertility and mortality.
To calculate the net coefficient Rn, the following formulas are used:
a) for one-year age groups:
where n x are age coefficients for women of age group X years; d -- the proportion of girls among births;
The average number of living women in the stationary population of life tables in the age interval from X to X+ 1;
b) for five-year age groups:
where are age-specific birth rates for women in age groups from X to X + 4;
The average number of living women from life tables in the age range from X to X+4 (+ +1 + +2 + +3 + +4);
c) for ten-year age groups:
where are age-specific birth rates for women in the age group from X to X + 9;
The average number of living women in a hospital population survives in the age interval from x to x + 9.
Example. The number of women in the stationary population of the Novosibirsk region is known (according to life tables) and age-specific birth rates:
Let's calculate the net reproduction rate. Let's determine the "expected" number of children.
With the share of girls among births d = 0.488 Rn = 135 5490.488:
100,000 = 0.66148, or rounded to 0.662.
Consequently, every 1000 rural women leave behind only 662 girls. The initial conclusion is confirmed that a regime of narrowed reproduction has been established in this population.
The advantage of the net coefficient is that it takes into account the birth rate in certain age groups of women at the time of compiling life tables, and when calculating it, the mortality rate of the population and the probability of surviving to the next age group are taken into account. In statistical practice, the following scale for assessing the net reproduction rate is adopted: at Rn = 1.0, simple reproduction occurs; at Rn > 1.0 -- extended, at Rn< 1,0 -- суженное.
B.S. Yastremsky established a relationship between the total fertility rate, the fertility rate (special birth rate, fertility rate) and population reproduction rates (Tables 2 and 3).
Table 2. Relationship between fertility rates
Table 3. Relationship between fertility and population reproduction rates
Consequently, the border between narrowed and simple reproduction lies between the meanings:
· special birth rate from 100 to 150 ‰;
· gross reproduction rate from 0.86 to 1.29 ‰;
· total fertility rate from 15 to 22 ‰.
The net reproduction rate can be calculated not only for the female, but also for the male population using the same methodology. In this case, it shows how many boys each man leaves behind, taking into account the fact that some of them will not live to reach the age of their father at the time of their birth.
To calculate the net reproduction rate of the male population by one-year groups, the formula can be used:
where are the age-specific birth rates of children in families for men of age group x years,
The number of living men in the stationary population of life tables in the age interval from X years to X + 1;
d M -- the proportion of boys among births.
The calculation is carried out similarly for the five- and ten-year age groups.
Table 4. Initial data for calculating the reproduction rates of the male and female population of the region, people
Note. Age groups: for women - 15-49 years old, for men - 18-55 years old.
Let's calculate the number of births per 1000 population (n x) as (N x:S x 1000).
|
Age group |
||
|
45 and older Average |
Hence the total fertility rate according to the formula:
51000 for women:
=(78,3 + 226,7 + 193,2 + 106,2 + 36,3 + 8,9 + 1,6)5:1000 = 3,26;
for men:
+ (23,0 + 234,3 + 231,2 + 146,6 + 68,3 + 18,2 + 5,7)5:1000 = 3,64,
those. Each woman leaves an average of 3.26 children during the entire fertile period of her life, a man - 3.64.
The gross population reproduction rate will be calculated using the formula R b =:
3,260,488 = 1,591;
3,640,512 = 1,864,
those. Each woman on average left behind 1,591 girls, a man -1,864 boys.
To move on to determining the net coefficient, let’s calculate the “expected” number of children: : 1000, for example,
for women: 78.3485 117: 1000 = 37,985;
for men: 23.0487 370: 1000 =11210, etc.
Net reproduction rate:
for women formula
for men formula
Consequently, every 1000 women, on average, leaves behind 1529 girls, taking into account the fact that some of them will not live up to the age of the mother at the time of their birth, and every 1000 men - 1724 boys, provided that some of them will not live up to the age of the father at the time their birth. The net coefficient of the male population is higher than the net coefficient of the female population by 0.196 points, or 12.8%.
In the second half of the 20th century. In the world, there was a downward trend in all three indicators of population reproduction, and for economically developed countries it exceeded the boundaries of simple reproduction (Fig. 1).
Rice. 1.
The first turning point in the modern demographic history of Russia was 1964, when the fall in the net reproduction rate of the Russian population crossed the generation replacement line. That same year, the mortality curve began to creep up, which ultimately led to the current shameful level of life expectancy for Russians.
Period X is a characteristic resonant surge caused by the politics and market conditions of the 80s: a slow, jerky rise, a small upper plateau and an accelerating collapse well below the point of initial growth. Noteworthy is the fact that the collapse of the population reproduction rate began long before the “criminal liberal government” came to power and the sharp deterioration in the socio-economic situation of the Soviet people.
Period Y-- is divided into two political eras: the Yeltsin era, when uncertainty grew and the socio-economic situation of the majority of the country's population worsened; and the Putin era - when certainty grew, the vertical of power strengthened, the socio-economic situation improved, and the optimism of the voting majority multiplied.
The graph clearly shows the growth of the curve since the post-default year 1999: there are still 8 years of pre-active demographic policy.
According to UN forecasts, by the period 2010-2014. Regions with reduced population reproduction will include Foreign Europe, Foreign Asia, Australia and Oceania. The highest net ratio will remain in Africa. And in America, 109 women will leave behind 109 girls.
In Russia, the process of narrowed reproduction is deepening (see Table 5.)
Table 5. Dynamics of the net population reproduction rate in the Russian Federation in 1960 - 2000
The narrowed reproduction of the urban population began by the end of the 1950s, and of the rural population - since 1993.
In 2000, every 1,000 women of fertile age left 529 girls in cities and 704 in rural areas.
According to the Demographic Yearbook, the total fertility rate for the period from 1991 to 2000 ranged across the CIS countries from 1.10 in Ukraine to 4.09 in Turkmenistan. In Europe in 1999, the lowest level of the indicator was in the Czech Republic - 1.12, the highest in France - 1.77. In Asia for 1995-2000. the highest level was reached by Iran - 5.30 and Saudi Arabia - 5.80, the lowest - Japan - 1.39; China had 1.80, India - 3.40. In Africa, the total fertility rate reached 3.81 in Algeria, 3.74 in Egypt, and 3.25 in South Africa (1995-2000). In America for 1995-2000. Canada had the lowest level of the indicator - 1.64, the highest - Mexico - 2.75; in the USA -2.02; in Australia - 1.80 (1996), in New Zealand - 1.97 (1997).
