Gross, net coefficients and other special indicators of population reproduction. Gross, net coefficients and other special indicators of population reproduction Population reproduction rate formula
Gross population reproduction rate
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 you can get a summary characteristic of the fertility of the female population, which is gross population reproduction rate- the number of girls that on average each woman will give birth to 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 has been approximately 0.487 (with a minimum value over these years of approximately 0.485 and a maximum of 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.
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 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 net population reproduction rate, or otherwise, Beck-Kuczynski coefficient . 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 rigorous 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 you to reduce the calculation of the net coefficient to simply entering the initial data. For example, the International Program Center of the U.S. Bureau of the Census (IPC of U.S. Bureau of the Census) has developed a system of electronic tables PAS (Population Spreadsheets Analysis), 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 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 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 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 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 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 R0 once in a while T, called average generation length.
Calculation of indicators of population reproduction in Russia for 1998 5
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,
Lx- 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 |
Lx/ l 0 |
d * Fx* Lx / 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.
| | |
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 coefficient 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 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
shows how many girls born to one woman in her lifetime, on average, will survive to the age of the mother at their birth, given the birth and death rates.
Great definition
Incomplete definition ↓
a general characteristic of the population reproduction regime, showing how many daughters a certain set of newborn girls will give birth to throughout their entire life ahead under a given fertility and mortality regime.
Great definition
Incomplete definition ↓
Net reproduction rate
a quantitative measure of the replacement of the mother generation by the daughter generation. It is calculated as the average number of daughters born to a woman in her entire life and surviving to the age of the mother at the time of their birth, given age-specific levels of fertility and mortality. The net population reproduction rate is equal to the gross population reproduction rate, adjusted using the numbers of survivors from the mortality table.
Great definition
Incomplete definition ↓
Net population reproduction rate
net population reproduction rate, Beck-Kuchinsky coefficient) is a quantitative measure of the replacement of the female generation, the generation of mothers, with the generation of daughters. The net population reproduction rate (Ro) occupies a central place in the system of population reproduction rates and is a general characteristic of the population reproduction regime. The idea of application and formula for calculating the net reproduction rate of the population was formulated by the German demographer and statistician R. Beck, and it was widely introduced into the practice of demographic analysis in the 1920-1930s by his student and follower, the German demographer and statistician R. Kuczynski and the American demographer and biologist A.J. Tray. At the same time, the French demographer P. Depois will propose to calculate the net population reproduction rate for real generations. The net population reproduction rate can be calculated for both the female and male population, but in the vast majority of cases it is used for the female population. It represents the average number of girls born to one woman in her lifetime who survive to the end of her reproductive period, given birth and death rates. This calculation formula is applied for one-year age intervals; if other intervals were used in the calculation (for example, 5-year), the resulting value must be multiplied by the appropriate value. In a simplified manner, the net population reproduction rate can be calculated using the formula: Ro = Rlx, where R is the gross population reproduction rate; lx is the number of women surviving to the average maternal age at childbirth, which ranges from 26 to 30 years. As a measure of the reproduction of a hypothetical generation, the net population reproduction rate is valid only for a stable population, that is, a population whose reproduction regime does not change over time. The size of such a population increases (decreases) by a factor of Ro over a time T equal to the average generation length. If Ro > 1, the population grows (expanded population reproduction; with Ro 1. O. ZAKHAROVA
Great definition
Incomplete definition ↓
NET REPLACEMENT RATIO OF POPULATION
NET RATIO OF POPULATION REPRODUCTION, net population reproduction rate, a quantitative measure of the replacement of the mother generation by the daughter generation, occupying the center. place in the system of population reproduction rates; a generalizing characteristic of the population reproduction regime, taking into account fertility and mortality. N.-k. V. n. (R0) is calculated separately for us. each gender. In the vast majority of cases, the net coefficient is used. reproducing women's stories about us. It represents cf. the number of girls born in a lifetime to one woman who survives to the end of the reproductive period at given levels of fertility and mortality:
where δ is the proportion of girls among newborns, x is age, f(x) is the age function of fertility, l(x) is the age function of woman survival, a and b are the boundaries of the reproductive period.
N.-k.'s calculations V. n. are performed according to the approximate formula:
where Fx is the same as f(x) on average for discrete age intervals from x to x + 1, i.e. age coefficients. fertility, Lx - avg. the number of living women according to the mortality table for the same intervals, and δ is taken to be independent of the age of the mother. Usually they deal with one-year intervals. If the values of Fx and Lx reduced to such an interval (i.e., to one year of age) are available only for n-year (for example, 5-year) age groups, then.
If the mortality table contains one-year Lx values, you can use their sums for each n-year interval:
Example of calculation of N.-k. V. n. based on Fx data for 5 year age groups of women for us. USSR in 1969-1970, see table.
Taking δ - 0.488 (see Sex ratio), we have R0 = 2.2815-0.488 = 1.113.
An approximate calculation of N.-k. is possible. V. n. using a simplified formula: , where R0 is the gross population reproduction rate, is the number of women surviving to the average age of the mother at the birth of children. This age varies little and is usually 28-30 years. If we take = 30, then for the given example R = 1.166, l30 = 0.954 (according to mortality tables 1968-71), R0 = 1.166*0.954 = 1.112.
Calculated for hypothetical generation, N.-k. V. n. the most complete interpretation is received within the framework of the model of reproduction of us, the regime of which does not change (stable population). Number such us. increases (or decreases) by R0 times during a time T equal to avg. generation length. If R0 > 1, num. us. grows (extended playback) if R00 = 1, number. us. does not change (simple reproduction).
In stable us. N.-k. V. n. associated with the true natural coefficient. growth of us. r by the ratio:
where e is the base of natural logarithms. In a real population, the reproduction modes of which are continuously changing, the relationship between population dynamics and the value of N.-to. V. n. is not so clear, because this dynamics also depends on the age structure of the population, which, in turn, determines the potential for population growth. If this potential is positive, then the number of us. can increase even when R00>.
The value of N.-k. V. n. to midday 19th century was exposed means. fluctuations, but, in contrast to the fertility and survival functions that determine this value, which reveal historical. a tendency towards directional changes, an average level around which the values fluctuated
N.-k. V. n., throughout history remained relatively stable and, as a rule, was close to the level of simple reproduction of us. (R0 = 1). For the initial phases of demographic transition is characterized by a temporary rise in N.-to. V. n., especially significant in developing countries in the 20th century. If in the 2nd half. 19th century in Western countries Europe, which was experiencing the early phases of the demographic revolution, the highest values of N.-to. V. n. were ok. 1.5, then in the 2nd half. 20th century in some developing countries they reach 3.0 or more (one of the main manifestations of the demographic explosion). The difference in the meanings of N.-k. V. n. in modern world is large (see Population reproduction). The worldwide process of reducing N.-to. V. And. can also be traced in the USSR, where its value decreased from 1.680 in 1926-27 to 1.104 in 1975-76. At the same time, large differences in the size of N.-to remain. V. n. for the union republics.
For the first time he formulated the net coefficient. reproducing us. R. Beck. In practice demographic. analysis of N.-k. V. n. was widely introduced in the 20-30s. 20th century R. Kuchinsky and A.J. Lotka (Beck-Kuchinsky coefficient). At the same time the French scientist P. Depois proposed to calculate N.-k. V. n. for real generations. To assess the influence of the initial age structure of us. on coefficient reproduction in the USSR, an integral coefficient was proposed (1976). reproducing us. as Rs = R0 * VN, where VN is the net demographic potential. growth. Logical The development of this scheme is the introduction of the amendment of A. Ya. Kvasha, who proposed multiplying the demographic potential. growth is not ordinary, but so-called. cleared net coefficient L. Henri as the product of R0 and the ratio of the life expectancy of the generation of daughters (e´0) and the generation of mothers (e0). At the same time, the corrected N.-k. V. n. (Rk) has the form:
Rk = R0 * VN * e´0/e0.
Great definition
Incomplete definition ↓
An indicator that also takes into account mortality is net population reproduction rate, or otherwise, Beck-Kuczynski coefficient . 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, a5 Lxf 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 (lx), because this is an approximate formula. In rigorous demostatistical analysis and mathematical applications of demography, it is the survival function that is used 1(x).
Despite several<угрожающий>In 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 you to reduce the calculation of the net coefficient to simply entering the initial data. For example, the International Program Center of the U.S. Bureau of the Census (IPC of U.S. Bureau of the Census) has developed a system of electronic tables PAS (Population Spreadsheets Analysis), 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.
The net population reproduction rate is equal to the gross population reproduction rate, adjusted using the numbers of survivors from the mortality table.
44. Inverse relationship between fertility and education and income: paradox or norm
According to the US Census Bureau, by 2040 the number of people over 65 will more than double to 1.3 billion (from just over 500 million today). This means many problems, the main one being the increase in government spending on health care for the elderly coupled with a significant reduction in the workforce. This is the inevitable price to pay for high income and increased life expectancy.
In most wealthy countries, fertility rates have long been below the 2.1 children per woman needed to maintain population levels. The situation is especially sad in South Korea, Japan, Italy and Spain: in 2005, the birth rate in these countries was 1.08, 1.26, 1.32 and 1.33, respectively. If nothing changes, within 40-45 years the population of these countries, excluding immigration, will be halved.
Previous research has shown that the higher the Human Development Index (HDI), a widely used measure of social progress, the fewer babies are born per woman.
The HDI scale takes into account life expectancy, GDP per capita and literacy rate. At the bottom are twenty African countries with ratings ranging from 0.3 to 0.48, while the twenty most successful countries in the world have a score of 0.93 to 0.97.
A trio of researchers led by Mikko Mirskila from the University of Pennsylvania (Philadelphia, USA) analyzed the latest data from most countries around the world in search of new trends. And such trends were found. It was found that when the Human Development Index approaches 0.86, the birth rate bottoms out and begins to rise again when it reaches 0.95. The average fertility rate of the twelve most successful countries was 1.8 children per woman in 2005. In some places these numbers continue to rise. Thus, in 2008, France surpassed the 2.0 mark for the first time in forty years.
The main reason is that women and couples find it easier to decide to have an “expensive” child thanks to a good education and a well-paid job. Interestingly, the same improvements in the socio-economic status of women in developing countries, on the contrary, lead to a decrease in fertility. At the same time, in very poor countries, 5-6 children per woman is a normal figure.
Japan and South Korea are likely to be exceptions to this trend: these countries have some of the highest HDI ratings and some of the lowest fertility rates in the world. This is probably due to the fact that, despite the economic successes of the state, the position of women there has not changed.
Other anomalies, such as Canada and Germany, where fertility lags behind similar rich countries, have not yet been explained.
45. General and total fertility rates: what is their difference.
Crude birth rate (CBR) is the number of births in a population during a period divided by the total number of person-years lived by the population during that period, or by the average population. Usually expressed as the number of births per 1000 population. For one-year time periods, the total fertility rate is calculated as the ratio of the annual number of births to the average annual population.
Total fertility rate, fertility rate- is the most accurate measure of the birth rate; this coefficient characterizes the average number of births per woman in a hypothetical generation over her entire life, while maintaining existing birth rates at each age, regardless of mortality and changes in the age composition. In conditions of low mortality, for simple replacement of generations, the total fertility rate must be at least 2.15. A total fertility rate above 4.0 is considered high, and below 2.15 low. The total fertility rate decreased globally from 4.95 births per woman in the first half of the 1960s to 2.5648 in 2005-2010. For more developed countries, this level of fertility was typical already in the early 1960s, and by the end of the century it had dropped to 1.57.
The highest total fertility rate in the world is in Niger - 7.75, the lowest in Macau - 0.91 (as of January 1, 2009).
