Absolute number of births formula. Indicators of the natural movement of the population. Population reproduction efficiency coefficient

When studying the movement of the population, the causes and consequences of changes in the number and structure of the population in various aspects are considered. The most important components of the population movement are: firstly, births, deaths, marriages and divorces, which unite the natural movement of the population under a common name, and secondly, migration is the movement of the population from one place of residence to another. The main task of population movement statistics is to characterize and explain these processes, which are necessary primarily as a basis for forecasting and making socio-economic and political decisions.

The natural movement of the population is characterized by a system of indicators that can be divided into two groups: 1) absolute; 2) relative. Absolute indicators include the number of births and deaths, the number of marriages and divorces, and relative indicators - coefficients calculated on the basis of absolute indicators. The following indicators of the second group are most often used: general fertility, mortality, marriage and divorce rates; age-specific birth and death rates; total fertility rate; infant mortality rates; infant mortality rates by main classes of causes; life expectancy at birth, etc.

Absolute indicators are obtained during the statistical processing of civil status acts, which are compiled in the registry office. Civil status acts contain a certificate of the fact of the event, characteristics of the persons with whom this event occurred, for those who were born - the characteristics of their parents, and for those who died under the age of one year - some characteristics of their mother. Accounting for these characteristics makes it possible to attribute a given event to one or another socio-demographic group of the population and to a specific place and time.

Of the information contained in the child's birth certificate, the following are used in statistical development: gender, date and place of birth, what account the mother had a child, and also alive or dead. Parents are registered with their age, date of birth, place of birth and place of residence, nationality, citizenship, the basis for recording information about the father.

Of the information contained in the act of death, the following are used: date, place and cause of death, gender, date and place of birth, citizenship. In addition, for those who died under the age of one year, the characteristics of the mother are taken into account: what kind of child she has and her age, marital status, level of education, nationality, where and by whom she works or source of livelihood, place of permanent residence.

When entering into and dissolving marriages, the following information is recorded, which is necessary for statistical data processing:

• when entering into marriages: surname (before and after marriage registration), first name, patronymic, date and place of registration, for each of those entering into marriage - date of birth, age, previous marital status, nationality, citizenship, place of birth, a document confirming the termination of a previous marriage;
• upon dissolution of marriages: surnames (before and after divorce), date and place of registration of the act of divorce, for each of the divorced - date of birth, age, nationality, citizenship, place of permanent residence.

The terms and procedure for registering demographic events are determined by the Federal Law of November 15, 1997 No. 143-Φ3 "On acts of civil status". In accordance with this Law, a number of characteristics necessary for the analysis of the demographic situation were excluded from acts of civil status. For example, now the programs for registering all events do not reflect information about the level of education and the source of livelihood, which makes it practically impossible to study the social differentiation of demographic processes.

In the study of demographic processes, an important role belongs to relative indicators, or demographic coefficients. To characterize the natural movement of the population, as already noted, the following demographic coefficients are used.

total fertility rate

where N- number of live births during a calendar year; S- average annual population.

Crude death rate

where M is the number of deaths in a calendar year.

Birth and death rates are expressed in ppm (‰) and characterize the number of births (deaths) per 1000 population.

Total rate of natural increase of the population

(2.3)

Pokrovsky's vitality coefficient

marriage rate

where AT - number of marriages.

Divorce rate

where R- the number of divorced marriages.

In table. 2.12 and in fig. Table 2.4 shows the main general indicators of the natural movement of the population of Russia for 1990–2008.

Table 2.12

Indicators of the natural movement of the population of Russia for 1990–2008

	Per 1000 population
	born		natural increase

Rice. 2.4.

1 – born (axis on the left); 2 – deceased (axis on the left); 3 – natural increase (axis on the right)

From Table. 2.12 it follows that since 2005 in Russia there has been a trend towards an increase in the birth rate and a decrease in the death rate of the population against the background of its negative natural increase. Therefore, we can talk about a favorable demographic situation in Russia.

From 1992 to the present, the mortality rate in Russia exceeds the birth rate, which leads to negative values ​​of the natural population growth rate, which means its natural decline. Yes, in 2008. KN-M was equal to - 2.5‰, which means a natural loss of 2.5 people for every 1000 people of the population.

Of particular interest are regional statistics. The diversity of historical, cultural, ethno-social, economic and other conditions predetermines a significant differentiation of demographic indicators.

Thus, the birth rate in 2008 varied from 9.0‰ in the Tula region to 29.3‰ in the Chechen Republic. An even greater gap between regions is noted in terms of the mortality rate: from 3.7‰ in the Republic of Ingushetia to 24.2‰ in the Pskov region. In table. 2.13 shows data on the birth rate by federal districts for 2008 in order to compare not only average levels but also the degree of differentiation of regions within each of the federal districts. For each federal district, the minimum and maximum values ​​of birth rates are given, as well as the range of variation calculated on their basis, the average value, the median, and the asymmetry coefficient of the birth rate.

Table 2.13

Characteristics of the birth rate in the regions of the Russian Federation in 2008

federal district	Number of regions	Fertility rate,%o
		minimum value	maximum value	range of variation	mean
Central
Northwestern
Volga
Ural
Siberian
Far Eastern

The lowest values ​​of the birth rate were noted in the regions of the Central (9.0‰) and Northwestern (8.8‰) federal districts, the highest - in the regions of the Southern (29.3‰) and Siberian (25.2‰) federal districts . Moreover, in 50% of the regions of the Central Federal District, the birth rate in 2008 did not exceed 10.4‰. The largest range of variation in birth rates was found in the regions of the Southern Federal District (18.5‰). On the whole, in the Russian Federation in 2008, in 50% of the regions (that is, in 42 regions), the birth rate did not exceed 12.2‰. When comparing the average and median values ​​of fertility rates for federal districts, the presence of asymmetry is obvious, and only in one federal district - the Volga Federal District - can one note the presence of right-sided asymmetry, i.e. fertility rates are shifting upwards. In other federal districts, the asymmetry is left-sided, i.e. fertility rates in their regions are shifting downwards. The highest average birth rate in 2008 was in the Siberian (13.7‰) and Southern (13.9‰) federal districts, and the lowest in the Central Federal District (10.3‰).

To study the influence of the regional factor on the level of fertility, the dispersion of fertility for each federal district (intragroup dispersion) is calculated; the results of calculations based on data for 2004 are presented in Table. 2.14.

Table 2.14

Analysis of the influence of the regional factor on the birth rate (according to data for 2008)

The regions of the Central Federal District are the most homogeneous in terms of birth rate (variation coefficient 5.56%), this indicator varies to the greatest extent in the regions of the Southern Federal District (variation coefficient 33.5%). In general, the regions of the Russian Federation are homogeneous in terms of the birth rate (the coefficient of variation is 26.73%). To identify the role of the regional factor in the formation of the variation in the birth rate in the Russian Federation, we present the values ​​of the intergroup and average of intragroup dispersions.

The intergroup dispersion of the birth rate, which estimates the variation in the birth rate under the influence of regional differences, in 2008 was 4.082, and the average of the intragroup dispersions according to the results of calculations was 6.735. The share of intergroup variance in the total variance (determination coefficient) is 0.39, i.e. 39.0% of the variation in fertility is due to regional differences. The empirical correlation ratio was 0.624, which gives reason to assume a fairly strong influence of the regional factor on the birth rate.

A more detailed analysis should be aimed at identifying differences in economic, ethno-national factors influencing the formation of the birth rate in different regions.

One of the most important goals of Russia's demographic policy should be to counter the decline in the population of the country and its individual territories. The undoubted severity of this problem led to the preparation by the Government of the Russian Federation of the Concept of the demographic development of the Russian Federation for the period up to 2015.

In February 2007, Rosstat conducted a sample survey "Family and Birth Rate" to provide information support for federal and regional targeted programs developed in accordance with this Concept. The results of this survey are still being developed, but some of the findings of the pilot survey "Family and Fertility" conducted by Rosstat in February-April 2006 have already been published. The observation unit was either a married couple, in which the woman was under 45 years old, or a mother with children, as well as adolescents aged 15–17 years. The pilot survey was conducted in three subjects of the Russian Federation: the Republic of Mari El, Nizhny Novgorod and Tver regions. The survey in the Tver region turned out to be the most productive, where 1035 people were interviewed, including 488 women, 395 men and 151 teenagers.

Important indicators determined by the results of the survey were the average desired and average expected number of children in different groups of respondents. These rates differ among men, women, and adolescents, with the lowest rates among adolescents (Table 2.15). Differences in the desired number of children by generation turned out to be clearly pronounced: for young men and women, this figure is significantly lower.

Table 2.15

The main results of the pilot survey "Family and fertility" in the Tver region (February - April 2006)

It was also found that the liberalization of attitudes towards marriage registration leads to lower reproductive orientations.

In general, two most important conclusions were made for the implementation of a demographic policy aimed at increasing the birth rate: improvement of living conditions may provide some increase in fertility, however changing need for children can give a significantly greater result than improving living conditions. Thus, when implementing a demographic policy aimed at increasing the birth rate, along with the adoption of economic measures, attention should be paid to the formation of public consciousness regarding the value of the family and the need for children.

As world experience shows, it is not possible to restore the birth rate of the population only by economic methods. It is necessary to form public opinion, orienting it towards the transition from small families to large families. The idea of ​​a two-child family as ideal and desirable is still preserved, however, the deterioration of the socio-economic living conditions of the population does not contribute to the realization of this need. Children are now becoming one of the factors of poverty and, accordingly, limiting the number of births in a family is a method of social self-defense. Now approximately 60% of children live in families with incomes below or at the subsistence level.

It should be noted that the interpretation of the general indicators of the natural movement of the population should be carried out taking into account their significant dependence on the age structure of the population. Therefore, the overall coefficients should be compared only if the compared populations practically do not differ in age structure.

At the first stage, the elimination of the influence of structural factors is carried out by excluding the so-called "uninvolved subsets", i.e. by calculating partial coefficients. They are calculated per 1000 people of a certain group of the population, identified by age, gender, profession or other characteristics. For example, the so-called fertility rate- the ratio of the number of live births to the average number of women aged 15 to 49, and age-specific fertility rates, determined by age groups as the ratio of the number of births per year to women of a given age group to the average annual number of women of this age.

Based on age-specific fertility rates, it is determined total fertility rate. It shows how many children, on average, one woman would give birth throughout the entire reproductive period (from 15 to 49 years) if the birth rate of the year for which the age coefficients are calculated is maintained at each age. The total fertility rate is determined by dividing the sum of partial age-specific fertility rates calculated for one-year groups by 1000. The value of the total fertility rate of 2.1 or less indicates that even simple reproduction of the population is not ensured. In table. 2.16 shows the fertility rates (age and total) for the Russian Federation. Since age-specific fertility rates are given in Table. 2.16 as averages for five-year intervals, then the sum of all coefficients for the corresponding year is multiplied by 5 and then divided by 1000.

Table 2.1 in

Age and total fertility rates in Russia for 1990–2008

	Births per 1000 women aged, years							total fertility rate

So, for 2002, the total birth rate

The total fertility rate does not depend on the age composition of the population and characterizes the average birth rate in a certain calendar period. In this regard, it is used for dynamic and regional comparisons of fertility levels.

All age and total fertility rates tend to decrease in their values ​​compared to the 1990 level.

The decline in the birth rate in Russia occurred throughout the 20th century. After the fall in the birth rate during the Great Patriotic War, the pre-war level was never reached. The maximum value of the total fertility rate took place in 1949 and amounted to 3.2. Over the following years, it constantly decreased, and by the beginning of the 1960s. became equal to 2.5 births per woman. In 1979, Russia was located in the middle part of the distribution of developed countries in terms of fertility, and the total fertility rate was 1.9. In the early 1980s the state has taken a number of measures aimed at increasing the birth rate: paid parental leave has been increased, family allowances and a number of other benefits have been introduced. As a result, by 1987 Russia took one of the leading positions in this indicator among the developed countries. However, the trend towards an increase in the birth rate only as a result of the administrative measures taken could not be long-term (since they prompted most families only to change the birth calendar of children, and not to increase their number). Since 1987, the decline in the total fertility rate began again, and although after 2000 there was a trend towards an increase in the total and some age-specific fertility rates, its level by 2005 was significantly lower than in 1990 (see Table 2.16).

During the intercensal period from 1989 to 2002, the total fertility rate decreased by almost 1.5 times: for women in cities - from 1.83 to 1.25, and in rural settlements - from 2.63 to 1.5.

In 2003, the total fertility rate in Russia was lower than in the developed countries of Europe. Thus, the highest total fertility rate was in Germany and amounted to 1.98, in France - 1.89 births.

Based on the total fertility rate is calculated gross reproduction rate of the population, characterizing the average number of girls born to a woman in her entire life. To determine this coefficient, the value of the total fertility rate is multiplied by 0.49 (the proportion of girls among those born). For 2002, the gross coefficient is 0.648 (1.3225 0.49).

In the period after 1993, there has been a relatively stable decline in the total fertility rate, associated with a gradual shift in births towards older ages. If in 1993 the average age of a mother at the birth of a child was 24.6 years, then in 1999 it was 25.6 years.

This process is accompanied by a decrease in the marriage rate and an increase in the age of marriage. If the marriage and divorce rates for men and women were 8.9 and 3.8‰ per 1,000 people in 1990, respectively, then in 2003 they were 7.6 and 5.5‰. The proportion of children born to women who are not in a registered marriage is growing: from 14.61% in 1990 to 29.71% in 2003. In general, these changes are similar to changes in the institution of marriage and family in most European countries. The main and extremely negative difference from the situation in our country is the persistence of a high number of abortions used as a means of birth control. In 1999, 2197 thousand abortions were registered in Russia, i.e. 57 abortions per 1000 women of reproductive age (from 15 to 49 years). For every 100 births, including stillbirths, there are 180 abortions in Russia. In terms of the frequency of abortions, Russia occupies one of the first places among European countries that regularly publish similar data. The highest rate among Western European countries was observed in Sweden: about 16 abortions per 1000 women. Thus, this factor becomes a serious obstacle not only to the growth of the birth rate, but also to the development of healthy generations.

One of the important factors in increasing the birth rate is a change in attitudes towards the institution of the family and marriage, including increasing the strength of marriages. Undoubtedly, the relationship between the fragility of marriage and the decline in the birth rate.

The intensity of marriages and divorces is characterized, as already noted, by marriage and divorce rates (see formulas (2.5) and (2.9)). These coefficients are used to calculate general coefficient of instability of marriages, which is also defined as the ratio of the number of divorces and marriages (Table 2.17).

Table 2.17

Marriages and divorces in Russia 1970–2008

	Per 1000 population		General coefficient of instability of marriages
		divorces

The data given in table. 2.17, indicate a trend towards a decrease in marriage rates and an increase in divorce rates. If in 1970 there were 10.1 marriages per 1000 population, then in 2000 - 6.2 marriages. At the same time, after 2000, positive changes were noted: the total marriage rate began to increase from year to year (from 6.2 marriages per 1,000 population in 2000 to 7.6 in 2003). At the same time, the number of divorces per 1,000 people increased (from 4.3 to 5.5). The coefficients of instability of marriages are characterized by a general tendency towards their growth. If in 1970 in the Russian Federation there were 297 divorces per 1,000 marriages, then in 2000 it was 694, and in 2002 it was already 845. trends.

According to the 2002 census, the number of married couples was 34 million. Of these, 3 million were unregistered marriages, this information was collected in 2002 for the first time. The number of women who indicated that they are married exceeded the number of men who answered yes to this question by 65,000 people.

Russia is ahead of the EU member states both in terms of the number of marriages per 1,000 population (in these countries, in 2007, the marriage rate varied from 3.2 to 8.8), and in the number of registered divorces per 1,000 population (in 2003, it was 3.8). in these countries, the divorce rate varied from 0.8 to 5.2).

When studying the mortality of the population, the general (see formula (2.5)) and partial coefficients are also used. General mortality rates by federal districts are given in Table. 2.18.

According to the data given in table. 2.18, the highest mortality rates occurred in the Northwestern (Pskov region), Central (Tver region) and Volga federal districts. At the same time, in the Central Federal District, in 50% of the regions, the mortality rate was higher (17.8‰). The most problematic demographic situation has developed here: the lowest birth rates and the highest death rates. The lowest values ​​of mortality rates were noted in the Southern (Republic of Ingushetia) and Ural (Yamalo-Nenets Autonomous Okrug) federal districts. The lowest average mortality rate in 2008 (12.1‰) took place in the regions of the Southern Federal District, while the average for the regions of the Russian Federation was 14.6‰.

Table 2.18

Characteristics of the mortality rate in the regions of the Russian Federation in 2008

federal district	Number of regions	Mortality rate, ‰
		minimum value	maximum value	range of variation	mean		asymmetry
Central
Northwestern
Volga
Ural
Siberian
Far Eastern
In general for the Russian Federation

Let's add the table. 2.18 indicators of the dispersion of the mortality rate in each federal district (intragroup dispersion) and give the values ​​of the coefficients of variation.

Table 2.19

Analysis of the influence of the regional factor on the mortality rate (according to 2004)

The highest variation in the mortality rate given in Table. 2.18 took place in the Southern and Ural Federal Districts (the coefficient of variation was 32.41 and 32.06%, respectively). In other federal districts, the regions are more homogeneous in terms of this indicator (the coefficient of variation is from 8.61 to 19.40%).

The intergroup variance in the total mortality rate, which estimates the variance in mortality under the influence of regional differences, in 2008 was 5.678, and the average of the intragroup variances according to the calculation results was 6.624. Therefore, the coefficient of determination will be equal to 0.462, i.e. 46.2% of the variation in the mortality rate is due to regional differences. The empirical correlation ratio is 0.679, which suggests a fairly strong influence of the regional factor on the mortality rate.

Grouping regions according to general birth and death rates makes it possible to identify regions with a favorable demographic situation, unlike other regions of Russia, and problem areas with a very high natural population decline. In table. Table 2.20 shows the grouping of regions by birth and death rates for 2004. In the lower left corner of the table, there are regions with rather low mortality and high birth rates for Russia. This is typical for the republics of Ingushetia, Dagestan, Chechen, Yamalo-Nenets and Tai-

Table 2.20

Grouping of regions of the Russian Federation by birth and death rates for 2004

Fertility rate	Death rate
									Total regions
				Moscow city	St. Petersburg. Belgorod; Volgograd; Rostov	Bryansk; Voronezh; Ulyanovsk; Kaluga; Lipetsk; Moscow; Orlovskaya; Penza; Tambovskaya; Kaliningrad Saratov; Kirovskaya. Republic Mordovia	Regions: Vladimirskaya; Ivanovskaya; Kostroma; Ryazan; Smolensk; Tula; Nizhny Novgorod; Yaroslavskaya; Leningradskaya	Tverskaya; Novgorod; Pskovskaya
			Kabardino-Balkarian Republic	Regions: Murmansk; Tomsk; Kamchatka; Magadan. Republics: Tatarstan;	Orenburg; Samara: Sverdlovsk; Sakhalin: Novosibirsk; Chelyabinsk.	Arkhangelsk; Vologda; Perm; Kurgan; Kemerovo. Republics:		Komi-Permyatsky Autonomous Okrug
				Karachay-Cherkess; North Ossetia Alania	Republics: Bashkortostan; Udmurt; Chuvash; Altaic; Krasnoyarsk; Seaside; Khabarovsk Krasnodar; Stavropol
	The Republic of Ingushetia. Yamalo-Nenets Autonomous Okrug	Khanty-Mansi Autonomous Okrug	Tyumen region. Republic of Karelia		Astrakhan; Irkutsk. Republic	Chita; Amur. Karyaksky autonomous
	The Republic of Dagestan	Taimyr Autonomous Okrug	The Republic of Sakha (Yakutia)	Evenk Autonomous Okrug	Ust-Orda Buryat Autonomous Okrug
16.7 and above	Chechen Republic			Tyva Republic. Aginsky Buryat Autonomous Okrug
Total regions

Myr Autonomous Okrug. In these regions, the birth rate exceeds the death rate. The regions with the highest death rates and the lowest birth rates are shown in the upper right corner of the table. Basically, these include the regions of the Central and Northwestern Federal Districts, where the death rate significantly exceeds the birth rate and, consequently, the natural population decline is high. In total, only in 15 regions out of 87, the death rate does not exceed the birth rate. The highest mortality is in the Pskov (24.2‰), Tver (23.3‰), Tula (21.8‰) and Ivanovo (21.4‰) regions, the lowest is in the republics of Ingushetia (3.7‰) and Dagestan (6.0‰) and Yamalo-Nenets Autonomous Okrug (5.7‰).

Age-specific mortality rates calculated as the ratio of the number of deaths at a given age during a calendar year to the average annual number of people of a given age. In addition to age coefficients, mortality rates by cause of death are determined.

Infant mortality rates are defined as follows:

where M 0 - the number of deaths under the age of one year out of those born in the year for which the coefficient is calculated; N 0 is the number of births in the same goal; M 1 – the number of deaths before one year in those born in the previous year; Ν 1 is the number of births in the previous year.

Along with this indicator are determined:

• – perinatal mortality rate - the ratio of the number of deaths per 1000 live and dead births;
• – infant mortality rates by main cause of death classes – the product of the proportion of deaths from a given cause among all deaths under the age of one year by the infant death rate (determined per 10,000 births).

The main factor in Russia's population decline is the high mortality rate. If in terms of the birth rate, Russia basically fits into the models of developed countries, then in terms of the mortality rate of the country's population it differs significantly from the global ones (Table 2.21).

Of the presented in table. 2.21 of the data it follows that in 2006 Russia did not have the highest birth rate, but in terms of the overall mortality rate it "outperforms" by 1.5-2.0 times the indicators of all other countries. Natural population decline takes place in Germany and Russia.

Table 2.21

Demographic coefficients in the most developed countries

	Per 1000 population
	number of births			number of deaths			natural increase (decrease)
United Kingdom
Germany

Our country is characterized by significant differences in age-specific mortality rates by sex.

Table 2.22

Age-specific mortality rates for men and women in 2008 (deaths per 1000 people of the respective age group)

All age-specific mortality rates for men are much higher than those for women. In addition, the gap in the values ​​of indicators increases with age.

One of the most acute problems in Russia is the high level of infant mortality, the deterioration in the health of newborns, the growth of pregnancy pathology and childbirth complications, despite a slight decrease in perinatal mortality.

At present, infant mortality rates in Russia are almost two to three times higher than in developed countries. Thus, in 2007 this coefficient in the UK was 4.8, Germany - 3.9, France - 3.6, Italy - 3.7. The lowest value of this indicator is in Luxembourg - 1.8. In addition, the trend towards changes in mortality rates in Russia differs from similar trends in the EU and the US, primarily in that the decline in infant mortality rates in our country is much slower. However, there are some positive developments in this area. If in the 1980s-1990s infant mortality decreased by 1.4-3.3% per year, then in 2007 it decreased by 7.84% per year, and in 2008 by 9.57% (Table 2.23).

Table 2.23

Infant mortality rates in Russia

	Deaths under one year of age per 1,000 live births			Mortality ratio of boys and girls	Dynamics of infant mortality rates, % to the previous year
			boys

With high rates of infant mortality during the period given in Table. 2.23 of the period, its differences by sex persist: infant mortality rates for boys exceed those for girls.

With a general downward trend in infant mortality rates since 2000, there has also been a reduction in the gap in mortality rates between boys and girls. Thus, in 2008, compared with 2000, the reduction in infant mortality rates for girls and boys was 43.18% and 45.09%, respectively.

Special coefficients reflect demographic processes much more accurately than general ones, however, with their differentiation, the clarity that is necessary for temporal and regional comparisons is lost.

For such comparisons, it seems necessary to bring the overall coefficients to a comparable form) ", eliminating the influence of the structure of the population on the value of the indicator. The use of standardized coefficients makes it possible to exclude the influence of differences in the structure. When comparing data but the population with an interval of one year or less, it makes no sense to resort to standardization , since over such a short period of time the structure of the population does not change significantly.But when comparing the coefficients with an interval of five years or more, or for the population of different territories, it is advisable to exclude differences in population structures.

Crude death rate is defined as follows:

(2.7)

where is the number of deaths at the age X in gody - the average number of people aged X per year f, - mortality rates for ages per year t, is the proportion of the population of the corresponding age group in the total population: P– number of age groups of the population.

From formula (2.7), it is obvious that the crude mortality rate is the arithmetic weighted average of the full series of age-specific mortality rates and depends on two factors: age-specific mortality rates and the age structure of the population. The influence of these factors on the change in the total mortality rate can be assessed using the indices of variable composition, fixed composition, and the influence of structural shifts on the dynamics of the coefficients. The initial data for the analysis are presented in table. 2.24.

Table 2.24

Age mortality rates of the population of Russia

Age, years	Number of deaths per 1000 population		Population structure, %
85 and over

Indices of variable () and fixed () compositions, as well as the index of the influence of structural shifts () are calculated using the following formulas:

Here, with the superscript "0" the indicators for 1990 are given, and with "1" - for 1998.

In 1998, compared with 1990, the overall mortality rate increased by 23.2%. At the same time, as follows from the above calculations, the change in the total mortality rate is significantly affected not only by changes in age-related mortality rates, but also by the dynamics of the age structure of the population. Due to the change in the latter, caused by an increase in the proportion of the population of older age groups (see Table 2.24), the overall mortality rate increased by 10.3%. The change in age-specific mortality rates led to an increase in the overall mortality rate by 11.7%.

From the above example, it follows that the age structure of the population in 1998 is used as a standardized structure (see fixed composition index). However, it is not always advisable to use the age structure of a given year to standardize indicators. In particular, for international comparisons, a generally accepted standard for recalculating coefficients should be applied. To solve such problems in statistical analysis, a direct or indirect standardization method is used.

At direct standardization method the object of replacement in the calculation of general coefficients is the age structure of the population. This method is especially useful when comparing death rates by cause of death, since the standardized death rate for groups of causes of death is the sum of the standardized death rates for each of the causes in the group. In practice, two standards are used: European and world (developed by the World Health Organization - WHO), given in Table. 2.25.

Table 2.25

European and world standards

Age groups, years	Standard			Age groups, years	Standard
	European				European
35-39 40-44	0,070 0,070	0,060 0,060		85 and over

At indirect method of standardization the object of replacement is age-specific mortality rates. The "third" population is usually taken as a standard, for which there are data on the age composition and age-specific mortality rates. When comparing coefficients across regions of a country, the population of the entire country or one of the regions being compared can serve as the standard.

Widespread in the analysis of demographic processes received demographic tables, which are a system of interconnected series of numbers ordered by age, organized as a description of the process of change with the age of some "theoretical" generation.

Mortality table is the result of a model calculation, with the help of which the life cycle of a conditional generation (100,000 people) is constructed. At the same time, it is assumed that the probabilities of death of this conditional generation in each year of life exactly coincide with the probabilities of death, predetermined empirically. Mortality tables are calculated for men, women or two iols in total. The layout of such a table is tab. 2.26.

Table 2.26

Mortality table layout

Age in years ( X)	Number of people surviving to age X(1)	The number of deaths in the transition from age X to age X + 1 (d x)	Probability of dying within the next year of life (s/y)	Probability of surviving to age A "+ 1 (R X)	Number of living aged X (Ι.χ)	Number of person-years of life ahead (T X )	Average life expectancy (e° X)

The indicators of mortality tables are divided into two groups. The first group includes indicators related to the exact age X years: the number of surviving, the number of person-years of life ahead and the average life expectancy (columns 2, 7, 8), and the second includes other indicators related to the age interval from X before x + Δx years (columns 3–6).

Based on the mortality tables, the following indicators are determined:

The main indicator life expectancy at birth, characterizing the number of years that, on average, one person from the generation born would have to live, provided that throughout the life of this generation the mortality rate at each age remains the same as in the years for which the indicator is calculated. Life expectancy at birth () is defined as follows:

Based on the analysis of the mortality table, the following patterns can be considered:

• dynamics of the probability of death by age groups with distribution by sex;
• the total number of deaths and its distribution by individual age classes. It is possible to determine the maximum in the distribution of the number of deaths by age, i.e. the age at which mortality is highest;
• the average age of the deceased, defined as the age at which half of the conditional generation of those born died. It can be defined as the sum of the number of deaths up to the age class in which the number of deaths reaches 50%, or by specifying in the column / the age at which the number of survivors falls below 50%.

Fertility tables represent a system of interrelated indicators for describing the process of childbearing in a certain theoretical generation of women (in Russia, tables of the birth rate of women are built) with a fixed number at the age of 15 years.

According to the birth tables, the following indicators are determined:

• age-specific fertility rates;
• total number of births at a given age, cumulative birth rates- the number of births per 1000 women by a given age, excluding the decline in the number of the female generation under the influence of mortality - the sum of age-specific fertility rates from 15 years to a given age;
• average number of births at a given age taking into account the decline in the number of the female generation under the influence of mortality - the sum of similar indicators from 15 years to this age;
• total (gross) reproduction rate of the female population - the product of the sum of age-specific fertility rates and the proportion of girls among those born in the years for which the coefficient was calculated;
• net (net) female reproduction rate - the sum of the products of age-specific fertility rates and the corresponding number of living women in each age group L x from the mortality tables for the same period, multiplied by the share of girls among those born in the CU years for which the coefficient is calculated;
• average age of mother at birth is the average of the mother's ages at childbirth, weighted by recurrent fertility rates.
• Group of eight in numbers: stat. Sat. - M., 2004.
• Peritanal mortality is the mortality of viable fetuses from the 28th week of pregnancy until the onset of labor in the mother and during childbirth, as well as of children during the first 168 hours of life.
• Russia and countries - members of the European Union. 2009: stat. Sat. - M .: ed. Rosstat, 2005. - P. 39.

1. Overall coefficient pexpectation = Total number of live births per year =

Average annual population

= = 11.2‰.

2. Coefficient pfertility (fertility) = =

The average annual number of women of childbearing

(fertile) age (15-49 years)

= = 2,07%

3. The total fertility rate is equal to the sum of age-specific fertility rates calculated for one-year or five-year age groups.:

(25,5*5 + 159*5 + 126*5 + 97*5 + 50*5 + 19,1*5 + 4,4*5)/1000 = 2,405.

4. Gross reproduction rate of the female population is the number of girls born to one woman during the entire reproductive period of life. It is equal to the product of the sum of age-specific fertility rates and the share of girls among those born in those years for which the coefficient is calculated.

= 2.405 0.477 = 1.15.

5. Mortality (Cumulative Mortality Rate) =Total number of deaths per year_ 0 = . Average annual population

= = 14,9%0.

6. Natural increase (decrease) of the population:

Coefficientnatural increase = Crude Fertility Rate - Crude Death Rate =

\u003d 11.2% o-14.9% o \u003d -3.74‰.

7. The number of children who died in the 1st year of life

Infant = during a year_____________ x 1000 =

mortality Number of live births in a given year

= = 23,2 ‰.

8. Stillbirth = Born dead within a year x 1000 =

Born alive and dead

= = 16.05‰.

9. Number of births Number of deaths per

Perinatal = dead + 168 hours of life x 1000 =

mortality Total number of live births and stillbirths

= = 22,3 ‰.

10. Neonatal Number of deaths in the first four weeks

mortality = life of a child (up to 28 days) in a given year_ x 1000 =

Number of live births in a given year

= = 16.3‰.

11. Early neonatal - Number of deaths at the age of 0-7 days

naya mortality =( up to 168 hours) this year_________ x 1000 =

(postnatal) Number of live births during the year

= = 6,32 ‰.

12. Late neonatal

naya mortality (per = The number of children who died at 2-4 weeks of age x 1000 =

2-4 week of life) Number of children, ro- - Number of children who died

Died alive in the 1st week of life

= = 10.1‰.

13. Postneon- The number of children who died in the period from the 29th day

steel = up to 1 year of age______________ x 1000 =

mortality The number of children who gave birth - - The number of children who died in

who survived the first 4 weeks of life

= = 6.96‰.

Population statistics and medical demography, Sharshakova, Dorofeev, 2009

total fertility rate

Total number of live births per year

Average annual population

Fertility or fertility rate

Total number of live births per year_____

The average annual number of women of childbearing

(fertile) age (15-49 years)

total fertility rate is equal to the sum of age-specific fertility rates calculated for one-year or five-year age groups.

Crude death rate

Total number of deaths per year ____

Average annual population

The values ​​of the total mortality rate are estimated on a special scale.

Table 5 - Crude mortality rates.

Crude death rate, 0 / 00	Estimated mortality rate
	Very tall
35.0 and up	Extremely high

Gross reproduction rate of the female population is the number of girls born to one woman during the entire reproductive period of her life. It is equal to the product of the sum of age-specific fertility rates and the share of girls among those born in those years for which the coefficient is calculated.

infant mortality rate

The number of children who died in the 1st year of life

Infant = during a year_____________ x 1000

mortality Number of live births in a given year

Scale for estimating the total infant mortality rate

Antenna - The number of stillborns in a year (or the number

steel = _ deaths before childbirth after 22 weeks of pregnancy) x 1000

Intrapartum = _______ Number of deaths in childbirth per year _______ x 1000

mortality Total number of live births and stillbirths

Number of births Number of deaths per

perinatal= dead + 168 hours of life x 1000

To measure the birth rate, a system of indicators is used to determine both its general level and dynamics, and its intensity, as well as its magnitude in various subpopulations (socio-economic and demographic groups). Fertility rates are divided into:

• indicators related to period time (usually a year);
• and indicators characterizing a certain cohort, or generation(if we are talking about a cohort by year of birth), or cohort

indicators.

The first characterize the birth rate observed over a certain period, the second - the birth rate characteristic of certain groups of women, their reproductive history.

Time period indicators are simpler than cohort indicators and are used more frequently. We will start with them and consider them in order of increasing complexity and amount of data required to calculate them.

Fertility rates for the conditional generation (fertility rates for the period)

Birth rates for a conditional generation are expressed as the ratio of the number of births that took place during a given period of time to the population in which these births occurred. Usually, the following indicators are distinguished:

• total fertility rate ( CBR);
• special birth rate ( GBR)
• age-specific fertility rates ( ASFR);
• total fertility rate ( TFR);
• fertility rates by birth order ( OSFR);
• age-specific marital fertility rates

These coefficients are calculated using either data relating to a particular year or averaging (adjusting to a year) data relating to a period of one or another duration (for example, 3 or 5 year time intervals). In any case, these coefficients are indicators of a conditional generation (or, in other words, periodic, transverse), since they all reflect the conditions of fertility in a particular period.

All these coefficients are interconnected with each other, but each of them reflects one or another aspect of the childbearing process and, therefore, have independent value.

Coefficient (index) of children

However, we will start with the simplest conventional periodic characteristic of fertility, which requires only data on the age structure of the population, which is the coefficient (or index) of children.

The childbearing rate is understood as the ratio of the number of children aged 0-4 years to the number of women of reproductive (15-49 years) age. Sometimes the number of children aged 0-9 years is taken as the numerator when calculating the fertility rate, and the number of women aged 20-49 years is taken as the denominator.

The birth rate, being a structural coefficient, is not included in the system of fertility indicators presented above, however, it can be used to characterize it in cases where data on the number of births are either missing or unreliable. The fertility rate is calculated using the following formula:

C /WR= °- 4

where C / UYa - fertility rate; SI() _ 4 - the number of children aged 0-4 years; В^ 15 49 - the number of women of reproductive age.

Table 6.2 shows data on the value of the childbearing rate in some countries as of July 1, 2005, according to the United Nations. The Pearson correlation coefficient between the birth rate and the total fertility rate reported by the UN is 0.974. The linear regression equation between the childbearing rate and the total fertility rate is as follows:

TFR = -0,148 + coefficient_detn x 7.259.

Childhood rate for some countries

Table 6.2

	Number of children aged 0-4 years, thousand people	population reproductive age, thousand people	Coefficient childhood
Afghanistan
Germany
Ireland
Uzbekistan
World at large

Source: Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World Population Prospects: The 2004 Revision and World Urbanization Prospects: The 2003 Revision, Population Database. panel 2. http://csa. un.org/unnn/n2k0data.asn.

In Russia, the value of the child-bearing rate according to the 2002 population census was 0.160, incl. in cities - 0.144 and in rural areas - 0.211, i.e. 46.3% more than 1 . The difference in the value of the childbearing rate from the estimates given in Table 6.2 is explained by a certain increase in the number of births in the country after 2000.

The birth rate can be used to initially estimate and predict fertility levels, especially in countries with poorly established vital records but with sufficiently accurate census data. It is also useful for making initial comparisons of fertility rates across countries: the fertility rate is high where fertility is high and low in countries where fertility is low. The disadvantage of the fertility rate is that it is extremely sensitive to fluctuations in infant and child mortality and to underestimation of the child population. Therefore, its use in countries with high infant and child mortality and unreliable statistics may lead to incorrect estimates and conclusions.

The indicators that will be discussed below, in contrast to the childbearing rate, directly characterize the process of fertility. The first and initial of these indicators is absolute number of births.

Absolute number of births

Absolute number of births shows how many children were born in a particular population in a certain period, usually a year. The value of the absolute number of births gives the first idea of ​​the "gross volumes" of the birth rate and allows them to be compared over different periods of time and different territories. Information on the absolute numbers of births is obtained during the registration of the vital movement of the population, processing the statistical registration forms of birth certificates.

However, the absolute number of births is an uninformative indicator, since it depends on the absolute population. It is impossible to judge the birth rate by the magnitude of the absolute number of births without comparing it with the total population. Similarly, it makes no sense to talk about the dynamics of the birth rate, based only on data on changes in the absolute number of births and without taking into account either the total population or changes in demographic structures. “You need to remember,” V.A. rightly says. Borisov, - what “ fertility" (as well as " mortality", “marriage” etc.) is always expressed only attitude the number of children born (usually only those born alive) to a particular population (either to the total population, or only women of a certain age, married, and so on)” 1 .

total fertility rate

Therefore, it is necessary to move to relative birth rates that would not depend on the population size, i.e. to fertility rates and probabilities.

Borisov V.A. Fertility // Population of the world: a demographic guide. M., 1990.S. 25.

The first, most simple and widely used relative fertility rate is total (rough) fertility rate. The total fertility rate is calculated as the ratio of the absolute number of births to the total number of person-years lived by the entire population in a period, usually a year.

Or, more simply, if we talk about a period equal to a year, the total fertility rate is the ratio of the absolute number of births to the average annual population (Table 6.3). For clarity, this value is multiplied by 1000, i.e. expressed in ppm (%about):

CM \u003d? x 1000% o,

where: AT - absolute number of births per year; R- average annual population; CBR is the total fertility rate.

For example, let's calculate the total fertility rate for Russia in 2004. The total number of births in 2004 was 1,502,477. The average annual population, according to Rosstat, in 2004 was 143,821,215 people. Hence the total fertility rate is:

CBR\u003d x 1000% o \u003d 10.45 % 0 .

The value of the total fertility rate strongly depends not only on the intensity of fertility, i.e. from the average number of children born to women, but also from demographic and other structures, primarily from age, sex and marriage. Therefore, it gives only the very first, approximate idea of ​​the birth rate. In this regard, the total fertility rate is also called rude its coefficient (hence its designation - CBR- from English. Crude Birth Rate). To eliminate this influence of demographic and other structures on fertility rates, it is calculated special and private coefficients, and total coefficient.

Special birth rate calculated, like other special coefficients, in relation to the part of the population that "produces" birth, i.e. in relation only to the number of women of conventional reproductive age (15-49 years). The special fertility rate is equal to the ratio of the total number of births per year to the average annual number

Dynamics of total fertility rates in Russia, 1960-2005, %about

Source: Demographic Yearbook of Russia 2005. M., 2005. S. 69-71. For 2005 - operational data of Rosstat ( http://www.gks.ru/bgd/free/B05 ОО/^ХУШУУ.ехе/Бгё/ 0120/08-00.1It).

of women of reproductive age, multiplied by 1000 %aboutSVYA \u003d -!? -xZh0% s,

where: GBR- special birth rate; AT- absolute

number of births per year; R 15 _ 49- average annual number of women

reproductive age.

The value of the special birth rate in the same 2004 was equal to:

GBR = JUZ4 // x 1000% o = 37.69% o.

The general and special fertility rates are related to each other by the following ratio: the general rate is equal to the special multiplied by the proportion of women in the reproductive population in the entire population:

CBR = AxGBR = GBR

where D is the proportion of women of reproductive age in the entire population, i.e. ^15-49

In 2004, the share of women of reproductive age in the entire average annual population was approximately 27.71%. From here we get: 37.69% o x 27.71% ~ 10.45% s.

Partial fertility rates are calculated to eliminate the influence of other demographic and non-demographic structures. Partial fertility rates are equal to the ratio of the number of births in a part of the population (in subpopulation) to the average annual size of this subpopulation. Partial coefficients can be both general and special. For example, in table. 6.3 shows the values ​​of the total fertility rates of the urban and rural population.

In demographic analysis, knowledge of the frequency of births of children in marriage and out of wedlock is of great importance, knowledge, in other words, of the levels of marital and extramarital births. Accordingly, the rates of marital and out-of-wedlock births are calculated, equal to the ratio of the number of those born in marriage and out of wedlock to the average annual number of women who are married and who are not married.

Special Marriage Fertility Rate:

x 1000 %about,

vvme =

where AT""- the number of births of children in marriage; - number of women

reproductive age, married.

Special rate of out-of-wedlock births:

where AT**- the number of births of children out of wedlock; ^15-49 - the number of women of reproductive age who are not married.

Indices t and g refer to marriage and illegitimate births, respectively.

When calculating the rates of marital and out-of-wedlock births, one should keep in mind the differences in determining the marital status of women when registering births in the civil registry offices and in the population census. If the first is determined purely formally by documents (marriage certificate), then during the census, as you remember, by the self-determination of a woman. In other words, there is some incompatibility between the numerator and denominator of a fraction. As a consequence, the calculation of marriage and out-of-wedlock fertility rates underestimates the level of the former and exaggerates the latter. And so the extramarital birth rate is better judged by the proportion of extramarital births among all births.

This proportion shows a steady upward trend and in 2004 in Russia was approximately equal to 29.8% of all births, incl. in urban settlements - 28.3%; in rural areas - 33.4%. The minimum value of extramarital births for the entire period of continuous observations (since 1960) was recorded in 1970 and was equal to 10.57%. In other words, for a quarter of a century, the level of out-of-wedlock births in Russia has almost tripled.

In a similar way, fertility rates (general and special) of the urban and rural population, and so on, can be calculated.

The general rule for calculating partial fertility rates, I repeat once again, is that the part of the absolute number of births that falls on the corresponding subpopulation is divided by its average annual number.

Age-Specific Fertility Rates

Among partial fertility rates, the most important place belongs to age-specific fertility rates, which measure the net intensity of fertility in a particular age group of women. Age-specific coefficients can be calculated for one-year age intervals, or for five-year (ten-year) age intervals. In the latter case, they are reduced to one year (averaged). Age-specific fertility rates are calculated as the ratio of the number of births to women of a certain age (x years) to their average annual number:

AU / K \u003d - ^ x 1000% o,

where is L-57 7 /? - age-specific fertility rates; p V- number

births to women ages + P years; R - average annual number of women ages + P years.

An example of calculating age-specific coefficients, as well as general and special, is given in Table. 6.4.

The calculation of age-specific fertility rates requires much more data than the calculation of general or specific fertility rates. This requires data not only on the total number of births per year, but also on their distribution by mother's age. In other words, in order to calculate age-specific coefficients in the country, there must be a reliable and accurate system for recording the vital movement of the population, which is far from always the case. Even in countries with well-established population statistics, data on the distribution of births by age of mother began to be collected only in the middle of the 20th century. For those cases when such data are not available, special mathematical models have been developed that make it possible to restore age-specific fertility rates from data on the total number of births in the country.

When calculating the age-specific fertility rates, as well as its special coefficient (which is also, in essence, by definition, the age-specific fertility rate for the age of 15-49 years), it is customary to attribute all births to mothers younger than 15 years of age at the age of 15 years (or 15-19 years, if coefficients are calculated for five-year age groups). Births to mothers whose age exceeds 49 years are attributed to the age of 49 or 44-49 years, respectively. This does not reduce the accuracy of determining the age-specific coefficients for these ages due to the very small number of births in the youngest (under 14 years old) and in the oldest (50 years and older) ages. However, if the purpose of the study is to study the birth rate in these age groups, then, of course, the age-specific coefficients for them are calculated according to the general rule.

Graph 6.2 shows the curves of changes in age-specific fertility rates for the population of Russia in 1958-2004. Differences in the form of curves characterize the process of fertility decline in Russia during this period. As can be seen from the graph, low fertility corresponds not only to a lower curve height, but also to its greater shift to the left, to the y-axis, i.e. left asymmetry.

Age-specific fertility rates make it possible to analyze the level and dynamics of the net intensity of fertility in a conditional generation, free from the influence of the age structure of both the population as a whole and women of reproductive age. This is their advantage over the general and special fertility rates. However, some inconvenience of age-specific coefficients is that their number is too large: if these coefficients are calculated for one-year intervals, then there are 35 of them, and if for five-year intervals, then seven. This circumstance makes analysis and comparison difficult. In order to overcome this difficulty and be able to analyze the level and dynamics of fertility using a single indicator, also free from the influence of the age structure, the so-called cumulative fertility rates are calculated, of which the most famous and widely used total fertility rate (TFR). The total fertility rate is calculated simply as the sum of the age-specific rates for ages 15 to 49:

HuSHTS

TRY = ^--.

Division by 1000 is done to bring the value of the coefficient to one woman. In practice, since age-specific fertility data are published in 5-year age intervals, the following formula is used:

5x? 5 AYAR

TRY =-!*_--

where 5 ANR x - age-specific fertility rates for 5-year-olds

age intervals.

The total fertility rate characterizes the average number of children that a woman of a conditional generation will give birth to during

Births per 1000 women of a given age

Chart 6.2

Age-specific fertility rates. Russia. 1958-2004. Births per 1 woman of reproductive age.

Source: Demographic Yearbook of Russia. 2005. M., 2005. S. 193.

the entire reproductive period, provided that the intensity of age-specific fertility that was observed in the year for which this indicator is calculated is maintained. The total fertility rate is calculated under the assumption that there is no mortality, i.e. under the assumption that all women of the conditional generation will remain alive until the end of the reproductive period.

The total fertility rate characterizes the average number of births per woman in a hypothetical generation over her entire life, while maintaining the existing levels of fertility at each age, regardless of mortality and changes in age composition. Total coefficients above 4.0 are considered high, less than 2.15 - low.

Population: Encyclopedic Dictionary. M., 1994. S. 199.

Since data on age-specific fertility are usually published for five-year age intervals and are given per thousand women of reproductive age, when calculating the total fertility rate, the values ​​​​of age-specific coefficients are multiplied by 5 and divided by 1000, which is reflected in the above formula. In some countries, however (for example, in the USA), the total fertility rate, like the age-specific rates, is calculated per 1,000 women. In this case, there is no need to divide by 1000. Table 6.4 shows an example of calculating the total fertility rate of the population of Russia in 2000. The value of this coefficient, given in Table 6.4, differs only by 0.001 from the official figure of Rosstat.

Figure 6.3 shows the dynamics of the total fertility rate in Russia in 1961-2004. As can be seen from the graph, the value of the total birth rate in the country, starting from the mid-1960s, was below the level of simple reproduction of the population. This means that depopulation in the country did not begin in the early 1990s, when the death rate for the first time exceeded the birth rate, but in the second half of the 1960s. The 1990s was just a time when depopulation moved from a hidden, latent form to an open one, became obvious to everyone, and not just to demographers.

in the world in the last quarter of the 20th century. there was also a radical decrease in the value of the total fertility rate. If in the first half of the 1970s. the average world value of the total fertility rate was equal to 5.03 births per 1 woman of reproductive age with a minimum value of 1.62, a maximum of 8.50 births and a standard deviation of 1.955 births per woman of reproductive age with a minimum value of 0.84,

Births per 1 woman of reproductive age

• 2.1 2,0
• 1.4 1,3 1,2 1,1 1,0

All population

Urban population

Rural population

TFR for PV

Chart 6.3

Dynamics of the total fertility rate in Russia in 1961-2004 Sources: Demographic Yearbook of Russia, M., Rosstat, 2005, p. 108.

Table 6.4

An example of calculating the general, special, total fertility rates and the average age of the mother at the birth of a child, Russia, 2000

Age interval	births		population	age odds fertility
				8 \u003d (3) / (4) x 1000% o
Share of women of reproductive age in the entire population, %
Average annual population
Total Fertility Rate (CBR), %o		CBR=-x 1000 = 10.4
Special Fertility Rate (GBR), %o		CBR=-x 1000 = 37.7
Total Fertility Rate (TFR) =		28,2 + 93,4 + 80,2 TFR= 5x- 45,9 + 17,6 + 2,9 + 0,1 +-= 1,341

Calculated by: Demographic Yearbook of Russia 2005. M., 2005. S. 54, 108, 193.

a maximum of 7.91 births and a standard deviation of 1.73161. and in 2000-05. respectively are: 1 quartile - 2.97 and 1.76; 2 quartile (median) - 5.54 and 2.71; 3rd quartile - 6.70 and 4.33 births per 1 woman of reproductive age.

And finally, if in the first half of the 1970s. Since approximately 10% of the countries in the world for which data are available had a total fertility rate less than what is necessary for simple population replacement, the share of such countries is currently approximately 35% (see also Chart 6.4, which shows the cumulative distribution of the countries of the world by the value of the total fertility rate) .

Cumulative distribution of the countries of the world by the value of the total fertility rate in 2000-2005.

Calculated by: Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World Population Prospects:

The 2004 revision. highlights. New York: United Nations. ESA/P/WP. 193. 24 February 2005 and World Urbanization Prospects: The 2003 Revision.

Table VI1-16. ( http://esa.un.org/unpp). Medium option.

total fertility rate summarizes age coefficients for Total reproductive period, i.e. for the entire interval of 15-49 years. But such summation can be made for any age within the reproductive period. The results obtained in this way are called cumulative birth rates at a given age and are calculated similarly to the total fertility rate.

A generalizing indicator of fertility for a period, or fertility for a given year, calculated by summing the age-specific fertility rates that form a function of fertility, is the total fertility rate, or simply the total fertility. The total fertility for a given year represents the number of children that 1,000 women would give birth to if there were no deaths and if the age-specific fertility rates observed in that year were maintained.

Multilingual Demographic Dictionary. English section. Liege, 1982.

The value of the cumulative and total fertility rates lies precisely in the fact that they allow one number, the value of which does not depend on the influence of the age structure, to characterize the birth rate in a particular country and thus make cross-country and inter-period comparisons.

Birth rates by birth order

In addition to the age of the mother, in the analysis of fertility, the number of children a woman gave birth to in the past, or the sequence or order of birth, is also important.

Birth order is the number of children born to a woman, including the last child.

Although birth order is of the greatest importance in cohort analysis of fertility, its role is also great in cross-sectional analysis, in the context of conditional generation. In demography, the following birth rates are used in order of birth for a conditional generation:

• special birth rate by birth order (GFR: OS);
• age-specific fertility rate by birth order (.ASFR: OS);
• the probability of having a child in a certain order ( PSFR). Special birth rate by birth order

is calculated as the ratio of the number of births of children / "- of that order to the average annual number of women of reproductive age:

GFR : OS=-x 1000%o,

where GFR : OS- special birth rate by birth order; Bj- the number of births of the /-th order; F l5 49- medium-

annual number of women of reproductive age. As can be seen from the definition of this indicator, the sum of special fertility rates by birth order is simply equal to the special birth rate:

vRJ = I : 05,

The special fertility rate by birth order is a very informative indicator in the analysis of the process of fertility decline, since in populations with low fertility, the values ​​of this coefficient for higher birth orders are practically equal to zero. On the other hand, one of the first indicators of the beginning of a decline in the birth rate is just a decrease in the coefficients for higher orders of birth.

Age-specific fertility rates by birth order are calculated as the ratio of the number of births of children of /-th order in women of age x years to the average annual number of women of this age:

L5/7? : 05 = - x 1000%o,

where V"x- the number of births /-of that order in women ages.

The sum of age-specific fertility rates by birth order is simply equal to the age-specific fertility rate for a given age.

Probability of having children in a certain order

The logical continuation of the analysis of the birth rate by birth order is the calculation of the birth rates of /-th order, the denominator of which is only the number of women with (/- 1) children:

/>5№ = ~g~g,

where IN 1- the number of births /-of that order, R‘~]- the average annual number of women with (/ - 1) children.

In other words, for example, the birth rate for the 3rd priority is equal to the ratio of the number of third births to the number of women with two children. These coefficients are usually called the probability of having children in the i-th order. They characterize the process of fertility in relation to those women who, before the birth of a child, already have one or another number of children. Here, the analysis of fertility for a conditional generation merges with a cohort analysis, since not only the current status of a woman is taken into account, but also the entire history of her previous births. That is why we will return to this indicator later, when we get acquainted with the birth rates of the real generation.

Birth calendar indicators of the conditional generation

In the analysis of fertility for a conditional generation, in addition to the coefficients discussed above, indicators are also used that characterize not the level, but the so-called timing, or calendar, fertility, i.e. its distribution over the entire interval of reproductive age. These indicators are as follows:

Share of total fertility n A x, attributable to a certain age interval (x + p) years. It is calculated as the quotient of the corresponding age-specific coefficient by the total fertility rate (here, the age-specific coefficients are expressed per 1 woman of the corresponding age):

P X.

"x y/y/? '

Cumulative share of total fertility ( Sit p A x) falling on the age interval ( x+n) years:

Sit P A X=X,A;

• mean age of mother at childbirth ( MMA):
  • 49 49

MMA = ^^t "MrSh xx A, = X

where t^drth- the middle of the age interval (x, x+n) years, or, which is the same, (x + 0.5 P).

In table. 6.5, using the example of data on age-specific and total fertility rates in Russia, the technique for calculating all these indicators is shown. The obtained value of the average age of the mother at birth differs only by 0.13 from the official data of the State Statistics Committee of the Russian Federation (25.9 years See: Demographic Yearbook of Russia 2005 ... P. 238.

Newell S. Methods and Models in Demography. London, 1988. P.40.

See: Source to tab. 6.4.

Demographic Yearbook of Russia 2005. M., 2005. S. 236.

Vital movement of the population is the change in population due to births and deaths.

The study of natural movement is carried out using absolute and relative indicators.

Absolute indicators

1. Number of births for the period(R)

2. Number of deaths per period(U)

3. Natural increase (decrease) population, which is defined as the difference between the number of births and deaths for the period: SP \u003d P - Y

Relative indicators

Among the indicators of population movement, there are: the birth rate, the death rate, the natural increase rate and the vitality rate.

All coefficients, except for the vitality coefficient, are calculated in ppm, i.e., per 1000 people of the population, and the vitality coefficient is determined as a percentage (i.e., per 100 population).

total fertility rate

Shows how many people are born during the calendar year on average for every 1000 people in the current population

Crude death rate

Shows how many people die during a calendar year on average for every 1000 people in the present population and is determined by the formula:

Mortality rate in Russia (number of deaths per 1,000 population) from 11.2 ppm in 1990 increased to 15.2 in 2006, and the birth rate decreased respectively from 13.4 to 10.4 ppm in 2006.

High mortality is associated with a steady upward trend in morbidity. In comparison with our ailments, they become chronic for 15-20 years. Hence the massive disability and premature mortality.

Natural increase rate

It shows the amount of natural increase (decrease) of the population during the calendar year on average per 1000 people of the present population and is calculated in two ways:

Vitality factor

Shows the ratio between fertility and mortality, characterizes the reproduction of the population. If the Vitality Factor is less than 100%, then the population of the region is dying out, if it is above 100%, then the population is increasing. This ratio is determined in two ways:

Special indicators

In demographic statistics, in addition to general coefficients, special indicators are also calculated:

marriage rate

Shows the number of marriages per 1,000 people during a calendar year.

Marriage rate = (number of people who got married / average annual population) * 1000

Divorce rate

Shows how many divorces occur for every thousand of the population during the calendar year. For example, in 2000 in Russia there were 6.2 marriages and 4.3 divorces for every 1,000 people.

To divorce rate = (number of persons divorced per year / average annual population) * 1000

infant death rate

It is calculated as the sum of two components (in ppm).

• The first is the ratio of the number of deaths under the age of one year from the generation born that year, for which the coefficient is calculated, to the total number of births that year.
• The second is the ratio of the number of deaths under the age of one year from the generation born in the previous year to the total number of births in the previous year.

In 2000, this indicator in our country was 15.3‰.

To infant mortality = (number of deaths of children under the age of 1 year / number of live births per year) * 1000

Age-specific fertility rate

Shows the average number of births per 1,000 women in each age group

Special birth rate (fertility)

Shows the average number of births per 1,000 women aged 15 to 49.

Age-specific mortality rate

Shows the average number of deaths per 1,000 people in a given age group.

total fertility rate

It depends on the age composition of the population and shows how many children, on average, one woman would give birth to throughout her life if the existing birth rate was maintained at each age.

Life expectancy at birth

One of the most important indicators calculated in the international. It shows the number of years that, on average, a person from the generation born would have to live, provided that throughout the life of this generation, age-sex mortality remains at the level of the year for which this indicator was calculated. It is calculated by compiling and analyzing life tables, in which the number of survivors and deaths is calculated for each generation.

Life expectancy at birth in 2000 was 65.3 years in Russia, including 59.0 for men; for women - 72.2 years.

Population reproduction efficiency coefficient

Shows the share of natural increase in the total turnover of the population

Brief theory

The population is one of the most important objects of statistical study. The tasks of population statistics include the study and analysis of the number, distribution, composition, reproduction and dynamics of the population, the determination of the prospective size of the entire population and its individual contingents. The main sources of population data are population censuses and current records of natural and migratory movements of the population.

The composition of the population is studied by demographic and socio-economic characteristics: gender, age, nationality, sources of livelihood, occupation, level of education, etc. For this, the relative values ​​of the structure (shares, specific weights) and coordination (indicators of the ratio of the number of men and women, boys and girls in the annual number of births).

The processes of birth and death that provide natural population growth, as well as the processes of marriage and divorce are called natural population movement. The movement of people within a country is called migratory movement of the population.

The initial characteristic of the natural and migration movement of the population are absolute values. The absolute numbers of births and deaths, marriages and divorces, arrivals and departures are derived from current records. Absolute indicators of population movement are interval indicators, they are calculated for certain periods of time, for example, for a month, for a year, etc. The annual numbers of the events studied are of the greatest importance.

Absolute Vital Rates This:

If the number of births exceeds the number of deaths, the natural increase is positive, and if the number of deaths is greater than the number of births, the natural increase is negative.

Absolute indicators of the migration movement of the population This:

To characterize the reproduction and migration of the population, a number of general demographic coefficients are used (fertility, mortality, natural increase, marriage, divorce, arrival, departure, migration increase, etc.), which are calculated as the ratio of the corresponding number of demographic events (total absolute population growth, the number of births, deaths, natural population growth, the number of registered marriages, divorces, the number of arrivals, departures, migration population growth, etc. during the calendar period) to the corresponding average population.

total fertility rate calculated by dividing the number of live births in a year by the average annual population - Shows how many people are born during a calendar year on average for every 1000 people in the present population.

Crude death rate is calculated similarly by dividing the number of deaths in a year by the average annual population. Shows how many people die during a calendar year on average for every 1000 people in the present population.

Natural increase rate(departed). Shows the amount of natural increase (decrease) of the population during the calendar year, on average, per 1000 people in the present population.

Along with the general coefficients, that is, those calculated for the entire population, for a more detailed description of the reproduction of the population, private (special) coefficients are determined, which, in contrast to the general coefficients, are calculated per 1000 people of a certain age, sex, professional or other group of the population.

So, when studying fertility, a special fertility rate is widely used - fertility rate, fertility:

- the number of live births per year;

The average annual number of women aged 15-49 years.

There is a clear relationship between general and special coefficients, therefore, through special coefficients, you can calculate the general ones. Thus, the total fertility rate is equal to the product of the special birth rate and the share of women aged 15-49 in the entire population.

Of great importance is the calculation of age-specific fertility rates (that is, fertility rates for certain age groups of women) and the total fertility rate, which characterizes the average number of children born to a woman in her entire life.

Vitality factor shows the ratio between fertility and mortality, characterizes the reproduction of the population. If the vitality factor is less than 1, then the population of the region is dying out; if it is higher than 1, then the population is increasing.

Turnover ratio- the number of births and deaths per 1000 people per year on average:

Population reproduction efficiency coefficient(as a share of natural increase in the total turnover of the population):

Total marriage rate calculated by the formula:

where is the number of marriages

General divorce rate:

- number of divorces

Marriage Stability Coefficient:

Migration intensity indicators characterize the frequency of cases of change of place of residence in the total population over a certain period. The following general characteristics of the intensity of migration per 1000 inhabitants per year are most often used:

arrival rate:

Retirement rate:

General coefficient of migration intensity(coefficient of mechanical population growth):

Migration turnover intensity coefficient:

Migration efficiency ratio:

General demographic coefficients have a significant drawback: their value is influenced not only by the intensity of demographic processes, but also by the characteristics of the age, sex and other structure of the population for which they are calculated. For example, of all the general coefficients of natural movement of the population, only the mortality rate gives a characteristic of the process taking place in the entire population, since all people are mortal. The denominator of the general fertility, marriage and divorce rates includes the part of the population that in the period under study did not generate demographic events reflected in the numerator, for example, children. Due to these reasons, general coefficients are suitable only for the most rough assessment of the intensity of the relevant processes, and for a deeper analysis, to characterize the reproduction of the population and assess the demographic situation in the region under study, it is necessary to use special and private indicators that are less dependent on the influence of structural factors.

Problem solution example

The task

The average annual population in the region was 20 million people, of which 2% are women aged 15-49 years. During the year, 12,000 people were born, 14,000 people died, including 182 children under one year of age, 2,000 arrived at their permanent place of residence, and 1,000 left.

Define:

1. Total fertility rate.
2. fertility rate.
3. Crude death rate.
4. Child mortality rate.
5. absolute population growth.
6. coefficient of natural growth.
7. The coefficient of mechanical growth.

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