Methods of demographic forecasting. Start in science Hypotheses and scenarios of demographic forecast

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Introduction

The relevance of research.

Traditionally, long-term population forecasting is the means by which population-to-resource projections are determined. The problem of any civilization is the ratio of resources and population. In the event of a shortage of the first, civilization is doomed to extinction. However, the modernization of life and fast the economic growth in a number developing countries and countries with transition economy in the foreseeable retrospective, they lead to the fact that these countries stand on a par with the developed ones, while continuing to remain different in culture, preserving their civilizational identity, different from the Western one. Recent political events on the world stage (election of US President Donald Trump, UK withdrawal from the EU) determine that we are moving from the globalization agenda to the creation of regional political and economic unions. In this regard, additional questions arise related to the long-term forecast: what will be the ratio of the population in largest countries ami?

Taking into account recent demographic trends (gradual growth of the world population), it can be argued that a strategy for the survival of mankind is needed, which ensures the growth of prosperity and the preservation of ecological balance. At the same time, there is a problem of the interaction of civilizations associated with the fact that the natural population decline begins in developed countries, and in conditions of successful catch-up development, it is the population that becomes an important resource that determines the comparative potential of countries and civilizations.

In this project, made on demographic development modern civilizations to determine global problems. The value of this project is due to the fact that the studied material can be applied in the study of geography at school.

Object of study: population as an element of demographic dynamics.

Subject of study: change in the population in the countries of the first "ten" for this parameter.

Purpose of the study: predict the change in the population of the countries of the world included in the top ten in this parameter.

Research objectives:

1. Study the sources on this issue;

2. Find out the population of China, India, USA, Indonesia, Brazil, Pakistan, Bangladesh, Nigeria, Russia, Japan;

3. Describe the essence of the age shift method for population forecasting;

4. Using this method, make a population forecast for the above countries.

Research hypothesis. An increase or decrease in population is in direct correlation with the average annual rate of general population growth.

Research methods. Analysis and synthesis, statistical.

1. Demographic forecast 1.1 Essence of the age shift method for population forecasting

In connection with the growing role of the demographic factor in socio-economic planning, prospective calculations of the size and composition of the population are relevant. Mathematical modeling is useful in solving this problem. The development and use of various kinds of mathematical models serve both to analyze the reproduction of the population as a whole, and to identify patterns in the development of certain demographic processes. When modeling, certain initial assumptions are made regarding the main components of the process (fertility, mortality, migration, etc.). On this basis, other characteristics of the population and its structure are calculated.

A special place in mathematical modeling is occupied by the method of shifting ages (or the method of components), developed by P. K. Welpton. S.G. Strumilin, A.Ya. Boyarsky, P.P. Shusherin, M.S. Bedny, S. Shcherbov, V. Lutz, W. Sanderson, and the United Nations Population Commission, State Committee Russian Federation in statistics, Center for Human Demography and Ecology.

The method of shifting age groups is quite effective for short-term forecasts with horizontal planning for a period of no more than 10 - 15 years.

The study was conducted on the basis of open statistical data. To achieve the goal of the study, using the method of shifting ages, we calculated the estimated population of the countries included in the top ten. Age movement is understood as the transition of persons of age X to the next age X + 1, while the number of these persons decreases due to mortality and a decrease in the birth rate, and also changes due to migration. Thus, the replacement of generations is ensured, which is decisive for reproduction. labor resources. In our case, we do not make shifts for individual age groups, but calculate for all age groups.

The countdown was carried out from the population in 2011 on the basis of the average total increase / decrease in the population for 2011-2015. based on the assumption that the increase/decrease in population will remain constant annually.

1.2 Forecast of the population of the studied countries

In this part of the work, we carried out a forecast of the population of the countries included in the top ten for this indicator. The methodology for this process has also been described above. The initial data for calculations included the population size for 2011, 2012, 2013, 2014 and 2015. A five-year sample makes it possible to determine the value of the average annual population growth, on the basis of which a population forecast will be made. These data are given in table. one.

Table 1.

Population of the leading countries of the world for 2011-2015

Source: 2.

From the tabular data, we can conclude that in general there is an increase in the population in these countries in 2015 compared to 2011 by 5%. Russia is consistently among the top ten largest countries in the world in terms of population. We deliberately did not reduce absolute values ​​to fractional indicators in order to maintain the accuracy of calculations.

Rice. 1. Change in the population of China.

The population of China increased from 2011 to 2015. The population increased by 3.9%. The trend is positive. China's population growth is affected by the 2016 ban on having a second child. Over the 36 years of this restriction, side effects have appeared. The negative consequence is that the number of able-bodied population decreases every year. And in a few years, a situation may occur when the number of pensioners will exceed the number of able-bodied persons responsible for filling China's pension budget.

The same situation with the population is observed in India. But here there was no narrowed reproduction of the population, so the age structure is younger.

Rice. 2. Change in the population of India.

The population increased from 2011 to 2015 by 8%. The trend is positive. But if in the two Asian "giants" the population grew due to natural increase Since the Asian mentality is not very to the liking of possible migrants from Western countries, the US population has increased mainly due to migrants.

Rice. 3. Change in the US population.

During the study period, the population increased by 2%. The trend is positive.

The situation is different in Indonesia.

Rice. 4. Population change in Indonesia.

From the graph, we can see that from 2011 to 2014 the population increased, but later from 2014 to 2015, the population fell sharply. Currently, the population has stabilized. We see the reasons for the sharp fluctuations in the socio-economic situation.

Brazil's population is also growing unevenly. There is no positive trend here, and the population is growing cyclically.

Rice. 5. Population change in Brazil.

According to the graph, we see that the population rose from 2011 to 2012, but then over the year it fell sharply, but later from 2013 to 2015 it began to increase. It increased by about 3%.

Rice. 6. Population change in Pakistan.

From the graph, we can see that the population of Pakistan has been increasing from 2011 to 2014. But later, from 2014 to 2015, the population fell sharply. It increased by about 3%.

Rice. 7. Population change in Bangladesh.

We can see that the population increased from 2011 to 2015. It increased by about 6%. The trend is positive.

Rice. 8. Population change in Nigeria.

According to the graph, we see that the population increased by 118% from 2011 to 2015.

Rice. 9. Change in the population of Russia.

According to the graph, we see that at first, from 2011 to 2012, the population decreased slightly, but later, from 2012 to 2015, it increased by 5%, including due to the annexation of Crimea and the stabilization of the birth rate. The trend is positive.

Rice. 10. Change in the population of Japan.

From the graph, we can see that in Japan from 2011 to 2012, the population increased dramatically, but later from 2012 to 2015, the population declined. The trend is negative.

After determining the demographic trends, we determined the values ​​of the total and average annual growth by years. These data are given in table. 2.

Table 2.

The values ​​of the total population growth for the countries studied

Based on the data, calculations were made of the projected population for 2016-2019. This is presented in Table. 3.

Table 3

Projected population

Demographic forecasting methods include:

1) extrapolation methods;

2) the method of shifting ages;

3) methods of statistical modeling.

The application of extrapolation methods for estimating the future population is based on the assumption that the identified trends in fertility, mortality, migration will be unchanged over the forecast period.

The most approximate estimates of the future population size using the extrapolation method can be obtained by means of generalizing dynamics indicators:

1) extrapolation based on the indicator of average absolute growth:

where?? – indicator of average absolute population growth;

St is the projected population in year t;

S0 is the population at the beginning of the forecast period;

t is the forecast period;

2) extrapolation based on the indicator of the average growth rate:

where ?xt– indicator of average absolute increase;

3) extrapolation based on the indicator of the average growth rate:

where ?xpr is an indicator of the average growth rate.

Age shift method called the method of calculating the age and sex structure of the population in the future. It is based on the use of data on age composition population and survival rates from mortality tables.

The essence of the age shift method is that the population age group x at a point in time t calculated as the product of the population of the age group ( x-) at a point in time (t-1) and the survival rate for a given age group, showing what proportion of persons aged ( x-1 ) will live to age x years:

If the age composition of the population on a certain date is known, then it is possible to calculate the estimated population at each age in a year, two, etc. (excluding migration).

To determine the possible number of births, data on the age composition of women aged 15–49 and special birth rates are used:

where ToR.spec.x is a special fertility rate for women aged X years;

?Sxt is the average number of women aged X years.

essence statistical modeling methods consists in applying for demographic forecasting regression models that characterize the dependence demographic phenomena from the selected factors.

A separate group includes mathematical modeling methods that involve the use of models based on the use of mathematical functions (for example, an exponential curve, parabola, etc.).

If the population at the beginning of a certain period is known, then the prospective population in t years can be determined based on the exponential law of population growth using the formula:

(RU)- natural population growth;

(P-V)– mechanical population growth;

?S– average annual population;

t is the forecast period.

The methods for calculating the total population have been presented above. Of great importance for the purposes of socio-economic planning is the forecast of the future composition of the population, primarily by age and sex. To calculate individual age groups (as well as by sex), the age shift method is used (abroad, more often called the component method).

The essence of the method is that the initial population, as it were, "moves" into the future, decreasing at the expense of the dead (and those who left) and replenishing at the expense of those born (and those who arrived). Therefore, for the forecast, it is necessary to know the basic size and structure of the population, as well as hypotheses regarding the trends in the reproduction and migration of the population in the forecast period.

The movement is carried out in time steps equal to the length of the age group. To do this, the size of the age group of the population at the beginning of the forecast period is multiplied by the coefficient of displacement (survival). The displacement coefficient is the ratio of two numbers of adjacent age groups: those living at the age of "x + 1" and "x" ( and ), taken from the mortality table. In this case, the migration balance should be taken into account.

The age shift model has the form:

, (7.17)

where is the size of the age group " ";

- the number of age group " ";

- coefficient of shifting to the next age (probability to live at the age of " ");

MS - migration balance.

Using the migration balance coefficient, the age shift model looks like this:

, (7.18)

Task 7.3. It is required to determine the prospective number of people aged 4 years at the beginning of 2009 by the age shift method, provided that the existing trends of natural and mechanical movement persist, if the following conditional data on the population size for the region at the beginning of 2005 are available. (table 7.1).

Table 7.1

Initial data for calculating the prospective population

Component method opens before developers demographic forecast wider possibilities. Unlike extrapolation and analytical, it allows you to get not only the total population, but also its distribution by sex and age*.

The component method was developed by the American demographer P.K. Welpton (R.K. Whelpton, 1893-1964). Cm.: Bogue D.J. Techniques for Making Population Projections: Age-Sex Projections. Chicago, 1980. P. 8. Reprinted in:Readings in Population Research Methodology. Volume 5. Population Models, Projections and Estimates. Chicago, 1993. P. 17-7-17-10.

The double name of this demographic forecasting method (the method of components, or the method of shifting ages) is due to the fact, firstly, that its application is based on the use of the demographic balance equation, which was discussed in Chapter 3:

where P 0 and P 1 - population, respectively, at the beginning and end of the period (year); AT- number of births for the period; D - number of deaths for the period; M i - migration inflow for the period; M 0 - migration outflow for the period. Wherein AT,D, M i and M 0 are called components of population change over a period (year).

Secondly, due to the fact that data on the number of individual age and sex groups move around each year at the next age, and the size of the zero age group is determined based on the forecast of the annual number of births and infant mortality.

The essence of the component method is to "track" the movement of individual cohorts in time in accordance with the given (forecast) parameters of fertility, mortality and migration. If these parameters are fixed at some initial time t 0 , then remaining unchanged throughout the period  then this uniquely determines the size and structure of the population at the time t 0 +  t

Starting from time t o, the population of each individual age decreases in accordance with the predicted age-specific probabilities of death. The number of deaths is subtracted from the initial population of each age, and the survivors become one year older. Projected age-specific fertility levels are used to determine the number of births for each year of the forecast period. Those born also begin to experience the risk of death in accordance with its accepted levels. The component method also takes into account age-specific migration rates (arrivals and departures).

The procedure is repeated for each year of the forecast period. This determines the population of each age and sex, the total population, the general birth and death rates, as well as the rates of general and natural increase. At the same time, predictive calculations can be made both for one-year age intervals

fishing, and for different age groups (5-year-olds or 10-year-olds). The technique of prospective calculations is exactly the same in both cases. Prospective calculations are usually made separately for the female and male populations. The population size of both sexes and its age structure is obtained by simply summing up the female and male populations. At the same time, all forecast parameters of fertility, mortality and migration may change for each year or interval of years of the forecast period.

In practice, population forecasting is carried out onbased on age data for each sex inseparately (on an age- specific basis). give birthbridge is expressed in its age-specific coefficientsentah. The strength of mortality is expressed in terms of ageprobabilities to live to the next ageta (as age- specific survival rations) separately formen and women. Migration is usually measured in terms of expected annual net migration,classified by sex and age. More thantemporary trend is the desire to clarifythread migration, highlighting, where possible, the influx andoutflow.

Calculations are made in terms of the "forecast cycle".zation", each of which is usually equal to 1 yearor 5 years. Starting with censuses or otherinput data, the demographer consistently takestakes data on births, deaths and migrationduring one forecasting cycle,then summing the results to get an estimatepopulation at the date marking the end of the cycle.Population at the end of the cycle, calculated usingthis operation, in turn becomes the outcomenym for the next cycle. Forecast cyclerepeated to get the population estimate fornext date in the future. This is repeated untiluntil the date for whichtorus and the forecast is built. A feature of this procedure is that the forecaster can usecall for each forecast cycle differentbirth, death and migration values. As soon as for each cycle the sets of vethe names of each of the components, the computational

The process is reduced simply to substituting the obtainedvalues ​​into the demographic balance equation.It follows from the above that the validity(validity) and utility (utility) forecast depends onthe accuracy of the source population estimate and the accuracyty predictions of future fertility parameters,mortality and migration.

Bogue D.J. Techniques for Making Population Projecttions: Age-Sex Projections. Chicago, 1980. P. 8. Reprinted in: Readings in Population Research Methodology.Volume 5. Population Models, projections and Estimates. Chicago, 1993. P. 17-7.

Let us show, for simplicity, how a prospective calculation is made using the example of one-year age intervals for the female population.

Let at some initial time t o (base year of projection) female population aged X years

is equal to R x 0 . During the year, the initial number will change: part of the population will die, another part of the population will leave this territory, someone, on the contrary, will come to live in it. As a result, the population of age (X+1) at a point in time t 1 will be equal to:

(L x and L x + l - number of people living in ages X and X+1 from mortality table), M s x - balance of age-specific migration.

The same procedure applies to all ages except for the age of 0 years.

The size of the age group 0 years at time t 1 is calculated taking into account both the birth rate and infant mortality and migration, since not all those born during the year will survive until the beginning of the next year, and since there is, albeit small, migration at this age too. First of all, the number of births during the year is calculated. This number, as is known, is equal to the sum of the products of age-specific fertility rates by the average annual number of women of the corresponding ages:

where AT- annual number of births; ASFR X - age-specific fertility rates; F x - the average annual number of women in

age X years. To get the number of girls born separately, AT multiplied by (1-5), where 8 is the proportion of boys born, which ranges between 0.507 and 0.517, but is usually taken to be 0.512 (this corresponds to a secondary sex ratio of 105 to 100). Then, the number of births thus obtained is corrected using the survival function adopted for the forecast, as well as using the net migration data for this age, obtaining the population of age 0 years by the beginning of the next year.

The procedure described above is iteratively repeated as many times as the number of years covers the forecast period. The population of each age, as it were, moves to the next, older age. That is why the component method is also called the “age shift method”.

This can be visualized as follows (Table 8.1):

Table 8.1

Demographic projection scheme usingshifting ages

As a result, for each year of the forecast period, both the total population and its age and sex structure are obtained, as well as, as mentioned at the beginning of this section, the general birth and death rates.

An indispensable condition for the application of the component method (age shifting) is the preliminary development of a pro-

forecasts of fertility, mortality and migration. However, if the application of this method in itself is a purely technical task, then forecasting the dynamics of demographic processes requires a lot of analytical work, knowledge of the patterns of changes in fertility, mortality, migration, and their relationship with socio-economic factors. You can even say that such forecasting is somewhat akin to art.

At present, the solutions of purely computational problems of applying the transfer method are completely transferred to the corresponding computer packages. In particular, it is necessary to point to such packages developed by the UN as DemProj and Spectrum, which make it possible to almost instantly predict the size and structure of the population. The US Census Bureau has developed a RUP computer program that implements the component method 17 .

However, to reiterate, purely computational procedures are the least complex and least interesting part of population forecasting. The meaning of the forecast is not in such calculations, but in forecasting trends in fertility, mortality and migration. In this case, of course, the first step in forecasting should be to assess the accuracy and reliability of data on the size and structure of the population for the base year, since if the information about this is incorrect, any forecast loses its meaning.

If the accuracy and reliability of the initial information on the size and structure of the population is not in doubt, then the next steps in forecasting are to put forward hypotheses about future trends in fertility, mortality and migration*. At the same time, it is necessary to link these hypotheses with each other, although state of the art demographic science does not allow fixing the links between fertility, mortality and migration with the accuracy and reliability necessary and sufficient for their effective use in forecasting 18 .

A feature of forecasting individual demographic processes is that their parameters are determined not for each year of the forecast period, but only for some of its points. After that, the obtained values ​​are interpolated for intermediate dates. In this case, very often interpolation is reduced simply to the assumption that the parameters of the de-

* Issues of forecasting migration are not considered here.

mographic processes between reference points. For example, the 1998 UN forecast for Russia proceeds from the fact that, according to the middle variant, the total fertility rate in the period between the five years of 1995-2000. and 2025-2030 will rise from 1.35 to 1.70 births per woman of reproductive age, and then until the end of the forecast horizon, i.e. until 2050, will remain at this level. Intermediate values ​​from 2000 to 2025. calculated by interpolation 19 .

Mortality prediction

The most developed methodologically is the forecasting of mortality. Therefore, let us briefly consider the main methodological methods for predicting the levels of demographic processes using the example of mortality. Mortality forecasting can be carried out in two ways: the first of them assumes that first the overall level of mortality, measured in terms of the average life expectancy of a newborn, is predicted, and then the age-specific mortality rates are estimated for each value of the average life expectancy of a newborn adopted in the forecast. The second way, on the contrary, assumes the reverse order of forecasting general and age-specific mortality levels: first, age-specific indicators are determined, and then, on their basis, a predictive value of the average life expectancy of a newborn is built.

In any case, however, the first of these stages, in turn, consists of two stages: (1) determining the value of the average life expectancy, or age-specific mortality rates, at a given date in the future and (2) determining the trend of this value between the base year and the year for which the calculation is made.

The second stage is basically a purely technical operation, solved using the well-known mathematical techniques of time series interpolation. Determining the future level of mortality (average life expectancy, or age-specific values ​​of mortality) is more creative and is a real scientific task, the solution of which requires a special study.

To determine the predicted values ​​of the average life expectancy, or age-specific mortality values, the following methods are most often used:

rapolation; method of the "law" of mortality; referential forecasting, or forecasting by analogy (in three varieties - (1) comparison with typical mortality tables; (2) comparison with a more “advanced” population and (3) comparison with an “optimal” mortality table calculated for “ideal” conditions) ; forecasting based on the analysis of the dynamics and the forecast of the causes of death 20 . The choice of a specific method depends on the goals of forecasting, the availability and reliability of demographic information, and, importantly, on the amount of resources available to the demographic forecaster.

The simplest method is extrapolation. If the values ​​of this indicator for past years are known, then for a relatively short period of time the future trend can be determined using extrapolation methods using certain mathematical functions. For example, in the case of predicting the average life expectancy, a logistic curve is usually used, since it approximates well the dynamics of this indicator.

When predicting age-specific mortality rates (for example, n q x - probabilities of dying in the age interval (X+ n) years) using certain methods, a certain correction factor is determined that shows the dependence of the selected parameter on time, and the base value of the predicted indicator is multiplied by it to obtain its value for the selected date. Then, if necessary, interpolation is used to obtain its values ​​for intermediate dates. The calculated predictive values ​​of mortality and average life expectancy are routinely used for age shifts.

The second method for predicting age-specific mortality is based on the use of the so-called. "mortality law", that is, a mathematical function that describes changes in the death rate depending on age 21 . Although the history of the "mortality law" dates back almost three centuries, in its modern form it is known as the Heligman-Pollard model *, proposed by the authors in 1980. The model describes changes in the level of mortality, represented by the ratio of the probability of dying at age X years from the mortality table to its supplement

* L. Heligman - English demographer; J.H. Pollard is an Australian demographer.

to 1, i.e. to the probability of surviving to the next age X+ 1

year (q x /1-q x). from age. It is a trinomial

each term of which describes the dependence on age, respectively, of infant mortality, mortality at the age of 15-40 years and mortality at the age of over 40 years.

Forecasting using the “mortality law” consists in determining its parameters (there are nine of them in the Heligman-Pollard model), their subsequent extrapolation to the depth of the forecast horizon, and substituting the predicted values ​​of the “mortality law” parameters into its formula to obtain the values ​​of age-specific mortality levels and, as a result, - average life expectancy. The calculated predictive values ​​of mortality and average life expectancy, as in the previous case, are used to shift ages.

The method of predicting mortality based on the use of its "law" has a number of significant limitations, which creates considerable difficulties for its practical use. More preferred are the methods discussed below, in particular the method of reference prediction, or prediction by analogy.

Its first variety - comparison with standard mortality tables - can be considered as a special case of both the "law of mortality" method and the method of comparison with a more "advanced" population. The forecasting technique in this case consists in selecting the most appropriate, in the opinion of the forecaster, system of standard mortality tables*. Then the parameters of the selected system are determined for a number of periods in the past (usually this is the average life expectancy), after which they are extrapolated to obtain forecast values. In the next step, using the selected system of model tables of mortality, age-specific mortality rates are calculated, which are then used to shift the ages. This method is most often used to predict mortality in the least developed countries, which are characterized by high mortality and low life expectancy.

For developed countries, a more suitable and commonly used

* J. Pollard even says that in "it is believed."

My version of reference forecasting is the comparison with more "advanced" populations, i.e., populations that are considered to be "ahead in their demographic development" of the country for which the forecast is made *.

The essence of this method can be briefly characterized as follows. First of all, a more “advanced” population with good demographic statistics for a long period in the past is selected. At the same time, there is reason to hope that the mortality history of the more “advanced” population will “repeat” for the population for which the forecast is being fulfilled. The mortality characteristics of the latter are compared with those of the more "advanced" population. The identified similarities are recorded. For example, it may turn out that the predicted population with some lag (say, 20-30 years) repeats the population that is more “advanced”. Then the levels of mortality that were characteristic of a more "advanced" population are used as predictive values ​​for the predicted population.

The application of the method of comparison with a more "advanced" population has a number of difficulties, the main of which is the choice of this most "advanced" population. This choice is critical to the success of predicting mortality in this case.

The last variation of the reference method is a comparison with the "optimal" mortality table, corresponding to some "ideal" conditions, the achievement of which is possible in relation to a given population.

The method is based on the recognition of the possibility of the existence of some "optimal" mortality table that describes this demographic process in relation to hypothetical "ideal" conditions. One of the first to raise the question of such a possibility was American demographers P.K. Welpton, H.T. Elbridge and J.S. Siegel in his 1947 US Population Projection. 23 Comparing age-specific mortality data for different states, they found low levels mortality after a certain period of time are repeated at the national level. Based on this observation, P.K. Welpton, H.T. Elbridge

* However, it is quite suitable for both developing and least developed countries.

and J.S. Siegel suggested that the average life expectancy of 68.4 years for men and 71.8 years for women can be considered (taking into account rising living standards and progress in health care) as the lower limit for this indicator in 2000.

Somewhat later (in 1952), the French demographer J. Bourgeois-Pichat asked whether the death rate could drop to 0, or was there a certain limit to this decrease, and if so, what was the limit? In search of an answer to this question, he proposed to divide the causes of death into two categories - exogenous (external, associated with living conditions) and endogenous (internal, associated with natural age-related changes in the body). Using six extended groupings of causes of death and data from Norway, J. Bourgeois-Pishcha estimated the marginal average life expectancy at 76.3 and 78.2 for men and women, respectively 24 .

Closer to our days, the English demographer B. Benjamin put forward several "extreme hypotheses" regarding possible progress in the structure of mortality by cause. On their basis, and using mortality data for England and Wales, he estimated the marginal average life expectancy of 81.3 and 87.1 for men and women, respectively 25 .

Forecasting based on the “optimal” mortality table comes down to the fact that first a suitable mortality table is selected, reflecting the possible progress in the fight against each of the groups of causes of death described by B. Benjamin. A decision is then made about how the projected population will reach the optimal age-specific mortality and how quickly this will happen. After that, predictive mortality values ​​are calculated and used to shift the ages.

The last of the forecasting methods listed above is forecasting based on the analysis of the dynamics and the forecast of the causes of death. The essence of the method, which assumes the availability of good mortality statistics by cause, is to decompose the age-specific probabilities of dying from the mortality table into partial probabilities of dying from individual causes of death and then predicting the dynamics of the latter (for each cause or class of causes separately). The obtained predictive values ​​of partial probabilities

The probability of death by cause is again integrated into the total probabilities of death for each age, which are used in the usual way to shift the ages 26 .

In conclusion, I would like to repeat once again that the choice of a specific method from those described above is determined both by the goals of forecasting, and by available demostatistical information, as well as by available resources.

Fertility forecasting

The most complex and creatively interesting stage of fertility forecasting is forecasting either the general level of fertility (usually in terms of its total coefficient), or its age-specific coefficients. It is at this stage that the theoretical concepts of the demographer-prognosticator, his understanding of the essence of the changes that occur with fertility, and the forces that them callers. Currently, various methods are used to predict the overall level of fertility, ranging from simple extrapolation of its trends into the future, to attempts to develop and apply mathematical models that take into account the relationship between the level of fertility and the socio-economic factors that determine it.

The latter would probably be the ideal solution to the problem of predicting fertility. In this case, the forecast values ​​of socio-economic factors would act as input parameters of the forecast, the output of which would be the values ​​of the total and age-specific fertility rates. Unfortunately, the task of creating such mathematical models has not yet been solved because of its incredible complexity and the need to use huge information and computing resources. One of the possible approaches to solving this kind of problems is the use of the multiple regression method. The essence of this approach is that, based on long-term data on fertility rates and a number of socio-economic indicators (for example, per capita income, the share of employed women, per capita income among women, the marriage rate, the prevalence of contraception, etc., etc. .p.) a multiple regression equation is constructed that relates the birth rate values ​​to the levels of the listed factors 27 .

Most fertility forecasts, however, are made using more accessible and less costly methods.

The simplest method is to extrapolate trends in the total fertility rate into the future using some mathematical function, for example, the same logistic curve. It is this function that is often used to predict fertility in developing countries that are undergoing a transition from high to low fertility. The basis for the application of the logistic function in this case is the long-term statistical dynamic series of fertility, characterizing its decline in those countries where it has already reached low levels. This decline from high to low is best described by the logistic curve. An example is a graph showing how Taiwan's birth rate declined from 1958 to 1987 (Figure 8.1). Having determined the trend of the total fertility rate, it is extended into the future. Then, using standard fertility tables, its age-specific coefficients are calculated corresponding to the obtained predicted values ​​of the total coefficients, thereby setting the input parameters for predicting the size and structure of the population using the component method (age shift). The extrapolation method is usually used to predict fertility in countries with a high level of it.

Another method for predicting age-specific fertility rates is the reference method (implemented mainly by comparison with more "advanced" populations. From a technical point of view, the use of this method for predicting fertility is similar to what was said above about predicting mortality. The only thing worth saying is that is that the comparison of the projected population is made not so much with the levels of age-specific or total fertility rates of "advanced" populations, but with the prevalence and characteristics of the practice of using contraceptives and artificial termination of pregnancy 28 .

In modern conditions, the data of special statistical surveys and sociological surveys, the purpose of which is to identify the reproductive intentions and orientation of the population, play an increasingly important role in predicting the birth rate. We have already discussed studies of this kind and their role in the study of fertility and the reproduction of the population as a whole. The results of these studies are used and

Chart 8.1

Actual and cleared with logistic

functions of the value of the total coefficient

fertility. Taiwan, 1958-1987 29

for forecasting purposes, in particular in our country. Thus, data from six surveys of women's opinions on the expected number of children in a family, conducted by the Laboratory of Demography of the Research Institute of the Central Statistical Bureau of the USSR (nowadays, the Research Institute of Statistics of the Goskomstat of the Russian Federation) in the period from 1967 to 1988, were used to predict the birth rate in the union republics of the former USSR.

In a time closer to us, data from the 1994 microcensus were used to predict fertility trends in Russia.30

8.4. POPULATION FORECASTSWORLD AND RUSSIA

Currently, practical work on the development of demographic forecasts is carried out by international organizations, government agencies and scientific institutions.

The most extensive work in this regard is carried out by the Population Division of the Department of Economic and Social Information and Policy Analysis of the UN Secretariat. This international body regularly, every two years, publishes forecasts of the size and structure of the population, as well as the main demographic processes for the world, in general, for the main regions and for all countries that are members of the UN. These forecasts are available in the form of the fundamental publication "World Population Prospects" 31 , as well as in the form of tables and graphs contained on the web pages of the UN 32 , a number of other international organizations, as well as many universities in the USA, Australia and other countries.

According to the UN forecast (revised 1998), by 2050 the population of the Earth will reach approximately 10.7 billion in the upper, 8.9 billion in the middle and about 7.3 billion in the low*, i.e. it is assumed that over the next half century the world population will increase approximately 1.2-1.8 times 33 . The 2000 projection gives slightly larger population figures for 2050. The high variant predicts 10.9 billion people in 2050, the medium variant 9.3 billion, and the low variant 7.9 billion 34 . The UN experts consider the middle version of the 1998 forecast to be the most probable, although the truth is likely to lie somewhere in the middle between the low and medium versions, given the tendency to overestimate the value of the global population growth rate, which is characteristic of most demographers-forecasters, including working for the UN. True, as can be seen from the above data, another error crept into the 1998 forecast. The authors of the forecast acknowledge that they somewhat overestimated the rate of decline in fertility in a number of developing countries 35 .

According to UN experts, 60% of the 77.8 million annual absolute growth of the world population is accounted for by only 10 countries, and 36% of it - by India and China 36 . At the same time, according to the 2000 forecast, 39 countries will have a smaller population in 2050 than at present. Largest population decline

* However, the low version of the forecast assumes that the world population will reach approximately 7.5 billion people by 2040, after which it will begin to decline.

expected in Estonia (-46.1%), Bulgaria (-43.0%), Ukraine (-39.6%), Georgia (-38.8%) and Guyana (-33.7%). Russia will reduce its number by 28.3% (sixth place in this sad list) 37 .

The "top ten" countries in terms of population over the next half century will change, according to the average variant of the 2000 forecast, as follows (Table 8.2).

The dynamics of the world's population, according to UN experts, will be significantly affected by the further spread of

Table 8.2

"Top ten" countries by population, 2000-2050gg. (thousands of people)

UN 2000 Revision Forecast G. Medium option 38

AIDS. According to the 2000 revision forecast, 45 countries will be most affected by this terrible disease (against 34 countries according to the 1998 forecast). In 1999, in these 45 countries, at least 2% of the population aged 15-49* were carriers of HIV (Human Immunodeficiency Virus). These 45 countries include 35 countries in sub-Saharan Africa (29 countries in 1998 forecast), India, Cambodia, Myanmar (Burma) and Thailand in Asia (Myanmar was absent in 1998 forecast), as well as 6 countries Latin America (forecast 1998

* In total, in 1999, according to the United Nations specialized agency on AIDS, there were 33 million adults living with HIV, of which 29 million, or 88%, lived in these 45 countries (WPP-2000. R. 9).

Brazil and Haiti only). The demographic effect of AIDS is expressed primarily in a sharp reduction in life expectancy. For example, in the 35 African countries mentioned, the demographic cost of AIDS is expressed in the loss of 6.5 years of life (48.3 years instead of 54.8 years, provided that there is no AIDS. In the 1998 forecast, these data were even more pessimistic: for the 29 countries mentioned Africa was expected to lose 7 years of life: 47 years instead of 54). The consequences of this disease are especially terrible in 9 African countries, where the proportion of HIV-infected people is equal to or exceeds 14% of the adult population: at present, the loss in the life expectancy of a newborn in these countries is 12.2 years (10 years according to a 1998 forecast). , by 2010-2015 they will rise to 19.6 years (17 years according to the 1998 forecast) 39 .

If this terrible cost of AIDS is expressed in terms of population losses, then, for example, in Botswana, where 36% of adults have AIDS or are HIV-positive (25% according to a 1998 forecast), the population by 2025 is expected to be 28 % less than it would be in the absence of this disease 40 .

However, even in these countries, population growth will not stop due to high birth rates. However, estimates of future fertility are the weakest point of UN projections, which do not take into account sociological data on reproductive behavior and therefore turn out, like many other predictive statisticians, “are not able to accurately determine the scale and speed of the spread of one-childhood in developed countries and the pace of transition to medium and small children - in developing countries” 41 . As a result, unrealistically high birth rates are included in the forecasts.

Another feature of the world's population in the middle of this century will be the further aging of the population, which will be the result of the combined effect of declining birth rates and rising average life expectancy. The world as a whole will enter a period of demographic old age no later than 2015, even according to the upper version of the forecast 42 . Particularly old will be the more developed regions of the world, in which the main factor in the aging of the population will be aging “from above”. The forecast of the number of the “oldest” (i.e., the population aged 80 years and older) carried out by UN specialists showed a sharp increase in the number and proportion of this age group.

py. So. the number of people aged 80 years and over will grow 5.5 times in the world over the next half century (from 69 million in 2000 to 379 million in 2050), including 5.2 of those aged 80-89 times (from 61 million to 314 million), at the age of 90-99 years - almost 8 times (from 8 million to 61 million), at the age of 100 years and older - 18 times (from 180 thousand to 3.2 million) . At the same time, the proportion of the “oldest” in developed countries is 5 times higher than in countries that are considered “less developed” according to the official UN classification 43 .

A lot of work on forecasting the population of the world and individual countries is carried out by the US Census Bureau. On his Web page, you can find data on the dynamics of the population of the world and all countries up to 2150. 44 As a kind of horror story, you can also find here the so-called demographic Hours, instead of time, showing how the population of the world and the United States is changing. As for Russia, in Table. 8.3 summarizes the main known forecasts of its population, made by both domestic authors and UN demographers.

All the forecasts presented in the table show a steady decline in the population of our country in the next half century. Although the specific forecast figures differ from each other, the commonality of population change trends assumed by different authors is a kind of mutual verification of each of the forecasts, at least in indicating the general direction of future demographic dynamics in Russia.

However, these same differences in specific forecast estimates also indicate a significant methodological weakness, especially in terms of developing specific forecast scenarios for the dynamics of demographic processes, primarily fertility.

In this regard, the work carried out in the early 1990s is particularly indicative. the official forecast of the Center for Economic Conjuncture under the Government of the Russian Federation, recognized by the majority of experts as completely untenable 45 .

Methodological weakness in the above sense is also characteristic of the forecasts of the State Statistics Committee of the Russian Federation, which from time to time demonstrate a decrease in the forecast values ​​of the population of Russia. One gets the impression that official forecasters simply follow the dynamics of the numbers of births, deaths and net migration, under the fluctuations of which they adjust.

Table 8.3

Russian population projections,million people 46

Demographic Yearbook of the Russian Federation 1998. Moscow, 1998. S. 375-377.

"Population Russia 1999. Seventh Annual Demographic Report. M., 2000. S. 170.

"" Ermakov S.P. General trends, regional peculiarities and long term forecast consequences of depopulation in Russia //Demographic processes and family policy: regional problems. Proceedings of the Russian Scientific and Practical Conference (Lipetsk, September 1999). M., 1999. S. 27-28. """ WPP-1. P.523.

WPP-2000. R. 28. * -2011 -2021 * -2025 -2040

correct their predictions. Even the only exception to the above-mentioned tendency to reduce the size of the population with each new forecast says that this is so: the figures for the medium and low versions of the 1998 forecast are higher than the corresponding values ​​for the 1996 forecast. This, in our opinion, reflects the expected then and actually began in 2000, a change in the sign of the dynamics of the number of births, associated with the action of purely structural factors - an increase in the number of women aged 20-24 years old, born in the first half of the 80s.

The methodological value of forecast scenarios is well illustrated by the description of scenarios for the future dynamics of fertility in the latest forecast of the Center for Human Demography and Ecology of the Russian Academy of Sciences 47 . Keyword in these scenarios "stabilizationtion. The differences between the low, medium, and high TFR forecasts come down only to the speed at which this is achieved. stabilization, as well as the levels at which it will occur. At the same time, the high version of the forecast assumes stabilization not as a result of a decrease in the birth rate, but as the completion of its certain growth, albeit to values ​​that are far from reaching at least the level required for a simple replacement of generations.

The motives for choosing such scenarios are not specified in any way, except for the unknown-based hope that “families will fully realize their reproductive intentions about the expected number of children expressed during the 1994 microcensus.” 48 Not to mention the fact that it is unlikely that survey data on the expected number of children in a family should be considered as an unconditional indicator of “reproductive intentions” (this indicator, let me remind you, is the result of a complex interaction between the need for children and existing living conditions, and also about what many demographers forget - the interaction between the respondent and the sociologist), although it reflects the need for children more accurately than others 49 , the transfer of the perception of living conditions in 1994 into the future raises doubts. In addition, even if the predictive value of the expected number of children is higher than other indicators of preferred numbers, it can actually be used only when living conditions do not change or change slowly and in the direction of improvement. In the era of their sharp negative for the vast majority of changes, as happened almost throughout the 90s. and especially in their first half, showing

The expected number can only be used as an upper (and unattainable) limit for the purpose of predicting fertility, to which reality can only more or less (rather less rather than more) approach. It is no coincidence that even in calm conditions, “the expected number at the start of a family is on average realized with a slight shortage by the end of the reproductive period” 50 . As for periods when the living conditions of families and their perception by the population are rapidly changing, then, I repeat once again, even the indicator of the expected number of children, not to mention others, cannot be considered an indicator of future levels of the total fertility rate. Conducted throughout the 90s. measurements of opinions about the reproductive intentions of the population speak about this better than any words and do not need special comments (chart 8.2).

In general, estimates of future fertility, as noted above, are the weakest point in almost all demographic forecasts that do not take into account sociological data on reproductive behavior and therefore turn out to be very far from the real scale and rate of spread of single-childhood and voluntary childlessness in our country.

Chart 8.2

Ideal and desired number of childrenaccording to surveys of women (VTsIOM), 1991-1999. 51

As a result, unrealistically high birth rates are included in the forecasts, which, in turn, overestimate the forecast estimates of the population of Russia. The main reason for this is the lack of attention and interest in the data of sociological studies of fertility, which alone can provide reliable and accurate information about the real reproductive intentions of the population and their dynamics.

The ideal solution to the problem of predicting fertility, as mentioned above, would be the development of a system of macro- and micro-mathematical models that take into account the relationship between the level of fertility and the socio-economic factors that determine it. In this case, the predicted values ​​of socio-economic factors would act as input parameters of a heterogeneous simulation model of fertility, which would result in the values ​​of total and age-specific fertility rates, which in turn would be used as the basis for forecasting the size and structure of the population.

Unfortunately, the task of creating such mathematical models has not yet been finally solved because of its incredible complexity and the need to use huge information and computing resources that our country, apparently, does not have. Perhaps the most advanced part of this system of demographic forecasting models is the development of stochastic fertility simulation models. However, their verification is difficult due to the lack of relevant sociological information about the parameters of reproductive behavior and their dependence on the values ​​of socio-economic factors necessary to determine the probabilities of events that form the reproductive process. A particular deficit is felt in relation to information relating to the 90s. last century - the time of radical political, economic and social changes in our country. The data of the VTsIOM surveys mentioned above cannot make up for this information deficit, since they are, in essence, not sociological studies of reproductive behavior, but only measurements of opinions regarding the preferred family size.

An attempt to make up for this deficit was an initiative project of the Department of Sociology of the Family of the Faculty of Sociology

12. Demographics

theta of Moscow State University, the purpose of which was to identify the dynamics of the lifestyle of urban families in Russia, to assess changes in their living conditions in the 1990s, as well as the characteristics of the reproductive behavior of families, including both the dynamics of the need for children, reproductive attitudes and motives, and its ( behavior) outcomes (births, contraception and abortion practices, etc.). The survey was conducted in 1999-2000. in several regions of the country. In total, more than 900 people, women and men, were interviewed, representing almost all types of families in terms of the number of children in them - from childless to those with more than three children.

An important characteristic of the surveyed population, from the point of view of the tasks of demographic forecasting, is the level of social mobility and orientation towards it. It was measured by a whole system of indicators, of which we will dwell here on only one - on the level of income desired by the respondents, since the latter, among other things, to some extent characterizes the main vector of the social orientation of the individual, satisfaction with the existing situation and orientation towards its change.

If the achieved level of income reflects the situation at the time of the survey and characterizes, rather, the past achievements of the family, which, of course, is very important and informative from the standpoint of identifying reproductive orientations. But from the point of view of their future dynamics, it seems more important to focus on the desired level of income, which reflect one of the most important aspects of social mobility, which is currently one of the powerful social values ​​that modern Russia targeting a growing number of people. The growth of orientation towards mobility, at the same time, is, as it were, alter ego weakening the focus on family values. That is why this indicator (orientation to the desired level of family income) is very important for assessing the predictive dynamics of reproductive orientation, and, consequently, future birth rates.

The survey showed that the vast majority of respondents are not satisfied with the current level of family income. This, however, is not surprising. Few people can say about themselves, especially now, that they are completely satisfied with the level of material well-being of their family. Something else seems surprising: the fact that the degree of dissatisfaction with the income of one's family grows as its level rises. This fact was recorded

already determined by the very first preliminary data of our survey 52 . It is fully confirmed by the final results of the study "Russia-2000". The greater the amount of income, the higher its desired level and the greater the gap between the available and the desired.

What does this mean for reproductive orientations and their future dynamics? It has been proven 53 that the growing gap between the desired and the real, between the level of aspirations and the level of achievements causes an increase in the likelihood that the current living conditions of the family will be assessed as unfavorable for the birth of another child in the family, in order to fully satisfy the family's need for children. Consequently, more income marks not only great achievements, but a deeper transformation of the system of life values, stronger and more significant orientations of the individual towards extra-family values ​​of personal success and prosperity.

At the same time, modern trends cause the spread of such orientations both in breadth and depth. Therefore, in the coming years and decades, we should expect not only an increase in the number of those who believe that their living conditions do not allow them to acquire at least one more child (and regardless of what these conditions “really”, i.e., what they seem to an outsider observer), but also a further decrease in the very need for children as a natural and inevitable result of reorientation to extra-family values.

The decline in the birth rate is not due to some incidental circumstances, but to a historically long and global process of reducing the need for children, caused by a change in the role and place of the family in society. This process has been repeatedly described in detail in the sociological and demographic literature, so there is no need to dwell on it here. According to sociological data, over the past half century there has been a steady and monotonous process of reducing the need for children, the value of which has decreased by about a third every 10-15 years, which is also confirmed by the data of our study.

Since there are no grounds to assert or at least hope that the factors of the family crisis have ceased or will cease to operate, the need for children will decrease in the future as well, unless, of course, a radical change occurs.

fundamental changes in the social structure, or a family policy specifically focused on strengthening the family with several children will not be launched. But the hope for this is very weak. On the contrary, we are witnessing the growth of egoistic individualism and orientation towards prestigious extra-family values ​​associated with personal success, wealth, even if not quite righteously acquired, and so on. The family, however, the farther, the lower it falls on the scale of social values. This is evidenced by the results of almost all sociological measurements. And forecasting the future dynamics and structure of the population of our country is simply obliged to take into account this sociological fact, which, without alternative, indicates that the need for children will decrease, and the growth of social mobility and orientation towards it, one of the aspects of which - income and orientation towards it - was considered above, will determine that the current living conditions of the family will be assessed as less and less favorable for increasing its number of children, no matter what they are. "in fact".

Therefore, it will not be a big mistake to say that, in relation to the next 10-20 years, one should proceed from the predicted value of the total fertility rate of 0.8-0.9 children per 1 woman of reproductive age. And this means that the most pessimistic population projections must be adjusted towards even more pessimism. There can be no doubt that the real population decline will be at least a third greater than that predicted by the low forecasts 54 .

And the depopulation caused by such changes will not be able to compensate for any decrease in mortality (except that one universal immortality is capable of this), nor any immigration policy, no matter how attractive it may be.

Only the awareness of the whole society of the threats that depopulation brings with it, only, so to speak, general mobilization to combat these threats, only the development and implementation of a democratically oriented family and demographic policy, the purpose of which is to revive in the new economic and social conditions a complete family with several children, are able, if not to reverse the depopulation, then at least stop it.

The main features of such a policy will be discussed in the next chapter of the manual.

Exponent extrapolation method

Extrapolation method by average growth rate

Extrapolation method based on the average absolute increase

Mathematical Methods

A. Extrapolation methods - the simplest forecasting methods based on the assumption that the average annual growth rate, average annual absolute and relative growth rates remain unchanged.

Extrapolation methods are used in demography to calculate the total population only in the absence of sharp fluctuations in births, deaths and migration.

Mathematical model according to this method has the form of a linear function:

where is the predicted population level;

– a basic level of population;

– absolute average annual population growth;

t is the forecasting period.

In reality, constant average annual absolute gains can only remain so for a short time, so population forecasting using this linear function can only be used in short-term forecasts.

The mathematical model by this method has the form of a power function:

where: is the average annual population growth rate.

This model assumes an annual change in the population by the same number of times, i.e. its growth (or decline) exponentially.

From the average annual growth rates, you can go to the average annual growth rates, and then the formula can be transformed as follows:

where is the average annual population growth rate.

By transforming the formula, you can determine population doubling period population halving period .

The mathematical model for this method has the form of an exponential function:

where: e is the base of the natural logarithm (2.7183);

where is the average annual population growth rate

The use of an exponential function is more preferable than a linear function and a power function, because this ensures that the population does not become negative.

B. Analytical method- based on the selection of the function closest in its graphical display to the empirical curve.

For example, it is often used logistic function ("logistics" from Greek - the art of calculating, reasoning), the peculiarity of which in demographic forecasting is that its increment decreases as the population grows.

The methods for calculating the total population have been presented above. Of great importance for the purposes of socio-economic planning is the forecast of the future composition of the population, primarily by age and sex. To calculate individual age groups (as well as - broken down by sex) use age shift method(abroad often called the component method).

The essence of the method is that the initial population, as it were, "moves" into the future, decreasing at the expense of the dead (and those who left) and replenishing at the expense of those born (and those who arrived). Therefore, for the forecast, it is necessary to know the basic size and structure of the population, as well as hypotheses regarding the trends in the reproduction and migration of the population in the forecast period.

The movement is carried out in time steps equal to the length of the age group.

To do this, the size of the age group of the population at the beginning of the forecast period is multiplied by the coefficient of displacement (survival). The displacement coefficient is the ratio of two numbers of adjacent age groups: those living at the age of "x + 1" and "x" (and ), taken from the mortality table. In this case, the migration balance should be taken into account.

The age shift model has the form:

where is the size of the age group " ";

- the number of age group "";

- the coefficient of movement to the next age (the probability of living at the age of "");

MS - migration balance.

Using the migration balance coefficient, the age shift model is as follows.