China population growth forecast
abstract
This paper solves the problem of population growth forecast in China. Leslie model is a common model for population prediction.
Type, but due to its shortcomings-the model is easily affected by the specific situation of a certain year and the prediction time is short.
The longer the span, the lower the accuracy of the model. A Leslie model based on weighted improvement is proposed.
The accuracy of Leslie model comprehensively uses the data of several years and distinguishes the time distance of the data to predict a certain year.
According to the data of China population survey in 20001-2005, it is predicted that
Population size and structure from 2006 to 2080; It is concluded that the peak of population appears around 2030, and the peak value is 14.3.
1 100 million, the peak of aging index will reach its peak around 2050.
Based on the interaction between population problem and economic and educational level, two characteristics of population are established.
The linear logarithmic equation of the relationship between GDP and per capita income is constructed, and the model parameters are fitted by multiple regression respectively.
Considering the problems of aging population and unreasonable population structure in China at present, a forecasting model is adopted.
According to the obtained data, we appropriately changed the value of the total fertility rate to reflect the influence of policy changes on the model.
It is concluded that if the second child is opened in 2025, the peak population will be delayed to 2050, with a peak value of 65.438+0.53 billion.
The degree of aging will also decrease.
Finally, the advantages and disadvantages of this model are evaluated.
Population forecast; Leslie model; Weighted model; multiple regression
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I. Restatement of the problem
1. 1 problem background
China is a populous country, and the population problem has always been one of the key factors restricting the development of our country. because
Since the implementation of the family planning policy in the early 1980s, the population has been effective to some extent.
Control, compared with the open policy for more than 20 years, has reduced the population by more than 400 million. At the same time, because most of the population is working at this stage.
China's GDP per capita has developed rapidly in the dynamic era. But due to 2005-2020, I am 20 years old.
The number of women of childbearing age aged -29 will reach a peak. At the same time, due to the independence during the implementation of the family planning policy,
Children are also entering childbearing age, and the current fertility policy will improve the fertility level, which leads to the middle school.
The arrival of the fourth baby boom in China.
Due to the implementation of the family planning policy for many years, the family composition presents a "4-2- 1" model, while the labor force
The burden of power is getting heavier and heavier. According to the survey in 2000, the proportion of the elderly population over 65 years old exceeded 7%. According to China,
By international standards, China has entered an aging society. The aging of China society is fast and large.
The characteristics of "getting old before getting rich" have a negative impact on future social and economic development and social security.
At present, the sex ratio of the population continues to rise. "108-11-165438" broke the balance of population sex ratio, and also gave
Social stability brings unstable factors.
A large number of rural people go to work in cities, which not only provides a lot of labor for cities, but also promotes the countryside.
Economic development. At the same time, the number of people with higher education has increased significantly, and the proportion of people with primary education has gradually increased.
Decline promotes the process of urbanization.
1.2 problems to be solved
Based on the above conditions and the processing of relevant data, the short-term effect of the model on population growth in China is established.
Period and long-term trend forecast.
Two. problem analysis
Population is influenced by population structure, birth rate, mortality rate, aging, economic level, urbanization, poverty and other factors.
Education level and other factors. Based on this, we first establish an improved weighted Leslie model.
Future population forecast considering age structure. Based on the data predicted by this model and the influence of aging index on population.
Make predictions about aging. On the basis of the basic model, from simple to complex, the influencing factors are gradually added.
After analysis and processing, a more comprehensive population forecast is finally obtained.
It is pointed out that the fertility rate of women of childbearing age in cities and towns in 2003 was obviously different.
It's too low to be realistic. After careful observation, we find that the data is roughly different from other years.
An order of magnitude, so we changed the fertility rate of women of childbearing age in the appendix from one thousand to one hundred in 2003. .
Three. Noun Interpretation and Symbolic System
three
2. 1 noun explanation
Sex ratio at birth: it is the ratio of the number of live-born boys to the number of live-born girls, and the number of girls usually used is 100.
When a corresponding number of baby boys. Under normal circumstances, the sex ratio at birth is determined by biological laws.
Held between 103 and 107.
Total fertility rate: the total fertility rate of women of different age groups in a certain period (such as a certain year), indicating each
A woman spends her reproductive period according to the fertility rate of all ages in a certain year, and the average number of children she may have is a balance.
One of the most commonly used indicators of fertility level.
Replacement level: refers to a fertility level, that is, the number of daughters born to the same group of women can just be replaced.
By themselves. Once the level of birth replacement is reached, birth and death will gradually become balanced, and there will be no international migration.
In the case of migration and emigration, the population will eventually stop growing and remain stable. The time required for this process
It changes according to the age structure of the population. At present, the fertility rate in almost all developed countries has reached or is very low.
At the replacement level. It is generally believed that the total fertility rate is 2. 1, that is, it has reached the level of fertility replacement. The reason is 2. 1.
Instead of 2.0 (one child corresponds to one parent), it is because there are slightly more boys at birth.
In terms of the number of girls, some girls will die before their childbearing age. The mortality rate in developing countries is relatively high, so,
The total fertility rate of birth replacement level is generally higher than 2. 1.
Birth rate: Also called total birth rate. Refers to a certain period, usually a year, when a specific area is newly developed.
The ratio of the number of births to the mid-term population or the average population in the same period is expressed in one thousandth. This article
The birth rate in this chapter refers to the annual birth rate, and the calculation formula is:
Birth rate = 0
× 100 0
Average population years
Number of years of newborn population
Among them, the number of newborns refers to the number of months of pregnancy when leaving the mother without considering any accidents.
Have you ever had any life phenomena such as breathing in the morning and evening or other baby figures? Average headcount year refers to the headcount at the beginning of the year.
The average number of people at the end of the year can of course be replaced by the number of people in the middle of the year.
Mortality: Also known as total mortality. Refers to the number of deaths in a specific area within a certain period of time, usually within one year.
The proportion of population to the average population in the same period is expressed as one thousandth. Appear in this article
Mortality refers to the annual mortality rate, and the calculation formula is:
Mortality rate = 0
× 100 0
Average population years
The years of death
Population aging: refers to the phenomenon that the proportion of the elderly in the population is increasing. Aging index: expressed by the formula as follows
Aging index = 0
× 100 0
life expectancy
Average age of population
four
2.2 Symbol system
K: age group, k = 0, 1, 2, …, 90.
According to the population structure data predicted by the improved Leslie model based on weighting, and then refer to foreign teaching.
According to the experience of education level development, we can predict the growth of China's per capita GDP and predict the per capita GDP.
Numerical values can in turn predict the natural population growth rate.
4.4 Suggestions for decision makers:
At present, the problems of aging population and unreasonable population structure in China are serious and need to be reformed in time.
Change some population policies to alleviate and solve these problems.
Principles of policy change
(1) The total peak population should be controlled at around1.500 million.
(2) Maintain sustained economic development.
(3) Avoid the rebound of low fertility level.
In order to avoid the rebound of low fertility level and the out-of-control population size, the policy opening time should not be too early.
In 2020. As we know, China began to implement the family planning policy in the early 1980s.
The implementation of the policy has been relatively common in ten years, and this group of only children will reach childbearing age around 20 15.
Age, in order to alleviate the problem of aging, and the problem that the only child is overburdened with supporting the elderly, to avoid continuous
Both generations are only children, and the policy opening should be no later than 2030. To sum up, we put the policy
The implementation time is scheduled for 2025.
The open population policy we are talking about is to allow the birth of a second child.
Almost all developed countries have reached the replacement level. It is generally believed that when the total fertility rate is 2. 1,
That is, it has reached the level of fertility replacement, so we set the policy-adjusted total fertility rate β (t) as 2. 1.
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It can be seen that after the policy adjustment, the population peak will be postponed to around 2050, and the population peak will be reached.
65.438+0.5 billion, in line with China's goal of controlling the peak population at around 65.438+0.5 billion. But also for our country.
Long-term development is beneficial.
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It can be seen that after the policy adjustment, the aging index has declined to a certain extent and can be slowed down to a certain extent.
Solve the problem of population aging.
It can be seen that the per capita GDP has not changed much before and after the implementation of the policy, which is due to the control of the population, and
The quality of the population and the level of urbanization are constantly improving.
V advantages and disadvantages of the model
5. Advantages of1mode
(1) The improved Leslie model based on weighting established in this paper makes full use of data and overcomes transitivity.
Leslie model only takes advantage of the limitations of data in a certain year, and also retains the population data in time.
Continuity, the prediction results prove that this improvement is feasible.
(2) The model does not blindly adopt the idea of weighting, but distinguishes control variables from state variables.
Physical properties are different and considered in different ways.
(3) The model not only predicts the data of population itself, but also studies the relationship between population growth and economic growth.
The parameters of the model have high fitting degree and significance.
(4) The model simulates policy changes by changing control variables, which makes the model more realistic.
It has important guiding significance.
(5) The model takes into account the differences between urban and rural areas and the sex ratio of the birth population, which is in line with the national conditions of China.
5.2 Shortcomings of the model
The (1) model does not consider the influence of population migration and environmental factors on the model.
(2) There is no sufficient theoretical basis for determining the weight.
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The extension direction of intransitive verb model
(1) The effects of population migration, environment and population quality improvement on the model can be considered.
(2) In terms of policy adjustment, the formulation of policies can be considered from "only having one child" to "opening a second child"
Super-policy can conditionally open the second child, such as allowing both husband and wife to be the only child's home.
The soft landing of this policy change can not only alleviate social contradictions to a certain extent, but also
In order to maintain the achievements of family planning and avoid the rebound of low fertility level.
(3) When determining the weight, it can be determined according to the repeated verification of historical data.
Seven. refer to
[1] Tan Yongji et al., Mathematical Model, Shanghai: Fudan University Press, 2005.2.
[2] Li Zheng, an empirical test of the economic and educational factors of population growth in China, Northwest Population, Volume 28,
The second issue in 2007
[3] Jiang Qiyuan, Mathematical Model, Beijing: Higher Education Press, 2003.
[4] Wang Mojie, MATLAB and Scientific Computing, Beijing: Electronic Industry Press.
[5] Liu Jiashu, an empirical analysis of the relationship between population structure and economic growth in China, Journal of Anhui University of Technology, No.24.
Volume 2, April 2007.
[6] Xue, Chen Yangquan. MATLAB to solve the problems of advanced applied mathematics. Beijing: Tsinghua University Publishing House,
2004.8。