Research on Prediction of China ’ s Population Development from 2008 to 2050

Population system is a typical grey system. In this paper, we establish two new grey models of population prediction: discrete grey increment model(DGIM) and grey increment model with new initial value(NGIM). By contrasting, we did simulation and test prediction through utilizing a large amount of data. The results indicate that the two new models prove more accurate than GM(1, 1) model and other models. According to the latest statistical data of China’s population from 1949 to 2007, we predict the population development of China up to the year 2050 based on the two new models. Evidence shows that at the end of 2008, 2010, 2020, 2030, 2040 and 2050 the total population will reach 1.32789, 1.3403, 1.3917, 1.428, 1.454 and 1.472 billion, respectively.


Introduction
China has the largest population in the world, reaching 1.32129 billion at the end of 2007(except Hongkong, Macao and Taiwan), which makes up one fifth of the world's total.The immense population acts as the leading factor controlling the socio-economic development.During the 58 years after the foundation of People's Republic of China, it has experienced a 21-year high-increment stage and a following 37-year low-increase stage (see Table 1and Figure 1).1949 to 1970 was a stage of high birth and low mortality rate instead of high birth and great mortality rates prior to 1949 and thus a period of sharp drop of crude mortality compared to the high birth rate of >30‰ to 37‰, where the sharp fluctuation is an exception in 1959 to1961 for natural disaster-hit years.The yearly increment of Chinese population had reached the first population peak of 23.21 million, when the yearly growth rate was 28.77‰ till 1980.The period from 1971 to present is one dominated by birth rate, which had formed a second population peak of 17.93 million till 1987, with mortality reduced to < 7‰, showing that the fast increase in population is suppressed, leading to significant decrease in the birth rate and natural augmentation.Total fertility rate (TFR) of women has been reduced from 5.8 to 1.8 since 1970s, which makes China enter into the low level of birth country half a century ahead of other developing countries (PRC, 2006).
Till the end of the 1990s the reproduction of population reached a stage of low birth rate, low mortality rate and low augmentation rate, an eventful change of the problem that China took a bit more than 30 years to realize compared to the period of nearly 200 years taken by foreign countries.China has achieved the struggling goals successfully, which are demanded by the white book "Population and development for the 21st century in China " of PRC State Council and the Fifteen Planning, to control the total population in 1.33 billion and to control the annual natural growth rate in 9‰ at the end of 2005(Research, 2007)).China has added up to reduce 400 million population after carrying out the policy of family planning 30 plus years, which delayed the world population date of 6 billion 4 years, suppressed the fast increase in population effectively, promoted the development of economy and society, strengthened the comprehensive national power and improved the living standard of people.We also made solid foundation for modernization construction and implement the well-off society in all round way.Meanwhile, we have made outstanding contribution for the world population's development and control.However, the problem of population's increase is still terribly grimness, as china has oversize population.In the period of the eleventh five-years planning, China will receive the forth birth population peak.From 1990 to 1999, the average annual net increase population was 12.73 million, and from 2000 to 2006 it was about 8.09 million.Those people will consume about thirty or forty percent of new increasing GDP, which exerts great pressure on socio-economic development.China's modernization requires population's increase in harmony with economy, society, resources and environment on a sustainable basis.Thus, the current basic tasks of most importance and urgency for building the overall society in all round way are to make a stabilization of low birth rate, to improve their quality and structure, to redistribute the population and to ensure the security of population.Consequently, scientific prediction of the future population situation is of great significance to the strategic decision-making for socio-economic development in our country.

Establishment of two new grey-increment models
We usually adopt the model of self-regression or the processing calculation method of population's age on the basis of time sequence analysis for the prediction of population.The premise of the self-regression model must be a smooth sequence.If not, the prediction precision might not be great, even lack of the prediction function as the irrational choice of the expositive variables or unreasonable design (Zhao, 2003, Fan, 2003).The processing calculation method of population's age is hard to calculate precisely, because it involves the structure of population's age, the mode of women's bearing, the mode of population's death and so on.Theory on grey systems has as its research object "uncertain systems with information partially known and partially unknown" that are small-sampled and poor-information, and the research is undertaken largely by extracting useful information from the generation and exploitation of the part of known information to realize the correct understanding of the system's operation pattern and viable control (Liu, 2004).The population system is a typical grey system and is thus suitable for being studied by using a grey model to extract and gain insight into an inherent law contained in synthesized greyness factors of primitive time series.The literatures (Men,2004, Men,2005) first brought forward the grey increment model of population's prediction, which gave full play in the contribution of increment information to the population increase.Thus, we got higher prediction precision.This article is based on the grey increment model, and is trying to establish two new grey prediction models with higher precision and more stability for extended and long-range predictions.
Assume the output of the population's system to be non-negative time series To make the economic increment information contribute as much as possible to economic growth and get still higher prediction precision, the authors do not construct a prognostic model based on the total population sequence shown in Table 1 but a special treatment of the raw series, i.e., a first-order accumulative subtraction operator, in order to separate the increment part. ( Followed by first-order accumulative addition of the increment time series (0)  x through 1-AGO (accumulating generation operator) to get a newly-generated sequence (1) x , namely,

1 Establishment of discrete gray increment prediction model (DGIM)
Make a discrete GM (1, 1) prediction model where 1 β and 2 β are coefficients to be determined, obtained through the following expression via the least squares method ( ) ( ) (1) (1), 1 (2), 1 ( 1), 1 , the solution is the time response function in the form And then the result is retrieved to the total by means of (0 The model presented here is called a discrete grey increment model(DGIM).When setting up a general GM(1, 1), the basic form (0)   (1) = is a continuous one.The parameters got from the basic form are put into the whitenization equation, which makes prediction precision degradation from the discrete form to the continuous form.Therefore, a general GM(1, 1) can get a high prediction precision only when the model is used for short-range prediction or the development coefficient -a is small.The model of discrete grey not only conquers this problem, but also solves the problem of GM(1, 1) about stability on a certain extent (Xie,2005).

2 Establishment of grey increment model with new initial value (NGIM)
Make (1)   Z mean generation of consecutive neighbors sequence of (1)  X , ( ( 2), (3), , ( )) where (1)   (1) (1) . We usually get 0.5 α = and establish the grey model Where a and b are coefficients to be determined, obtained through the following expression via the least squares method 1 ˆ( , ) ( ) The solution is the response function in the form Where (1) ( ) x m d mean select m from 1 to n in turn.After comparing we can choose m, which makes the response function the least average error, and establish the best prediction model.When 1 m = , it is just the general GM(1,1).In the common condition, we can get satisfactory prediction precision, when m n = .Then the result is retrieved to the total by means of (0) (0) (0) ( 1) ( ) ( ) p t p t x t + = + .We call it the grey increment model with new initial value (NGIM) as we adopt (1) ( ) x n to be the new initial value.The initial value (0) (1) x of the general grey model is not related to its prediction of it, which does not make good use of the original sequence's information, so it doesn't fit for the least information principle of the gray system theory.Thus, it also produces some errors in the prediction.According to the theory of new information first, we can improve the prediction precision of grey model by putting large weight on new information.Meanwhile, we can make full use of the "least information", optimize and improve the model by means of the initial value (1) ( ) x n replace the original value (0) (1) x .Thus, we can improve the prediction precision effectively.We adopt the above two new gray increment models in the following passage, to make demonstration research on the short-term, medium-term and long-term prediction of China's population (Zhang, 2002, Dang, 2005).

1 Testing Prediction of the Population of China from 2005 to 2007
To select a suitable model, we single out 5~9 dimensions short series to construct general-type GM (1, 1) model, DGIM model and NGIM model for experimental prediction of the total population of China from 2005 to 2007.Test shows that the 6-dimension model gives the closest result, which is thus taken for use, with the values from all the gray prediction models summarized in Table 2, 3 and 4. Comparison of tests of table 2 to 4 indicates that models of DGIM and NGIM have higher prediction accuracy and better effect than other models.In 2007, the accuracy of two models reached 99.997% and 99.990% separately.
To sum up, it is superior to other models in some respects: a) High precision accuracy and stability are maintained in extended and long-range predictions (far exceeding other ordinary models); b) No large quantities of data are demanded in collection [Five to eight samples can be chosen for model establishing, which is especially fit for the occasion that data are difficult to get]; c) It is flexibility and handy in model operation [with small calculation].Consequently, models of DGIM and NGIM are ideal and economic new tools for population prediction.Tests show that the mean fitting precision of Model ( 1) is 98.45% and Model (2) is 98.21%.The two new models satisfy first-grade accuracy requirement for the use of the extended and long-range prediction of the total population of the country, with the predictions shown in Table 5.

2 Population prediction and demonstration analysis of China in the future
Compared with table 5, the results of two new model-based predictions are much close.It indicates the feasibility of two new models used.To reduce the relative error, we can utilize the combination of the two new grey models to indicate the total population in the relevant years by putting the values of NGIM as the upper limit, that of DGIM as the lower limit and the mean of them as the prediction.
It needs to state that the natural growth rate in PRC National Statistics Bureau equals the annual net-increase individuals divided by yearly averaged total population (the births minus deaths in the involved year), and the increase rates in Tables 6 are acquired approximately by the prediction of net growth in a year divided by the total number of the preceding year.

Conclusions and discussions
From the above, we see that utilization of DGIM and NGIM model is able to make the effect on increment information prominent and weaken effect of disturbing factors, thus revealing the operational law of the system used for higher precision of the prediction.At the same time, the two new models are new ideal tools in population predictions for their absoluteness, facility and easy control.Not all raw data are used for establishing a grey model and different dimensions (or lengths) produce different values of a and b, leading to different predictions that constitute a prognostic grey interval.
According to grey modeling theory, the established grey model is significative when ( 2,1) a ∈ − . One-step forecast precision is above 98% and two to five step forecast precisions are above 97% as 0.3 a ≤ , while one to two step forecast precisions are above 90% and ten-step forecast precision is above 80% as 0.3 0.5 a < − ≤ (Liu, 2004).In a word, the established GM (1,1) can be used in the extended and long-range prediction while ( 2,1) a ∈ − and 0.3 a ≥ − .Thus, choosing the grey model with appropriate dimensions is the key to improve experimental prediction and actual effect.At the end of 2007, the actual population of China is 1.32129 billion, and the first step prediction precision is as high as 99.997% in this paper by testing.Therefore, the effect of prediction is quite satisfactory.
In keeping the normal operation of the present population system, the following conclusions are available: (1) The natural growth rate of the population on a yearly basis is expected to reduce to 4. 97‰ in 2006-2010 compared to 11.60‰ in 1990-1995, 9.12‰ in 1996-2000 and 6.25‰ in 2000-2005, respectively.And the rate would be lowered to about 4.6‰ in 2010 and 2.5‰ in 2025 that is equivalent to the figure reached in developed countries.
(2) The annual net increase in population in China is expected to decline from 6.60 to 6.16 million in 2008-2010, about 3.10 million persons in 2030, no more than 1.60 million persons in 2050.
(3) The population is about 1.32789 billion at the end of 2008 and no more than1.3405billion at the end of 2010.So we can completely accomplish the restrictive target of the total to be kept inside 1.36 billion at the end of 2010 and annual natural growth rate of 8‰ during 2006-2010.At the end of 2020, the total would be 1.3917 billion, while it would exceed 1.4 billion at the end of 2023.India will become the largest population country instead of China as reported.At the end of 2030, 2040 and 2050 the total would be 1.428, 1.454 and 1.473 billion, respectively.It can be expected that the total would not exceed 1.48 billion persons with the persistent and efficient implementation the policy family planning, on the basis of markedly prosperous socio-economic situation, pronouncedly raised spiritual civilization and significantly improved qualification of national citizenship in the future.
As shown by the thematic slogan for World's 6 Billion Population Day in 1999, the selection of mankind's birth policies affects the choice of their future in the end.And the essence of the population problem is the development.But the drop in birth rate and stability depend eventually on socio-economic development.We come to the conclusion that the present stage for the population development is in the third interval of the second period (1970 to present).The characteristic of the period is slowly declining at lower birth rate into a stabilized low-rate stage.With fast advance in economy, improved living standard and health care, the crude death rate in China would be slowly declining to the bottom limit of 6.2‰ and maintained at 6.2~6.3‰ in a long time.A chief factor that determines the growth in the future 40~50 years is birth rate.Consequently, the only strategic decision-making is to strictly control the birth rate for keeping lower rate as our serious target on a long-term basis.Although the mission is prolonged and arduous, we should not be lax.
Currently, the structure of the population is becoming increasingly prominent in the process of solving the issue, as follows: (1) Baby sex pro rata is serious lopsided and goes beyond the range 103~107, high to 119:100.Now male is 18 million more than female in the nubile period and we can forecast that in 2020, the male will be 20 million more than the female at the age of 20~45.China goes through a longest duration with the highest baby sex pro rata.It will induce adverse effect to social stability and harmony (Xin,2007) .
(2) There are 0.8~1.2 million invalids every year, 30% dead, 40% lifelong defective, and only 30% can be cured or corrected, so we loss about 1 billion every year.Proportion of invalids is higher and the total population of invalids has exceeded 60 million as reported, amount to the population of France.
(3) Data provided by National Elder Committee indicates that the population of people older than 60 is 143 million, about 11% of total population.As the Ministry of Affairs reported, the population of the people over the 65 years old is 104.19 million at the end of 2006.It is 7.9% of the total population and raises 0.2% compared with last year.The population of the old people will be 240 million at 2020.It indicates the society of aging is coming ahead, but the whole society has not prepared completely (Xin, 2007).
Besides that, we are facing such problems as qualities of the population out of phase with development, social consequences from population fluidness and ex-and immigration for development, employment, spreading of diseases as AIDS endangering the population's security, etc.Although the increasing quantities of the population have effect on the economic increase, the population's structure and qualities are also the keys.We shall continue to put into strict control the population augmentation and stabilization of birth rate at lower level and place the focus on bettering the population's structure, establishing systems of sound child rearing and social security in an attempt to overall raise the qualities of population, mobilize all departments and the whole society for integrative management of the problem to stepwise realize a long-term harmonic development of population, resources and society.As noted by Mr. Zhao Baige at Oct 9th, 2006, Assistant Director of the National Committee of Population and Planned Birth, China will meet the three population peaks (Xin, 2006): laboring age, aging and total of the population one after another next half century to follow and we should be ready for the challenge.

From
the above comparison, we select a DGIM model and a NGIM model on a 6-dimension basis by data from 2002 to 2007 separately, Comparison of various grey models-based predictions for China's total population for 2007 (Units: 10 4 persons)

Table 3 .
Comparison of various grey models-based predictions for China's total population for 2006 (Units: 10 4 persons)