摘 要

人口是影响经济发展的重要因素。由于我国地域辽阔，人口基数大，各地差异较大，这使我国的人口控制变的艰难。自我国1978年计划生育政策实行以来，人口数量已得到有效控制，但是我国人口又出现了新的问题：人口老龄化的快速骤增。为了缓解这一状况，2014年开始我国陆续施行“单独二胎”政策，2016年开始又开始施行“全面二胎”政策。这将会导致我国人口数量和结构发生巨大的变化，因此我们需要对我国人口作出准确的预测，这对国家控制人口健康，实现和谐发展具有重要的战略意义。

人口预测本身具有较大的复杂性，它与许多因素直接或间接相关。因此我们选择不需要考虑所有因素的灰色模型来对人口总量进行预测，构建了灰色预测人口模型，并选用我国1995-2014年的数据对未来10年和40年的人口总数进行了拟合求解。从该模型中得到相对比较准确的预测结果是：2024年我国人口会达到14.56亿。该结果表明灰色模型对我国人口的短期拟合非常好误差很小，但是对长期预测的结果却偏离现实：我国的人口总数在未来无限制直线增长。将灰色预测模型改进成新陈代谢模型，但依然不能消除灰色模型过度依赖原始数据的弊端。

为了预测二胎政策对我国人口数量和结构的影响，我们按年龄分组运用leslie模型进行人口预测。本文分别对原计划生育、“单独二胎”、“全面二胎”三种政策下的人口数量和结构进行了预测和比较。从我国2015年的人口结构分析中可以看出：我国的人口结构明显分布不均，存在较大的人口男女比例失衡，年龄分布不均，有明显的高峰与低谷问题。在第一种政策下我国的人口会在2028年左右达到14.59亿并有一个明显的拐点，在此之后人口数量开始随时间加速下降，人口抚养比在2025年左右开始下降并在2027年达到最低点，随后开始持续上升；在施行“单独二胎”政策以后，人口增速增加，人口拐点出现明显提前，并且人口一直持增长，不再下降，人口抚养比的增速一开始大于之前，随后增速放缓，慢慢接近并小于原计划生育水平；“全面二胎”之后，人口增长不再有明显的拐点，只是在中间某个阶段增速有所放缓，而人口抚养比在2025年之前增速持续增加，在2025-2034年期间处于平稳下降状态，自2034年后开始缓慢上升。

本文分别对三种政策下的人口总量、人口结构和人口抚养比等问题进行了比较研究，研究结果表明我国即将进入老龄化社会，分析两种新政策对人口走向的影响得出的结论是：新的人口政策对我国人口年龄分布不均，有明显的高峰与低谷问题有很好的改善作用，能促进我国人口平稳正常发展。

关键词：人口增长；灰色模型；Leslie人口模型；人口抚养比

Abstract

Population problem is an important factor that affects economic development. Since our country has a vast territory and a large population base, there exists signicantly different in different regions, which makes it difficult to control the population. Since the implementation of the family planning policy in 1978, the population has been effectively controlled. But it has also led to the emergence of new problems in our country, the rapid arrival of population aging makes the social pressure surge. In order to alleviate this situation, our country began the implementation of a separate two child policy in 2014, and began to implement the "comprehensive child" policy in 2016. Our country's population quantity and the structure will have huge changes, therefore we need to make the accurate forecast to our country population. which has an important strategic significance for the country to control the healthy and harmonious development of population.

The population prediction itself has great complexity, which is directly or indirectly related to many factors. We can't put all the factors into the prediction process, so we choose the gray model to predict the total population. In this paper, the grey GM (1,1) model is used to fit the population of the population in the next 10 years and 40 years, Using the data in 1995-2014 in our country. The relatively accurate data obtained from this model prediction is that in 2024 the population of our country will reach the 1 billion 456 million. We can find that in the grey model short-term fitting on the population of our country is very good and the error is very small, but for long-term prediction results has deviated from the reality: China's total population in the future without limitation to a similar linear growth from the results obtained. After the model improvement, we developed the metabolic model, but we can not eliminate the disadvantages of the gray model too dependent on the original data.

In order to predict the effects of the two child policy on the quantity and structure of population in our country, We use LESLIE model to predict population according to age group. In this paper, the comparison of the predicted and the original family planning policy, the second single child policy, "comprehensive child" policy of population quantity and structure are investigated. It can be seen from the analysis of China's population structure in 2015: The population structure of our country is obviously uneven distribution. There is a large proportion of the population imbalance between men and women and uneven distribution of age, there is a clear peak and trough problem. In the first policy China's population will be reached 1 billion and 459million around 2028 and there is an obvious turning point, After that, the population began to accelerate down over time, the population dependency ratio began to decline around 2025 and reached its lowest point in 2027, and then continued to rise; After the implementation of the single child policy, The growth rate of population increase, the inflection point of population appeared in advance, And the population has continued to grow, not falling, The growth rate of the population dependency ratio was greater than before, and then the growth rate slowed down, slowly close to and less than the original level of family planning; After the "comprehensive child policy implementation, there is not a significant turning point in Population growth, but the growth has slowed in the middle of a certain stage. The growth rate of population dependency ratio continued to increase over the year before 2025, and decline in a steady state during the period of 2025-2034 , Which began to slowly rise since 2034.

In this paper, the total population, population structure and population dependency ratio of the three policies are compared and studied, which shows that our country is about to enter the aging society. The new population policy has a very good effect on the uneven distribution of population age in China, and has a good effect on the peak and trough, which is drawn from the analysis of the influence of the two new policies on the trend of population. It can promote the normal development of China's population.

Key Words: Population growth; grey model; LESLIE population model; population dependency rat

目 录

摘 要 I

Abstract II

目 录 1

第1章 绪论 1

1.1 研究背景及意义 1

1.2 国内外研究现状 2

第2章 灰色预测人口模型 4

2.1 我国出生率、死亡率、自然增长率的变化 4

2.2 灰色预测人口模型简介 4

2.3 灰色系统的人口预测建模 5

2.4 灰色预测人口模型检验 6

2.5 中国人口预测与实证分析 6

2.6 基于灰色人口预测的新陈代谢模型 8

2.7 本章总结 9

第3章 Leslie人口模型 11

3.1 原计划生育政策下的leslie人口模型 11

3.1.1 模型的建立 11

3.1.2 模型的求解 12

3.2 2015年人口数量和结构分析 15

3.3 “单独二胎”政策下的leslie模型 16

3.3.1 模型的建立 16

3.3.2 模型的求解 16

3.4 “全面二胎”政策下的leslie模型 18

3.4.1 模型的建立 18