﻿ 厦门GDP和人口的房价关系探究——基于切比雪夫多项式和库兹涅茨曲线

# 厦门GDP和人口的房价关系探究——基于切比雪夫多项式和库兹涅茨曲线A Study on the Relationship between GDP and Housing Price in Xiamen

Abstract: House price is one of the most concerned topics in people’s daily life. Among the top five cities in China’s housing prices, except Xiamen, the GDP in the first half of 2019 has exceeded trillion Yuan. So, can house prices reflect the economic development level of a city? Can the future trend of GDP also predict the future trend of house prices? In addition, will the future population growth of Xiamen also affect the trend of housing prices? In this paper, we try to predict house prices from two perspectives. This article attempts to predict housing prices from two perspectives. We use Python programs and Chebyshev polynomials to predict Xiamen’s population and GDP, and use the obtained population and GDP prediction values as independent variables, and then make two separate predictions of housing prices.

1. 引言

2. 数据来源及研究方法

2.1. 数据来源

Table 1. Xiamen’s total population, average housing prices and GDP changes

2.2. 研究方法

2.2.1. 用切比雪夫多项式预测厦门GDP及人口的变化

${T}_{0}\left(x\right)=1$ (1)

${T}_{1}\left(x\right)=x$ (2)

${T}_{n+1}\left(x\right)=2x{T}_{n}\left(x\right)-{T}_{n-1}\left(x\right)$ (3)

Figure 1. Chebyshev polynomial image

$p\left(x\right)=\text{}{a}_{0}{T}_{0}\left(x\right)+{a}_{1}{T}_{1}\left(x\right)+{a}_{2}{T}_{2}\left(x\right)+{a}_{3}{T}_{3}\left(x\right)\cdots$ (4)

$\left(T-2012\right)/\left(2022-2012\right)=\left(x+1\right)/2$ (5)

$x=\left(T-2012\right)/\left(2012-2022\right)\ast 2-1$ (6)

2.2.2. 用库兹涅茨曲线预测厦门的房价

3. 结果分析

3.1. 拟合结果

Figure 2. Xiamen population forecast map

Figure 3. Xiamen house price forecast map

Figure 4. Xiamen GDP forecast map

Figure 5. Xiamen GDP forecast house price chart

3.2. 结果分析

3.2.1. 人口原因

1) 前期

2) 后期

3.2.2. GDP与实体经济

Figure 6. 2017 national large and medium cities’ house price income ratio deviation ranking

4. 结论与建议

4.1. 税收

4.1.1. 购房环节强调差别化的税收调控政策

4.1.2. 住房持有环节施行房地产保有税

4.1.3. 住房转让环节对投资性住房转让课以重税

4.2. 房源

2018年5月上旬，住房和城乡建设部约谈了成都、太原两市政府负责人，强调要有针对性地增加有效供给，大力发展中小套型公寓，抑制投机炒作，支持和满足群众刚性住房需求。同年下旬，住房和城乡建设部再次重申房地产调控目标不动摇，力度不放松。

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