住房价格及其与住房抵押贷款关系研究
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摘要
近年来中国房价持续上涨,2006年1季度与1999年1季度相比,全国平均房价上涨了42.93%,是同期CPI涨幅的5.6倍。在房价高涨的同时,个人住房抵押贷款也急速上涨,截止2005年底,全国个人住房抵押贷款余额1.84万亿,是1999年初的43倍。住房作为人类生活的必需品和居民财富的重要组成部分,近年来急涨的房价引起了政府重视,群众关心和社会关注。经济学家和政策制定者面临如下无法回避的问题:(1)中国住房价格的变动规律是什么?(2)房价与住房抵押贷款同步高涨,到底二者之间关系如何,是否存在因果关系,如果存在因果关系,那么孰为因?孰为果?对以上问题的回答关系居民购房决策,关系对住房抵押贷款风险的判断,关系住房金融政策的制定。而要正确回答以上问题,必须建立在对中国住房价格运动规律及其与住房抵押贷款关系的科学认识的基础上。
本文从分析我国住房价格时间序列特征入手,研究住房价格的运动规律,在此基础上,运用泛化回归神经网络(GRNN)方法建立住房价格预测模型,并运用变参数协整、多变量协整以及误差修正模型,对住房价格与住房抵押贷款的关系进行了深入系统的研究。
本文主要的研究工作及由此形成的结论包括以下六个方面:
(一)分析了选题的背景和意义,综述了国内外有关住房价格预测、住房价格与其影响因素关系研究已有文献,总结了现有文献主要研究成果和经验,分析了目前我国住房价格及其影响因素关系研究中存在的问题,指出了可行的研究方向。
(二)运用J-B检验、自相关函数、以及ADF和PP检验对我国住房价格时间序列的正态性、自相关性和稳定性等进行了系统研究,研究结果发现:我国住房价格时间序列呈右偏和尖峰的分布特征,呈现高度的自相关性和微弱的均值回复性,并且正自相关系数持续期很长,负相关系数在很长滞后期出现,住房价格时间序列有长记忆性特点。住房价格时间序列是非平稳序列,而住房价格一阶差分序列平稳,因此住房价格时间序列是一阶单整序列。当滞后期一定长(≥9个月),北京和上海两地住房价格变化互为Granger因果关系,说明两地住房价格存在相同的影响因素。我国住房价格时间序列有显著的自相关性,说明住房价格时间序列的前后数据之间有依存关系,可以利用过去及当前的住房价格对未来的住房价格作出预测,也说明了在住房价格预测中技术分析是可行的。
(三)回顾了国内外关于住房市场有效性研究文献,借鉴国外住房市场弱式有效性游程检验方法,对北京和上海两地住房市场的有效性进行检验,发现上海住房市场拒绝有效市场假设,而北京住房市场接受弱式有效市场假设。在关于住房价格时间序列特征分析中,北京住房价格与上海住房价格一样呈现显著的自相关性。在资本市场上,证券价格的自相关性可以用资本市场无效解释。但是在住房市场上,实证结果发现仅靠有效市场理论无法对住房价格自相关性作出合理的解释。因为住房市场不同于证券市场,所以对住房市场的研究不能完全照搬对资本市场的研究方法。对住房市场而言,即使是一个有效的市场,由于住房市场本身的特殊性,住房供给滞后调整、住房市场上非理性预期、住房融资的首付款约束等都可能引起住房价格调整时滞。
(四)根据住房价格时间序列一阶单整的特性和自相关性,以上海为例,建立了住房价格预测的ARIMA模型,并利用该模型进行了预测,发现ARIMA模型对上海住房价格预测的精度不高,解释能力不强。鉴于ARIMA模型预测能力上的局限性,本文将泛化回归神经网络方法(GRNN)用于住房价格预测,GRNN网络的高度非线性映射能力和快速运算能力,比较适合复杂系统的仿真。通过GRNN网络预测结果和ARIMA模型预测结果的对比分析,发现GRNN网络方法预测相对误差为0.37%,而ARIMA预测的相对误差为1.96%,说明经过大量样本反复训练的GRNN网络较好地仿真了上海住房价格的行为模式,GRNN模型比ARIMA模型更适合于上海住房价格预测。当然,以上结论仅是从对上海住房价格预测对比中得到的,GRNN网络预测方法是否适合于我国其他地区的住房价格预测还有待于进一步验证。ARIMA模型方法和GRNN模型方法本身并没有优劣之分,选择什么样的模型主要取决于所要研究的系统特征。符合住房价格时间序列数据生成系统特征的模型,能反映住房价格的行为模式,预测能力就强。相反,不符合住房价格时间序列数据生成系统特征的模型,即使再先进、再复杂,在房价预测上效果也不一定好。
(五)以上海为例对我国住房住房价格与住房抵押贷款及其组成之间的关系进行研究。第一步:假定住房价格与住房抵押贷款之间的数量关系不随时间变化,运用1996年8月～2006年8月的统计资料进行实证研究,发现住房价格与住房抵押贷款及其组成部分之间不存在长期协整关系。第二步:运用标准Granger因果检验对住房价格与住房抵押贷款之间的因果关系做了研究。研究表明:住房抵押贷款总余额是住房价格的Grange原因,但反方向的因果关系不成立;商业性个人住房贷款余额是住房价格的Grange原因,但反方向的因果关系也不成立。仔细分析这一结论,发现在研究期内上海住房市场不是一个平稳的市场。因停止实物分房,居民家庭的住房需求增加。为支持住房制度改革央行制定了《个人住房抵押贷款管理办法》并且取消了商业银行信贷规模直接控制,加上商业银行间业务竞争日益激烈,居民得到住房抵押贷款变得越来越容易。受上述政策变化影响,住房价格与住房抵押贷款的关系处于不断变化之中,经历了一系列的结构变迁。虽然房改政策和住房金融政策出台有具体时间,但是市场消化吸收的过程难以把握,而且各种影响因素错综复杂,所以无法通过在线性方程中加入哑元变量分析变化因素,而是利用变参数模型比较合适。因此,在第三步:本文去掉基本模型中的常参数假定,用时变参数来代替常参数,假定住房价格与住房抵押贷款的关系系数为AR(1)状态转换形式,利用卡尔曼滤波算法对时变参数模型进行估计。结果表明:住房价格与住房抵押贷款之间存在随时间变化的协整关系—在2000年以前,住房价格与住房抵押贷款之间的关系规律性不明显;但是2000年以后,住房抵押贷款对住房价格的正向影响逐步增强并呈上升趋势。通过残差图、均值和标准差比较,时变参数模型的估计效果比常参数模型好,时变参数模型能够更好地描述住房价格与住房抵押贷款之间的关系。
同时,上述实证证明了上海住房市场的变结构特征,也进一步论证了为什么ARIMA模型不适合于对上海住房价格的预测研究。更重要的该实证结果可以帮助我们认清一个现实问题。当前大家比较关注房价泡沫对金融稳定的威胁,实际上,在促成房价泡沫的因素当中,过于宽松的货币政策和过度的金融支持是重要因素之一,要避免房价泡沫需要从金融政策上防患于未然。尤其是在金融制度变迁、不确定性和信息不对称性的背景下,金融机构的竞争和短视,导致大量贷款投向住房投资(投机),直接导致住房价格的剧烈波动。解决居民住房问题必须要有住房抵押贷款供给作为支持,但同时需要注意金融支持过度问题,因此,建议始终坚持“住房金融以支持居民自住住房购买为主,限制用于投资性(投机性)购房”的原则,要求商业银行对投资性(投机性)购房实行差别化的高利率政策,同时加强对商业银行个人住房抵押贷款业务的窗口指导和监督,避免出现金融支持过度。另外,根据我们的研究,房价不是住房抵押贷款快速增长的Grange因,说明了近年来住房抵押贷款的急涨主要源于申请抵押贷款购房的业务量增长,而非来自于作为抵押物的住房价格增长,住房抵押贷款余额不是被高房价推高的,因此,研究期内住房抵押贷款对抵押物价值的依赖度不高,风险不大。
(六)以住房价格生命周期模型为基础,以上海为例,构建了城镇化指标,建立了住房价格与人均可支配收入、收入预期(失业率)、住房抵押贷款利率和城镇化等变量之间的多因素关系模型,采用E-G两步法协整分析技术和误差修正模型,研究了住房价格与人均可支配收入、收入预期、抵押贷款利率和城镇化等变量之间的长期均衡关系和短期影响关系。研究结果表明:这些变量之间存在长期均衡关系。长期看,收入预期(失业率)、抵押贷款利率、城镇化和抵押贷款余额是决定和影响住房价格水平的主要因素。从影响程度看,1%的抵押贷款余额增长,将导致0.21%的住房价格增长;1%的农村人口减少,将导致0.17%的住房价格增长;收入预期(失业率)下降1个百分点,住房价格将增加0.74%;住房抵押贷款利率提高1个百分点,住房价格下降0.08%。其中收入预期(失业率)和抵押贷款余额对住房价格的影响较大,而且这两个变量短期内也对住房价格变化产生影响。均衡误差修正项系数为14%,说明上海住房市场价格调整速度比较快,每一个月份调整偏离长期均衡的14%。滞后2期住房价格变化对当期价格变化影响弹性为0.42,滞后3期住房价格变化对当期价格变化的影响弹性为0.34,滞后4期住房价格变化对当期价格变化的影响弹性为0.20,揭示了住房价格调整过程是一个有粘性的价格调整过程,滞后住房价格变化是促使住房价格短期波动的主要原因,证明了住房市场不符合有效市场假说,住房市场上购房者的预期是非理性预期。购房者根据以往的住房价格及其变化对未来的房价作出预测,在房价大幅上升阶段,容易产生投机泡沫,房价可能大幅度地偏离其长期均衡价值,加上现阶段上海住房市场缺乏长期性购买力支撑,房价调整速度比较快,上海住房市场的“繁荣-衰退”循环比较脆弱,政府应该给予住房市场更多关注,以确保一个平稳发展的住房市场。
本研究的创新性体现在以下四个方面:
(一)弱式有效性实证结果发现,资本市场有效性理论不能用来解释住房价格的自相关性。本文从住房市场固有属性出发,系统地分析了住房价格自相关性的原因,即住房供给滞后调整、住房市场上非理性预期、住房融资的首付款约束等都可能引起住房价格调整时滞。
(二)将泛化回归神经网络方法(GRNN)用于住房价格预测中,通过与ARIMA预测结果的对比分析,得出GRNN模型在上海房价预测中优于ARIMA模型,证明了上海住房市场的非线性特征。
(三)运用时变参数协整关系的估计和检验方法,建立了住房价格与住房抵押贷款关系的时变参数模型,得出住房价格与住房抵押贷款之间具有随时间变化的长期均衡关系以及时变参数模型在描述二者关系方面优于常参数模型的结论。
(四)构建了城镇化指标,并且用城镇失业率作为收入预期的代理变量,建立了上海住房价格与城镇人均可支配收入、收入预期、抵押贷款利率、抵押贷款总余额以及城镇化等变量之间的多因素模型,运用E-G两步法协整分析和误差修正分析,得出住房价格与收入预期、抵押贷款利率、抵押贷款总余额以及城镇化等变量之间存在长期均衡关系。城镇居民人均可支配收入与住房价格没有显著的相关关系。在影响住房价格的因素中,城镇化和抵押贷款余额是决定和影响住房价格水平的主要因素。
总的来看,本论文的研究在关于我国住房价格运动规律的认识方面,以及住房价格与抵押贷款关系研究方面给出了一些新的结论,这对于制定住房及金融相关政策、促进我国住房市场的健康发展,实现社会和谐与稳定有着相当的理论价值和积极的实践意义。
In recent years, housing prices in China have increased rapidly. The average housing price in China had increased by 43.95% from Spring 2006 to Spring 1999, 5.6 folds of the increasing rate in CPI during that same period. Meanwhile, the amount of home mortgage loans had increased rapidly. The balance of China's home mortgage loans is 1.84 quadrillion at the end of 2005, 43 folds of that at the beginning of 1999.The rapid increase in housing prices has drawn attention of the central government and concerns the public. Economists and policy makers are facing the following questions. 1) What are the trends in the movement of China's housing prices? 2) What are the relationships between housing prices and mortgage loans? They increase synchronously. Are there any causal relationships between the increases of them? If so, which is the cause, which is the result? Answers to the above questions will affect the decision making of housing purchasers, risk analysis of mortgage loans, the formulation of monetary policies. Correct answers to the above questions must be base on scientific knowledge of the relationships between the movement of China's housing prices and mortgage.
In this thesis, studies on the movement of housing prices are performed by the housing price time series features. Based on this, in-depth and systematic studies on the relationships between housing prices and mortgage are given through a housing price forcasting model founded on generalized regression neuro network (GRNN) and time varying parameter , multivariate error correction models.
Following are the six main contributions of the thesis.
1) The background and significance of the topic are analyzed. Literature on housing price forecasting, housing price movement and its determinant factors are reviewed. Drawback in existing research in China on housing prices and their determinant factors are analyzed. Feasible research directions are given.
2) Nomal distribution , autocorrelation, stationarity of the time series data of China's housing prices are systematically studied through J-B test, autocorrelation function, and ADF and PP tests. The studies show that the distribution of the time series data of China's housing prices is right-skewed and has peaks. A high degree of autocorrelation and weak mean reversion have observed. The positive autocorrelation coefficient lasts for a long time. There is a long lag in the negative autocorrelation coefficient. When the lag period is at least 9 months, the changes in housing prices in Shanghai and Beijing are mutually related by Granger causal relationship. That means that same factors affect the housing prices of both cities. There is notable autocorrelation in the time series data of China's housing prices. That means that the data of China's housing prices are dependent. And it is possible to forecast the housing prices by historical and current housing prices. It also implies that technical analysis can be applied to housing price forecasting.
3) Literature on market efficiency is reviewed. The efficiency of Beijing and Shanghai's housing market is tested. Results show that effective market hypothesis is opposed by the housing market in Shanghai, but housing market in Beijing supports weak effective market hypothesis. There is notable correlation in the time series data of Beijing's housing prices, as well as in that of Shanghai's housing prices. For the capital market, autocorrelation between the prices of securities can be explained by market in efficiency. However, for the housing market, experiments show that only market efficiency along can not explain the autocorrelation of housing prices. Because housing market is different from stock market, research methodology for capital market can not be used to study housing market without modification, even if the housing market is an effective market, because of its special characters, lag in housing supply, unrealistic expectation, restrictions on down-payment, etc. will cause lag of housing price movement.
4) ARIMA model for housing price forecast is established based on the characters of the time series data of housing prices in Shanghai. Experiments show that ARIMA model can not provide accurate forecasts and explanation. Because of the limitation of the forecasting ability of ARIMA model, Generalized regression neural network (GRNN) model is used in this thesis for housing price forecasting. Because GRNN network can produce highly nonlinear mapping and fast calculation, it is suitable for simulation of complex system. The relative error of forecasting by GRNN network is 0.37%, that by ARIMA model is 1.96%. That shows that through repeated training with large training set, GRNN can simulate the movement of housing prices in Shanghai better. So GRNN network is more suitable for the forecasting of Shanghai's housing prices than ARIMA model. Of course, the above conclusion is drawn only from the comparison of the two forecasting models for Shanghai's housing prices. whether GRNN model is suitable for forecasting housing prices in other areas in China needs further tests. ARIMA is not superior to GRNN, and vise versa. Which model to use depends on the characters of the system. The forecasting results are better if the model fits the data generation model for the time series of the housing prices and it models the movement of housing prices. Otherwise, a more advanced and complicated model may not produce good forecasting results if it doesn't fit the data generation model for the time series of housing prices.
5) The relationships between housing prices and the mortgage and its composition are studied based on the data in Shanghai's market. First, assume that the relationships between housing prices and mortgage are not changed over time. Experiments using the statistical data from August 1996 to August 2006 show that there is no long-term correlation between housing prices and mortgage loan and its components. Second, the casual relation between housing prices and mortgage is examined through standard Granger casual test. Results show that the balance of mortgage loans is the Grange cause of housing prices, not the other way around. The balance of commercial home mortgage loans is the Grange cause of housing prices, not the other way around as well. A close look at the conclusion reveals that Shanghai's housing market is not a stable market. Because of the termination of physical distribution of housing, consumer demand for housing increases. To support the reformulation of housing policies, central bank has developed“regulations for home mortgage loans”, and canceled direct control of the size of the loans of commercial banks. Plus more and more fierce competition between commercial banks, it is more and more easily for consumers to get home mortgage loans. Due to the above policy changes, the relationships between housing prices and mortgage changes all the time. The structure of the relation has undergone a series of changes. Although policies for housing reform and housing financing reform will be introduced in a specific time, it is not certain how the market will absorb these policies. In addition, the influence factors are complicated; so it is not possible to analyze the reasons for change via linear functions with dummy variables. Models with time varying parameters are more suitable. So in the third step, the assumptions of constant parameters are deleted. And these constant parameters are replaced by time-varying parameters. Assume the parameters of the relations between housing prices and mortgage is in AR(1) state transition form. The time variable parameter model is estimated by the Kalman filter. Results show that there is correlation changing over time between housing prices and mortgage.Before 2000, there is no obvious relation between housing prices and mortgage. However, after 2000, positive effects from mortgage to housing prices gradually increase and have upper-word trend. Based on comparisons of residuals, mean, and standard deviation, time varying parameter model can achieve better forecasts and describe the relations between housing prices and mortgage better than constant parameter models.
Meanwhile, the above experiments prove that Shanghai's housing market features variable structure and further verify why ARIMA model is not suitable for forecasting research on Shanghai's housing prices. More importantly, these experiments results help us recognize a real problem. Currently, public is concerned about the threat of housing bubble against the stability of economy. Few people realize that over rapid financial deregulation and excessive financial support is one of the important factors that contribute to the housing bubble. Prevention of housing bubble should resort to financial policies. Especially during the period when financial policies are undergone changes and uncertain, information are asymmetrical, and financial firms compete with each other and are short-sighted, a large quantity of loans are invested in (speculated on) housing. This directly leads to the turbulence of housing prices.To solve the housing problem, home mortgage is an important tool.However, excessive financial support should be prevented. Therefore, this thesis suggests that the following principles should always be sticked to: housing financing should mainly support consumers to buy their own housing Commercial banks should be required to set differentiated high interest rates for consumers to do housing investment (speculation).Meanwhile, window guidance and supervision of home mortgage business in commercial banks should be enhanced to prevent excessive financial support. In addition, according to our study, housing price is not the Grange cause of the rapid growth of mortgage loans. It demonstrates that the rapid growth of housing mortgage in recent years comes from the growth of mortgage application, not from price increasing of the property mortgaged. And the balance of mortgage is not pushed by high housing prices. Therefore, current mortgage loans are not highly dependent on the property mortgaged and are not high-risk.
6) Based on life cycle model, the urbanization index is established using data from Shanghai. Multi-factor relation model of housing prices, per capita disposable income, income expectation (unemployment rate), mortgage loan balance, mortgage interest rate, and urbanization index, etc., is established. Long-term balance relation and short-term impact of housing prices, per capita disposable income, income expectation , mortgage interest rate, and urbanization index, etc are analyzed through E-G two-step cointegration analysis and error correction model. Results show that there is long-term balance relation between these variables. In the long-run, income expectation (unemployment rate), mortgage interest rate, urbanization index, and balance of mortgage loans are main determinant factors of housing price. The degree of impact is as follows. 1% increase in the balance of mortgage loan will lead to 0.17% increase in housing prices; 1% decrease in rural population will lead to 0.17% increase in housing prices; income expectation (unemployment rate) decreasing by 1 percent will lead to housing prices increasing by 0.74%; if mortgage interest rate increases by 1 percent, housing prices will decrease by 0.08%. Among them, income expectation (unemployment rate) and balance of mortgage have greater impact on housing prices. These two variables have impact on housing prices in the short term as well. Error correction coefficient is 14%, which shows that the adjustment rate of Shanghai's housing market is fast. Each month, adjustment is 14%. Impact elastic of two-period lagged changes in housing prices to current housing prices is 0.42; that of three-period lagged changes in housing prices is 0.34, that of four-period lagged changes is 0.20. That shows that the housing price adjustment process is a sticky price adjustment process. Lagged housing price changes are main contribution to short-term fluctuations of housing prices. It proves that housing market doesn't fit the effective market hypothesis. On the housing market, consumer expectations are irrational. Consumers predict future housing prices based on previous housing prices and their movement. During the period when housing prices are increased substantially, bubbles will likely appear, and housing prices may deviate from their long-term value substantially. In addition, current Shanghai's housing market lacks the support of long-term purchase power, and the adjustment rate of housing prices is fast. The“prosperity- recession”cycle of Shanghai's housing market is relatively weak. Government should pay more attention to the housing market to insure a stable growing housing market.
Following are the 4 innovative contributions of this thesis.
1) Weak-form efficiency experiments show that the market efficiency theory of capital market can not explain the autocorrelation of housing prices. Starting from inherent attributes, this thesis systematically studied the reasons of autocorrelation of housing prices, i.e. lagged adjustment of housing supply and demand , irrational expectation on housing market, restriction on down-payment of housing financing, etc. will lead to lags in housing price adjustment.
2) GRNN neural network model is applied to housing price forecasting. Through comparison of its results and that from ARIMA forecasting, we conclude that GRNN model is better than ARIMA model in predicting Shanghai's housing prices, and demonstrate the non-linearity of Shanghai's housing market.
3) Time-varying parameter model of the relations between housing prices and housing mortgage are established. we conclude that there are long-term balance relations between housing prices and housing mortgage, and time-varying parameter model can better describe the relations between them than constant parameter models.
4) Urbanization index is introduced. Using unemployment rate as the proxy variable of income expectation, multi-factor models of Shanghai's housing prices and per capita disposable income, income expectation (unemployment rate), mortgage loan balance, mortgage rate, and urbanization index, etc., is established. Through E-G two-step cointegration analysis and error correction model, we show that there is long-term balance relation between housing prices and per capita disposable income, income expectation (unemployment rate), mortgage loan interest rate, and urbanization index, etc. There is no obvious correlation between per capita disposable income and housing prices. rbanization and balance of mortgage loans are determinant factors of housing prices. Overall, this thesis draw some new conclusions of the relations between housing prices and mortgage in the area of China's housing price movement. It has quite a great theoretical value and positive practical significance for establishing housing policies and related financial policies, promoting the healthy development of China's housing market.
本文从分析我国住房价格时间序列特征入手,研究住房价格的运动规律,在此基础上,运用泛化回归神经网络(GRNN)方法建立住房价格预测模型,并运用变参数协整、多变量协整以及误差修正模型,对住房价格与住房抵押贷款的关系进行了深入系统的研究。
本文主要的研究工作及由此形成的结论包括以下六个方面:
(一)分析了选题的背景和意义,综述了国内外有关住房价格预测、住房价格与其影响因素关系研究已有文献,总结了现有文献主要研究成果和经验,分析了目前我国住房价格及其影响因素关系研究中存在的问题,指出了可行的研究方向。
(二)运用J-B检验、自相关函数、以及ADF和PP检验对我国住房价格时间序列的正态性、自相关性和稳定性等进行了系统研究,研究结果发现:我国住房价格时间序列呈右偏和尖峰的分布特征,呈现高度的自相关性和微弱的均值回复性,并且正自相关系数持续期很长,负相关系数在很长滞后期出现,住房价格时间序列有长记忆性特点。住房价格时间序列是非平稳序列,而住房价格一阶差分序列平稳,因此住房价格时间序列是一阶单整序列。当滞后期一定长(≥9个月),北京和上海两地住房价格变化互为Granger因果关系,说明两地住房价格存在相同的影响因素。我国住房价格时间序列有显著的自相关性,说明住房价格时间序列的前后数据之间有依存关系,可以利用过去及当前的住房价格对未来的住房价格作出预测,也说明了在住房价格预测中技术分析是可行的。
(三)回顾了国内外关于住房市场有效性研究文献,借鉴国外住房市场弱式有效性游程检验方法,对北京和上海两地住房市场的有效性进行检验,发现上海住房市场拒绝有效市场假设,而北京住房市场接受弱式有效市场假设。在关于住房价格时间序列特征分析中,北京住房价格与上海住房价格一样呈现显著的自相关性。在资本市场上,证券价格的自相关性可以用资本市场无效解释。但是在住房市场上,实证结果发现仅靠有效市场理论无法对住房价格自相关性作出合理的解释。因为住房市场不同于证券市场,所以对住房市场的研究不能完全照搬对资本市场的研究方法。对住房市场而言,即使是一个有效的市场,由于住房市场本身的特殊性,住房供给滞后调整、住房市场上非理性预期、住房融资的首付款约束等都可能引起住房价格调整时滞。
(四)根据住房价格时间序列一阶单整的特性和自相关性,以上海为例,建立了住房价格预测的ARIMA模型,并利用该模型进行了预测,发现ARIMA模型对上海住房价格预测的精度不高,解释能力不强。鉴于ARIMA模型预测能力上的局限性,本文将泛化回归神经网络方法(GRNN)用于住房价格预测,GRNN网络的高度非线性映射能力和快速运算能力,比较适合复杂系统的仿真。通过GRNN网络预测结果和ARIMA模型预测结果的对比分析,发现GRNN网络方法预测相对误差为0.37%,而ARIMA预测的相对误差为1.96%,说明经过大量样本反复训练的GRNN网络较好地仿真了上海住房价格的行为模式,GRNN模型比ARIMA模型更适合于上海住房价格预测。当然,以上结论仅是从对上海住房价格预测对比中得到的,GRNN网络预测方法是否适合于我国其他地区的住房价格预测还有待于进一步验证。ARIMA模型方法和GRNN模型方法本身并没有优劣之分,选择什么样的模型主要取决于所要研究的系统特征。符合住房价格时间序列数据生成系统特征的模型,能反映住房价格的行为模式,预测能力就强。相反,不符合住房价格时间序列数据生成系统特征的模型,即使再先进、再复杂,在房价预测上效果也不一定好。
(五)以上海为例对我国住房住房价格与住房抵押贷款及其组成之间的关系进行研究。第一步:假定住房价格与住房抵押贷款之间的数量关系不随时间变化,运用1996年8月～2006年8月的统计资料进行实证研究,发现住房价格与住房抵押贷款及其组成部分之间不存在长期协整关系。第二步:运用标准Granger因果检验对住房价格与住房抵押贷款之间的因果关系做了研究。研究表明:住房抵押贷款总余额是住房价格的Grange原因,但反方向的因果关系不成立;商业性个人住房贷款余额是住房价格的Grange原因,但反方向的因果关系也不成立。仔细分析这一结论,发现在研究期内上海住房市场不是一个平稳的市场。因停止实物分房,居民家庭的住房需求增加。为支持住房制度改革央行制定了《个人住房抵押贷款管理办法》并且取消了商业银行信贷规模直接控制,加上商业银行间业务竞争日益激烈,居民得到住房抵押贷款变得越来越容易。受上述政策变化影响,住房价格与住房抵押贷款的关系处于不断变化之中,经历了一系列的结构变迁。虽然房改政策和住房金融政策出台有具体时间,但是市场消化吸收的过程难以把握,而且各种影响因素错综复杂,所以无法通过在线性方程中加入哑元变量分析变化因素,而是利用变参数模型比较合适。因此,在第三步:本文去掉基本模型中的常参数假定,用时变参数来代替常参数,假定住房价格与住房抵押贷款的关系系数为AR(1)状态转换形式,利用卡尔曼滤波算法对时变参数模型进行估计。结果表明:住房价格与住房抵押贷款之间存在随时间变化的协整关系—在2000年以前,住房价格与住房抵押贷款之间的关系规律性不明显;但是2000年以后,住房抵押贷款对住房价格的正向影响逐步增强并呈上升趋势。通过残差图、均值和标准差比较,时变参数模型的估计效果比常参数模型好,时变参数模型能够更好地描述住房价格与住房抵押贷款之间的关系。
同时,上述实证证明了上海住房市场的变结构特征,也进一步论证了为什么ARIMA模型不适合于对上海住房价格的预测研究。更重要的该实证结果可以帮助我们认清一个现实问题。当前大家比较关注房价泡沫对金融稳定的威胁,实际上,在促成房价泡沫的因素当中,过于宽松的货币政策和过度的金融支持是重要因素之一,要避免房价泡沫需要从金融政策上防患于未然。尤其是在金融制度变迁、不确定性和信息不对称性的背景下,金融机构的竞争和短视,导致大量贷款投向住房投资(投机),直接导致住房价格的剧烈波动。解决居民住房问题必须要有住房抵押贷款供给作为支持,但同时需要注意金融支持过度问题,因此,建议始终坚持“住房金融以支持居民自住住房购买为主,限制用于投资性(投机性)购房”的原则,要求商业银行对投资性(投机性)购房实行差别化的高利率政策,同时加强对商业银行个人住房抵押贷款业务的窗口指导和监督,避免出现金融支持过度。另外,根据我们的研究,房价不是住房抵押贷款快速增长的Grange因,说明了近年来住房抵押贷款的急涨主要源于申请抵押贷款购房的业务量增长,而非来自于作为抵押物的住房价格增长,住房抵押贷款余额不是被高房价推高的,因此,研究期内住房抵押贷款对抵押物价值的依赖度不高,风险不大。
(六)以住房价格生命周期模型为基础,以上海为例,构建了城镇化指标,建立了住房价格与人均可支配收入、收入预期(失业率)、住房抵押贷款利率和城镇化等变量之间的多因素关系模型,采用E-G两步法协整分析技术和误差修正模型,研究了住房价格与人均可支配收入、收入预期、抵押贷款利率和城镇化等变量之间的长期均衡关系和短期影响关系。研究结果表明:这些变量之间存在长期均衡关系。长期看,收入预期(失业率)、抵押贷款利率、城镇化和抵押贷款余额是决定和影响住房价格水平的主要因素。从影响程度看,1%的抵押贷款余额增长,将导致0.21%的住房价格增长;1%的农村人口减少,将导致0.17%的住房价格增长;收入预期(失业率)下降1个百分点,住房价格将增加0.74%;住房抵押贷款利率提高1个百分点,住房价格下降0.08%。其中收入预期(失业率)和抵押贷款余额对住房价格的影响较大,而且这两个变量短期内也对住房价格变化产生影响。均衡误差修正项系数为14%,说明上海住房市场价格调整速度比较快,每一个月份调整偏离长期均衡的14%。滞后2期住房价格变化对当期价格变化影响弹性为0.42,滞后3期住房价格变化对当期价格变化的影响弹性为0.34,滞后4期住房价格变化对当期价格变化的影响弹性为0.20,揭示了住房价格调整过程是一个有粘性的价格调整过程,滞后住房价格变化是促使住房价格短期波动的主要原因,证明了住房市场不符合有效市场假说,住房市场上购房者的预期是非理性预期。购房者根据以往的住房价格及其变化对未来的房价作出预测,在房价大幅上升阶段,容易产生投机泡沫,房价可能大幅度地偏离其长期均衡价值,加上现阶段上海住房市场缺乏长期性购买力支撑,房价调整速度比较快,上海住房市场的“繁荣-衰退”循环比较脆弱,政府应该给予住房市场更多关注,以确保一个平稳发展的住房市场。
本研究的创新性体现在以下四个方面:
(一)弱式有效性实证结果发现,资本市场有效性理论不能用来解释住房价格的自相关性。本文从住房市场固有属性出发,系统地分析了住房价格自相关性的原因,即住房供给滞后调整、住房市场上非理性预期、住房融资的首付款约束等都可能引起住房价格调整时滞。
(二)将泛化回归神经网络方法(GRNN)用于住房价格预测中,通过与ARIMA预测结果的对比分析,得出GRNN模型在上海房价预测中优于ARIMA模型,证明了上海住房市场的非线性特征。
(三)运用时变参数协整关系的估计和检验方法,建立了住房价格与住房抵押贷款关系的时变参数模型,得出住房价格与住房抵押贷款之间具有随时间变化的长期均衡关系以及时变参数模型在描述二者关系方面优于常参数模型的结论。
(四)构建了城镇化指标,并且用城镇失业率作为收入预期的代理变量,建立了上海住房价格与城镇人均可支配收入、收入预期、抵押贷款利率、抵押贷款总余额以及城镇化等变量之间的多因素模型,运用E-G两步法协整分析和误差修正分析,得出住房价格与收入预期、抵押贷款利率、抵押贷款总余额以及城镇化等变量之间存在长期均衡关系。城镇居民人均可支配收入与住房价格没有显著的相关关系。在影响住房价格的因素中,城镇化和抵押贷款余额是决定和影响住房价格水平的主要因素。
总的来看,本论文的研究在关于我国住房价格运动规律的认识方面,以及住房价格与抵押贷款关系研究方面给出了一些新的结论,这对于制定住房及金融相关政策、促进我国住房市场的健康发展,实现社会和谐与稳定有着相当的理论价值和积极的实践意义。
In recent years, housing prices in China have increased rapidly. The average housing price in China had increased by 43.95% from Spring 2006 to Spring 1999, 5.6 folds of the increasing rate in CPI during that same period. Meanwhile, the amount of home mortgage loans had increased rapidly. The balance of China's home mortgage loans is 1.84 quadrillion at the end of 2005, 43 folds of that at the beginning of 1999.The rapid increase in housing prices has drawn attention of the central government and concerns the public. Economists and policy makers are facing the following questions. 1) What are the trends in the movement of China's housing prices? 2) What are the relationships between housing prices and mortgage loans? They increase synchronously. Are there any causal relationships between the increases of them? If so, which is the cause, which is the result? Answers to the above questions will affect the decision making of housing purchasers, risk analysis of mortgage loans, the formulation of monetary policies. Correct answers to the above questions must be base on scientific knowledge of the relationships between the movement of China's housing prices and mortgage.
In this thesis, studies on the movement of housing prices are performed by the housing price time series features. Based on this, in-depth and systematic studies on the relationships between housing prices and mortgage are given through a housing price forcasting model founded on generalized regression neuro network (GRNN) and time varying parameter , multivariate error correction models.
Following are the six main contributions of the thesis.
1) The background and significance of the topic are analyzed. Literature on housing price forecasting, housing price movement and its determinant factors are reviewed. Drawback in existing research in China on housing prices and their determinant factors are analyzed. Feasible research directions are given.
2) Nomal distribution , autocorrelation, stationarity of the time series data of China's housing prices are systematically studied through J-B test, autocorrelation function, and ADF and PP tests. The studies show that the distribution of the time series data of China's housing prices is right-skewed and has peaks. A high degree of autocorrelation and weak mean reversion have observed. The positive autocorrelation coefficient lasts for a long time. There is a long lag in the negative autocorrelation coefficient. When the lag period is at least 9 months, the changes in housing prices in Shanghai and Beijing are mutually related by Granger causal relationship. That means that same factors affect the housing prices of both cities. There is notable autocorrelation in the time series data of China's housing prices. That means that the data of China's housing prices are dependent. And it is possible to forecast the housing prices by historical and current housing prices. It also implies that technical analysis can be applied to housing price forecasting.
3) Literature on market efficiency is reviewed. The efficiency of Beijing and Shanghai's housing market is tested. Results show that effective market hypothesis is opposed by the housing market in Shanghai, but housing market in Beijing supports weak effective market hypothesis. There is notable correlation in the time series data of Beijing's housing prices, as well as in that of Shanghai's housing prices. For the capital market, autocorrelation between the prices of securities can be explained by market in efficiency. However, for the housing market, experiments show that only market efficiency along can not explain the autocorrelation of housing prices. Because housing market is different from stock market, research methodology for capital market can not be used to study housing market without modification, even if the housing market is an effective market, because of its special characters, lag in housing supply, unrealistic expectation, restrictions on down-payment, etc. will cause lag of housing price movement.
4) ARIMA model for housing price forecast is established based on the characters of the time series data of housing prices in Shanghai. Experiments show that ARIMA model can not provide accurate forecasts and explanation. Because of the limitation of the forecasting ability of ARIMA model, Generalized regression neural network (GRNN) model is used in this thesis for housing price forecasting. Because GRNN network can produce highly nonlinear mapping and fast calculation, it is suitable for simulation of complex system. The relative error of forecasting by GRNN network is 0.37%, that by ARIMA model is 1.96%. That shows that through repeated training with large training set, GRNN can simulate the movement of housing prices in Shanghai better. So GRNN network is more suitable for the forecasting of Shanghai's housing prices than ARIMA model. Of course, the above conclusion is drawn only from the comparison of the two forecasting models for Shanghai's housing prices. whether GRNN model is suitable for forecasting housing prices in other areas in China needs further tests. ARIMA is not superior to GRNN, and vise versa. Which model to use depends on the characters of the system. The forecasting results are better if the model fits the data generation model for the time series of the housing prices and it models the movement of housing prices. Otherwise, a more advanced and complicated model may not produce good forecasting results if it doesn't fit the data generation model for the time series of housing prices.
5) The relationships between housing prices and the mortgage and its composition are studied based on the data in Shanghai's market. First, assume that the relationships between housing prices and mortgage are not changed over time. Experiments using the statistical data from August 1996 to August 2006 show that there is no long-term correlation between housing prices and mortgage loan and its components. Second, the casual relation between housing prices and mortgage is examined through standard Granger casual test. Results show that the balance of mortgage loans is the Grange cause of housing prices, not the other way around. The balance of commercial home mortgage loans is the Grange cause of housing prices, not the other way around as well. A close look at the conclusion reveals that Shanghai's housing market is not a stable market. Because of the termination of physical distribution of housing, consumer demand for housing increases. To support the reformulation of housing policies, central bank has developed“regulations for home mortgage loans”, and canceled direct control of the size of the loans of commercial banks. Plus more and more fierce competition between commercial banks, it is more and more easily for consumers to get home mortgage loans. Due to the above policy changes, the relationships between housing prices and mortgage changes all the time. The structure of the relation has undergone a series of changes. Although policies for housing reform and housing financing reform will be introduced in a specific time, it is not certain how the market will absorb these policies. In addition, the influence factors are complicated; so it is not possible to analyze the reasons for change via linear functions with dummy variables. Models with time varying parameters are more suitable. So in the third step, the assumptions of constant parameters are deleted. And these constant parameters are replaced by time-varying parameters. Assume the parameters of the relations between housing prices and mortgage is in AR(1) state transition form. The time variable parameter model is estimated by the Kalman filter. Results show that there is correlation changing over time between housing prices and mortgage.Before 2000, there is no obvious relation between housing prices and mortgage. However, after 2000, positive effects from mortgage to housing prices gradually increase and have upper-word trend. Based on comparisons of residuals, mean, and standard deviation, time varying parameter model can achieve better forecasts and describe the relations between housing prices and mortgage better than constant parameter models.
Meanwhile, the above experiments prove that Shanghai's housing market features variable structure and further verify why ARIMA model is not suitable for forecasting research on Shanghai's housing prices. More importantly, these experiments results help us recognize a real problem. Currently, public is concerned about the threat of housing bubble against the stability of economy. Few people realize that over rapid financial deregulation and excessive financial support is one of the important factors that contribute to the housing bubble. Prevention of housing bubble should resort to financial policies. Especially during the period when financial policies are undergone changes and uncertain, information are asymmetrical, and financial firms compete with each other and are short-sighted, a large quantity of loans are invested in (speculated on) housing. This directly leads to the turbulence of housing prices.To solve the housing problem, home mortgage is an important tool.However, excessive financial support should be prevented. Therefore, this thesis suggests that the following principles should always be sticked to: housing financing should mainly support consumers to buy their own housing Commercial banks should be required to set differentiated high interest rates for consumers to do housing investment (speculation).Meanwhile, window guidance and supervision of home mortgage business in commercial banks should be enhanced to prevent excessive financial support. In addition, according to our study, housing price is not the Grange cause of the rapid growth of mortgage loans. It demonstrates that the rapid growth of housing mortgage in recent years comes from the growth of mortgage application, not from price increasing of the property mortgaged. And the balance of mortgage is not pushed by high housing prices. Therefore, current mortgage loans are not highly dependent on the property mortgaged and are not high-risk.
6) Based on life cycle model, the urbanization index is established using data from Shanghai. Multi-factor relation model of housing prices, per capita disposable income, income expectation (unemployment rate), mortgage loan balance, mortgage interest rate, and urbanization index, etc., is established. Long-term balance relation and short-term impact of housing prices, per capita disposable income, income expectation , mortgage interest rate, and urbanization index, etc are analyzed through E-G two-step cointegration analysis and error correction model. Results show that there is long-term balance relation between these variables. In the long-run, income expectation (unemployment rate), mortgage interest rate, urbanization index, and balance of mortgage loans are main determinant factors of housing price. The degree of impact is as follows. 1% increase in the balance of mortgage loan will lead to 0.17% increase in housing prices; 1% decrease in rural population will lead to 0.17% increase in housing prices; income expectation (unemployment rate) decreasing by 1 percent will lead to housing prices increasing by 0.74%; if mortgage interest rate increases by 1 percent, housing prices will decrease by 0.08%. Among them, income expectation (unemployment rate) and balance of mortgage have greater impact on housing prices. These two variables have impact on housing prices in the short term as well. Error correction coefficient is 14%, which shows that the adjustment rate of Shanghai's housing market is fast. Each month, adjustment is 14%. Impact elastic of two-period lagged changes in housing prices to current housing prices is 0.42; that of three-period lagged changes in housing prices is 0.34, that of four-period lagged changes is 0.20. That shows that the housing price adjustment process is a sticky price adjustment process. Lagged housing price changes are main contribution to short-term fluctuations of housing prices. It proves that housing market doesn't fit the effective market hypothesis. On the housing market, consumer expectations are irrational. Consumers predict future housing prices based on previous housing prices and their movement. During the period when housing prices are increased substantially, bubbles will likely appear, and housing prices may deviate from their long-term value substantially. In addition, current Shanghai's housing market lacks the support of long-term purchase power, and the adjustment rate of housing prices is fast. The“prosperity- recession”cycle of Shanghai's housing market is relatively weak. Government should pay more attention to the housing market to insure a stable growing housing market.
Following are the 4 innovative contributions of this thesis.
1) Weak-form efficiency experiments show that the market efficiency theory of capital market can not explain the autocorrelation of housing prices. Starting from inherent attributes, this thesis systematically studied the reasons of autocorrelation of housing prices, i.e. lagged adjustment of housing supply and demand , irrational expectation on housing market, restriction on down-payment of housing financing, etc. will lead to lags in housing price adjustment.
2) GRNN neural network model is applied to housing price forecasting. Through comparison of its results and that from ARIMA forecasting, we conclude that GRNN model is better than ARIMA model in predicting Shanghai's housing prices, and demonstrate the non-linearity of Shanghai's housing market.
3) Time-varying parameter model of the relations between housing prices and housing mortgage are established. we conclude that there are long-term balance relations between housing prices and housing mortgage, and time-varying parameter model can better describe the relations between them than constant parameter models.
4) Urbanization index is introduced. Using unemployment rate as the proxy variable of income expectation, multi-factor models of Shanghai's housing prices and per capita disposable income, income expectation (unemployment rate), mortgage loan balance, mortgage rate, and urbanization index, etc., is established. Through E-G two-step cointegration analysis and error correction model, we show that there is long-term balance relation between housing prices and per capita disposable income, income expectation (unemployment rate), mortgage loan interest rate, and urbanization index, etc. There is no obvious correlation between per capita disposable income and housing prices. rbanization and balance of mortgage loans are determinant factors of housing prices. Overall, this thesis draw some new conclusions of the relations between housing prices and mortgage in the area of China's housing price movement. It has quite a great theoretical value and positive practical significance for establishing housing policies and related financial policies, promoting the healthy development of China's housing market.
引文
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