外文翻译--香港住宅市场合理价格和泡沫的实证研究

本科毕业论文外文翻译
外文题目：Detecting rational bubbles in the residential housing markets of Hong Kong
出处：Economic Modelling，2001，1(18)：61-73
作者：Hing Lin Chan Shu Kam Lee Kai Yin Woo
原文：
Abstract
This paper attempts to conduct an empirical study for detecting misspecification errors and rational bubbles in the residential housing markets of Hong Kong. We focus on a fundamental model that defines market fundamental price as a sum of the expected present value of rental income, discounted at a constant rate of return. Testable implications for detecting misspecification errors and/or price bubbles are explored through the flow and stock approaches. In addition, the paper attempts to identify the amount of misspecification and bubble components in the property price data of Hong Kong.
Keywords: Bubbles; Housing market; Modelling
1.Introduction
The total land area of Hong Kong is approximately 1075 km2. However, 80% of the territory is considered too hilly for property development. Therefore, only a tiny portion of the total supply could be used for residential purpose. The need to accommodate a total population of 6 800 000 people on a meager 50 km2of residential land has made Hong Kong one of the most densely populated cities in the world. Without doubt, land is one of the scarcest resources in Hong Kong. How to use the resource efficiently is, therefore, an important question. In a market economy, price is one of the most important pieces of information for formulating government policies. However, if the prices contain bubbles, misguided policies might be made as
a result. This problem is particularly important for Hong Kong because the government has, over the years, intervened extensively in the housing sector, despite its well-known reputation as being one of the most ‘laissez faire’ market economies in the world. These intervention measures include, for example, provision of public housing, restriction on supply of residential lands and rent controls in some years. As a result, housing prices are influenced to a significant degree by the government policy. It is, therefore, important to ascertain whether bubbles have existed in the residential housing markets.
Apart from the above, there are other reasons that motivate us to study this problem. For example, the Hong Kong property markets play an important role in the economy. Several official figures can illustrate this point. First, more than 45% of all bank loans are directly tied to properties. More than half of those loans are mortgage loans, which totaled in excess of HK$500 billion as at the end of 1997 (Hong Kong Government, 1998a).In additional, the real estate sector contributes approximately 10.2% of the GDP in 1996(Hong Kong Government, 1998b).Finally, income from land auction, rate and stamp duty accounted for approximately 24% of total Government revenue in 1997r1998.1 Because of these important relationships, the devastating effects associated with a bursting bubble, might be quite far-reaching as well as long-lasting. Clearly, there is a need for the authorities to avert the formation of price bubbles in the property markets. Another reason to study this problem is that the prices of residential property in Hong Kong were highly volatile over the last decade. For example, in 1991, the real price for the overall property market rose by 40%. Another drastic change occurred in 1995 when the price fell by 16.2%. It was then followed by remarkable increases of 18.9 and 20% in the next 2 years and a rapid fall of 50% in 1998.Given these drastic fluctuations, it is interesting to investigate whether price bubbles have been formed in this highly volatile period.
Despite the importance of this problem, not many studies have been done on detecting rational bubbles in the residential markets of Hong Kong. Most of the earlier papers, such as Peng and Wheaton (1994) and Mok et al. (1995) concentrated on studying the property price without taking the possibility of bubbles into account. In view of this, our paper attempts to fill this gap. To do that, we arrange the discussion
in the following manner. Section 2 will discuss the methodology. In particular, we focus on a fundamental model that defines market fundamentals as the sum of the expected present value of rental income, discounted at a constant rate of return. The methods of how to detect misspecification errors an/or speculative bubbles will be discussed. In Section 3, we will present the empirical result. In particular, the magnitudes of misspecification and bubble components will be presented. Section 4 will conclude the major findings of the paper.
2. Methodology
2.1.Model specification
We treat property as a good investment, which produces a stream of rental incomes over its lifetime. The current value of a property is therefore determined by the present value of current rental income and next period’s expected market price. The following equation formalizes this relation:
P t =)(1t t t P D E Ω++δ (1)
where Pt is the real value of property at date t , δ is the constant ex ante real discount rate, E (．∣t Ω) denotes rational expectations based on t Ω , which is a full information set available to the market representatives at time t , and Dt represents the real rental income during the period t .
Eq.(1) can be solved by recursively substituting forward for E(P 1+t )and using the law of iterated expectations. The solution is given in Eq.
2.2. Noise detection
In this paper, we follow the signal extraction method of Durlauf and Hall (1989a,b) and Durlauf and Hooker (1994) to investigate the existences of St and B t by the use of the flow and stock test. To carry out the flow test, let us first consider the perfect foresight fundamental price P.
Because of Eq., r is known as one period excess return on holding property. Once the information of r is available, it is possible to conduct the flow test. To begin with, let Lt ( x )be the information set available at time t, which is a subset of t Ω .Projection of r onto Lt (x ) captures the fitted value of St . since t 4 and _et 4 are, by definition, orthogonal to Lt (x ). Therefore, under the null hypothesis, r is orthogonal to Lt (x ). Failing to reject this hypothesis implies that St is zero.
The implementation of the stock test, however, relies on Eq. from which we know
that the projection of P onto L(x).can capture the fitted values of B t and St. Therefore, the null hypothesis assumes that P is orthogonal to Lt( x). Failing to reject the null hypothesis implies that the total model noise,
Bt + St, is zero.
To sum up, there are three possible outcomes when these two tests are taken together. Firstly, if both flow and stock orthogonal conditions are not rejected, price follows fundamental price solution. That is, the total model noise is zero.Secondly, in the case where the flow projection is zero but the stock projection is non-zero, the model noise contains Bt only. In other words, the price sequence is consistent with the general solution Eq. Thirdly, if both orthogonal conditions are rejected, we can confirm that St is present but further analysis for the existence of Bt is required.
3.Empirical studies
3.1.Noise detection
The implementation of the flow and stock tests requires the construction of r and P. Since we deal with moment (orthogonal) conditions, the generalized method of moments (GMM) is needed to construct r. To do that, we first estimate δvia GMM, using the flow projections themselves as given by the following orthogonality conditions,
The role of the GMM estimator is to help select an optimal δso that the sample correlations between the Lt(x) and r are as close to zero as possible. This can be done by varying δto minimize the following criterion function (Hansen, 1982):
where m is the sample moment condition, W is a weighting matrix and N refers to the number of sample observations. A necessary (though not sufficient) condition to obtain an asymptotically efficient estimate of δis to set W equal to the inverse of the covariance matrix of the sample moments, m. However, since the GMM’s estimates are sensitive to the choice of the bandwidth parameter, we therefore use heteroskedasticity and autocorrelation covariance matrix estimators that make use of automatic data-dependent band-width selectors (Newey and West, 1994).
The data for this study are taken from the Hong Kong Government Property Review. They contain data on monthly averaged rentals and quarterly averaged prices of the private domestic properties within the class A, which is defined as those
apartments whose sizes are less than 39.9 m2. The rentals are exclusive of rates, management and other charges. Since the urban areas of Hong Kong consist of three main regions: Hong Kong Island, Kowloon and New Kowloon, we will include all of them for analysis. The sample period runs from the first quarter of 1985 to the third quarter of 1997 for empirical testing, with additional data from the fourth quarter of 1997 to the third quarter of 1998 for the construction of the perfect foresight price. 3.2.Estimation of S t and B t
Since we have obtained the estimates of B t, we can further examine the time series property of the Bˆt by using the N1and N2test statistics of Bhargava (1986).The purpose of conducting N1and N2tests is to examine whether the bubble estimates follow, without and with drift, respectively, random walk against the alternative of explosive patterns. The results of these tests, summarized in Table 5, accept the null hypothesis for all the three regions in Hong Kong. In other words, the bubble estimates, Bˆt , do not exhibit linearly explosive property, which indicates that the price bubbles in Hong Kong residential housing markets are not deterministic. This is not surprising since bursting bubbles are more commonly observed than deterministic bubbles. In order to illustrate how the bubbles explode and burst over time, we plot Bˆt of the three urban regions in Figs. 4-6. In general, Bˆt moved from 1985 towards the peaks in 1991-1992 but burst afterwards. Starting from 1995, however, Bˆt exploded again reaching the peaks in 1997.
4.Conclusion
This paper reports empirical studies for the existence of unobservable misspecification errors and explosive rational bubbles in the property markets of the three urban regions in Hong Kong. We assume that the property price is composed of fundamental, rational bubble and misspecification error components. The signal extraction approach of Durlauf and Hall (1989a, b) is employed for uncovering the unobservable model noise. Since both the nulls of the flow and stock tests are rejected, this means that the misspecification error exists in the model noises. To measure the sizes of each component in the model noise, we have used the formula of Hansen and Sargent (1980) to calculate the misspecification error. On the other hand, the bubble component is calculated by the projection of P. The paths of the bubbles show that the
bubbles exploded most sharply between 1990 and 1992 and between 1995 and 1997. 译文：
香港住宅市场合理价格和泡沫的实证研究
摘要
这篇文章倾向于指导揭开香港住房市场的设定误差和合理泡沫的实验研究。

我们关注有关市场基本价格的重要模型。

这种模型把市场的基本价格定义为预计的租赁收入现值和固定盈利率的折扣的总和。

通过研究流量和库存的方法可以验证设定误差和价格泡沫研究的意义。

此外，这篇文章还打算在香港房产价格的数据中鉴定设定误差的数量和泡沫的组成部分。

关键字：泡沫；住房市场；模型
1.介绍
香港的总面积大约为1075平方千米。

但是，80 %的土地是丘陵不适合房产开发。

因此，在提供可以利用的土地中只有一小部分可以作为住房土地。

一片不到50平方千米的住房土地要容纳6800000的人口，这使得香港成为世界人口密度最大的国家之一。

不用怀疑，土地是香港最稀缺的资源。

怎样有效率的利用这个资源是一个非常重要的问题。

在市场经济下，价格是政府制定政策的最重要的信息依据之一。

但是，如果存在价格泡沫，那政府就会被误导制定错的政策。

这个问题对香港政府来说非常的重要。

因为政府已经对住房市场进行宏观调控好几年了，尽管香港是世界有名的放任自由的市场经济。

近几年的调控措施中包括提供公共住房，限制住房土地的供给，房租管理。

但结果却差强人意，房产价格在政府政策的影响处于白热化的阶段。

因此，查明住房市场是否存在泡沫现象是非常重要的。

除上述原因外，还有另一些原因促使我们去研究这个问题。

例如，香港的房产市场在整个经济中有很重要的地位。

一些官方的数据可以证明这个观点。

首先，超过45%的银行贷款和房产有关，超过一半的贷款是住房贷款。

到1997年，住房贷款的总数超过了5000亿港币。

（香港政府，1998a）。

另外，1996年香港的不动产拉动GDP10.2%（香港政府，1998b）。

最后，1997年和1998年，房产拍卖
收入和印花税收入大约占政府总收益的24%。

由于这些复杂的关系，泡沫的破碎将会带来沉重的影响，这影响也会持续很久。

无疑的，当局应该避免房产市场的价格泡沫的构成。

另一个研究这个问题的原因是香港在过去十年里的住宅房地产价格波动剧烈。

例如，1991年住宅房地产的实际价格上升了40%。

1995年房价又急剧下降了16.2%。

接着2年内又分别明显的上升了18.9%和20%，1998年又急剧下降50%。

根据这些剧烈的波动现象，去调查在这非常波动的时期是否已经形成了价格泡沫令人关注。

尽管这个问题非常重要，但探究香港住房市场的合理泡沫的研究还是不多的。

最早期的论文有彭粲和惠顿(1994)和莫孙俐 (1995)对资产价格泡沫的可能性考虑的专门研究。

鉴于此,本文试图填补这一差距。

要这麽做,我们就安排以下方式的讨论。

第2部分将讨论的是方法论。

特别要讨论的是这种把市场的基本价格定义为预计的租赁收入现值和固定盈利率的折扣的总和的模型。

如何检测不合理的误差或投机泡沫的方法也会被讨论。

在第三节,我们将介绍实证研究的结果。

特别是不合理的误差的大小和气泡的组成部分。

第4部分将总结本文的研究发现。

2. 方法论
2.1模型设定
我们把财产当作是不错的投资,它一生可以产生一连串租赁收入。

物业的现值因此由现在租赁收入的现值和下个时期的预期市场价格决定的。

下列方程说明了这个关系:
P
t =)
(1t
t
t P
D
EΩ
++
δ (1)
Pt是在房地产在日期t的真正价值, δ是事前真正的贴现率,E(。

∣)是指基于理性预期tΩ,这是一个完整的资料集可供市场代表在t时期利用, Dt代表在t时期真正的租金收入。

等式。

(1)可以解决递归的替代了E(P),并利用迭代的律法期望。

等式给出了解决的方法。

2.2噪音检测
在本文中,我们遵循Durlauf and Hall (1989a,b) and Durlauf and Hooker (1994)的信号提取方法利用组织的流动和股票测试探讨St和Bt的存在。

进行流量测试前,我们先来考虑一下完美预测的基本价格P。

根据公式,r是持有房产的一时期超额回报财产。

一旦r的信息是可行的,它
可以进行流量测试。

首先,让Lt(x)是在t时期是可以利用的信息,并是tΩ的子集。

假设x在Lt（x）上得St的拟合值。

t4和_et4必然正交于Lt(x)。

因此在零假设下，r与Lt(x)相交。

这个假设存在意味着St等于零。

实施股票测试,依靠公式我们知道把P投射到L(x)可以得到拟合值Bt和St.因此,这个零假设是假设P正交于Lt(x)。

这个假设的存在意味着总模型的噪音,Bt+St等于零。

综上所述,当这两测试放在一起时，存在三种可能的结果。

首先,如果流量和库存正交存在,价格服从基本的价格方案。

也就是说,总模型噪声为零。

其次,在流量预测为零而库存预测不为零的情况下,模型噪声只包括Bt。

换句话说,价格序列是公式的通解。

第三,如果两个正交条件都不成立,我们能够确认St的存在,但进一步分析Bt的存在是必要的。

3.实证研究
3.1噪声探究
实施流量和库存的测试需要构建r和p.因为我们处理正交条件,最普遍的方法（GMM）是构建r。

我们通过GMM初步估计δ,并在以下正交条件中利用流量预测其本身，
利用高斯混合模型(GMM)去估量是为了选择一个最佳的δ,使Lt(x)和r的试样关系近乎于零。

这可以通过变化δ的值使准则函数最小化 (Hansen,1982)。

在m是样本矩条件下,W是称重矩阵，N指的是试样的观察结果的总和。

令W等于样本矩的协方差矩阵逆的倒数m是得到一个渐近有效的估计值δ的必要 (尽管不是充分)条件。

然而,由于高斯混合模型(GMM)的统计对带宽参数的选择非常敏感,因而我们要使用异方差性和自相关协方差矩阵函数并充分利用自动的具有数据的图象的宽带选择符（Newey 和West,1994）.
本研究的数据来自于香港政府财产审查。

它们包含月平均租金和季平均私有家庭财产的价格。

我们把这一类人定义为那些公寓面积不到39.9平方米。

这里的住房租金不包括差饷，管理费和别的费用。

由于香港市区包括三个主要地区:香港岛、九龙和新九龙,我们将对这三个地区都进行分析。

采样周期从1985年第一季度到1997年第三季度是实证研究时期,并有从1997年第四季度到1998年第三季度的额外数据是为构建完美的预测价格
3.2 St和Bt的评估
既然我们已经得到了Bt的估计值,我们可以利用Bhargava(1986)的N1和N2
的校验统计学更进一步检查Bt的时间数列的财产。

进行N1及N2测试的目的是为了检测泡沫是否具无规律分布并对爆炸的模式有选择的趋势。

这些测试结果总结在表5中,原假设包括香港的三个区域。

换句话说,泡沫的评估Bˆt,不具有线性爆炸性的特性,这表明价格泡沫在香港住宅房屋市场是不确定性的。

这并不奇怪,因为我们通常观察泡沫破裂而不是确定性的泡沫。

为了说明泡沫是如何爆炸,并随着时间的推移如何爆炸,我们在表格4-6中把B^t划分为三个城市地区。

一般来说, Bˆt从1985年移向1991-1992的顶峰，接着破裂。

但是从1995年以来, Bˆt爆炸点再一次达到1997年的顶峰。

4.总结
本文的实证研究记录了香港三个城市地域房产市场的不合理房价和突发性泡沫。

我们假设房产价格是由基本的、理性的泡沫以及不合理的部件组成。

利用了Durlauf的信号提取方法和Hall(1989a,b)的观察难以发觉的噪声模型。

并通过假设流量和库存测试的不存在,意味着在噪音模型中存在不合理的误差。

为了测量噪音模型中每个组成部分的大小,我们采用Hansen和Sargent(1980)的公式计算不合理的误差。

另一方面,泡沫成分的计算依照P的投影。

泡沫的路径表明了气泡最突出地爆炸期在1990年至1992年和1995年到1997年。