Chapter 2 Literature Review
2.3 Review of Housing Bubble Factors
2.3 Review of Housing Bubble Factors
According to the past literatures, there are plenty of studies exploring the relationship between housing bubbles and other variables. These researches showed that many factors contributed to housing bubbles. This section mainly reviews three kinds of these factors: investment, supply/demand and policies.
(1) Investment
The factors of investment refer to the relevant indexes in the financial market.
The changes of these factors not only influence the cost of real estate investment, but also adjust the investors’ anticipation of the house market. Roche (2001) employed regime-switching models to explore housing bubbles in Dublin. The results found that the economic boom, low interest rates and more returning emigrants would push up the demand for houses in Irish. They also pointed out that once the supply of houses was not adequate to the demand, house prices would inevitably increase. So the Irish government should design policies to raise the supply of houses. Li and He (2011) built two non-linear smooth transition regressions with the money supply M2 and weighted inter-bank rate (IBOR) to examine the non-linear dynamic relation between the house price and the monetary policy in China. The empirical results found that the asymmetric non-linear impact of money supply M2 on house prices was notable but massive money supply could only make house prices change a little. Besides, the weighted inter-bank rate had a substantially weak relationship with housing prices.
Evidently, the housing policies only depending on M2 and IBOR would not be effective. Tsai and Peng (2011) applied the panel cointegration test to discuss the relationship of the bubble with mortgage rate, money supply, inflation rate, homeownership rate and user cost of housing. This study found that expansionary monetary policy lead to speculations and also resulted in bubbles in Taiwan housing market.
Liang and Gao (2007) used error correction model and panel data model to explore the factors which determined real estate price fluctuation. The conclusion indicated that the effect of credit policy on house prices were stronger in the east and west of China. And the impact of interest rate policy is significant but small.
Furthermore, GDP was positively related to house prices, which meant that the
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development of real estate market depended on the economic conditions. Agnello and Schuknecht (2011) employed Multinomial Probit model to detect booms in housing prices in eighteen industrialized countries from 1980 to 2007. The estimates suggested that domestic credit and interest rates had a significant impact on the probability of booms and bust occurring.
(2) Supply/Demand
As mentioned above, the supply and demand of houses are determined by macroeconomic environment. By the factors of supply/demand we mean population, unemployment and so on. The mismatch in supply and demand influenced house price directly. Thus lots of researches explore how the macroeconomic factors affect housing prices or housing bubbles. For example, Quigley (1999) studied the linkages between house prices and general economic conditions by basic regression models.
The results suggested that the housing prices would become higher when household income, construction permits and the number of household increased. However, if the owner-occupied vacancy rates were higher, the housing prices decreased. Malpezzi (1999) establish a simple error correction model to investigate housing price changes.
This study found that price changes depended on the measured disequilibria in previous periods. Moreover, the rapid-growing population and income resulted in higher conditional price changes while higher mortgage rates lowered price changes.
Chen and Patel (2002) attempted to explain the strong investment demand and short-run variability in housing prices. And then they indicated that the household income, construction cost and house supply were important house price determinants in the long-run equilibrium as well as the money supply and stock prices affected the house prices effectively in the short-run dynamic. Besides, the non-linear model that they used helped to estimate the short-run fluctuations in house prices but the forward-looking expectations mechanism could not help.
(3) Polices
The exorbitant housing price is unfavorable for steady economic development.
Therefore the government will try to control real estate market through housing polices, which also affects housing bubbles. But it is difficult to quantize the housing
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policies. Few researches employ econometric model to investigate the relationship between price bubbles and housing policies. Wang and Huang (2013) attempted to explore the long-run impacts of the house purchase restrictions and property tax on housing prices. The theoretical prediction showed that the house purchase restrictions might curb housing prices but the effect was limited. Also, it was indicated that property tax might reduce the short-run housing prices but increase the long-run house prices possibly. At last, they employed 70 cities’ panel data to examine the impact of the house purchase restrictions on house prices and the empirical result was consistent with the theoretical one.
From the literatures above, the researches that investigate the factors affecting the housing bubbles usually focus on the perspectives of investment and supply/demand.
According to the results of these studies, the relations of housing bubbles to investment variables and supply/demand variables are easy to see. This is explained by the fact that the housing bubbles are pushed up mainly by speculation which has a high correlation with these factors.
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Chapter 3
Research Method and Data Information
This chapter is divided into two parts. The first part shows the methods for the housing bubbles measurement and the empirical analysis. And the second part describes the variables selected in the empirical analysis.
3.1 Research Method
The purpose of this study is to measure the status of the housing bubbles in the three selected cities and to explore the equilibrium relationship between the housing bubbles and other variables. Based on the literature review，this study defines housing bubbles as the comparison between fundamental values and market prices. According to Lin (2012), the fundamental value of real estate can be calculated by annual rents and reasonable capitalization rate. And the funds which are used to purchase houses usually consist of equity and mortgage. Thus, weighted average cost of capital can be regarded as the reasonable capitalization rate which is adopted by most market participants. In the empirical analysis section, we employ Johansen cointegration method to analyze the housing bubbles of these three cities and other variables respectively. If they have the cointegration relationship, Vector Error Correction Model (VECM) is applied for further study. Otherwise, they should be interpreted through Vector Autoregressive (VAR) model. Finally, we use Granger Causality test to find out the lead/lag relationship between the housing bubbles and the variables. In short, the general process of empirical analysis is as follows:
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Figure 3- 1 Process of Research Method
3.1.1 Capitalization Rate
In real estate appraisal, the capitalization rate is commonly used to value an income generating property. The capitalization rate, which is sometimes referred to as the “cap rate”, is the ratio between the net operating income (NOI) and the transaction price or the current value (Brueggeman and Fisher, 2011). The formula is:
𝑟 =𝑃𝑟𝑖𝑐𝑒(𝑉𝑎𝑙𝑢𝑒)𝑁𝑂𝐼 (3.1)
Generally, NOI is calculated by rental income from operating expenses. According to the equation above, we can estimate the value of real estate by determining the NOI and dividing by an appropriate 𝑟.
3.1.2 Weighted Average Cost of Capital
In general, the investors use both equity and loan to finance their investments.
They must take into account the loan interest they need to pay and the opportunity cost of keeping the money. Accordingly, they expect that their total earnings are more than the costs of capital. To evaluate an investment project, the investors usually discount the future cash flows at the weighted average cost of capital (WACC). The WACC is the minimum return that a project must satisfy its investors (Ross et al., 2009). The formula of WACC works out to be:
Structural Change Unit Root Test Cointegration Test VECM
Granger Causality Test
VAR
Yes No
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𝑅0 =𝐸𝑉× 𝑟𝐸+𝐷𝑉× 𝑟𝑀 (3.2)
In this expression, the cost of equity is 𝑟𝐸 and the cost of loan is 𝑟𝑀; 𝐸/𝑉 represents the proportion of equity and 𝐷/𝑉 represents the loan-to-value ratio.
The income tax base is calculated by NOI from the expenses of interest and depreciation. In other words, interest is tax deductible which can cut the average cost of capital. So the formula of after-tax WACC is as follow：
𝑅0 =𝐸𝑉× 𝑟𝐸 +𝐷𝑉× 𝑟𝑀× (1 − t) (3.3)
where t is the income tax rate. Since the WACC is the minimum acceptable return, NOI divides by WACC is the reasonable price accepted by most investors.
3.1.3 Cointegration Test
In 1987, Engle and Granger proposed the theory of cointegration, which provides a new way to build up models for non-stationary series. Although the non-stationary time series can be rendered stationary through differencing the series, the differencing series does not have direct economic meanings. However, cointegration which refers to linear combinations of non-stationary time series is an alternative method of achieving stationary. It is noticeable that the series must be integrated of the same order. Furthermore, cointegration implies that there exist long-run equilibrium relationships between the variables.
Engle and Granger also proposed a testing procedure to confirm whether the non-stationary series are cointegrated. The Engle-Granger test employs the residuals of regression to perform the unit root test. Suppose {yt} and {xt} are I(1), we build up a regression model as follow:
𝑦𝑡 = 𝛽0+ 𝛽1𝑥𝑡+ 𝑒𝑡 (3.4)
In this equation, yt is the dependent variable; xt is the independent variable and et is the error term. Then, we use the {et} sequence which is the estimated residuals from the regression equation above to perform the unit root test. The regression of the
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residuals can be expressed as:
∆𝑒̂𝑡= 𝑎1𝑒̂𝑡−1+ 𝜀𝑡 (3.5)
If the estimated result can reject the null hypothesis |𝑎1| = 0, then we can make a conclusion that the variables are cointegrated.
However, the Engle-Granger procedure cannot make the separate estimation of multiple cointegrating vectors. In this two-step method, since the coefficient 𝑎1 is obtained by the residuals of another regression, the errors produced in step1 are carried into step 2. Fortunately, Johansen cointegration test which is proposed in 1991 can avoid the defects above.
Johansen cointegration test, which is based on VAR approach, uses the maximum likelihood estimation to examine cointegration relationships between the non-stationary time series. This approach can interpret the multiple long-run equilibrium relationship more robustly. Assuming a VAR model of order p and n variables can be expressed as follow:
𝑦𝑡 = 𝛼1𝑦𝑡−1+ 𝛼2𝑦𝑡−2+ ⋯ + 𝛼𝑝𝑦𝑡−𝑝+ β𝑥𝑡+ 𝜀𝑡 (3.6)
where 𝑦𝑡 is a vector of non-stationary I(1) series; 𝑥𝑡 is a d-vector of exogenous variables; 𝜀𝑡 is disturbance vector. Through subtracting 𝑦𝑡−1 on both sides of the equation (3.6), we can obtain a new equation as:
∆𝑦𝑡 = 𝜋𝑦𝑡−1+ ∑𝑝−1𝑖=1 𝜋𝑖∆𝑦𝑡−𝑖+ β𝑥𝑡+ 𝑢𝑡 (3.7)
where π = ∑𝑝𝑖=1𝛼𝑖 − 𝐼 and π𝑖 = − ∑𝑝𝑗=𝑖+1𝛼𝑗. In the equation (3.7), we need to pay attention to the rank of the long-run impact matrix π which equals to the number of cointegrating vectors. Then we can obtain the number of cointegration relationships by examining the non-zero characteristic roots of π. Therefore, Johansen proposed the Trace and Maximum Eigenvalue test to determine the number of cointegration.
𝜆𝑡𝑟𝑎𝑐𝑒(𝑟) = −𝑇 ∑𝑘𝑖=𝑟+1ln(1 − 𝜆𝑖) (3.8)
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𝜆𝑚𝑎𝑥(𝑟) = −𝑇 ln(1 − 𝜆𝑟+1) (3.9)
where T is the number of observations and λr is the value of characteristic roots. The null hypothesis of the Trace test is H0: rank≤r. On the other hand, the null hypothesis of the Maximum Eigenvalue test is H0: rank=r.
3.1.4 Vector Error Correction Model
Engle and Granger proposed Vector Error Correction Model (VECM) that is the combination of cointegration and error correction model. VECM provides robust interpretations of both long-run and short-run dynamics. Hence, VECM is an appropriate model for a system of cointegrated variables. The system of cointegrated series can be expressed by VECM as follow:
∆𝑦𝑡= 𝛼𝑒𝑐𝑚𝑡−1+ ∑𝑝−1𝑖=1 𝜋𝑖∆𝑦𝑡−1+ 𝜀𝑡 (3.10)
𝛼𝑒𝑐𝑚𝑡−1 is the vector of error correction terms, which equals to 𝛽′𝑦𝑡−1. It can show the long-run equilibrium relationships between the variables. And the coefficient 𝛼 represents the rate of adjusting deviations. For a more brief explanation, we assume a VECM with two series (y1 and y2) which have no lagged differences. Then the set of equations can be written as:
∆𝑦1𝑡 = 𝛼1(𝑦2𝑡−1− 𝑏𝑦1𝑡−1) + 𝜀1𝑡 (3.11a)
∆𝑦2𝑡 = 𝛼2(𝑦2𝑡−1− 𝑏𝑦1𝑡−1) + 𝜀2𝑡 (3.11b)
In the equations, 𝛼1 and 𝛼2 represent the adjustment rate. The variable on the right side of the equations is the error correction term. In the long-run equilibrium relationship, this term should be zero. Hence, once the series (y1 and y2) deviate the equilibrium, the error correction term changes. The coefficients 𝛼1 and 𝛼2 make the deviating series return to the long-run equilibrium.
3.1.5 Vector Autoregressive Model
If there is no cointegration between the time series, Vector Autoregressive (VAR)
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model is appropriate to explore the dynamic interrelationships between the series.
According to the theory of VAR, it requires all the series are stationary. Therefore, the non-stationary series need to be differenced firstly. In the VAR model, every endogenous variable is expressed by the lag values of all the variables. Hence, VAR can predict the relationships between the interrelated series and analysis the impulse of random disturbances on variables. The mathematical expression of VAR can be expressed as:
𝑦𝑡 = 𝛼1𝑦𝑡−1+ ⋯ + 𝛼𝑝𝑦𝑡−𝑝+ 𝛽𝑥𝑡+ 𝜀𝑡 (3.12)
In this equation, 𝑦𝑡 represents the vector of endogenous variable; 𝑥𝑡 represents the vector of exogenous variable; p is the selected lag order and 𝜀𝑡 is the vector of disturbances. Especially, different 𝜀𝑡 at the same period can be interrelated but would not related to its own lag value and the variables on the right side of the equation (3.12).
3.1.6 Granger Causality Test
In the econometric analysis, some variables may be significantly related with no economic meaning. This is a common problem in the field of econometric. Thus, in 1969, Granger proposed the Granger causality test to judge the causal relationship of variables. In the Granger causality test, the key to note is that how much the current y can be interpreted by the lagged value of x. If the related coefficient of x and y is significant, we can say that y is caused by x. Based on the theory of Granger causality test, if x is the reason of y, x should precede y. The Granger causality equation is defined as:
∆𝑦𝑡 = 𝛼0+ ∑𝑝𝑖=1𝛼𝑖∆𝑥𝑡−𝑖+ ∑𝑝𝑗=1𝛽𝑗∆𝑦𝑡−𝑗+ 𝜀𝑡 (3.13)
where 𝑦𝑡 is the dependent variable; 𝑥𝑡 is the independent variable and p is lag terms.
The null hypothesis of Granger causality test is H0: 𝛼1 = 𝛼2 = ⋯ = 𝛼𝑝 = 0. If the result of the test accepts the null hypothesis, the variable x cannot cause the variable y which means x is an exogenous variable for y.
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interest rates of mortgage and per-capita disposable income in the three cities.First of all, the real estate industry is capital-intensive. Both the developers and investors are deeply dependent on financing. When the central bank expands the credit scale, the home buyers can get more money from financial institutions easily.
Then the demand for houses increases significantly and the housing prices rise accordingly. As long as the easy credit policies continue, the housing bubbles would constantly accumulate. Thus, this study expects that total loans of financial institutions are positively correlated with the housing bubbles.
Secondly, interest rate is one of the indispensable macro-control means in China.
And in the real estate investment, interest rates of mortgage affect the capital costs which cannot be ignored. If interest rates rise, the carrying costs of houses will rise proportionately. Then the speculators change their minds to sell houses at the appropriate price, instead of hoarding properties. It is likely to reduce housing bubbles.
Hence, it is considered that the increase of mortgage rates might lead to declines in housing bubbles.
Lastly, personal income is one of the indicators of economic development. When the economy develops, people's income should increase, which in turn promotes economic development. Furthermore, the domestic economy and real estate industry should also be complementary to each other. Therefore, this study anticipates that personal incomes have a positive relationship with housing bubbles. However, there are obvious income disparities in different cities. Consequently, we select per-capita disposable incomes in Beijing, Shanghai and Guangzhou respectively.
3.2.2 Data Source
The data employed in this study range from January 2007 to November 2012, 71 samples in total. Because the status of housing bubbles is not published data, we
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repayment term of home loan, the lending rate of over 5 years is usually employed as the mortgage rate. The per-capita disposable incomes in the three cities are provided by GTA CSMAR database. Total loans of financial institutions and interest rates of mortgage are reported by People’s Bank of China monthly. However, the original data of disposable incomes is quarterly. Thus, we need to convert the quarterly data into monthly data by Eviews statistical software. Table 3-1 shows the brief information of the variables used in this study.Table 3- 1 The Variable Descriptions
Variable Code Source Time Period Direction
Housing Bubbles in
Income in Beijing INCOME_BJ CSMAR 2007Q1-2012Q4 +
Per-capita Disposable
Income in Shanghai INCOME_SH CSMAR 2007Q1-2012Q4 +
Per-capita Disposable
Income in Guangzhou INCOME_GZ CSMAR 2007Q1-2012Q4 +
Total Loans of
Financial Institutions LOAN People's Bank
of China 2007.1-2012.11 +
Interest Rates of
Mortgage INT People's Bank
of China 2007.1-2012.11 −
3.2.3 Data Analysis
It is helpful for further study to understand the characteristics of the data. The descriptive statistics of variables are shown in Table 3-2, including the mean, median, maximum, minimum and standard deviation. However, the characteristics of the housing bubbles in the three cities will be discussed later because the status of the housing bubbles is going to be calculated in the next chapter. From Table 3-2, INCOME_BJ, INCOME_SH, INCOME_GZ and LOAN have increased a lot during
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the research period, which accords with China’s economic growth situation. In addition, since interest rates are controlled by the central bank strictly, interest rates of mortgage do not change much certainly.
Table 3- 2 Descriptive Statistics of Variables
Variable INCOME_BJ INCOME_SH INCOME_GZ LOAN INT
Mean 2502.652 2591.438 2472.467 432881.8 0.067
Median 2473.880 2537.386 2424.446 425622.6 0.068
Maximum 3328.044 3818.363 3778.754 666868.3 0.078
Minimum 1767.888 1767.024 1644.325 243944.1 0.059
Std. Dev. 438.053 513.065 516.104 130845.4 0.007
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Chapter 4
Measure of Housing Bubbles
This chapter consists of three parts. The housing prices and rents in Beijing, Shanghai and Guangzhou from 2007 to 2012 are presented in the first part. The second part introduces the parameters used for calculating fundamental values. And the last part describes the situation of housing bubbles in three cities and analyzes the causes of changes.
4.1 Trends of Housing Prices and Rents
The data of housing prices in three selected cities comes from the monthly market report of China Real Estate Information Corporation (CRIC), as reported in Figure 4-1. As we all see, from January 2007 to November 2012, the housing prices had kept increasing in Beijing, Shanghai and Guangzhou. Beijing’s housing price rose from
￥9446/m2 to ￥21447/m2 while the housing price in Shanghai increased from
￥9548/m2 to ￥21863/m2. Also Guangzhou’s housing price rose from ￥8622/m2 to
￥12821/m2. In 2008, China’s real estate market was influenced by the subprime mortgage crisis and the housing prices fell a little bit. However, after several months, the housing prices perked up again, which meant that the real estate market had got out of the depression.
The housing rents in China’s real estate market are not transparent. So it is quite difficult to obtain the data of housing rents as long as we need. Under this circumstance, we decide to convert the housing rental index into the actual rents.
Firstly, we get the housing rents in November 2012 by CityRE Data. Secondly, the trend of the housing rental index is acquired in the China Real Estate Index System.
At last, according to the data above, we figure out the housing rents in three selected cities which range from January 2007 to November 2012 (as shown in Figure 4-2).
Compared with the housing prices, the rents grew at a slow rate.
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Figure 4- 1 The Housing Prices in Beijing, Shanghai and Guangzhou Source: CRIC
Figure 4- 2 The Housing Rents in Beijing, Shanghai and Guangzhou Source: CityRE and CREIS
According to the direct capitalization method, the market capitalization rates in
According to the direct capitalization method, the market capitalization rates in