房價、利率與總體經濟的波動

倪仁禧,劉景中,錢美容

(1.德明財經科技大學財金學院?台灣台北114)

(2.德明財經科技大學財金學院?台灣台北114)

(3.德明財經科技大學管理學院?台灣台北114?

摘 要；房地產傳統以來均被視為地域性顯著且缺乏流動性?但2007年美國的次

級房貸問題產生時卻衝擊全球股匯市。2008年美國大型金融公司逐一破產後更引發

全球金融危機?全球經濟活動陷入嚴重的衰退。房地產市場與總體經濟波動關係為

何?是否具有國際傳導特性?本文以時間序列VAR模型分析美國、中國、香港及台灣

房屋市場及總體經濟波動關係。發現美國GDP成長率變化有助於預測中國、香港、

台灣GDP成長率波動?而區域型的GDP成長率變化均能顯著影響三者之房價指數。

中國及台灣股價指數變化具有顯著預測美國及香港股價指數?而各地區股價指數均

有顯著影響房價指數效果。美國及至於利率市場方面?美國與中國及台灣利率互有

顯著預測效果?而中國及台灣利率亦能顯著預測香港利率走勢?而利率變化對房價

指數在各區呈現負面衝擊效果。在房屋市場指數方面?台灣與香港房屋價格指數可

用來預測美國及中國房價波動?而香港、台灣及中國三者房價指數均互有顯著預測

波動效果。

關鍵字；房屋價格指數(House Price Index)、向量自我迴歸模型(Vector Autoregression

Model)、向量誤差修正模型(Vector Error Correction Model)、共整合

(Cointergartion)、因果關係效果(Granger-Causality effect)

House Price？Interest Rates and Macroeconomic Fluctuation

NI JEN SHI, LIU JIN CHUNG, CHYAN MEI RONG

(1.Finance College, Takming University of Science and Technology, Taipei 114, Taiwan) (2.Finance College, Takming University of Science and Technology, Taipei 114, Taiwan) (3.Management College, Takming University of Science and Technology, Taipei 114, Taiwan)

Abstract；Housing is the quintessential non-tradable asset, and customarily it is categorized as asset with regional limiting characteristics and less liquidity. But, the

Sub-prime mortgage in 2007 had a big impact on global stock and foreign exchange

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markets. In 2008, some US giant, famous financial conglomerate bankrupted one after another, even caused global financial crisis, and put global economy into serious recession. What is the degree of the influence of housing market to macro economy? Does the prosperity of housing market carry international transmission mechanism? This paper uses Time-Series models of VAR Model, to study the interrelationship between housing market and macro-economy for US, Hongkong, Mainland China and Taiwan.. finds that the changes of U.S. GDP growth rates are helpful to predict the volatility of GDP growth rates of China, Hong Kong and Taiwan. And, the regional-based GDP growth rates can significantly affect the price index of the three objects. The changes of China and Taiwan stock indexes could significantly predict the changes of U.S AND Hong Kong stock indexes. And, all regional stock price indexes all have significant effects to house price indexes. For the interest rate market, there is a mutual predictable function between United States and Taiwan, and between the United States and China. The interest rates of Taiwan and China are helpful to predict the interest rate of Hong Kong.The impacts of the changes of interest rates to the house price indexes showed a negative signal for each area. For the housing market index, the housing price index of Taiwan and Hong Kong could be used to predict the house price fluctuations of the United States and China. There is a significantly mutual predictable function among Hong Kong, Taiwan and China for the volatility effects of house price indexes.

Key words: House Market Index, VAR Model, Vector Error Correction Model,

Cointegration, Granger-Causality effect

第一作者?倪仁禧 (1964.7.1出生)?男?台灣省彰化縣?副教授。主要研究方向:國際金融及不動產金融。

jenshi@takming.edu.tw。

第二作者?劉景中 (1973.05.02出生)?男?台灣省新北市?助理教授。主要研究方向:金融 經濟學。

michael@takming.edu.tw。

第三作者?錢美容(1970.03.16出生)?女?台灣省台東縣?服務業經營管理研究所碩士生。主要研究方向:金

融及不動產。091151@mail.bot.com.tw

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1 Introduction

After the impact of the Burst of Internet Bubbles in 1999 and the terrorist attack of 911 in 2001, the U.S. economy was trapped in a predicament situation. The real economic growth rate was 4.83% in 1999, slipped to 1.08% in 2001. After that, the interference of those incidents of the Enron (Enron) and other companies accounting fraud scandals in 2002 and the invasion of Iraq in 2003, added the U.S. economy more uncertainties and difficulties. To prevent the economy get into recession, the Federal Reserve Board (FED) cut interest rate 13 times consecutively. The basic interest rate fallen from 6.5% to 1%, from 2000 to 2003. And, low interest rate financial market provided an active loan and funding environment. The loan amount increased fast. The scales of real estate companies’ operations expanded quickly. Then, the subprime mortgage market continued exaggerating. However, in order to restrain inflation the FED changed the policy of low interest rate financial environment. The FED raised the basic interest rate 17 times consecutively, from 2004 to 2006, pushing the rate hiking to 5.25%. Rising interest rate increased the burden on borrowers. Since 2006, the default rate of subprime mortgage increased gradually. In 2007, the second largest subprime mortgage company, New Century Financial Corp. filed for bankruptcy. The crisis of subprime mortgage surfaced. The investors were panic to sell houses, resulting in the collapse of house prices in U.S. The house price index was 225.45 high in June 2007, down to 197.28 in December 2008. The financial crisis emerged from domestic markets in 2008, through the path of international transmission, triggered global financial crisis and put global economic activity into a serious recession. From September 2007, the FED restarted the interest rate cutting cycle, continuously cutting 8 times, as of October 2010 the basic interest rate maintained as low as of 0-0.25% only.

The nature of the liquidity of real estate is different from the one of stocks, bonds, and foreign exchange. Real estate is the quintessential non-tradable asset, and it is a

typical asset with sectional boundary liquidity. But, the collapses of prices of offices of U.S. in early 1990s, and prices of houses in 2008, and the crisis of subprime mortgage in 2008 caused U.S. stock market slumped and put global financial market serious recession. Whether the real estate is the same as other assets possess an asset liquidity? Morris and Heathcote (2004) pointed out that for the general public the housing is the main asset, and the big price volatility in asset markets, not only impacts the macro-economy of a country also has a tremendous influence on financial stability. Case et al. (1999) pointed out that

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real estate prices, and local GDP component and international GDP component are significantly interrelated. The fluctuations of international house prices should be partially interpreted as facing the international economy circle collectively.

Is there a causal relationship between interest rates and house prices? Is that house price responses first, or the other way? Kan and Donald (1980), Harris (1989), Cooper (2004) found that the effect of interest rate and house price is the inverse relationship. Kenny (1999) pointed out that the effect of interest rates and house prices is a positive relationship. What is the relationships of real estate to security markets and to macro-economy? Okunev J., P. Wilson, Zurbruegg R. (2002) found that Australia's real estate market and the stock market influences with each other. Kakes and Willem (2004) found that the housing market of the Netherlands affects the stock price, and thus significantly affects the economy. Bonnie (1998), Parker (2000), Iacoviello (2005) studied that the interrelationships among house price, interest rate, stock price and macro-economy, and found that a stable economy was under the control of interest rate, and the housing market changes significantly affected the macro-economy. Beltratti and Morana (2010) thought that housing prices and macro-economy developments were in different directions. Otrok and Terrone (2005) studied that the linkage factors of international housing price and found that it the movement of global interest rates. Taylor (2007) pointed out that big fluctuations in interest rates will lead to house price fluctuations. And, Bernanke (2010) thought that the mobile interest rate, the interest-paying only mortgage increase continuously and underwriting standards continue lowing were the factors that led to the big house price fluctuations in U.S. Then the collapse of house prices in U.S. triggered the global economy crisis. Bernanke, Boivin and Eliaz (2005), and Mumtaz and Surico (2009) studied of the impact of international transmission mechanism, probing of macroeconomic variables with cross-border mobility connection.

This paper, by using 3 major economies of the Asian region, Hong Kong, China, Taiwan and the United States as the objects, analyses fluctuations, path and influence of transmission of house prices, interest rates and macro-economy. This paper is divided into four parts, the first one is introduction, the second is to use price index, interest rates, stock index and the GDP growth rate of the United States, Hong Kong, China and Taiwan to run the VAR model and VECM model. The third is the empirical analysis. Finally, is the conclusion.

2 Theoretical Model

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(1) VAR MODEL

Sims (1980) proposed the VAR (vector autoregression, VAR) model. The model is according to data characteristics, rather than the default priori theory, and the variables are treated as endogenous variables. Using a regression equation indicates interactions between variables.The lag items of the variables contain all the information so that each regression equation can use the lag items as explanatory variables. This paper referred Bonnie (1998), Hui and Yue (2006) to constructed VAR model. Variable information is the price index, stock indices, interest rates and real GDP growth rate. Using time series theoretical model and empirical methods studies the influence of house prices, interest rates, and macro-economy. VAR model is determined as follows:

q

~Y= C++ (1) AYtt，it？ii，1

Where, Y is to be investigated variables which cosists of (n×1) endogenous t

variable vector, Y is Y to the amount of the first i-deferred items consisting of (n×1) t？it

~vector, A is (n×n) of the coefficient matrix, is (n×1) ector composed of one-time t

forecast error.

11121314YHH~??YHYH??AAAA????C??tt？11111t：?：?：?：?：?21222324YII~YIYIAAAACtt？1t1111：?：?：?：?：?= +++ (2) YSS31323334：?：?：?~：?：?YSYSCAAAAtt？1t1111：?：?：?：?：?YGDPGDP41424344~YGDPYGDPCAAAA：?：?：?t，?tt？1，?，?，?，?1111

(2) VECM and Cointigration

Engle and Granger (1987) proposed random walk of individual variables, even non-stationary, but if the correlation of Cointegration exists between variables. Then, each sequence of variables would integrate into a stable sequence. In long time, the linear combinations between the variables will base on short-term dynamic adjustment to achieve the long-run equilibrium. Although a short term fluctuations might push the variables away from the equilibrium level. However, in the long term, the degree of the deviation will fade gradually and the equilibrium level will come back again. Granger’s

representative Theorem is Vector Error Correction Model, VECM. VECM’s theorem is

that for any cointegration relationship existing variable group I (1), Vector Error Correction Model (VECM) applies. Adding error correction items to VAR model can be used to measure the effects of short term and long term variables (Brooks, 2008). VAR

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model adds error correction items to be the Cointegration - error correction model, as follows (3):

！Y，(Y？，！Y？，！Y？...，！Y？~ (3) tt？P1t？12t？2k？1t？(P？1)t

pi

(，(A)？I，，(A)？I？ ，ik，ijk，1ij，1

，Equation (3) is a first differentiation VAR model with error correction item, I is t？p

'，(，：；unit matrix. is measurable short-term impact. But, can be used to measure i

：long-term effects. is the error correction adjustment speed (Adjustment Speed). In the

：non-equilibrium state, the greater of the means that the adjustment of the average

speed faster. is the co-integration vector (cointegration vector) matrix. The rank of ；

determines the number of cointegration vectors. The rank of (π )can be divided into (

the following three cases:

(1) rank (π) = p, and π is full rank, indicating that vector Yis a constant sequence. t

(2) rank (π) = 0, and the rank of π is zero, indicating that vector Y do not have a t

long-term cointegration relationship.

(3) when 0

variables

There are two main Cointegration test ways. One is proposed by Engle and Granger (1987). In two stages, use least square method to estimate cointegration vectors. The other is proposed by Johansen (1988, 1991), called Maximum Likelihood Method. Using the rank of cointegration vectors measures the relationship of cointegration. Johansen uses Gaussian vector autoregressive model, the unrestricted and Gaussian errors included model, as a starting point. Use the corresponding error correction equation of the Model to be the maximum likelihood estimation basis, and use the statistics of two likelihood test ration to confirm the number of cointegration vectors. Use the maximum likelihood

ˆˆ?(function to estimate, and find out the root of characteristics. Then, use the matrix of

rank to test the existing of cointegration among variables. The tests of statistics are the Trace test and the Maximum Eigenvalue Test.

(1)、trace test，

H，among the variables, the number of the cointegration vectors is N at most. (H，00

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rN) (

H，indicating that among n variables, at most N kind of long-term cointegration trend 1

relationships.

?n

ln(1？?)? (r) = -T (4) ，itracei，r？1

(2)、maximun eigenvalue test ，

H，rank (π) = r, r co-integration vectors. 0

H，rank (π) = r +1, r +1 co-integration vectors. 1

?

?(r,r？1) =-T ln(1 (5) ？?)maxr？1

?T is total number of samples.is the i estimate of the ith eigenvalue. r is the ?i

number of cointegration vectors. When the value of trace test or the maximun eigenvalue test is very large, reject the null hypothesis.

3 Empirical Analysis

(1) basic information

This paper studies major variables of the United States, China, Hong Kong and Taiwan. For U.S., FAHA housing price indexes (USH), Dow Jones Industrial Average Stock Index (USS), the FED basic interest rate (USI), real GDP growth rate (USGDP). For China, Real Estate Climate Index Sales Price Index (CHH), Shanghai A Share Index (CNS), the People's Bank base rate (CNI), real GDP growth rate (CNGDP). For Hong Kong, private residential price index (HKH), the Hang Seng Index (HKS), Bank Base Rate (HKI), real GDP growth rate (HKGDP). For Taiwan, Sin-Yian House Price Index (TWH),the weighted stock price index (TWS), the discount rate (TWI), real GDP growth rate (TWGDP). Samples taken period is from the first quarter of 1998 to the third quarter of 2010, amount to 51 quarters of data.

Table 1, Table 2, Table 3 and Table 4 are the description of the data of the variables for the four areas. The coefficients of skewness of the U.S. house price index, U.S. GDP growth rate, Hong Kong GDP growth rate, Taiwan house price index, Taiwan GDP growth rate are negative, non-symmetrical distribution of the left side. The coefficients of skewness of Hong Kong house price index, China house price index, the U.S. FED basic interest rate, the Hong Kong Base Rate, People's Bank of China base rate, Taiwan

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rediscount rate, U.S. Dow Jones Industrial Average Stock Index, the Hang Seng Index in Hong Kong, China Shanghai A Share Index, Taiwan weighted stock price index, China's GDP growth rate are positive, non-symmetrical distribution of the right side. The coefficients of kurtosis of People's Bank of China base rate, China Shanghai A Share Index, U.S. GDP growth rate, and Taiwan GDP growth rate show a peak of more than 3 distribution, leptokurtic distribution. the rest show a low fat tail distribution. Jarque-Bera test statistic value of the normal distribution show that except U.S. house price index, Dow Jones Industrial Average Stock Index, Hong Kong House price index, the Hang Seng Index in Hong Kong, China house price index, China GDP growth rate, Taiwan house price index, and Taiwan weighted stock index, the rest are not in the area of the normal distribution test. Ljung-Box Q statistics show that the sequence with a significant level of 1% will hold the characteristics of first-order sequence.

Table 1 US Common Sample Descriptive Stats

USH USI USS USGDP

51 51 51 51 Observations

104.0123 3.132353 10306.17 2.315882 Mean

105.7212 3 10435.48 2.73 Median

111.9021 6.5 13895.63 5.38 Maximum

93.50892 0.25 7591.93 -4.11 Minimum

5.141757 2.099019 1419.154 2.139161 Std. Dev.

-0.46158 0.021342 0.253085 -1.31771 Skewness

2.066414 1.512236 3.133384 4.786447 Kurtosis

；；；；Jarque-Bera 3.663093 0.58225 4.707434 21.54086

Sum 5304.63 159.75 525614.7 118.11

Sum Sq. Dev. 1321.883 220.2941 1.01E+08 228.8004

；；；；；；；；；；；；Q(1) 48.797 46.754 35.145 43.157 ；；；；；；；；；；；；Q(2) 89.96 84.176 56.254 70.363

Table 2 HK Common Sample Descriptive Stats

HKH HKI HKS HKGDP

51 51 51 51 Observations

103.2125 6.679216 15254.46 3.423529 Mean

99.05349 6 14230.14 4.8 Median

132.8407 10 27812.65 12 Maximum

73.32372 5 7883.46 -8.1 Minimum

16.55839 1.784044 4840.478 4.912783 Std. Dev.

0.34542 0.476642 0.652661 -0.71909 Skewness

1.748628 1.70147 2.786244 2.625055 Kurtosis

；；4.341783 3.717807 Jarque-Bera值 5.51423 4.694036

Sum 5263.839 340.64 777977.4 174.6

Sum Sq. Dev. 13709.02 159.1406 1.17E+09 1206.772

；；；；；；；；；；；；Q(1) 34.397 45.545 42.234 36.388

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；；；；；；；；；；；；Q(2) 80.265 71.83 53.923 52.098

Table 3 CN Common Sample Descriptive Stats

CNH CNI CNS CNGDP

51 51 51 51 Observations

104.3392 5.925882 2139.067 9.631373 Mean

104.3 5.85 1809.96 9.1 Median

111 7.92 5827.66 14.5 Maximum

98.9 5.31 1135.12 6.5 Minimum

3.370405 0.758006 1018.255 2.284862 Std. Dev.

0.351453 1.317738 1.845997 0.523013 Skewness

2.12185 3.641376 6.643151 2.240066 Kurtosis

；；；；；；2.688602 3.552303 Jarque-Bera值 15.63383 57.16966

Sum 5321.3 302.22 109092.4 491.2

Sum Sq. Dev. 567.9816 28.72864 51842208 261.0298

；；；；；；；；；；；；Q(1) 39.029 35.753 40.514 41.856 ；；；；；；；；；；；；Q(2) 63.395 54.110 64.695 72.848

Table 4 TW Common Sample Descriptive Stats

TWH TWI TWS TWGDP

51 51 51 51 Observations

104.1092 2.772059 6672.995 4.163137 Mean

105.0473 2.375 6522.19 5.47 Median

119.9686 5.25 9854.95 13.59 Maximum

86.19345 1.25 3636.94 -8.56 Minimum

7.954405 1.339474 1479.56 4.559298 Std. Dev.

-0.19135 0.476892 0.083461 -0.9514 Skewness

2.484248 1.784347 2.278179 4.203192 Kurtosis

；；；； Jarque-Bera 0.876458 1.166388 5.073473 10.77014

Sum 5309.571 141.375 340322.8 212.32

Sum Sq. Dev. 3163.628 89.70956 1.09E+08 1039.36

；；；；；；；；；；；；Q(1) 29.211 46.275 31.646 29.814 ；；；；；；；；；；；；Q(2) 44.304 82.062 45.715 34.384

Note，

(1)、Q(1)、Q(2) is Lag 1、Lag 2 Ljung-Box Q-Stat

；；；；；；(2)、Significant at the 1% level？ Significant at the 5% level？ Significant at the 10% level。

Table 5 shows the coefficient matrix of variables of United States, China, Hong

Kong and Taiwan. For U.S., the correlation coefficients of U.S. house price index to the

FED basic interest rate and the GDP growth rate were 0.32 and 0.45. The correlation

coefficients of the FED interest rate to the Dow Jones Industrial Average Stock Index and

GDP growth rate were 0.38 and 0.56. The correlation coefficient of Dow Jones Industrial

Average Stock Index to the GDP growth rate was 0.22. For Hong Kong, the house price

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index to the bank base rate was negatively correlated. The correlation coefficients of the house price index to GDP growth rate and the Hang Seng index were 0.55 and 0.45. The correlation coefficient of the Hang Seng Index to the GDP growth rate was 0.43. For China, The correlation coefficients of the house price index to the Shanghai A Share Index and GDP growth rate were 0.26 and 0.70. The correlation coefficient of People’s

Bank base rate to the Shanghai A Share Index was 0.35.The correlation coefficient of the Shanghai A Share Index and the GDP growth rate was 0.5.For Taiwan, the correlation coefficient of the house price index to re-discount rate was negatively correlated. The correlation coefficients of the house price index to the weighted stock price index and GDP growth rate were 0.22 and 0.37. The correlation coefficient of re-discount rate to the weighted stock price index was 0.39. The correlation coefficient of the weighted stock price index to the GDP growth rate was 0.44 .

Table 5 House Price Index、Interest rate、Stock index And GDP Growth Rate Correlation Coefficient Matrix

house Interest rate Stock index GDP

US

USH 1 0.322149 0.051468 0.45497

USI 0.322149 1 0.381701 0.563358

USS 0.051468 0.381701 1 0.228104

USGDP 0.45497 0.563358 0.228104 1

Hong Kong

KHH 1 -0.3295 0.545588 0.452491

HKI -0.3295 1 -0.08146 -0.07788

HKS 0.545588 -0.08146 1 0.42736

HKGDP 0.452491 -0.07788 0.42736 1

China

CNH 1 0.100832 0.256246 0.698092

CNI 0.100832 1 0.354141 0.185672

CNS 0.256246 0.354141 1 0.498969

CNGDP 0.698092 0.185672 0.498969 1

Taiwan

TWH 1 -0.48384 0.218059 0.372364

TWI -0.48384 1 0.388695 0.038071

TWS 0.218059 0.388695 1 0.443699

TWGDP 0.372364 0.038071 0.443699 1

(2) Unit root test and the best selection of lagged period

To avoid the phenomenon of spurious regression generated in the progress of the empirical analysis model, the data is subject to unit root test to select integrated order of time sequence of the variables to ensure the stationary series of the data. In this paper, AugmentedDickey-Fuller (ADF) test and Phillips-Perron test unit root test (unit root test) are used. Model has the following three:

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