Exuberance and spillovers in housing markets: Evidence from first- and second-tier cities in China

Accepted Manuscript Exuberance and spillovers in housing markets: Evidence from first- and second-tier cities in China I-Chun Tsai, Shu-Hen Chiang PII:

S0166-0462(17)30445-3

DOI:

https://doi.org/10.1016/j.regsciurbeco.2019.02.005

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REGEC 3437

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Regional Science and Urban Economics

Received Date: 9 November 2017 Revised Date:

30 January 2019

Please cite this article as: Tsai, I.-C., Chiang, S.-H., Exuberance and spillovers in housing markets: Evidence from first- and second-tier cities in China, Regional Science and Urban Economics (2019), doi: https://doi.org/10.1016/j.regsciurbeco.2019.02.005. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Exuberance and Spillovers in Housing Markets: Evidence from First-

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and Second-tier Cities in China

Professor

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I-Chun Tsai

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Department of Finance

National University of Kaohsiung, Taiwan e-mail: [email protected]

Shu-Hen Chiang* Professor

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Department of Finance

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Chung Yuan Christian University, Taiwan

*Corresponding author, email: [email protected].

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Exuberance and Spillovers in Housing Markets: Evidence from First- and Second-tier Cities in China

Abstract

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Over the last few decades, exuberance (bubble) and spillovers (ripple effects) have both been observed in the overheated housing market. However, surprisingly few attempts have so far been made to integrate these two concepts to further explore

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China’s housing market frenzies. According to growth poles, the causality between exuberance and spillovers in real estate markets is that capital is initially concentrated

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in first-tier cities, but the housing-price exuberance then leads to spillovers to second-tier cities. Using housing price and rental data encompassing four first-tier and six second-tier cities on a month-by-month basis, we apply recursive unit root tests to examine the degree and timing of housing booms. At the same time, a rolling-window

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spillover index is used to evaluate ripple effects among these cities. Our estimates indicate that Beijing as a first-tier city first exhibits episodes of exuberance, which are

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then transmitted to second-tier cities.

Keywords: Exuberance; Housing booms; Spillover index; Generalized sup ADF;

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First- and second-tier cities

1

ACCEPTED MANUSCRIPT 1. Introduction

China’s overheated real estate market has attracted a global interest over whether it is a bubble waiting to burst (Glaeser et al., 2017). In fact, development of China’s

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residential asset is considerably young due to its privatization and commercialization after the 1997 Asian financial crisis (Chen et al. 2011b). Inextricably intertwined interactions among several factors caused an unprecedented housing frenzy. These

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elements include China’s 10% average annual rate of economic growth since the open-door policy of 1978 that has led to an excessive domestic saving (Wei and

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Zhang, 2011), the traditional belief that “land is wealth” (Zhang et al., 2012), and a lack of diversified investment goals (Chiang, 2014). In addition, the 2008 Global Financial Crisis (GFC) forced the Chinese government to implement an expansionary monetary policy associated with a loosening credit management, which channeled

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much more financial resources into the real estate sector, especially into the housing market. Wu, et al. (2012) even mentioned that China is experiencing increases in high housing prices far ahead of those in the United States during its spectacular

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1995–2006 boom-and-bust period. Similarly, Glaeser et al. (2017) stated that housing prices in the United States grew by 5% annually from 1996 to 2006, whereas housing

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prices in some Chinese cities grew by 13% annually from 2003 to 2013. In this situation, the authorities have repeatedly revealed their desire to reduce the continuous upward pressure on real estate prices, but their actions have ceased to be effective. What is more, China is now the second largest economy in this era of globalization, and its real estate sector plays an extraordinary role in economic growth.1 All these

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Glaeser et al. (2017), for example, pointed out that in 2014, the construction industry in China accounted for 16% of urban employment, namely, 29 million workers; a percentage far exceeding that for construction employment in the United States. 2

ACCEPTED MANUSCRIPT things make it clear that the importance of how to carefully evaluate and clearly comprehend the overheated housing market with the Chinese characteristics deserves explicit emphasis. Over the past few decades, numerous attempts have been focused on an

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exorbitant housing-price appreciation from two angles, namely, exuberance (bubble) and spillover (ripple) effects. The former stresses that high housing prices that apparently deviate from economic fundamentals indicate that a bubble exists in a

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particular city (Shiller, 2000), whereas the latter suggests that high housing prices are easily transmitted from one city to other cities (Meen, 1996). Since exuberance and

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spillover are both introduced to probe into soaring housing prices, this raises the question whether the integration of exuberance and spillovers can fully explain what has happened in this emerging economy. Although this issue regarding the integration of housing price dynamics within a city (exuberance) and across cities (spillovers) has

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never been examined, we observe two growing trends, which direct us to take a closer look at the housing market by considering exuberance and spillovers together. One is that the theory of growth poles proposes a possible solution, whereby national

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resources are first concentrated in special locations and first-tier cities are the notable examples of China’s development. 2 These rapidly growing cities then generate

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spillovers to second-tier cities. This view seems to be applicable to the occurrence of housing frenzies, whereby investment capital must first be channeled into first-tier cities to cause their housing prices to skyrocket and these prices increases will then start to spill over to second-tier cities with the rising housing prices and eventually becomes a national issue. In other words, growth pole theory suggests that exuberance

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The most typical realization of growth poles is China is based on a policy argument that national resources are concentrated in first-tier cities resulting in a high rate of economic growth and this is generally referred to as “urban-biased” policy (Yang, 1999; Ke and Fser, 2010; Chiang, 2018). 3

ACCEPTED MANUSCRIPT should first exist in the housing markets of first-tier cities, and then this information is transmitted to second-tier cities. Another opportunity stems from new advances in empirical estimations in order to track the process of exuberance and spillovers in a timely manner, by use of generalized version of the sup augmented Dickey–Fuller test

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(SADF) test, namely, the GSADF test (Phillips, et al., 2011, 2015) as well as the spillovers index (Diebold and Yilmaz, 2009, 2012). It is important to note that GSADF test and spillovers index established under the same rolling window

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framework are used to calculate time-varying bubbles in a specific city and time-varying spillovers across cities, respectively. To sum up, using GSADF test and

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spillover index to the evolution of exuberance and spillovers becomes available to examine the effectiveness of growth-pole argument that exuberance leads spillovers. Based on the above, we implement GSADF test and DY spillover index simultaneously to evaluate China’s housing market. From our estimation results,

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compelling evidence is found by Beijing to prove the authenticity of our viewpoint on the grounds that the emergency of exuberance is first identified in this housing market, which becomes the most essential source of the spillovers to the second-tier cities,

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especially in 2014. We firmly believed that integrating the concepts of the bubbles and spillovers can provide brand new economic meanings and policy implications

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regarding currently overheated housing market in China. The remainder of this paper is organized as follows. In Section 2, we review

exuberance and spillover effects of housing market. In Section 3, time-varying GSADF test and spillover index are both outlined. In Section 4, the data regarding economic conditions and housing prices in first- and second-tier cities are described and analyzed. In Section 5, the estimation results are reported and some policy implications are also discussed. Finally, a review of the conclusions reached follows 4

ACCEPTED MANUSCRIPT in Section 6.

2. Review of the Literature

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Since we attempt to combine exuberance with spillovers to develop some new insights into China’s housing market, and so related researches on these two topics are

estimations in this section.

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2.1 Housing bubbles and exuberance

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surveyed by comparing traditional time-series econometrics with new time-varying

Ever-increasing housing prices always instill dread regarding the reasonableness of housing price appreciation, and this is an initial motivation underlying the concept of a bubble. A bubble is defined being a result of housing prices largely deviating

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from economic fundamentals. The theoretical foundation for a bubble is mainly constructed on the rational bubbles of Blanchard and Watson (1982), Shiller (1984), and Tirole (1985) under the assumption of the efficient market hypothesis.3 Rational

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bubbles occur when an investor is willing to pay more for housing than the fundamental value of that housing. Researches usually use a discount model from

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income or rent to compute reasonable housing prices, namely, fundamental values, and it is the remaining part that constitutes the bubble. In practical works, the price-to-income ratio or price-to-rent ratio is often applied to simply understand the relative position of housing prices. In the empirical study, Campbell and Shiller, (1987) first proposed using a cointegration test of a present-value model to justify no bubble. Diba and Grossman

3 Black et al. (2006) additionally mentioned momentum behavior as an irrational bubble theory. 5

ACCEPTED MANUSCRIPT (1987) applied unit root tests to look for stock bubbles in the S&P index from 1871 to 1986 and they also rejected the presence of bubbles. Diba and Grossman (1988) again reported that cointegration between stock prices and stock returns indicated the absence of any bubble. As far as the housing market is concerned, Malpezzi (1999),

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McCarthy and Peach (2004), Gallin (2006) and Mikhed and Zemcik (2009) all indicated that there is a long-run relationship between housing prices and income in the United States. Similarly, Black et al. (2006) also preclude the existence of

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explosive rational bubbles using United Kingdom data. In sum, there is little evidence to prove the existence of rational bubble based on the concept of income.

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In the case of housing prices and rents, Clark (1995) first used cross-sectional data for the United States to investigate the relationship between housing prices and rents based on the present value model. Capozza and Seguin (1996) analyzed the interaction between housing prices and rents to evaluate the efficiency of the housing

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market. Gallin (2008) showed a cointegration between housing prices and rents; at the same time, he claimed that rent-price ratio can be used to predict future prices well. Alternatively, Campbell and Shiller (1998) developed a model based on the

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relationship between the housing price and the price-to-rent ratio. Plazzi et al. (2006) examined the predictive ability of the price-to-rent ratio to housing prices. Engsted

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and Pedersen (2015) applied a dataset comprising 18 OECD countries to check the ability of the price-to-rent ratio to predict hosing prices and they found that the price-to-rent ratio is good at forecasting housing prices. Since a long-run equilibrium between housing price and rent can be achieved or the price-to-rent ratio can be regarded as a good predictive index of housing price, there is still little evidence from rational bubble according to the rental data. Although various published studies from the above have failed to grasp rational 6

ACCEPTED MANUSCRIPT bubbles, Evans (1991) argued that a bubble may be reflected in the presence of periodic collapses and this is why traditional time-series approaches, which need to rely on long-term data to obtain reliable results, cannot efficiently identify financial bubbles that are characterized by periodic collapses. To improve this problem, Phillips

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et al. (2011) presented a recursive strategy based on ADF tests to capture a mildly explosive form of rational bubble and this new type of ADF test is referred to as the sup ADF (SADF) test that is based on a rolling-window approach to successfully

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detect the existence of explosive stock prices in the Nasdaq, especially for multiple bubbles. Furthermore, Phillips et al. (2015) proposed a new generalized version of the

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SADF with a double-sup window selection criterion to recognize more possible bubbles than ones by the SADF test in the case of the S&P 500 index. To sum up, this newest index, namely, GSADF test possesses numerous advantages compared to the traditional time-series method. First, a rolling-window approach is used to actively

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investigate the evolution of housing prices and bubble. Second, applying a generalized date-stamping mechanism can identify more possibilities of a chronology of exuberance. Thirdly, we can only focus on the testing of a single variable; thus, it is

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easier to evaluate and analyze. Based on these benefits, this dynamically rolling and recursive test is widely applied to search for time-varying bubbles in different cases,

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such as stock markets (Phillips, et al., 2011), commodity futures markets (Etienne et al., 2014), and housing markets in an international context (Pavlidis, et al., 2016). As far as China’s housing market is concerned, numerous studies have

addressed the bubble issue. Hui et al. (2006) applied cointegration and causality among housing prices and market fundamentals (demand and supply) to estimate the bubbles of China’s big cities, and found evidence of a housing bubble in Shanghai, rather than in Beijing. Ren et al. (2012) quoted the concept of a rational bubble to test 7

ACCEPTED MANUSCRIPT the housing prices of 35 cities and their dynamic panel data estimation indicated that no rational bubble existed. Tsai et al. (2015) used data from 35 cities to show that some mega cities, such as Beijing, Tianjin, and Shenzhen, had real estate market bubbles, while Liu et al. (2016) applied the GSADF test for 70 cities to find that the

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first-tier cities were not bursting. However, Glaeser et al. (2017) investigated the forces of demand and supply in China’s housing market and concluded that the

market is bursting or not.

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2.2 Spillovers among housing markets

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government is the most pivotal element in determining whether China’s housing

Another question in the face of an overheated housing market concerns spillovers among local housing markets.4 Spillover behaviors actually complicate and exacerbate the housing bubble problem on the grounds that an overheated housing

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market in one city may be transmitted to other cities by spillover effects and this eventually causes high housing prices to become a big problem. Meen (1999) proposed many reasons, including equity transfer, arbitrage, and migration, to explain

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spillover behaviors among local housing markets. Since spillovers may lead to high housing prices in numerous cities, causality tests can be further used to search for

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source cities.

Based on the importance of spillovers among local housing markets, a

considerable number of studies have proved the significance of spillovers in various countries. In the United Kingdom, scholars have proven that spillovers objectively exist and regional housing prices have spread from the South East (greater London) region out to other regions (MacDonald and Taylor, 1993; Alexander and Barrow,

4 Spillovers are also referred to as the ripple effect or spatial diffusion in real estate research. 8

ACCEPTED MANUSCRIPT 1994). In the Australian case, Tu (2000) found that segmented housing markets are reflected in limited interactions among many cities, whereas Liu et al. (2008) and Costello et al. (2011) have suggested that housing price diffusion exists in most capital cities. Chen et al. (2011a) employed the Toda-Yamamoto (TY)

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causality test to search for the origin of the ripple effect in Taiwan. In the case of

the United States, Gupta and Miller (2012) estimated spillovers among three Western cities and then identified Los Angeles as the source city. Yunus and

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Swanson (2013) used nine housing markets to investigate the convergence of regional housing indices with lead–lag relationships. Brady (2014) confirmed

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that spillovers exist among states; moreover, he found that spillovers were stronger after the late 1990s by dividing subsample periods to present structural changes.

More specifically, Meen (1999) suggested that a spillover implies that

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regional housing price relativities should be stable variables in the long run based on unit root tests. Cook (2003) found that the asymmetric behavior of regional housing price relativities can be stable based on momentum threshold

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autoregressive (MTAR) asymmetric unit root tests. Stevenson (2004) also used the MTAR unit root test to show a stable Irish housing price ratio at the regional

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level. Holmes and Grimes (2008) used the first principal component based on regional–national differentials to revise the unit root test and still saw a stable housing differences. Lee and Chien (2011) applied a panel seemingly unrelated unit root test (SURADF) to support the stationary of five cities in Taiwan. Balcilar et al. (2013) used linear, nonlinear, and Bayesian unit root tests to prove stable housing price relativities from cities in South Africa. Furthermore, housing price diffusion mechanisms can be observed among 9

ACCEPTED MANUSCRIPT neighboring markets, for example, central cities and their suburbs. Clapp and Tirtiroglu (1994), Clapp et al. (1995), and Dolde and Tirtiroglu (1997) applied the concept of spillovers between neighboring towns within metropolitan areas in the United States. Pollakowski and Ray (1997) suggested that only the Greater New York

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metropolitan area supports intrametropolitan housing price diffusion. Gallet (2004) applied unit root tests to investigate the convergence of local housing prices in the Los Angeles metropolitan area using regional housing price relativities. Jones and

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Leishman (2006) investigated the lead–lag relationships among towns and cities in the Strathclyde region in the United Kingdom. Oikarinen (2008) argued that the diffusion

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mechanism from a central city to the surrounding area is strong in Finland. In the case of China, Chiang (2014) applied a causality test to search for the source of spillovers among six mega cities. Lee et al. (2016) introduced a SURADF unit-root test to examine housing prices in Chinese cities. Gong et al. (2016) utilized

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the Pan-Pearl River Delta as their sample to find little evidence of spillovers among cities within this area. Finally, Weng and Gong (2017) additionally considered spatial correlation as well as multivariate volatilities to find strong spillovers among ten cities,

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including first- and second-tier cities in China. As mentioned previously, spillovers among regional housing markets have been

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examined by traditional time-series econometrics, for example, vector autoregression (VAR), cointegration, causality and unit root tests to determine the existence and direction of spillovers across regional housing markets. However, the previous literature seems to lack an in-depth examination of the time-varying and dynamic processes of spillovers and we believe that time-varying spillovers could better account for housing frenzies in China. With this mind, Diebold and Yilmaz (2009, 2012) used a generalized VAR to calculate variance decomposition among urban 10

ACCEPTED MANUSCRIPT housing markets using a rolling-window approach to obtain time-varying spillovers. Their time-varying estimation of spillovers has been applied in many fields, for example, in relation to international and Chinese stock markets (Zhou, 2012), national and regional housing markets (Tsai, 2015), and different financial assets (Chiang et al.,

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2017).

Since exuberance (bubbles) and spillovers (ripple) both tend to occur as consequences of fast-growing housing prices, it is reasonable to expect that

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exuberance and spillovers in housing markets should be highly related. However, no studies have yet combined these two notions to derive new and meaningful

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implications. Thus, we propose an argument from growth pole theory, whereby financial capital is first concentrated in first-tier cities, which results in exuberance and housing bubbles; then, local overheated housing markets start to spill over to second-tier cities. Finally, we plan to introduce the GSADF test and spillover index

argument.

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using housing price and rental data in China to verify the authenticity of this

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3. Measuring Bubbles and Spillovers: The Rolling-window Approach

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To fully investigate the overheated housing market, some critical studies have

recently started to apply the rolling-window approach to evaluate the extent of bubbles and spillovers, most notably Phillips et al. (2011, 2015) and Diebold and Yilmaz (2009, 2012, 2014), respectively. The feature of the rolling-window approach is to first choose a specific sample size as a window to obtain the first estimated parameter. Then, we move this window by dropping the first observation and adding a new observation to retain a constant sample size and the data in this new window are 11

ACCEPTED MANUSCRIPT used to estimate the second-round parameter. This estimation process is rolled until the last observation is added to the estimation period. In other words, by using the rolling-window approach we can receive a sequence of exuberances and spillovers

section, we will provide their basic strategies and analyses.

3.1 Explosive episodes using a new ADF test

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across a period covering many important economic and political situations. In this

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Over the past few decades, little evidence on bubbles has been found. For example, Diba and Grossman (1987, 1988) and Campbell et al. (1997) applied

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time-series econometrics to prove no explosive behavior based on financial-asset prices. These results are, however, apparently inconsistent with the development in financial market, such as the occurrences of financial cries and housing frenzies. Evans (1991) proposed periodically collapsing bubbles to explain why a bubble

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cannot be detected through the use of traditional time-series estimation on the grounds that the bubble generally exists within a specific and short period, rather than over the long term, while the time-series method relies on long-run data to estimate reliable

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outcomes. This notion of periodic collapses encouraged Phillips et al. (2011) to build a new ADF unit root test using a rolling window calculation. In our opinions, there are

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at least three benefits to be derived from searching for the bubble by means of these new recursive ADF tests. The first point is that applying a rolling or recursive approach surely represents a good choice in relation to the periodic-collapse characteristic of the bubble. The second point is that using the ADF unit root test as the basis to determine whether the bubble exists is very intuitive based on the fact that the unit root test is mainly used to examine a variable’s stability. In the meantime, the bubble is defined in terms of there being a significant deviation from the fundamental 12

ACCEPTED MANUSCRIPT housing price. The final point is that using these new ADF tests by rolling window approach can additionally identify the episodes (intervals) of exuberance. It is important to note that these right-tailed unit root tests should be used to test the price-to-rent ratio or price-to-income ratio, rather than housing prices alone

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(Phillips et al., 2015; Engsted et al., 2016; Pavlidis et al., 2016) on the grounds that rational bubble, which arises due to housing prices being higher and rising more rapidly than their fundamentals, such like measured in terms of rent or income, causes

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these ratios to explode. This is a good case where very high housing prices associated very high housing rents may not be defined by the bubble. To sum up, Phillips et al.

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(2011) and Phillips et al. (2015) derived two univariate tests based on the ADF test: the supremum (sup) ADF (SADF) and generalized sup ADF (GSADF) tests, respectively to check whether the housing price lies in the status of the bubble, i.e., explosive forms based on price-to-fundamentals ratio. In this paper, one may notice

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that we choose the price-to-rent ratio to evaluate the degree of exuberance. Initially, their approach follows a random walk with an asymptotically negligible

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drift in terms of the price-to-rent ratio (P/R) in (1):

(1)

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P/R = dT  +
P/R

+ ε , ε ~iid
0, Σ

where d is a constant, T is the sample size and η > 1/2 is used to control the magnitude of the intercept. We further insert a transient dynamics to investigate the degree of exuberance using a rolling-window approach, i.e. the regression from the sample starts from the r  fraction of the total sample (T) and ends at the r fraction due to r = r + r , where r is the window size of T. Thus, this empirical regression model is expressed as in (2): 13

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Δ
P/R = α , + β ,
P/R

+ ∑%$& φ$ , Δ
P/R $ + ε

(2)

To examine exuberance behavior in housing market, we introduce the concept of unit roots through the use of the null hypothesis: β , = 0, against the alternative

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hypothesis, namely, mildly explosive behavior: β , > 0, so that

1 2 ,2 0



ADF = 34
01

(3)



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2 ,2

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In other words, this is a right-tailed statistic. Phillips and Yu (2011) suggested a recursive procedure based on (3) on subsamples of the price-to-rent ratio data since r5 is the smallest sample window fraction and this new test statistics is referred to as the sup ADF (SADF) test using a fixed start point as in (4) below:

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sup  SADF
r5  = r ∈ :r , 1;ADF5  5

(4)

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The SADF test statistics can be compared with critical values: when its value is larger than the critical value, an explosive event starts to emerge. Otherwise, when its

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value is lower than the critical value, the end date of this exuberance can be detected. However, Phillips et al. (2015) argued that for multiple episodes of exuberance,

the SADF may suffer from low power and inconsistency and hence fail to detect the emergence of bubbles. Accordingly, they proposed a generalized sup ADF (GSADF) test with a more flexible window than the SADF with only a fixed starting point to allow both the ending point and the starting point to change as in (5). To obtain the GSADF test statistics, Phillips et al. (2015) proposed a recursive backward SADF 14

ACCEPTED MANUSCRIPT (BSADF) regression operation as in (6).

sup sup   GSADF
r5  = r ∈ :r , 1;, r ∈ :0, r − r ;ADF = r ∈ :r , 1;SADF  5

 5  5

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sup  BSADF
r5  = r ∈ :r , 1;SADF  5

(5)

(6)

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The GSADF is still a right-tailed test, i.e., it rejects the null hypothesis in favor of explosive behavior. Phillips et al. (2015) suggested that the GSADF can capture

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more opportunities of multiple bubbles and hence the GSADF test is adequate when searching for time-varying bubbles here.

Finally, we would like to lay special emphasis on how to search for periods with explosive behavior, namely, date-stamping strategy. Phillips et al. (2015) defined the

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origination (r?4 ) and termination (r?) @ points of exuberance as

inf F Br : BSADF
r5  > CV G H r ∈ :r5 , 1; 

r?@ =

inf F Br : BSADF
r5  < CV G H r ∈ :r?4 , 1; 

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r?4 =

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F

where CV G denotes
1 − αJ  critical value of the BSADF test statistic based on :Tr ;. However, we may notice that the SADF and the GSADF tests both stem from non-standard limiting distributions, so critical values are only obtained case by case by use of a bootstrap simulation.

3.2 Time-varying spillovers Diebold and Yilmaz (2009) first proposed a spillover measure by means of 15

ACCEPTED MANUSCRIPT forecast error variance decompositions (FEVDs) from the VAR model. Dielbold and Yilmaz (2012) further suggested using generalized VAR methodology to solve the problem of variable ordering. Hereafter, this approach has been referred to as DY spillover index. However, when we use DY spillover index, it is first necessary to

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answer a new question as to why FEVDs can account for spillovers. This is simply because the FEVD is used to calculate the contribution of every variable shock to the forecast error variance of a specific variable. In other words, higher explained powers

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of other variables to this variable’s variance directly imply that there are stronger spillovers of other variables in relation to this variable. If this view is valid, the related

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DY spillover indices based on FVEDs can reveal the size and direction of spillovers simultaneously as follows.

First, we can consider a covariance stationary VAR (p) of housing returns (Z)

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with N cities and p lags:5

p

(

Z t = ∑ Φ i Z t −i + ε t , ε t ~ 0, σ 2 i =1

)

(7)

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where ε is a random error with zero mean and equal variance, namely, σ . Using

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moving average representation, (7) can be re-written as

∞

p

i =0

i =1

Z t = ∑ Ai ε t −i , where Ai = ∑ Φ i At −i

(8)

Under a generalized VAR system, we can further compute the H-step-ahead FEVD by θ ijg (H ) 5

as in (9).

VAR or generalized VAR methods both require that all variables must be stationary. To meet this requirement, housing returns (∆lnP are used to calculate the spillover index in this paper. 16

ACCEPTED MANUSCRIPT σ −jj1 ∑ (ei/ Ah σ 2 e j ) H −1

θ ijg ( H ) =

2

h =0

H −1

∑  e A σ / i

h =0

h

2

′ Ah ei  

(9)

By virtue of the non-unity sum of the FEVD, the normalization of (9) is

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~ implemented by a new version of the FEVD ( θ ijg ) to surely sum up to 1 from

θ ijg ( H )

~

θ ijg ( H ) =

N

∑θ

(H )

(10)

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j =1

g ij

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generalized VAR as in (10).

Now that using FEVDs can represent the effects of spillovers, we can construct

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the first spillover index, namely, the total spillover index ( S g ) as in (11):

N

~g

∑θ

S g (H ) =

i , j =1 i≠ j N

~g

∑θ

ij

(H )

(H )

N ~ , where ∑ θ ijg ( H ) = N i , j =1

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i , j =1

ij

(11)

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The total spillover is derived by computing spillovers “from” or “to” other cities

by use of the variance decomposition of housing return in a specific city, minus its own explained power. Thus, the magnitude of the total spillover between zero and unity reflects “average” degree of spillovers over N cities. A higher value for the total spillover index points to more active spillovers among cities. However, past studies regarding the ripple effects only focus on the direction, but not the magnitude of spillovers among cities. This is the first advantage of the DY spillover index. 17

ACCEPTED MANUSCRIPT In addition to the total spillover index being able to let us know about the magnitudes of total spillovers among N cities, we can also know more about the “two-way” directions of the interactive relationships among urban housing markets,

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that is to say, directional spillovers by city i “from” other cities as in (12), namely, S ig. and directional spillovers by city i “to” other cities as in (13), namely, S .ig , while past studies only estimated the outcome of the net spillovers. This is the second advantage

N

N

~

S ig. ( H ) =

j =1 j ≠i N

~g

∑θ

i , j =1

N

ij

~

N

~g

∑θ

(H )

(H )

N

ji

~g

∑θ

=

(H )

j =1 j ≠i

ji

(12)

(H )

N

(13)

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i , j =1

ij

N

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S .ig. ( H ) =

j =1 j ≠i

=

∑ θ jig ( H ) j =1 j ≠i

~g

∑θ

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∑θ ijg ( H )

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of the DY spillover index.

By analogy, according to spillovers or “to” other markets in (13) minus

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spillovers or “from” other markets in (12), we can obtain a net index, which is referred to as or “net spillovers” ( S ig ), as in (14). Using net spillovers can let us know about the position of a city based on the spillovers or ripple effects of housing markets on the grounds that a positive (negative) net spillover index implies that this city is a provider (receiver) of housing spillovers

S ig ( H ) = S .ig ( H ) − S ig. ( H ) 18

(14)

ACCEPTED MANUSCRIPT Just as Diebold and Yilmaz (2012) have emphasized that the traditional time-series econometrics only estimate a single fixed-and-average parameter, the third contribution of DY spillovers is to propose the rolling-window method in order to investigate the impacts of economic events or draw comparisons between new and old

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policies. As mentioned above, all these advantages cause us to choose the DY spillover index as our estimation method for spillovers among urban housing markets.

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4. Data Description

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In this section, we not only demonstrate the sources and description of the housing price and rental data in the ten cities, but we also go into details about past housing-related policies in order to offer the key to an understanding China’s real

4.1 Data sources

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estate market.

Each month, the SouFun company collects urban housing price indices from the

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China Real Estate Index System (CREIS); those prices were used in this study. We may notice that various types of real estate price indices are officially announced; for

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example, the urban composite price index is the weighted-average value of residential, office, and retail price indices on a new-housing basis. Although Chiang (2014) and Weng and Gong (2017) selected the urban composite index to estimate spillovers among cities, we choose the residential price index, as did Hui et al. (2006), to focus on China’s housing market. Moreover, these indices are calculated using the Laspeyres index; the base point is 1,000 in Beijing in December 2000. The CREIS database also provides a second-hand housing price index and a housing rent index. 19

ACCEPTED MANUSCRIPT We therefore decide to quote residential price index and housing rent index in order to compute the price-to-rent ratio to check the bubble in China on the grounds that higher price-rent ratio implies that the housing price may deviate more from its fundamental part, namely, the housing rent.6

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We gathered the housing prices of numerous Chinese cities and classified the cities into different ranks, namely, first-tier and second-tier cities, to analyze possible exuberance and spillovers across different urban ranks.7 First-tier cities are defined

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by many aspects, such as powerful economic influences over broader regions, innovative ability, high-quality education, a high proportion of service industry,

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especially financial sector. Second-tier cities are defined by lower levels of the above factors than the four first-tier cities. Due to the data limitations of the CREIS database, only ten cities with long time-series data were selected to estimate the bubbles and spillovers with a rolling-window calculation. These ten cities were further classified

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into four first-tier cities and six second-tier cities, respectively. The first-tier cities were Beijing, Shanghai, Guangzhou, and Shenzhen which are all located in the coastal region: Beijing lies in the North, Shanghai lies in the East and Guangzhou and

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Shenzhen are both in the South. The second-tier cities were Tianjin, Chongqing, Chengdu, Nanjing, Hangzhou, and Wuhan which are located in different regions:

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Tianjin, Nanjing, and Hangzhou are located in China’s coastal region; Chongqing and Chengdu are both located in China’s western region; and Wuhan is the only city in China’s central region, as depicted in Figure 1. These economically powerful cities are diversely distributed in three regions of China, and hence their dynamic relations can represent China’s housing market.

6

Although housing rent and household income can both be used to evaluate fundamental housing prices, the monthly income data of the four first-tier cities in China are not available. 7. Generally speaking, Chinese cities are divided into first-, second-, third-, and fourth-tier levels. 20

ACCEPTED MANUSCRIPT [Insert Figure 1]

4.2 Economic outlook All of these cities, with the exception of Nanjing and Hangzhou, have resident

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populations of over ten million inhabitants, and tremendous production abilities, as noted in Figure 2 which depicts the regional gross products (RGPs) of these ten cities in 2015. The top four RGPs just correspond to the four first-tier cities, namely,

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Shanghai, Beijing, Guangzhou, and Shenzhen, in that order. Among the second-tier cities, Tianjin and Chongqing had the largest RGPs; both of those cities are directly

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controlled by the government. Figure 3 depicts real estate investment in the ten cities in 2015 and it differs from Figure 2 because Beijing and Chongqing are the two cities with the most real estate investment. We further computed a ratio of real estate investment to RGPs from Figure 4 and it is found that the top four cities all belonged

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to the second-tier cities (Hangzhou, Wuhan, Chongqing, and Chengdu, in that order). That is to say, many second-tier cities have notably higher real estate investment potential than the first-tier cities. This result seems to imply that housing frenzies can

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generate spillover from the first-tier cities to the second-tier cities now. Finally, we classify investment to understand the distribution of local real estate markets based on

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three different uses: residences, offices, and retail spaces, as given in Table 1. It is clear that China’s housing market has a drastically dominant position in the second-tier cities, whereas office real estate is much more popular in the first-tier cities, especially in international cities such as Beijing and Shanghai. [Insert Figures 2, 3 and 4] [Insert Table 1]

21

ACCEPTED MANUSCRIPT 4.3 Real estate policy from 2005 to now After the Asian financial crisis, China’s housing was commercialized step by step by China’s government from 1998 to 2000. The fact that housing prices continued to rise rapidly attracted the attention of authorities. China’s government decided to apply

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a macroeconomic control policy (2004–2007) to stabilize economic development, especially housing prices. Moreover, the State council announced eight directives and six directives in 2005 and 2006, respectively, to control the speed of housing price

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inflation. Nevertheless, the GFC of 2008 compelled the government to exercise an expansionary monetary policy associated with loosening mortgage credit quotas.

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Consequently, as housing prices in many cities kept on rising since 2009, the authorities again issued four directives to prevent excessive liquidity from entering the real estate market. For example, the State council announced 11 new directives and eight new directives in 2010 and 2011, respectively to restrain the excessively

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high housing prices with strong restrictions on loans. However, as China’s economic growth apparently revealed a downside risk as well as a slowing pace of housing market in 2014, the authorities suddenly changed their tactics by abating the earlier

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policy to restrict housing loans during the 2014-2015 period and this strategy again led to overheated housing markets after 2015. Since then, housing prices in many

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cities have hit their highest recorded values. These unprecedentedly high housing prices forced the Chinese government in 2016 to propose the most serious limits on loans and purchase orders associated with restricted selling periods ranging from 5 to 8 years. At the same time, the central government at the first time ordered every local or city government to implement local regulations against real estate speculation. As stated above, many of the measures adopted to control housing prices have been invalid, while any housing revitalization plan has always been particularly 22

ACCEPTED MANUSCRIPT effective, even spiraling out of control. It would be better to say that housing frenzies in China are fully reflected by these traits.

4.4 Data Description

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Table 2 lists simple statistics regarding housing price indices and Figure 5 illustrates the time series of housing prices for the ten cities; the data for these housing price indices range from April 2005 to June 2017.8 First, the housing price variation

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of first-tier cities is larger than that of second-tier cities; in particular, Beijing and Shenzhen have larger housing price variations than other first-tier cities: the index

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fluctuation range for Beijing is 1191–4510 and the range for Shenzhen is 1176–4904. Second, it is found that the coefficients of variation (CVs) for these cities are 0.34, while the CV for Shanghai is only 0.2. Of the second-tier cities, it is worth noting that the CV for Wuhan with the fluctuation range of 527–1526 arrives at 0.26. This is

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because, by comparison from Figure 5, it can be seen that the upward trend of housing prices in Wuhan is steeper than in other second-tier cities. [Insert Table 2]

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[Insert Figure 5]

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Finally, from Figure 5, the most evident economic downturns appeared in most

cities in 2014. As mentioned in Section 4.3, following the recession of the housing market in 2014 due to the worries about low economic growth in China, the policies that were formulated to control housing prices were cancelled in succession from the second half of 2014 to 2015. Consequently, all ten cities exhibited noticeable 8

As far as housing price index is concerned, Beijing and Shanghai can be traced to 1996, Tianjin, Chongqing, Guangzhou and Shenzhen can be traced to 2000 and other second-tier cities can only be traced to 2004 or 2005. To maintain data consistency, we decide to apply these housing prices of these ten cities from April 2005 to June 2017. 23

ACCEPTED MANUSCRIPT increases after 2015.

5. Empirical evidence

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In this section, the evolution of spillovers from first-tier cities to second-tier cities and exuberance of every first-tier city are both chased using rolling-window approach in Section 5.1 and Section 5.2, respectively. In turn, a graph with DY

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spillovers and the GSADF test statistics are completed to decide the lead-lag relationship between exuberance and spillovers in Section 5.3. Finally, some

in housing markets in Section 5.4.

5.1 Time-varying spillovers index

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important policy implications are proposed to understand and solve China’s troubles

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To estimate the correlation between these ten cities using a VAR model, we tested the characteristics of the return rates of the housing price indices. Table 3 indicates that two unit root (ADF and PP) tests of the housing returns of the ten cities

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significantly rejected the nonstationary hypotheses; therefore, the housing return was surely stationary. We continued to use these ten housing returns to estimate a

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generalized VAR model, which is used to calculate the variance decomposition. Based on this, we can further obtain the DY spillover index (Diebold and Yilmaz, 2012) to show the ripple effect.9

The measurements of the spillover effects in the ten cities are listed in Table 4 during the overall sample period (2005-2017). The values in the 10 × 10 grid in the center of Table 4 are the FEVDs using the VAR model as (7). In the rightmost column,

9

The lags of the VAR model are two periods based on the Schwarz information criterion (SIC). 24

ACCEPTED MANUSCRIPT we summed up the total of each city “from” other cities, whereas the “contribution to others” in the bottom row shows the totals of every city “to” other cities. [Insert Tables 3 and 4]

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In Table 4, the ten cities do not exhibit large differences in terms of the spillover effects from other cities, based on the fact that the proportion of variation in housing returns that can be explained “from” other cities was 64%–72%. The total spillover

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index is the average value across the ten cities given in the lower right corner, 69%. Notably, Table 4 can see the spillovers “to” other cities and Beijing and Shenzhen

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both display the greatest effects to other cities, and Chongqing shows the smallest spillover effect to other cities. At the same time, the spillover effects of first-tier cities to other cities were stronger than those of second-tier cities. The spillover effects of the four first-tier cities to other cities are, for example, Beijing (114%), Shenzhen

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(107%), Shanghai (94%), and Guangzhou (75%) orderly. These values are all far greater than the influences of second-tier cities to other cities. In second-tier cities, the cities with the strongest spillover effects to other cities were Hangzhou (67%), which

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is near Shanghai, and Tianjin (65%), which is near Beijing. Finally, compare “contribution to others” as in (13) to “from others” as in (12), it is clear that there are

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positive values across all four first-tier cities, while negative values are found in all six second-tier cities. In other words, there are stronger ripple effects from the first-tier cities than from second-tier cities. Subsequently, we employed rolling windows of 40 months to estimate the total spillover indices as shown in Table 4, and thereby observe changes in the total spillover indices of the ten cities from September 2008 to June 2017.10 The estimated

10

Although our housing price data across ten cities are collected since April 2005, our window size 25

ACCEPTED MANUSCRIPT results are plotted in Figure 5, which well illustrates that the total spillover indices were all higher than 70% and this effects clearly decreased at the beginning of 2014, greatly increased in June of this year, and then maintained a high level of approximately 80% until June 2017. This result is completely consistent with the

loan policy later and please refer to section 4.3.

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[Insert Figure 5]

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downside risk of China’s economic growth in 2014 associated with a loosening credit

To devote to the spillovers of every first-tier city “to” second-tier cities, the

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housing returns of each first-tier city as well as six second-tier cities are separately utilized to reestimate a generalized VAR model, in order to obtain the resolution of the FEVDs, and to further calculate the net spillover indices in Table 5 using the net spillover effect of city O to city P in (14), namely, the effect of city O to city P in (13)

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minus the effect of city O QRST city P in (12) on the grounds the net spillovers can stand for final spillover effects of a first-tier city to second-tier cities. It is interesting to note that the differences among the net spillovers of first-tier cities to second-tier

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cities are quite remarkable in that they range from 2% to 52%: Beijing had the largest net spillover effect to second-tier cities, in particular Wuhan; moreover, it also had the

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largest net spillover effect to every second-tier city. Shenzhen had the second highest net spillover effect to second-tier cities, and it had larger net spillover effects on Wuhan and Chengdu. Contrarily, Shanghai was subject to the net spillover effects from Hangzhou and Nanjing, and Guangzhou was also subject to by the net spillover effects from Tianjin and Hangzhou. [Insert Table 5] here is 40 months in order to estimate all the parameters of this generalized VAR model. Thus, our rolling-window estimators of spillovers are obtained since September 2008. 26

ACCEPTED MANUSCRIPT To sum up, the spillovers always prevail in housing markets in China due to total spillovers of around 70%. Regardless of the total spillovers to other cities and net spillovers to second-tier cities, it is obvious that Beijing is the main source city among the ten cities and this result is similar to the study of Chiang (2014). The next section

of our argument that exuberance leads to spillovers.

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will examine the possibilities of local housing market bubbles to prove the reliability

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5.2 Price-to-rent ratio and episodes of exuberance using the GSADF

It is clear from Section 3.1 that the price-to-rent ratio is the first step in

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examining the emergence of housing bubble. We must therefore collect an adequate housing rent index to compute the price-to-rent ratio of China’s four first-tier cities. Unlike the data from the housing price index that have been available since April 2005, the housing rent indices in the four first-tier cities are only recorded since

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January 2006. Figure 6 therefore illustrates the price-to-rent ratios of the four first-tier cities from January 2006 to June 2017, giving a total sample of 138. From a comparison between Figure 6 with Figure 4, it is found that the differences in the

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price-to-rent ratios are greater than the differences in housing prices. Before 2007, the price-to-rent ratios were at a low level, while from 2012 to 2013, the price-to-rent

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ratios increased dramatically. In 2014, housing prices were corrected, and the price-to-rent ratios decreased rapidly. After 2014, however, the differences between the four cities became more apparent. In particular, the price-to-rent ratios for Guangzhou were distinctly lower than those for the other three cities. [Insert Figure 6]

More importantly, we hope to understand the evolution and episodes of housing 27

ACCEPTED MANUSCRIPT bubbles by testing the price-to-rent ratio for every first-tier city by means of the GSADF test, which has been introduced in Section 3.1. Our window size is 23 observations based on the smallest ratio of total sample (138), namely, 0.01 +

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1.8Y according to Phillips et al. (2015), and so our first window covers the √138 period from January 2006 to November 2007. Thus, the rolling-window GSADF test can be calculated from November 2007 to June 2017 with 115 values of the GSADF

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statistics.

The estimated results are listed in Table 6, and the results prove that except for

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Beijing, the other three first-tier cities did not significantly reject the null hypothesis, namely, no explosive form based on the GSADF test. In other words, according to the price-to-rent ratio and the mildly explosiveness, Beijing is the only city to exhibit a possible exuberance and bubble and this result totally corresponds to estimation outcome for the total and net spillovers in Section 5.1. At the same time, based on a

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generalized data-stamping strategy from Phillips et al. (2015) in Section 3.1, we further determine that the episodes of exuberance for Beijing ranged from March 2012 to January 2014 in Table 6. This result is important for investigating the lead-lag

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relationship between exuberance and spillovers in the next subsection.

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[Insert Table 6]

5.3 Lead-lag relationship between time-varying exuberance and spillovers We apply GSADF test to check the emergence of housing exuberance and the

outcome is that Beijing is the only city to show the bubble phenomenon during the 2012-2014 period. The estimations were based on the method proposed by Phillips et al. (2015) for the structural change intervals of the GASDF tests ( r1 and r2 ). These were constructed in Backward SADF statistic (BSADF) tests in section 3.1. To 28

ACCEPTED MANUSCRIPT present the stable state of price-to-rent ratio, we can plot the first line from the results of the BSADF statistics for Beijing as shown in Figures 7. Moreover, we want to implement a rolling-window of 40 months to estimate a generalized VAR among seven cities, including Beijing and six second-tier cities.

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Then we can calculate all results from total spillover of Beijing “to” the six second-tier cities. These data of rolling-window spillovers from Beijing to six second-tier cities can be used to plot the second line of the time-varying spillovers

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from September 2008 to June 2017 as shown in Figure 7.11

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[Insert Figure 7]

Figure 7 indicates that after the first quarter of 2012, the fact that the housing price spillover effect of Beijing decreased is caused by exuberance in this market. By the second quarter of 2014, the pressure of rising housing prices rapidly spilled over

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to second-tier cities, and the spillover effect increased to 80% on the grounds that housing prices in Beijing were corrected to a state without exuberance after the first quarter of 2014. At that point, exuberance was no longer a concern. This result seems

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to prove the validity of our argument that exuberance leads to spillovers. In other words, the overheated housing market generally follows a longer path first bursting

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out in a city and then spilling over to other cities.

5.4 Economic meanings and policy implications Based on past academic studies, it is clear that there are two distinct and separate characteristics: exuberance and spillovers in overheated markets. We attempt to

11

Due to space limitations, graphs of other three first-tier cities with two lines based on the GSADF

tests and DY spillover index are omitted here and they are available from the authors upon request. 29

ACCEPTED MANUSCRIPT propose an integrated story by combing these notions to investigate China’s housing frenzies. According to Beijing’s experience, a housing frenzy initially stems from exuberance or bubble in a first-tier city; in turn, this overexcited emotion in response to an increasing housing price then begins to spill out to second-tier cities. Eventually,

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the question regarding overheated housing market is expanded from local to national scale. To sum up, the conclusion is that the local exuberance of a first-tier city is spilled out to other second-tier cities.

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From the econometric study, since exuberance leads spillovers, how to set up a timely warning of local housing bubble must be our top priority due to local

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exuberance constituting the origin of spillovers out to other cities. This is the reason why the GSADF test, which is proposed by Phillips et al. (2015), attracts much interest in the real estate research. As far as the authorities are concerned, we suggest that the local authorities as the front office, rather than the central government should

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watch and control local housing price as soon as possible on the grounds that exuberance or bubble actually stems from local housing market. In other words, a splendid local governance on housing market must be emphasized to avoid

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overheated housing market. Unfortunately, past policies to control high housing prices in China were all initiated by the central government and this may be the reason why

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the housing policies in the past have mostly been ineffective. Furthermore, according to the concept of portfolio, local exuberance is similar to

local-specific risk and spillovers will give rise to market (systematic) risk.12 At the national level, local exuberance seems to be able to be overlooked by diversification and the only relevant risk is systematic risk due to spillovers. This may be why little attention is often paid to exuberance in a specific city, especially in China as a 12

In fact, Diebold and Yilmaz (2014) mentioned that higher spillovers results in higher market risk, so they used a new term: “connectedness” to emphasized the consequence of spillovers. 30

ACCEPTED MANUSCRIPT planned economy under the control of the central government. However, this viewpoint from portfolio theory must be conservative from two angles. On the one hand, it is well-known that there are imperfect adjustments in the real estate market, for example, indivisible assets, low liquidities and no short sales. Thus, diversification

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can be limited in the real estate market and exuberance in a city still deserves to be noteworthy. On the other hand, there is sufficient evidence to prove the existence of strong spillover effects in housing market in many international cases, especially

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China. In other words, according to the fact that strong spillover effects reveal high correlations among local housing markets, exuberance in a city can give rise to

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overheated housing market with high risk through a high degree of spillovers. It follows from what has been said that given the limitation of diversification and high correlations, the importance of controlling exuberance cannot be overemphasized, just as “a single spark can start a prairie fire.”

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Finally, it is generally established that housing frenzies in China broke out as the result of the huge accumulation of excessive liquidities, so how to diversify housing risk by opening more investment channels and directing idle capital to other forms of

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consumption spending are two further critical points in the face of overheated housing

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market in China.

6. Conclusion

In this study, we have used monthly housing price index data of four first-tier cities and six second-tier cities to analyze the relationship between exuberance and spillover effects in local housing markets. We have simultaneously employed two types of dynamic testing methods to separately quantify the indices of local 31

ACCEPTED MANUSCRIPT exuberance and spillover effects in housing prices. The empirical results of this paper indicate that the spillover effects of first-tier cities are stronger than those of second-tier cities, and that among the four first-tier cities, the spillover effect for Beijing is the strongest. This may be related to the

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pressure of housing market bubbles by examining the price-to-rent ratio of first-tier cities. More importantly, through empirical testing, we have accounted for the centrifugal effect of first-tier cities on the housing price diffusion of second-tier cities

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using two rolling-window indices, namely, the GSADF and spillover index, respectively. It is clear during the 2013-2014 period that exuberance first appears and

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then increases in spillovers to second-tier cities after 2014 serve to reduce the pressure of exuberance in the first-tier cities. This result is consistent with our reference to the relationship between exuberance and spillovers.

Finally, since the overheated housing market goes through the phases of local

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exuberance to spillovers, local authorities need to play a critical role in creating a stable and healthy housing market by blocking expectation of increasing housing

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ACCEPTED MANUSCRIPT Table 1: Composition of real estate markets in the ten cities (2015) Unit: % Residence

Office

Retail

Beijing

58.10

27.64

14.26

Shanghai Guangzhou Shenzhen

61.77 71.27 74.84

22.30 11.65 13.25

15.93 17.09 11.91

Average

66.50

18.71

Tianjin

77.82

6.70

15.48

Nanjing Hangzhou Wuhan

82.35 70.19 78.08

6.61 14.02 8.28

11.04 15.79 13.63

Chongqing Chengdu

74.46 71.56

6.34 8.33

19.19 20.11

Average

75.74

8.38

15.87

14.79

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EP

TE D

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Second-tier cities

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First-tier cities

1

ACCEPTED MANUSCRIPT Table 2: Simple statistics of housing price indices Shanghai

Shenzhen

Guangzhou

Tianjin

Mean Maximum Minimum

2929 4510 1191

2385 3439 1561

2944 4904 1176

1980 3013 982

1527 2005 895

Std. Dev. CV Skewness Kurtosis

995.2 0.34 -0.18 1.88

479.33 0.20 0.17 2.61

995.86 0.34 0.28 2.51

513.15 0.26 -0.09 2.18

271.02 0.18 -0.74 3.01

Chongqing

Hangzhou

Nanjing

Wuhan

Chengdu

Mean Maximum Minimum

850 1050 580

1757 2312 1203

1196 1722 706

1016 1546 527

877 1073 611

Std. Dev. CV Skewness

136.73 0.16 -0.64

297.84 0.17 -0.36

264.2 0.22 0.13

269.49 0.27 -0.12

120.81 0.14 -0.51

Kurtosis

2.1

2.29

2.41

2.34

1.92

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Beijing

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Table 3: Unit root tests of housing returns over the ten cities Beijing ADF unit root test

-7.17 (0.00)

Shanghai

Shenzhen

Guangzhou

Tianjin

-9.42 (0.00)

-7.53 (0.00)

-8.71 (0.00)

-6.44 (0.00)

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PP unit root test

-9.62

-7.49

-9.24

-12.41

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

Hangzhou

Nanjing

Wuhan

Chengdu

-5.22 (0.00)

-9.83 (0.00)

-10.03 (0.00)

-5.69 (0.00)

-9.60

-10.32

-10.37

-10.21

-8.23

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

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-7.39

Chongqing

ADF unit root test

-6.46 (0.00)

PP unit root test

Notes: ADF and PP tests are adopted to test the null hypothesis of a unit root in the series. Intercept is included in the testing equation, and the lag lengths of the unit root models are selected by Schwarz Information Criterion. Entry in parentheses stands for the p-value. 2

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Shenzhen

Guangzhou

Tianjin

Beijing Shanghai Shenzhen Guangzhou Tianjin Chongqing

27.6 15 15.5 13.8 10.7 10.4

13.3 27.9 18.1 13.9 12.9 4.9

16.8 17.8 28.1 16 10.6 8.3

13.1 11.5 12.5 31.4 6.9 6.1

7.1 8.6 9.2 8.2 32.2 3.9

Hangzhou Nanjing Wuhan Chengdu

12 11.1 14.6 10.9

13 4.3 9.2 4.5

11.6 5.9 10.4 9.3

6.7 4.9 8.3 5.3

114

94

107

From Others

7.7 11.1 8.2 7.9 7.5 8.2

4.5 3.4 2.1 2.2 6.4 9.2

5.6 2.8 1.6 3.1 4.8 9

1.9 0.4 2.6 2.1 5.3 8

72 72 72 69 68 68

29 4.7 6.7 4.4

8.4 36.5 3.7 12.4

7 9.9 32.2 9.3

1.6 14.8 2.3 32.6

71 64 68 67

65

25

67

52

53

39

69%

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Chengdu

3 5.4 1.2 5.3

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to others

2.2 1.4 2.2 1.4 2.8 32

Wuhan

7.8 2.6 11.6 6

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Contribution

Chongqing Hangzhou Nanjing

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Shanghai

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Beijing

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Table 4: Total spillover effects among ten cities

3

ACCEPTED MANUSCRIPT Table 5: Net spillovers to second-tier cities Beijing

Shanghai

Shenzhen

Guangzhou

52.8

50.6

51.8

56.7

Tianjin Chongqing Hangzhou Nanjing

8.7 8.2 6.7 4.2

4.1 2.7 -1.1 -2.3

-2.6 5.6 1.3 3.1

-3.9 4.4 -4.5 1.9

Wuhan Chengdu

12.7 11

4.3 2.5

8.9 6.8

2.2 1.8

52

10

Influence by itself

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The total net influence

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The net influence on the second-tier city

4

2

ACCEPTED MANUSCRIPT Table 6: Results of the GSADF tests Cities

Statistic

Period

Beijing SADF GSADF

-0.1665 2.3614**

Sample through 2008/01 Sample from 2012/03 to 2014/01

-1.6148 1.2086

Sample through 2010/04 Sample from 2014/09 to 2016/10

-2.2898 1.3871

Sample through 2017/01 Sample from 2014/07 to 2016/09

-0.6826 1.7226

Sample through 2008/01 Sample from 2012/01 to 2013/11

SADF GSADF

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Shanghai

SADF GSADF

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Shenzhen

SADF GSADF

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Guangzhou

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EP

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Notes: The symbol ** denotes significant at the 5%, which is according the asymptotic one-sided p-values of Phillips et al (2015).

5

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Figure 1: Locations of ten cities

Chengdu Chongqing

Hangzhou Nanjing

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Tianjin

EP

Wuhan

Shenzhen

Guangzhou

Shanghai Beijing

0.00

500.00

1000.00

1500.00

2000.00

2500.00

Unit: billions (CNY).

Figure 2: RGPs of ten cities in 2015

1

3000.00

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Chengdu Chongqing Wuhan Hangzhou

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Nanjing Tianjin Shenzhen Guangzhou

Beijing 0.00

100.00

200.00

400.00

500.00

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Unit: billions (CNY).

300.00

SC

Shanghai

Figure 3: Real estate investment (REI) in ten cities in 2015

Chengdu

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Chongqing Wuhan Hangzhou Nanjing

Shenzhen Guangzhou

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Shanghai

EP

Tianjin

Beijing

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Unit: %.

Figure 4: Ratios of REIs to RGPs in ten cities of 2015

2

ACCEPTED MANUSCRIPT Beijing

Shang hai

Shenzhen

5,000

3,500

5,000

4,000

3,000

4,000

3,000

2,500

3,000

2,000

2,000

2,000

Guang zhou 3,500 3,000 2,500 2,000

1,000

1,500 06

07

08

09

10

11

12

13

14

15

16 17

1,500

1,000 06

07

08

09

Tianjin

10

11

12

13

14

15

16 17

1,000 06

07

08

09

Chongqing

2,200

1,100

2,000

1,000

10

11

12

13

14

15

16 17

06

07

08

09

Hangzhou

10

11

12

13

14

15

16 17

Nanjing

2,400

1,800 1,600

2,000

1,800

900

1,400

1,600 800

1,600

1,200

1,400 1,000 1,200 600

1,000 800

800

500 06

07

08

09

10

11

12

13

14

15

16 17

800 06

07

08

09

Wuhan

10

11

12

13

14

15

16 17

13

14

15

16 17

600

06

07

08

09

10

11

12

13

14

15

Chengdu

1,600

1,100

1,400

1,000

1,200 900 1,000 800 800

400

600 06

07

08

09

10

11

12

13

14

15

16 17

06

07

08

09

10

11

12

16 17

06

07

08

09

10

11

12

13

14

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700

600

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700

1,200

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Figure 5: Housing price indices of the ten cities

90.0

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87.5 85.0 82.5

77.5

AC C

75.0

EP

80.0

72.5

70.0 2008

2009

2010

2011

2012

2013

2014

Figure 5: Total spillovers (10 cities)

3

2015

2016

2017

15

16 17

ACCEPTED MANUSCRIPT 2.2 2.0 1.8 1.6

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1.4 1.2

0.8 06

07

08

09

10

11

13

14

15

16

17

Shanghai Guangzhou

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Beijing Shenzhen

12

SC

1.0

Figure 6: The Price-to-rent ratios across the ten cities

0

75

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AC C

-2

80

70 65 60 55

EP

4 2

85

-4

-6 2007 2008

2009

2010

2011

2012

BSADF

2013

Ripple

Figure 7: Beijing

4

2014

2015

2016

2017

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Highlights

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1. Exuberance (bubble) and spillovers (ripple effects) are often used to examine the overheated housing market.

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2. Two concepts should exist a meaningful causality relationship.

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3. Appling two rolling-window indices can explore into China’s housing market in a timely manner.

4. Empirical results support our argument that exuberance, which first appears,

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eventually leads to spillovers to other cities.