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Price bubbles and policy interventions in the Chinese housing market

Abstract

The recent dramatic increases in house prices have led to considerable attention being focused on housing markets in China. Using a unique dataset of city-level house prices and rents, this paper investigates the presence of price bubbles in major Chinese city housing markets. Our findings show evidence of price bubbles in most housing markets, even though the bubbles might be, to a large extent, mitigated by strong government intervention. In order to distinguish rational bubbles from irrational bubbles, we extend the existing work to allow a deterministic time trend and break points in the unit root test of house price–rent ratios. As a consequence, our results demonstrate that the price–rent ratios in most of the sample cities are no longer non-stationary, implying the non-existence of rational bubbles in the housing markets.

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Notes

  1. See Wu et al. (2012) for a detailed description of the history of Chinese housing market.

  2. Shanghai Security News, reprinted in Sohu News (http://news.sohu.com/20090317/n262835241.shtml).

  3. The key to detect a housing bubble is dependent on where there exists a stable relationship between housing prices and fundamental factors such as personal incomes, population, or housing rents. Case and Shiller (2003) provide a detailed discussion on the relationship between housing prices and the fundamental factors. When these fundamental factors cannot interpret the variations in housing prices, this implies a large likelihood of the presence of housing bubbles.

  4. See Davis (2014) and Bradsher (2014).

  5. It is noteworthy that China is a large country with a huge population and land area. It has a complicated administrative system, and its cabinet, namely the highest administrative organization, is the State Council, which is composed of various ministries, commissions and the central bank. The State Council, and its ministries, commissions, or administrative offices are authorized to make managerial rules and policies, while the ministries or commissions have responsibility to perform their administrative functions in their respective fields. This helps understand why there might be several regulatory bodies that make housing policies shown in Table 1.

  6. To suppress speculative housing demand, on Apr. 17, 2010 the State Council issued the rules imposing limitations on housing purchase and loan eligibility by adopting legal, administrative and tax measures, and China’s major city governments correspondingly localized these rules subsequently. For example, on February 16, 2011 the Beijing municipal government released its stringent home-purchase limitation rules. According to the policy, a Beijing-Hukou family who has owned more than one housing unit was directly forbidden from purchasing one additional housing unit in this city. A non-Beijing-Hukou family who has owned one housing unit or more was also banned from buying an extra housing unit in this city, if its members had no temporary residence permits or did not pay society insurance or personal income taxes over past five consecutive years.

  7. According to the figures released by China's Ministry of Civil Affairs, as of 2014 there were 288 prefecture-level cities and 361 county-level cities in mainland China. Our study attempts to detect housing bubbles in major Chinese cities. We believe that the housing market conditions of these major cities have significant effects on the whole economic state in this country.

  8. We know that since a house can be regarded as a mixture of multiple bundles of housing characteristics such as structural, proximity, and neighborhood attributes, a hedonic method may be used to regress house price or rent on these housing attributes in order to build quality-adjusted housing price or rent indexes. However, the use of the hedonic approach usually requires a great deal of the actual housing transaction data. Although the database we use is one of the largest real estate databases in mainland China, it does not offer detailed information on the actual housing transactions in the major cities such that we cannot estimate hedonic-based housing price and rent indexes. Since there is a relatively short development history in the Chinese housing market, the quality-adjusted housing price indexes have not yet constructed for the major Chinese cities. In effect, so far, only in the very limited number of Western countries have this type of housing price indexes been constructed and released regularly to reflect the variations in the pure housing prices (Hill 2013).

  9. See Phillips and Sul (2007) for a detailed discussion on the definition of the relative transition measure.

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Acknowledgments

The authors would like to thank conference participants at the 2014 Global Chinese Real Estate Congress (GCREC) for helpful comments.

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Correspondence to Gang-Zhi Fan.

Appendices

Appendix 1: Present value model

Assuming a two-period model, the house price–rental relation can be written as:

$$ P_{t} = \frac{{E_{t} \left[ {P_{t + 1} + D_{t + 1} } \right]}}{1 + r} $$
(5)

where \( P_{t} \) denotes the asset price at time t, \( D_{t} \) the housing rental income at time t, and r the constant discount rate. A rational investor may evaluate the price of an asset as the present value of its next period price plus rental income. Recursively solving this equation, we obtain

$$ P_{t} = \theta (1 - \alpha )\sum\limits_{i = 0}^{\infty } {\alpha^{i} E_{t} (D_{t + i} )} $$
(6)

where \( \alpha = \frac{1}{1 + r},\theta = \frac{\alpha }{(1 - \alpha )} = r^{ - 1} \). Campbell and Shiller (1987) rearrange this equation as an empirically testable form:

$$ P_{t} - D_{t} \theta = \theta \sum\limits_{i = 1}^{\infty } {\alpha^{i} E_{t} (\varDelta D_{t + i} )} $$
(7)

Since both asset prices and rental incomes usually evolve as nonstationary I(1) processes, a long-run cointegrating vector (\( 1, - \theta \)) exists if the present value model holds. Alternatively, by Campbell and Shiller (1988), because

$$ r_{t + 1} \approx \log \left( {P_{t + 1} + D_{t + 1} } \right) - \log \left( {P_{t} } \right) $$

a logarithm transformation for this equation can generate

$$ p_{t} - d_{t} = - r_{t + 1} + \varDelta d_{t + 1} + \ln (1 + e^{{p_{t + 1} - d_{t + 1} }} ) $$
(8)

where the lower case letters represent the logarithms of the upper case variables. By means of a first-order Taylor expansion, we can linearize model (8) as the following expression:

$$ p_{t} - d_{t} \approx - r_{t + 1} + \Delta d_{t + 1} + k + \rho (p_{t + 1} - d_{t + 1} ) $$
(9)

where \( \rho = \frac{{e^{{\bar{p} - \bar{d}}} }}{{1 + e^{{\bar{p} - \bar{d}}} }} \) and \( k = \ln (1 + e^{{\bar{p} - \bar{d}}} ) + \rho \left[ {\bar{p} - \bar{d}} \right] \), \( \bar{p} \) and \( \bar{d} \) are unconditional mean of each variable. Under this log-linear form, a stationary log price-to-rent ratio process implies the nonexistence of a rational bubble in housing prices, while failing to reject a unit root hypothesis indicates the presence of such a bubble.

Appendix 2: Zivot and Andrews (1992) test

The null hypothesis for the test is:

$$ H_{0} :y_{t} = \mu + \beta t + y_{t - 1} + \varepsilon_{t} $$
(10)

The following augmented regression is considered when testing for unit roots:

$$ y_{t} = \mu + \theta DU_{t} (\lambda ) + \beta t + \gamma DT_{t} (\lambda ) + \alpha y_{t - 1} + \sum\limits_{j = 1}^{k} {c_{j} \varDelta y_{t - j} + \varepsilon_{t} } $$
(11)

where \( \text{for}\;\lambda \in (0,1),DU_{t} (\lambda ) = 1\quad \text{if}\;{\text{t}} > T\lambda ,0\;\text{otherwise, and}\;DT_{t} (\lambda ) = t - T\lambda \quad \text{if}\;t > T\lambda ,0\;\text{otherwise}. \)

Zivot and Andrews (1992) calculate sequentially one-side t-statistics for testing \( \alpha^{i} = 1 \) and select the minimum value as the test statistic. The break point is selected as the point generating a minimum t-statistic: \( t_{{\hat{\alpha }^{i} }} \left[ {\lambda_{\inf }^{i} } \right] = \mathop {\inf }\limits_{\lambda \in \varLambda } t_{{\hat{\alpha }^{i} }} (\lambda ) \).

Appendix 3: Club convergence

Panel data, Y it , we can decompose it into a systematic component (g it ) and a transitory component (a it ) as,

$$ Y_{it} = g_{it} + a_{it} $$
(12)

which can in turn be transformed into a time-varying factor representation:

$$ Y_{it} = \left( {\frac{{g_{it} + a_{it} }}{{\mu_{t} }}} \right)\mu_{t} = \delta_{it} \mu_{t} $$
(13)

where \( \delta_{it} \) is an idiosyncratic component and \( \mu_{t} \) is a common component. The idiosyncratic component measures the distance between \( Y_{it} \) and the common component. If the factor \( \delta_{it} \) converges to a constant \( \delta \), then there will be convergence clubs. Scaling the common factor \( \mu_{t} \), the PS method introduces a relative loading or transition coefficient:

$$ h_{it} = \frac{{Y_{it} }}{{\frac{1}{N}\sum\nolimits_{i = 1}^{N} {Y_{it} } }} = \frac{{\delta_{it} }}{{\frac{1}{N}\sum\nolimits_{i = 1}^{N} {\delta_{it} } }} $$
(14)

This relative transition parameter has a cross-sectional mean of unity; and when \( \delta_{it} \) converges to a constant, \( h_{it} \) converges to unity. The variance of this transition parameter \( H_{t} = \frac{1}{N}\sum\nolimits_{i = 1}^{N} {\left( {h_{it} - 1} \right)}^{2} \) converges to zero in the long run (t → ∞).

The PS method also allows for a test of convergence starting from the following regression

$$ \log \left( {{{H_{1} } \mathord{\left/ {\vphantom {{H_{1} } H}} \right. \kern-0pt} H}_{A} } \right) - 2\log L\left( t \right) = \hat{c} + \hat{b}\log \left( t \right) + u_{t} $$
(15)

In (15) \( L(t) \) is a slowly varying function, defined as \( \log \left( t \right) \) for \( t = \left[ {rT} \right] \),…, T, where \( \left[ {rT} \right] \) denotes the integer part of \( rT \), and \( r \) is a positive number. PS also show that the parameter \( b \) equals twice the convergence rate \( a \). The one-sided \( t \)-statistics for \( \hat{b} \) using HAC standard errors can be constructed, and the (one-sided) null hypothesis of convergence is rejected at the 5 % level if \( t_{b} < - 1.65 \).

To accommodate any possibility of sub-group convergence, PS introduce a systematic way of clustering based on repeated log-t regressions. It is a four-step process, namely, ordering, forming core group, seizing membership and stopping rule (see Phillips and Sul 2007 for more details).

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Zhang, D., Liu, Z., Fan, GZ. et al. Price bubbles and policy interventions in the Chinese housing market. J Hous and the Built Environ 32, 133–155 (2017). https://doi.org/10.1007/s10901-016-9505-6

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Keywords

  • Housing bubble
  • Price–rent ratio
  • House price
  • Policy intervention
  • Club convergence

JEL Classification

  • R31
  • R38
  • E31