Convergence and spillover of house prices in Chinese cities

ABSTRACT

The issue of house price convergence in 34 Chinese cities is investigated. We augmented the convergence model with contemporaneous spatial dependence in house prices and found that price convergence and positive spatial spillover are both present. We explicitly addressed the endogeneity problem by introducing a Bayesian instrumental variable setup, which was estimated with particle filtering techniques. From a growth poles perspective, the empirical evidence indicates that the spread effect in regional house prices outweighs the backwash effect. The identified positive spatial spillover has two effects on the growth of house prices in Chinese cities. First, the spillover elevates the trajectories of the steady-state growth paths of house prices. Second, the spillover narrows the gaps between the growth paths of house prices in neighbouring cities. Shocks to the socio-economic variables of a city generate their own effects on domestic house prices that dominate the effects arising from cross-city price feedbacks, thus mitigating the prospect of level convergence. Our findings also suggest a collaborating role between time and spatial dependence parameters. The identification of inter-city spillover, which is a conditioning factor for regional house price convergence, offers implications to policies that are most likely to be effective in reducing regional disparity.

KEYWORDS:

• China house prices
• spatial dynamic panel model
• convergence
• spillover

JEL CLASSIFICATION:

• R12
• R21
• C5

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Following past studies (e.g. Abraham and Hendershott 1994; Capozza et al. 2002; Rodda and Goodman 2005), steady-state house price is defined as the fundamental value for housing determined by economic conditions.

² Core regions are places where favourable conditions for expanding employment opportunity and other economic activities exist. These conditions include a developed public infrastructure and current external economies.

³ Different from previous studies (e.g. Henry and Barkley 1997) that investigated the urban–rural development linkages, the current study examines the spread and backwash effects across a system of cities and their immediate surrounding area.

⁴ This technical constraint is not unique to our study. Including only the first-order spatial lag in the model is a rather common practice in past-related studies. For instance, in a brief survey conducted by Kukenova and Monteiro (2008), none of the reviewed models simultaneously contained both first- and second-order spatial lags, and majority of them did not have a second-order lag.

⁵ China Data Online is compiled by the China Data Center, University of Michigan, using data from China Statistical Yearbook. The city-level sale price index of houses is available until 2009. We compiled the sample until 2008 to avoid the possible effect of the global financial crisis on the real estate market. The sample cities are Beijing, Changchun, Changsha, Chengdu, Chongqing, Dailan, Fuzhou, Guangzhou, Guiyang, Haikou, Hangzhou, Harbin, Hefei, Hohhot, Jinan, Kunming, Lanzhou, Nanjing, Nanning, Ningbo, Qingdao, Shanghai, Shenyang, Shenzhen, Shijiazhuang, Taiyuan, Tianjin, Urumqi, Wuhan, Xiamen, Xi’an, Xining, Yinchuan and Zhengzhou.

⁶ To show that y_t in Equation (6) is equal to the growth rate of the house price index, let h_t = p_t/p₀ be the price index, where p_t is the actual house price in t (t = 0 is the base year). The growth rate of h_t = ln(h_t/h_{t– 1}) = ln(h_t) – ln(h_{t– 1}) = ln(p_t) – ln(p_{t– 1}) = ln(p_t/p_{t– 1}) = y_t.

⁷ http://www.distancecalculator.globefeed.com/China Distance Calculator.asp.

⁸ Alternatively, the high expected inflation and nominal interest rates signify that nominal house prices tend to increase.

⁹ We have experimented with the inclusion of t – 2 endogenous variables as instruments in Equation (5), and found counter-intuitive patterns in the direct–indirect effects and signs of coefficients. A possible reason is that the second-order lags of the instruments are weakly related to the endogenous variables given the large time gap separating them. We have also tried an alternative specification of setting the endogenous variables not as contemporaneous factors but as first lag inputs while retaining the first-order autoregressive transitional dynamics. The results largely resemble those of the chosen model reported in this article.

¹⁰ The lagged terms of the endogenous variables can be replaced with instruments if they are readily available.

¹¹ The order of reduction is from $\left[\left(\tilde{k}+1\right)N\right]\left[\left(\tilde{k}+1\right)N+1\right]/2$ to $\left[\left(\begin{array}{c}\tilde{k}+1\\ 2\end{array}\right)+\tilde{k}+1\right]N$. Reducing the dimension can make the numerical computation of likelihoods easier.

¹² In a Bayesian analysis, the importance of the prior distribution diminishes as the sample size grows. In the context of particle filtering applied in this study, the filter becomes asymptotically optimal as the number of particles increases (i.e. partition of the state space becomes increasingly fine) (e.g. Crisan and Miguez, 2014).

¹³ Typically, log-likelihoods are highly feasible computationally in high-dimensional problems.

¹⁴ Moran’s I index ranges between – 1 and +1. A positive (negative) value indicates a positive (negative) spatial correlation (e.g. Li, Calder, and Cressie 2007).

¹⁵ The estimation is under the assumption that the convergence parameter is time invariant. To explore the possibility of a time-varying convergence parameter, we re-estimated the model using observations $t=\{1,2\}$ and $t=\{2,3\}$ separately and determined that the values of β from the two subsamples are – 0.0143 and – 0.0246, respectively. Considering that the actual convergence parameter is β₀ = β – 1, the speed of convergence is indeed stable over the sample period.

¹⁶ Here is a possible misnomer as all rounds are supposed to take effect instantaneously.

¹⁷ The raw values presented in Figure 1 are unweighted. Different from the MCMC estimates that give equal weights to all sampled points, the particle-filtering algorithm employed in our study attaches small weights to pairs of $\beta$ and $\rho$ (i.e. particles) that violate the stationarity condition, in which the weights are functions of the likelihoods. The pairs of $\beta$ and $\rho$ that violate the stationarity condition have a slight effect on the posterior estimates because they receive small weights and the chance of their values being drawn in the re-sampling step of the algorithm is small.

¹⁸ No comparable data for 2000 are available. The data can be found in the official website of the National Bureau of Statistics of China. http://www.stats.gov.cn/was40/gjtjj outline.jsp.

¹⁹ North: Beijing, Hohhot, Shijiazhuang, Taiyuan and Tianjin. South: Guangzhou, Haikou, Nanning and Shenzhen. East: Fuzhou, Hangzhou, Hefei, Jinan, Nanjing, Ningbo, Qingdao, Shanghai and Xiamen. West: Chengdu, Chongqing, Guiyang, Kunming, Lanzhou, Urumqi, Xi’an, Xining and Yinchuan. Central: Changsha, Wuhan and Zhengzhou. Northeast: Changchun, Dailan, Harbin and Shenyang.

²⁰ To curb the increasing house prices in major cities, for instance, non-local-registered families that have not paid local social security or income taxes for several years are banned from buying local properties in major cities. Whalley and Zhang’s (2004) simulation suggests that abolishing the hukou system can enhance rural–urban labour migration and thus positively affect urban house prices.

²¹ The plan was a strategic decision made by the Chinese government following its earlier decision to prioritize the development of the eastern region, develop the central region through urbanization and rejuvenate the old industrial bases.

Additional information

Funding

The work described in this article was supported by a grant from the Hong Kong Research Grant Council [Project #: PolyU 5917/13H].