Chapter 4: Does local governments’ budget drive housing prices up in China? . 45
4.2 A model of housing activity and local government’s budget deficit
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the housing price properties and their determinants at the both national and regional level.
Based on following reasons, this Chapter focus on China’s housing market at national and regional level. First, the movements of regional housing prices are more correlated with regional economic fluctuations rather than with national ones. Secondly, it is commonly believed that China's regional differences have become a growing problem.
The major 35 cities account for nearly half of national GDP. Nevertheless, top five cities that contribute to China’s economy most – Beijing, Shanghai, Shenzhen, Tianjin, and Guangzhou are all located in the Eastern China. Thirdly, Shen and Liu (2004) claims that the fundamental factors have different explanatory powers across different cities.
The rest of this Chapter is structured as follows. Section 4.2 conducts a theoretical model based on the behavior of the housing market participants and then relates the theoretical model to the PSTR models. Section 4.3 describes the estimation procedure and presents the linearity test. Section 4.4 describes the dataset in details. Section 4.5 performs the methodology and presents detailed description of the empirical results.
The final section concludes the Chapter.
4.2 A model of housing activity and local government’s budget deficit
In this section, we follow Wu et al. (2015) closely to present a simple partial equilibrium model as a motivation of our empirical study.
4.2.1 Households
A representative household living in a city derives utility from the quantity of housing consumed, the non-housing good, and from the city with the quality of life measured
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by the quality of air (𝐴𝑖𝑟) and local public amenities such as government spending on education (𝐸𝑑𝑢) . To achieve max utility level, the consumer subjects to budget constraint as well as flow of funds constraint. Disposable income(𝐷𝐼), housing prices (HP), interest rate (Int), and CPI growth rate (CPI) are all related to the constraint.
Hence, for a city with the number of population (Pop) and the sex ratio (Sex),15 the aggregate housing demand for each city 𝑖 at time 𝑡 is therefore: 𝐻𝑖𝑡𝑑 = 𝐻𝑖𝑡𝑑(𝐻𝑃𝑖𝑡, 𝐸𝑑𝑢𝑖𝑡, 𝐷𝐼𝑖t, 𝐴𝑖𝑟𝑖𝑡, 𝑃𝑜𝑝𝑖𝑡, 𝑆𝑒𝑥𝑖𝑡, 𝐼𝑛𝑡𝑖𝑡, 𝐶𝑃𝐼𝑖𝑡).
For this housing market, specified by Wu et al. (2015) for the China’s housing market, it is assumed the price of goods, services, and taxes are the same wherever one is located.16
4.2.2 Builders
Builders maximize profits by converting the raw land to urban use and building houses.
Housing prices (HP), available lands(𝐿), land prices(𝐿𝑃), and construction costs (Con) are relevant to the builders in deciding whether to construct the houses or develop the land. Additionally, financial costs measured by interest rate (𝐼𝑛𝑡𝑖𝑡) and CPI growth rate (CPI) reflect the costs of borrowing until sale of the house should be taken into account.
Therefore, housing supply and land demand for each city 𝑖 at time 𝑡 is therefore:17𝐻𝑖𝑡𝑠 = 𝐻𝑖𝑠(𝐻𝑃𝑖𝑡, 𝐿𝑖𝑡, 𝐶𝑜𝑛𝑖𝑡, 𝐼𝑛𝑡𝑖𝑡, 𝐶𝑃𝐼𝑖𝑡); 𝐿𝑑𝑖𝑡 = 𝐿𝑑𝑖𝑡(𝐻𝑃𝑖𝑡, 𝐿𝑃𝑖𝑡, 𝐶𝑜𝑛𝑖𝑡,
15 Wei and Zhang(2011) and Wei et al. (2012) claim that the sex ratio imbalance is contributed to China’s soaring house prices, because households with a son (or the bachelors) tends to buy the house in order to get the stronger competitive position in the marriage market in China.
16 According to the recent China Household Finance Survey (CHFS) estimated that the
homeownership ratio in urban China was up to 90% in 2014. For the reason, in this section, we ignore the rental market.
17 Our housing supply function is quite similar to Poterba (1984) which take q theory-related approaches to modelling housing supply. The net investment in housing structure is a function of real house prices, construction cost and credit availability in Poterba models.
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𝐼𝑛𝑡𝑖𝑡, 𝐶𝑃𝐼𝑖𝑡).
4.2.3 Local government
As stated above, the local government’s role is the core of China’s land system since China’s real east market is based on the land-use rights being transferred to the local government for a period of time. Local government's monopoly in land supply enables it to expropriate land below market price or to keep land prices at an artificially high level (Bertaud 2012; Hu 2016). With more financing needs, the local government has a stronger incentive to generate local revenue from lands sales. As a result, land supply is positively related to the local government’s budget deficit (BD). However, state participation in housing activities may lead to a misallocation (Wang 2011). According to World Bank (2014), the increasing aggressive requisitioning of farmland in order to convert it into urban land development will result in an unstable urban growth and a waste of land resources. Also, Hu (2016) points out that the continuing conversion of farmland to nonagricultural use has raised lots of concern. In other words, farmland conversion for urban development leads to other losses as agriculture revenue. For simplicity, in our model, we use labor productivity of the primary sector (AP) as the measurement of the cost that created from the local government’s land sale.
Last, suggestion from Wu et al. (2015), agriculture GDP share (AR) is also needed to be taken into account. The land supply for each city 𝑖 at time 𝑡 is therefore: 𝐿𝑖𝑡𝑠 = 𝐿𝑠𝑖𝑡(𝐵𝐷𝑖𝑡, 𝐿𝑃𝑖𝑡, 𝐴𝑃𝑖𝑡, 𝐴𝑅𝑖𝑡)
4.2.4 Asymmetric effect and threshold model
The real estate market is in equilibrium when housing supply equals housing demand
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and land supply equals land demand. Consequently, the corresponding reduced form of housing price function then defined as follows:
𝐻𝑃𝑖𝑡 = 𝛼𝑖 + 𝑋𝑖𝑡′𝛿 + 𝜀𝑖𝑡 (1)
where 𝛼𝑖 stands for city-level fixed effects which account for the heterogeneity between cities such as geography, culture, and social norms, and it is also constant over time. The vector 𝑋𝑖𝑡 stands for the set of potential determinants discussed earlier, 𝜀𝑖𝑡 is an i.i.d. city-specific random disturbance with zero mean and a variance 𝜎𝜀2𝑖.
Equation (1) implies that all regression parameters are constant for the set of model. As we mentioned earlier that the households, builders, and local government may not respond symmetrically over the real estate cycle, the linear assumption will not be complete in accordance with the real situation.Threfore, we are applying the PSTR model to housing prices, and the empirical PSTR model can be formulated as follow:
𝐻𝑃𝑖𝑡 = 𝛼𝑖+ 𝛿0′𝑋𝑖𝑡+ 𝛿1′𝑋𝑖𝑡 𝑔(𝑞𝑖𝑡; 𝑐) + 𝜀𝑖𝑡 (2)
where 𝑞𝑖𝑡 denotes a threshold variable with 𝑐 as a threshold parameter. Based on the previous discussion, 𝑞𝑖𝑡 is corresponding to the growth rate of housing price, and the transition function 𝑔(𝑞𝑖𝑡; 𝑐) associates with the indicator function:
𝑔(𝑞𝑖𝑡; 𝑐) = { 1 𝑖𝑓 𝑞𝑖𝑡 ≥ 𝑐
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (3)
In a panel framework, a logistic or an exponential specification can be applied for the transition function:
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parameter 𝛾 determines the slope of the transition function. For the logistic transition function(𝑚 = 1), the model has two extreme regimes separating low and high housing growth rate with single monotonic transition from 𝛿0 to 𝛿0+ 𝛿1 as housing growth rate increases. For the exponential transition function (𝑚 = 2), the model has three regimes separating low, middle, and high housing growth rate, while the regression coefficients are assumed to be the same in the two opposite regimes. The parameter 𝛾 can be also interpreted as the speed of the transition from one regime to another one.When 𝛾 → 0, the transition function approaches a constant and the model reduces into a homogenous or a linear panel regression model with fixed effects. When 𝛾 → ∞, the PSTR model converges towards the two-regime panel threshold regression (PTR) proposed by Hansen (1999).18