How Much Are Amenities Worth? An Empirical Study on Urban Land and Housing Price Differentials across Chinese Cities

Abstract

As China is transitioning from a planned economy to a market-based economy, over the past 30 years, China’s economy has experienced the same type of changes that led to amenity-driven housing and land markets in more developed countries. This paper examines the effect of different types of amenities on urban land and housing prices across Chinese cities in 2020. When firms and households value some amenities, the assumption is that the preference for these amenities will be valued and reflected in both land and housing markets. We conduct a cross-sectional analysis of urban land and housing prices in prefecture and higher-level cities in China. We extend the Roback model to explore the extent to which the different land rents and housing prices reflect the compensations for interregional amenity differences across Chinese cities. We include two types of amenities: natural amenities and locally produced amenities. We perform two-stage least squares (2SLS) estimations and compute the implicit prices of various amenities for households and firms. The empirical results show that a range of amenities is valued by both households and firms, resulting in higher housing and industrial prices.

1. Introduction

In the past three decades, unprecedented urbanization occurred in China and this phenomenon has attracted the attention of many researchers since it has changed many facets of China’s urban and rural worlds. Market-oriented mechanisms began to form and mature and have been strengthening China’s market economy. Market forces have also created substantial regional heterogeneity in urban land and housing prices across Chinese cities. For example, the average price of urban industrial land in the Pearl River Delta, one of most industrialized regions in China, was more than 65% higher than the national average of urban industrial land, and the average price of urban residential land in the Pearl River Delta was a few times higher than the national average.

Since land and housing prices play important roles in social and economic development, the topic of land and housing markets has attracted much attention from academia. There has been an ongoing interest in the determinants of factors that influence the real estate markets. Most previous studies have investigated land and housing markets separately. For housing market studies, Abraham and Hendershott investigated variations of house prices in about thirty metropolitan areas in the USA and found that the rate of change in employment, real income growth, real construction cost inflation, and changes in real after-tax interest rates could explain housing price changes well [1]. Huang et al. pooled macroeconomic and urban economic data on Chinese cites from 1999 to 2012 and controlled for geological, environmental, and social diversity in their multi-step estimation of property prices [2]. Their results suggest that bank lending and local amenities such as higher education, green infrastructure, healthcare, and climate positively affect house prices. Wang et al. employed a cross-sectional dataset of county-level housing prices to study the direction and strength of the association between housing prices and their potential determinants in China [3]. They found that the positive effects on housing prices include the proportion of renters, floating population, wage level, the cost of land, the housing market, and city service level. Another example of study on intercity variations in housing prices looks at how air pollution adversely impacted property values. Zou employed air pollution and housing price data covering 282 prefecture-level cities in China and confirmed negative capitalization of air pollution into cross-city housing prices [4]. Yang et al. conducted a geographically weighted regression (GWR) analysis on the relationships between residential land price and three major impact factors (i.e., immigrant population, gross domestic product (GDP), and investment in residential buildings) using data from 105 cities in China and showed that the GDP has more significant influence on residential land price than other factors and the influence of the three factors on overall variation in residential land price increased over time [5].

Although land and housing price variations have been investigated in the land and the housing markets separately, some researchers argue that single-market differentials are partial prices and are unreliable measures of amenity values in an interregional context [6]. Potepan explained why housing prices, rents and urban land prices vary so dramatically between US metropolitan areas using a two-stage least squares model of a metropolitan housing market with three interrelated submarkets of rent, housing prices, and urban land prices. The results suggested that the three submarkets do interact and that household income and construction costs are the most important factors causing housing prices, rents, and land prices to vary between metropolitan areas. Combining Potepan’s real estate model with Roback’s spatial equilibrium approach, Bischoff proved the interdependency of housing prices, rental prices, building land prices, and income through one simultaneous equilibrium analysis [7,8,9]. Results showed significantly positive interaction effects between income and real estate prices. In particular, the expectation of population growth seems to be one of the most important determinants to interregional prices. Other studies account for impacts of population migration accompanied with China’s urbanization. Deng et al. studied China’s land and housing price differentials using a dynamic competitive spatial equilibrium framework featured with endogenous rural-urban migration [10]. Garriga et al. evaluated how changes to city migration policies and land supply regulations affected the speed of urbanization and house price appreciation [11]. Their results show that making migration policy more egalitarian or land policy more uniform would promote urbanization but also would contribute to larger house price dispersion.

In order to understand the Chinese land and housing markets, it is important to examine which factors contribute to land and housing price differentials across Chinese cities and, more specifically, what amenity attributes are valued by households and firms in China. By doing so, we will add to the knowledge of the relationships between urban amenities and urban land and housing prices across Chinese cities. Under this context, this paper aims to explore the question of whether amenities play a role in determining price variations in China. In answering this question, we offer several contributions to the literature. First, this study concentrates on the role of amenities in affecting Chinese housing and land markets, which began to attract attention from researchers given that amenities are thought to be increasingly important as China becomes wealthier. Second, both natural amenities and consumer amenities are considered. Finally, we stress the interdependence between the decisions of firms and households in both housing and land submarkets in our analysis.

We extend and apply the Roback model to explore the extent to which the different land rents and housing prices reflect the compensations for interregional amenity differences across Chinese cities. Economists [7,8] have argued that, to a large extent, nonpecuniary characteristics of locations, in the form of consumer amenities [12,13] or producer amenities [14,15], can be used to explain pecuniary differences across locations in wages and land or housing rents in well-developed market economies. Here we are interested in investigating if nonpecuniary amenities are capitalized into rents in a transitional economy, particularly in China. We thus apply the Roback model and conduct a cross-sectional analysis of urban land and housing prices in prefecture and higher-level cities across China. In essence, our model stresses the interdependence between the decisions of firms and households in determining interregional rent differentials. We investigate the effects of a set of broadly defined urban amenities, such as climatic and environmental amenities, public services, regional and intra-urban transport systems, industrial agglomeration, and business services on urban land and housing prices across Chinese cities.

The paper is organized as follows: the next section describes a theoretical model; the third develops empirical specifications and describes the data and variables; the fourth provides model estimates; and the final section concludes the study.

2. Theoretical Model

Although land and housing price variations have been investigated in the land and the housing markets separately, single-market differentials are partial prices and are unreliable measures of amenity values in an interregional context [12]. With interaction between the urban labor and land markets, cities offer tied bundles of wages, land and housing rents, and amenities that affect households’ utility and firms’ productivity. Roback developed a model to show that wages and rents vary across locations in order to equilibrate household utility and firm costs [7]. Households and firms compete for a fixed number of locations, with households attempting to maximize well-being and firms attempting to minimize costs by their location decision.

Based on Roback’s model, we also solve the individual’s maximization problem with the indirect-utility function. Household valuations of alternative locations, indexed by i, can be derived from an indirect-utility function $V\left(W_i,R_i,p_i,{\mathbf{a}}_i^c\right)$, where W_i is the wage rate in city i, R_i is the rental payment of residential land, p_i is the price of a composite good determined by international markets, and ${\mathbf{a}}_i^c$ is a vector of local amenities for households (such as climate, public services, and environment quality).

Firms in city i produce y_i sold at a constant price level of q, according to constant returns to scale production function which requires inputs such as labor, n_i; land, l_i’; and capital, k_i. Producer amenities ${\mathbf{a}}_i^f$, such as transportation services and other public infrastructure services, are also assumed to affect production technology. It is necessary to note that ${\mathbf{a}}_i^c$ and ${\mathbf{a}}_i^f$ may overlap. For ease of exposition, we denote ${\mathbf{a}}_i^c=({\mathbf{a}}_i,{\mathbf{a}}_i^{\prime })$ and ${\mathbf{a}}_i^f=({\mathbf{a}}_i,{\mathbf{a}}_i^{″})$, in which ${\mathbf{a}}_i$ are amenities affecting both economic agents while ${\mathbf{a}}_i^{\prime }$ and ${\mathbf{a}}_i^{″}$ are assumed pure consumer amenities and producer amenities, respectively. The price of labor is the same as the wage rate W_i and the price of land is denoted as R′_i. Capital, with a constant interest rate r, is assumed to be completely mobile. Assuming the tax rate of profit is t_i, the profit is then given by $(1-t_i)(q{y}_i-W_i{n}_i-R_i^{\prime }{l}_i^{\prime }-r{k}_i)$. Therefore, the profit function associated with a representative firm in city i is given by $\mathsf{\Pi }\left(W_i,R_i^{\prime },t_i,{\mathbf{a}}_i^f\right)$. In Roback’s (1982) theoretical model and the subsequent empirical analyses, R′_i is assumed to equal R_i and both R′_i and R_i can be substituted by housing price $R_i^h$.

We can now characterize the equilibrium. Again, both capital and labor are assumed to be completely mobile across cities. Equilibrium is characterized by equal utility across workers and equal profits across firms so that no agents have incentives to move. However, wages and land rents may vary in equilibrium to compensate workers and firms for interregional differences in amenities. We thus have:

$$V\left(W_i,R_i^h,p_i,{\mathbf{a}}_i^c\right)=\overline{V}$$

(1)

$$\mathsf{\Pi }\left(W_i,R_i^h,t_i,{\mathbf{a}}_i^f\right)=\overline{\mathsf{\Pi }}$$

(2)

From Equations (1) and (2), we can express the implicit functions of W and R by the following set of simultaneous equations:

$$R^V=f\left(W,p_i,{\mathbf{a}}_i^c\right)$$

(3)

$$R^{\pi }=g\left(W,t_i,{\mathbf{a}}_i^f\right)$$

(4)

Substituting (3) and (4) in (1) and (2), respectively, and differentiating the resulting equations with respect to W yield

$$\frac{\partial f}{\partial W}=-\frac{\partial V}{\partial W}/\frac{\partial V}{\partial R}>0\hspace{1em}\frac{\partial g}{\partial W}=-\frac{\partial \mathsf{\Pi }}{\partial W}/\frac{\partial \mathsf{\Pi }}{\partial R}<0$$

(5)

Clearly, (5) indicates that the wages should be higher with increases in housing price in order for consumers to maintain the same level of utility and wages paid should be lower with increases in land price in order for firms to maintain the same level of profits. Thus, Equation (3) is an upward sloping line representing combinations of W_i and R_i which equalize utility at a given level of ${\mathbf{a}}_i^c=({\mathbf{a}}_i,{\mathbf{a}}_i^{\prime })$ while Equation (4) is a downward sloping line for iso-profit combinations of W_i and R_i at a given level of ${\mathbf{a}}_i^f=({\mathbf{a}}_i,{\mathbf{a}}_i^{″})$. In equilibrium, the iso-utility and profit curves must cross each other (see Figure 1).

Figure 1 also illustrates the effects of different quantities of amenities on the equilibrium levels of wages and rents (holding other things constant). The figure shows that cities with a higher level of consumer amenities (${\mathbf{a}}_i^c=({\mathbf{a}}_i,{\mathbf{a}}_i^{\prime })$), holding other things constant) attract an influx of population, resulting in a larger size of labor supplied in the city. The increase in labor leads to lower wages (w¹) while the increase in population results in higher housing prices (R¹). Altogether, these factors lead to a lower level of utility for the city residents. When utility drops to the average level of all cities, population migration stops. Similarly, cities with a higher level of amenities for firms (${\mathbf{a}}_i^f=({\mathbf{a}}_i,{\mathbf{a}}_i^{″})$, holding other input prices constant) would enable producers in these cities to obtain a higher level of profits. The increase in profits induces producers from other cities to move in, resulting in increased demand for labor and land, which lead to higher wages (w²) and rents (R²) and thus lower profits. When profits drop to the national average, producers stop moving in. This perfectly determines W_i and R_i as functions of ${\mathbf{a}}_i$, ${\mathbf{a}}_i^{\prime }$, and ${\mathbf{a}}_i^{″}$ given a certain utility level and profit margin.

The equilibrium levels of wages and rents can be solved from Equations (3) and (4). That is, given the equilibrium condition $R^V=R^{\pi }=R$, (3) and (4) define two reduced form equations:

$$R_i=R\left(p_i,t_i,{\mathbf{a}}_i,{\mathbf{a}}_i^{\prime },{\mathbf{a}}_i^{″}\right)$$

(6)

$$W_i=W\left(p_i,t_i,{\mathbf{a}}_i,{\mathbf{a}}_i^{\prime },{\mathbf{a}}_i^{″}\right)$$

(7)

Thus, the differences in the equilibrium levels of wages and housing prices across cities can be explained by differences in exogenous variables, {p_i, t_i, a_i, a_i′, a _i″}.

The above theoretical framework provided a means of imputing the implicit prices of consumer amenity attributes, $\frac{\partial V}{\partial {\mathbf{a}}^c}/\frac{\partial V}{\partial W}$, which is the amount of income needed to compensate a household for a marginal change in amenities. Specifically, substituting (6) and (7) in (1), differentiating the equation with respect to consumer amenity, ${\mathbf{a}}^c$, and by Roy’s identity, the implicit price of ${\mathbf{a}}^c$, or compensating differential, can be written as

$$P_{{\mathbf{a}}^c}=\frac{\partial V}{\partial {\mathbf{a}}^c}/\frac{\partial V}{\partial W}=-\frac{\partial W}{\partial {\mathbf{a}}^c}-\frac{\partial V}{\partial R}/\frac{\partial V}{\partial W}\frac{\partial R}{\partial {\mathbf{a}}^c}=h\frac{\partial R}{\partial {\mathbf{a}}^c}-\frac{\partial W}{\partial {\mathbf{a}}^c}$$

(8)

where $h=-\frac{\partial V}{\partial R}/\frac{\partial V}{\partial W}$ is housing consumption per capita. Similarly, the implicit price of producer amenity ${\mathbf{a}}^f$ can be expressed as

$$P_{{\mathbf{a}}^f}=\frac{\partial \mathsf{\Pi }}{\partial {\mathbf{a}}^f}=-\frac{\partial \mathsf{\Pi }}{\partial W}\frac{\partial W}{\partial {\mathbf{a}}^f}-\frac{\partial \mathsf{\Pi }}{\partial R}\frac{\partial R}{\partial {\mathbf{a}}^f}=n\frac{\partial W}{\partial {\mathbf{a}}^f}+h^{\prime }\frac{\partial R}{\partial {\mathbf{a}}^f}$$

(9)

where n is the amount of labor employed and h′ is the area used for production.

The above implicit prices can be estimated using cross-sectional or time-series data on wages, rents, and location-specific attribute data [16]. The main strategy in the recent empirical literature has been to estimate separate reduced form Equations (6) and (7) for the housing rents and wages as functions of amenities. It is worth noting that in literature [17,18], an alternative estimation method has been used. Instead of reduced form equations, structural equations are employed so that housing and land rents are functions of the endogenous wage premium in the area, in addition to exogenously determined amenity features. In this approach to estimation, the structural equations can be implicitly defined as

$$V\left(W,f\left(W,{\mathbf{a}}^c\right),{\mathbf{a}}^c\right)=\overline{V},\hspace{1em}\mathsf{\Pi }\left(W,g\left(W,{\mathbf{a}}^f\right),{\mathbf{a}}^f\right)=\overline{\mathsf{\Pi }}$$

(10)

Totally differentiating (10) with respect to a^c and a^f, respectively, and using (5) yields

$$P_{{\mathbf{a}}^c}=\frac{\partial V}{\partial {\mathbf{a}}^c}/\frac{\partial V}{\partial W}=-\frac{\partial V}{\partial R}/\frac{\partial V}{\partial W}\frac{\partial f}{\partial {\mathbf{a}}^c}=\frac{\partial f}{\partial {\mathbf{a}}^c}/\frac{\partial f}{\partial W}$$

(11)

$$P_{{\mathbf{a}}^f}=\frac{\partial \mathsf{\Pi }}{\partial {\mathbf{a}}^f}=-\frac{\partial \mathsf{\Pi }}{\partial R}/\frac{\partial \mathsf{\Pi }}{\partial W}\frac{\partial \mathsf{\Pi }}{\partial W}\frac{\partial g}{\partial {\mathbf{a}}^f}=-n\frac{\partial g}{\partial {\mathbf{a}}^f}/\frac{\partial g}{\partial W}$$

(12)

3. Empirical Analysis

3.1. Empirical Specifications

While the theoretical model developed for US urban land markets assumes that households and firms interact and compete for a fixed number of locations, commodity housing developers and industrial firms in China are not bidding for land in the same land markets. Regulation for Conveyance of State-Owned Land Through Tender Offer, Auction, and Posting mandates that only urban land use rights for residence, commerce, tourism, and entertainment be conveyed in an open market transaction. The rights to land use for industry, transportation, warehousing, and certain public purposes continue to be sold through bilateral negotiation. According to the data from 2020 China Statistical Yearbook for Land and Resources, for the prefecture level cities, the average land price for the land sold through bilateral negotiation is around 40% of the average land price for the land conveyed in an open market transaction. Apparently, Chinese characteristics of land markets present some difficulties when estimating reduced form equations. Therefore, following some of the early studies [17,18], the structural equations are used to estimate the implicit prices of amenities.

The theory has been silent on the specification of estimating equations. Many authors have contributed to discussing the “optimal” specification. Different functional forms have been tested to find the best fit [13]. Malpezzi recommends a log-linear specification [19]. Employing microdata from Hong Kong, Leung et al. show that the log-linear specification can provide a consistently high adjusted R². Both Malpezzi and Leung et al.’s datasets are large and are used for hedonic price estimations [19,20]. In our analysis, we tested both the linear and the log-linear specifications, and the linear form returned slightly better R². Therefore, in this exploratory analysis, we chose to adopt the linear form. Simultaneous Equations (3) and (4) are rewritten as follows and serve as the point of departure for our empirical specification.

$$R^h={\gamma }_0+{\gamma }_{1}W+\mathsf{\gamma }\cdot \mathbf{a}+{\mathsf{\gamma }}^{\prime }\cdot {\mathbf{a}}^{\prime }+{\epsilon }_1$$

(13)

$$R^{\prime }={\eta }_0+{\eta }_{1}W+\mathsf{\eta }\cdot \mathbf{a}+{\mathsf{\eta }}^{″}\cdot {\mathbf{a}}^{″}+{\epsilon }_2$$

(14)

where R^h and R′ are commodity housing prices and prices of industrial land sold through bilateral negotiation, respectively, and ${\epsilon }_1$ and ${\epsilon }_2$ are assumed to be iid random errors. Because W is a RHS endogenous variable, we will perform two-stage least squares (2SLS) estimations.

With 2SLS estimates, we further compute the implicit prices of various amenities for households and firms. By (11) and (12), the implicit prices of ${\mathbf{a}}^c$ and ${\mathbf{a}}^f$ can be estimated using parameter estimates of Equations (13) and (14), respectively,

$${\widehat{P}}_c=\frac{1}{{\widehat{\gamma }}_1}\left(\begin{array}{c}\widehat{\mathsf{\gamma }}\\ {\widehat{\mathsf{\gamma }}}^{\prime }\end{array}\right)$$

(15)

$${\widehat{P}}_f=-\frac{n}{{\widehat{\eta }}_1}\left(\begin{array}{c}\widehat{\mathsf{\eta }}\\ {\widehat{\mathsf{\eta }}}^{″}\end{array}\right)$$

(16)

It can be shown that the implicit prices evaluated this way are equivalent to those imputed from OLS estimates of reduced form equations. Specifically, ${\widehat{\gamma }}_1=1/h$ is the inverse of per capita housing consumption and ${\widehat{\eta }}_1=-n/h^{\prime }$ is the producer’s labor-land input ratio. The reduced form equations are $R={\alpha }_0+\mathsf{\alpha }\cdot \mathbf{a}+{\mathsf{\alpha }}^{\prime }\cdot {\mathbf{a}}^{\prime }+{\mathsf{\alpha }}^{″}\cdot {\mathbf{a}}^{″}+{\epsilon }_1$ and $W={\beta }_0+\mathsf{\beta }\cdot \mathbf{a}+{\mathsf{\beta }}^{\prime }\cdot {\mathbf{a}}^{\prime }+{\mathsf{\beta }}^{″}\cdot {\mathbf{a}}^{″}+{\epsilon }_2$. The OLS are assumed to be unbiased. Based on (8) and (9) the implicit prices of a_c and a_f are ${\widehat{P}}_c=h[\widehat{\mathsf{\alpha }}{\widehat{\mathsf{\alpha }}}^{\prime }]{}^{\prime }-[\widehat{\mathsf{\beta }}{\widehat{\mathsf{\beta }}}^{\prime }]{}^{\prime }$ and ${\widehat{P}}_f=h^{\prime }[\widehat{\mathsf{\alpha }}{\widehat{\mathsf{\alpha }}}^{″}]{}^{\prime }+n[\widehat{\mathsf{\beta }}{\widehat{\mathsf{\beta }}}^{″}]{}^{\prime }$ respectively. Because ${\mathbf{a}}^{\prime }$ is pure consumer amenities and ${\mathbf{a}}^{″}$ is pure producer amenities, two restrictions $h{\widehat{\mathsf{\alpha }}}^{″}-{\widehat{\mathsf{\beta }}}^{″}=0$ and $h^{\prime }{\widehat{\mathsf{\alpha }}}^{\prime }+n{\widehat{\mathsf{\beta }}}^{\prime }=0$ hold. On the other hand, the 2SLS of structure Equation (13) first estimates instrument variable of W, $\widehat{W}={\widehat{\beta }}_0+\widehat{\mathsf{\beta }}\cdot \mathbf{a}+{\widehat{\mathsf{\beta }}}^{\prime }\cdot {\mathbf{a}}^{\prime }+{\widehat{\mathsf{\beta }}}^{″}\cdot {\mathbf{a}}^{″}$, and substitutes $\widehat{W}$ in (13) for W to produce the second stage estimates, $\widehat{R}={\widehat{\gamma }}_0+{\widehat{\gamma }}_1\left({\widehat{\beta }}_0+\widehat{\mathsf{\beta }}\cdot \mathbf{a}+{\widehat{\mathsf{\beta }}}^{\prime }\cdot {\mathbf{a}}^{\prime }+{\widehat{\mathsf{\beta }}}^{″}\cdot {\mathbf{a}}^{″}\right)+\widehat{\mathsf{\gamma }}\cdot \mathbf{a}+{\widehat{\mathsf{\gamma }}}^{\prime }\cdot {\mathbf{a}}^{\prime }$. Comparing the 2SLS estimates with (13), it is clear that ${\widehat{\gamma }}_1{\widehat{\mathsf{\beta }}}^{″}={\widehat{\mathsf{\alpha }}}^{″}$ and ${\widehat{\gamma }}_1[\widehat{\mathsf{\beta }}{\widehat{\mathsf{\beta }}}^{\prime }]{}^{\prime }+[\widehat{\mathsf{\gamma }}{\widehat{\mathsf{\gamma }}}^{\prime }]{}^{\prime }=[\widehat{\mathsf{\alpha }}{\widehat{\mathsf{\alpha }}}^{\prime }]{}^{\prime }$. Further, comparing ${\widehat{\gamma }}_1{\widehat{\mathsf{\beta }}}^{″}={\widehat{\mathsf{\alpha }}}^{″}$ with restriction $h{\widehat{\mathsf{\alpha }}}^{″}-{\widehat{\mathsf{\beta }}}^{″}=0$ for the reduced form estimates reveals ${\widehat{\gamma }}_1=1/h$, i.e., the parameter of the structural equation is the inverse of per capita housing consumption. Rearranging ${\widehat{\gamma }}_1[\widehat{\mathsf{\beta }}{\widehat{\mathsf{\beta }}}^{\prime }]{}^{\prime }+[\widehat{\mathsf{\gamma }}{\widehat{\mathsf{\gamma }}}^{\prime }]{}^{\prime }=[\widehat{\mathsf{\alpha }}{\widehat{\mathsf{\alpha }}}^{\prime }]{}^{\prime }$ yields $(1/{\widehat{\gamma }}_1)[\widehat{\mathsf{\gamma }}{\widehat{\mathsf{\gamma }}}^{\prime }]{}^{\prime }=(1/{\widehat{\gamma }}_1)[\widehat{\mathsf{\alpha }}{\widehat{\mathsf{\alpha }}}^{\prime }]{}^{\prime }-[\widehat{\mathsf{\beta }}{\widehat{\mathsf{\beta }}}^{\prime }]{}^{\prime }=h^{\prime }[\widehat{\mathsf{\alpha }}{\widehat{\mathsf{\alpha }}}^{″}]{}^{\prime }-[\widehat{\mathsf{\beta }}{\widehat{\mathsf{\beta }}}^{\prime }]{}^{\prime }$, indicating that two methods, i.e., OLS of reduced form equations with the restriction and 2SLS of structural equations, yield the same estimates of implicit prices of consumer amenities. By the same token, it can be shown that the two approaches are equivalent in producing estimates of implicit prices of producer amenities.

3.2. Data and Variables

The core of the dataset for the empirical analysis is composed of the following sources: China Statistical Yearbook for Regional Economy 2019 (R), China Statistical Yearbook for Land and Resources 2018–2020 (L), China Statistical Yearbook for Cities 2020 (C), China Statistical Yearbook for Urban Construction 2020 (U), Climate Contour Maps 2020 (CM), and China Meteorology 2020 (M) with the letters in parentheses abbreviating the data sources. These sources allow us to exploit a variety of data relevant to location-specific urban amenities. The variables, descriptions, measurements, and data sources are listed below.

Housing_price: commodity housing prices in 2019, in RMB/m² (R). This variable measures the average selling price of commodity houses in each city in 2019.

Industrial_land_price: prices of industrial land sold through bilateral negotiation, in 10,000 RMB/hectare (L). The variable is calculated by dividing the sum of land values by the sum of land area for industrial land sold through bilateral negotiation between 2018 and 2020. We take the average price of land values from three years for the following two reasons. First, there is significant fluctuation in land prices even for adjacent years; second, some cities would have to be omitted if we employed land prices from only one year. In order to minimize possible data errors due to data coding or other factors and to construct a larger set of data covering more cities, we employ data gathered from three years.

Adj_city_wage: the 2020 average wage of all employees adjusted by composition of employment sectors in the city (C). In addition to the mechanism hypothesized above, wage rates differ considerably across sectors. Thus, differences in sectoral composition also contribute to wage differentials. Data suggest that employment composition varies significantly across cities. For example, nationwide the mining sector accounts for only 4.1% in total employment, while there are 28 cities with more than 20% of employees working in the mining sector, six of which are actually over 40%. To minimize the impact of having varied employment sectors on average wage, we create the adjusted average wage variable in two steps. First, we compute the hypothesized wage for city i, $W_i^h={\displaystyle {\sum }_{k=1}^K{\overline{W}}^k[Em{p}_i^k/Em{p}_i]}$, where ${\overline{W}}^k$ is the average wage of sector k in the nation, the inside brackets are the local employment ratio in sector k, and subscript i is the city index. Second, we define the adjusted average wage to be $W_i-W_i^h+\overline{W}$. The adjustment essentially removes the effects of sectoral composition on the average wage.

As noted in the literature [8], theory does not state which amenity attributes are valued by consumers and producers and by how much; theory only tells us how people behave in response to amenities. For this reason, when choosing amenity attributes for households and firms, we carried out extensive experiments with a large set of variables which were selected either because they were suggested in the literature or they account for some unique features of Chinese cities. As a result of our exploration, we include two types of amenities: natural amenities and locally produced amenities [21].

The natural amenities are climatic conditions and environmental attributes. Climatic conditions of cities are valued by households as significant amenities [13,16,22,23,24]. In this study, we have the following variables measuring climatic conditions and environmental attributes.

Jan_temp: average temperature in January (CM).

Jul_temp: average temperature in July (CM).

Precipitation: average annual rainfall or snowfall (M).

Altitude: elevation of a city measured in meters above the sea level (M). We include this variable to account for variation in the altitude of Chinese cities. Since most cities in western China at high altitudes have harsh climatic conditions, the coefficient of this variable is expected to be negative.

Coast: a binary variable indicating if a city’s urban district is adjacent to the coastline or if the city has a seaport. The variable was constructed by manually examining provincial maps. The parameter estimate is expected to be positive.

It is necessary to note that other studies have also included variables such as humidity [13] to quantify climatic conditions. In our dataset, we found that humidity is highly correlated with precipitation. Thus, we do not include humidity for multicollinearity concerns.

The estimated housing price equation also accounts for amenities that are locally produced. Specifically, we use the following variables to measure air pollution, social interaction, and public services in our analysis.

SO₂_density: emission density of SO₂, computed by the total amount of SO₂ emissions in the city divided by city area (C). This variable is used to account for environment quality.

Urban_non_ag_popu_density: non-agriculture population density in the urban built district (C). Density of population is an indicator of agglomeration. More population in the city facilitates better social interactions and may be valued as amenities [25].

Pupil_teacher_ratio: ratio of students and teachers in each city (C). This measure is a proxy for education quality [22], one of the amenities greatly valued by home buyers.

Hospital_bed_psn: number of hospital beds per capita in each city (C). This variable measures quality of public health services, valued by city residents [22].

Built_green_coverage: percentage of urban land that is designated as urban green space such as open space, parks, and greenbelts (C).

Urban_bus_psn: number of buses per capita operated in the urban built district (C).

Finally, we include one variable on cost of living in the estimated housing price equation:

Minimum_wage: minimum monthly wage set by government in each city. Gyourko and Tracy and Gabriel et al. employ a cost of living index compiled by the National Bureau of Labor Statistics (BLS) and the ACCRA Cost of Living Index, respectively, to make comparisons of cost of living across cities [22]. The higher the cost of living, the less desirable/attractive is the city, other things being equal. Since we do not have data on a cost-of-living index in China, we used data on minimum wage, provided by the Ministry of Human Resources and Social Security, as a proxy for the cost of living.

In the following, we list the variables of amenity attributes likely valued by firms. Recent studies have established relationships between urban quality of life and quality of business environment [15]. Nevertheless, the literature is still deficient in investigating how firms value city specific amenities. Relying on previous studies on migration and business environment [21,26] and determinants of economic growth [27,28], we identify variables related to transport efficiency, regional location, information and financial services, level of agglomeration, and income tax on enterprises as amenities (or disamenities) valued by firms. In addition, we include one variable to account for different levels of marketization across Chinese cities.

Three variables are used to measure transport efficiency in cities.

High_way_density: length of rated highways divided by the area of the jurisdiction (R). This variable is employed to measure the level of ease in transporting raw materials and goods for transactions. Needless to say, lower costs of moving goods enabled by more major roads provided in the area is one important amenity attribute for the firms.

Urban_bus_psn: in our land price equation, this variable is a proxy for intra-city commuting cost.

The dummy variable, coast, is also included in the industrial land price equation, assuming that a city on the coast or with a seaport would benefit from lower transport costs.

The following two variables measure availability of information and services to firms.

Service_labor_ratio: share of labor working in service sectors (C). In this study, the service sector is defined as the following four sectors: telecom and information technology, business and commercial services, research and technical consulting, and financial services. Glaeser et al. find that these employment sectors can enhance information transmission, which in turn could increase production efficiency [29]. We thus hypothesize that the coefficient of this variable is positive.

College_students_psn: percentage of college students in the urban population (C). Assuming that more college students can facilitate information transmission, we include this variable as a proxy for availability of information and knowledge.

The next two variables measure agglomeration of labor.

Manufacture_labor_share: local share of manufacturing employment in the nation (C). Agglomeration of labor is an attribute valued especially by firms in manufacturing [30,31]: with more workers in the manufacturing sector, it is more convenient for the workers to acquire better skills and for the producers to hire trained labor. We hypothesize that the coefficient of this variable is positive.

Urban_non_ag_popu_density: this variable is included to test whether knowledge spillovers among workers and lower transaction costs enabled by increased agglomeration of population are valued by producers.

As suggested in the literature [29], corporate tax is included.

Tax_rate: city-wide average corporation tax rate (C). To develop the average corporate tax for each city, we need to consider the presence and the share of foreign enterprises in the cities. According to the Income Tax Law for Enterprises with Foreign Investment and Foreign Enterprises, the income tax on enterprises with foreign investment established in Special Economic Zones (SEZs) and/or Economic and Technological Development Zones (ETDZs) are levied at a reduced rate of 15 percent; the income tax on enterprises with foreign investment in Coastal Economic Open Zones (CEOZ) are levied at a reduced rate of 24 percent; and the income tax on domestic enterprises are levied at a rate of 30 percent. We assume that foreign enterprises are always levied at the most favorable rate whenever two or more rates apply. As an example, if a city is designated as ETDZ and CEOZ at the same time, then the average rate is calculated by the following formula: (Revenue by foreign enterprises × 15% + Revenue by state-owned enterprises × 30%)/Total revenue.

Finally, we include one variable to measure the extent to which the government controls local economies.

Employment_state_owned_ratio: percentage of manufacturing employees working in state-owned (or controlled) enterprises (SOEs) in each city (C). This variable is used as a proxy for the openness of market economy across Chinese cities. SOEs account for very different shares of local economies.

Our final sample includes 254 observations of prefecture level cities.

Table 1. Descriptive statistics of all variables (n = 254).

Variables	Unit	Mean	Minimum	Maximum	Standard Deviation
Endogenous variables
Housing_price	RMB yuan/m2	9860	2206	30,587	5938
Industrial_land_price	RMB 10,000 Yuan/hectare	781	102	2452	179
Adj_city_wage	Yuan per year	30,282	14,057	60,460	5785
Amenities for households
Jan_temp	°C	1.5	−27	23	8.8
Jul_temp	°C	27.0	16	30	2.6
Precipitation	mm	962	75	2705	532
Altitude	meter	310	2	2392	485
So2_density	ton/km2	9.4	0.05	72.98	10.23
Pupil_teacher_ratio	na	20.98	3.8	38.09	5.34
Hospital_bed_psn	# of beds/10,000 person	86.76	16.97	221.23	34.87
Built_green_coverage	%	29.97	5.98	67.99	8.78
Minimum_wage	RMB Yuan per month	1002	880	2200	286
Amenities for firms
High_way_density	1/km	0.58	0.03	2.64	0.35
Service_labor_ratio	%	9.76	3.13	20.67	3.38
College_students_psn	%%	583	0.00	2453	472
Manufacture_labor_share	%	0.57	0.01	6.77	0.55
Tax_rate	%	26.68	14.81	28	2.40
Employment_state_owned_ratio	%	55.34	17.66	86.86	14.32
Amenities for both households and firms
Urban_bus_psn	# of buses/10,000 person	6.224	0.32	102.8	7.216
Coast	na	0.09	0	1	0.28
Urban_non_ag_popu_density	10,000 person/km2	1.1239	0.2989	4.2125	0.4731

presents descriptive statistics for all the above-described variables. The statistics show that the average housing price is RMB 9860 Yuan per square meter and the average industrial land price is RMB 781 Yuan per square meter. The statistics also show that there are large variations in both housing and industrial land prices: the highest housing price is more than 13 times higher than the lowest housing price and the highest industrial land price is about 24 times higher than the lowest land price. The average annual urban wage is RMB 30,282 Yuan and the highest wage is about 4 times higher than the lowest wage. Evidently, Chinese cities vary significantly in housing prices, industrial land rents, and wages. Through our empirical analysis, we seek to understand the extent to which these variations in rents and wages are explained by amenities valued by households and producers.

4. Results

Table 2. Regression estimates of housing and land prices.

	Housing_Price			Industrial_Land_Price
Independent Variables	Estimate	t	Pr(>|t|)	Estimate	t	Pr(>|t|)
Intercept	598	0.40	0.69	−147	−0.84	0.40
Adj_city_wage	0.37	15.77	0.00	−6.06 × 10−3	−1.84	0.06
Jan_temp	3.79	2.21	0.03	---	---	---
Jul_temp	−3.12	−0.83	0.40	---	---	---
Precipitation	−0.06	−2.90	0.00	---	---	---
Altitude	−0.03	−2.57	0.01	---	---	---
So2_density	−15.9	−10.32	0.00	---	---	---
Pupil_teacher_ratio	−1.14	−0.13	0.90	---	---	---
Hospital_bed_psn	1.38	2.90	0.00	---	---	---
Built_green_coverage	2.25	9.74	0.00	---	---	---
Minimum_wage	−1.36	−1.73	0.09	---	---	---
Urban_bus_psn	13.65	1.98	0.05	0.30	0.33	0.75
Urban_non_ag_popu_density	209.58	1.99	0.05	13.41	1.00	0.32
Coast	376.87	1.90	0.06	36.87	1.92	0.06
High_way_density	---	---	---	99.43	2.48	0.01
Service_labor_ratio	---	---	---	9.40	8.65	0.00
College_students_psn	---	---	---	0.89	5.79	0.00
Manufacture_labor_share	---	---	---	78.49	5.01	0.00
Tax_rate	---	---	---	7.83	2.21	0.03
Employment_state_owned_ratio	---	---	---	−0.76	−1.35	0.18
# of observations	254			254
Joint R-squared	0.64			0.64

presents 2SLS regression results which account for the endogeneity of the wage variable in simultaneous Equations (13) and (14). The joint McElroy R² of the system is 0.64. Since the purpose of this study is to explore how amenities contribute to variations in housing and land rents, we only discuss the results of the housing price and land price equations. We then present the results of the implicit prices of each amenity attribute.

4.1. Results of the Commodity Housing Price Equation

Table 2 shows that the estimated coefficient of the wage variable is significant and positive with a value of 0.37. This indicates that the household’s indifference curve in Figure 1 is upward sloped. To maintain the same level of utility, annual household wages need to increase by RMB 0.37 Yuan to compensate for the increase of RMB 1 Yuan in housing price per square meter.

One purpose of this study is to explore the extent to which amenities contribute to variations in housing prices across cities. The estimated equation shows that many of the natural amenities are significant. The climate variables perform quite well: average temperature in January has a positive coefficient and both precipitation and altitude have significant negative coefficients. These estimates are consistent with the prior notion that warmer weather in winter is amenable and that more rain and higher altitude are considered disamenities by households. Average temperature in July is insignificant, alluding to the fact that many southern cities in China have had strong real estate markets in recent decades. Consistent with previous studies, emission density of SO₂ has a strong negative coefficient, suggesting that lower environmental quality is viewed as a disamenity. The estimated coefficient of the binary variable for coastal cities is positive and significant at the p = 0.10 level. The estimate indicates that the average housing price in coastal cities increases by about RMB 377 Yuan per square meter. Apparently, amenable environment attributes in coastal location have been capitalized in housing prices in China.

The results of the public service variables are shown below. Student-teacher ratio is insignificant. This might allude to the variable lacking construct validity, failing to measure the amenity attributes as intended. Percentage of urban land designated as green space is significant and positive. Number of buses serving the urban built-up district has a significant positive coefficient, consistent with the notion that better transit service in the city is valued by city dwellers [32]. Urban population density, with its estimated coefficient significant at the p = 0.05 level, is viewed as positive amenity by households as indicated in previous research [28]. Number of hospital beds per capita is significant, demonstrating the importance of medical services. Finally, minimum wage, the proxy for living cost, is negative and significant at the p = 0.10 level, consistent with our expectation that higher non-housing cost of living is a disamenity to residents. The mixed results suggest that some of the amenity attributes are clearly valued by households while others may not be.

Overall, the estimates suggest that values of natural amenities, environmental quality, and some public services have been capitalized in urban commodity housing prices.

4.2. Results of the Industrial Land Price Equation

The estimated industrial land price equation has a negative coefficient for wages, indicating a downward sloping iso-profit curve in Figure 1. We have also regressed the industrial land price model using data for 2018, 2019, and 2020 separately, and consistently produced a negative coefficient on wages. This implies that the result is fairly robust.

In this part of analysis, we are interested in the extent to which amenities for production contribute to the variations in industrial land prices across cities. Measures of regional transport efficiency have mixed results. The variable of highway density has a significant positive coefficient, suggesting that regional transport efficiency is valued by firms. Better access to the highway system enables firms to earn higher profits and, as a result, the firms are willing to pay higher prices for industrial land. On the other hand, the urban bus service variable is insignificant, indicating that public transit service within the urban built district is not valued by firms as an amenable condition in the production process. The variable of regional location, Coast, has a positive coefficient and is significant at the p = 0.10 level. Two measures of the availability of information and services to firms perform remarkably well. The share of labor working in service sectors has a strong positive coefficient, which suggests that a more service-oriented industrial structure improves firms’ ability to make a profit. The percentage of college students in the city also has a strong positive coefficient, implying that greater capacity in higher education improves knowledge spillover, which is favored by producers. The measure of agglomeration of labor in manufacturing has a very strong positive coefficient. This is consistent with previous empirical findings [21]. The estimated coefficients of the variables of urban population density and percentage of employees working in state-owned enterprises are not significant. Surprisingly, average corporation tax rate has a positive and significant coefficient. This result is contrary to the theory that higher tax rate lowers profits and thus films need to be compensated by lower input costs. Upon a close examination of the data, we find that in coastal cities with more open economies, there are disproportionately more foreign enterprises and joint ventures that are granted the lowest corporation tax rate. In addition, in these cities, bilateral negotiation resulted in lower land prices while auction prices were significantly higher. Evidently, cities levying favorable corporation income taxes on firms also grant these firms land use rights at discounted prices. It seems that cities with more open economies are more devoted in attracting foreign investments by both measures.

In short, the estimates of the industrial land price equation reveal a pattern that higher (lower) wages and lower (higher) land prices compensate each other. Produced amenities, including accessibility to intercity transport facilities, coastal location, business services, and college education, are capitalized in land prices. On the other hand, intracity bus service and population density are statistically irrelevant to industrial land prices.

4.3. Implicit Prices for Consumer and Producer Amenities

Table 3. Implicit prices of amenities for both households and firms.

	Amenities for Households		Amenities for Firms
Variables	Implicit Price of One Unit of Change	Implicit Price of One Standard Deviation	Implicit Price of One Unit of Change	Implicit Price of One Standard Deviation
Jan_temp (1 °C warmer in January)	106.32	878	---	---
Jul_temp (1 °C hotter in July)	---	---	---	---
Precipitation (1 mm more annual precipitation)	−1.28	−786	---	---
Altitude (1 m higher in altitude)	−2.09	−1001	---	---
So2_density (one more ton per km2)	−78.96	−753	---	---
Pupil_teacher_ratio (one percentage change in student teacher ratio)	---	---	---	---
Hospital_bed_psn (one more bed per 10,000 people)	25.32	479	---	---
Built_green_coverage (one percentage change urban green land)	36.21	360	---	---
Minimum_wage (one more Yuan monthly)	−6.00	−500	---	---
Urban_bus_psn (one more bus per 10,000 people)	67.42	409	---	---
Coast (being on coast)	3479	532	9863	2044
Urban_non_ag_popu_density (10,000 more people per km2)	988	421	---	---
High_way_density (one more km per capita)	---	---	10,103	2567
Service_labor_ratio (one percentage change in service employment)	---	---	1876	3099
College_students_psn (one more college student per 10,000 people)	---	---	5.68	1753
Manufacture_labor_share (one percentage change in manufacturing employment)	---	---	11,099	5276
Tax_rate (one percent higher of tax rate)	---	---	978	2109
Employment_state_owned_ratio (one Percentage change in state enterprise employees)	---	---	---	---

reports the implicit prices that are imputed using the estimates in Table 2 and Equations (15) and (16). Each entry in Table 3 reveals the marginal price, P_c or P_f, for a respective amenity attribute. Note that P_c is not affected by wage and, in evaluating P_f of (16), we chose n = 1, i.e., P_f now measures the increase in per capita profit. For example, the average person would be willing to pay RMB 67.42 Yuan more for one more urban bus per 10,000 people. The average firm would be earning an extra RMB 9863 Yuan per employer for being in a coastal city or a city with seaport. To remove the effects of different measurement scales on the estimated prices of amenities, we also provide the estimated compensating differential for one standard deviation change in the amenity from its mean value. One standard deviation change in the natural amenities including altitude, precipitation, and temperature in January produces the largest implicit differential in residents’ well-being across Chinese cities. On the other hand, one standard deviation change in the locally produced amenities including information and service availability and level of agglomeration produces the largest implicit differential in profitability among industrial firms across these cities. Comparing contributions of amenities to the housing and land markets, variations in these amenity attributes have a more sizable impact on firms’ profitability than on consumer well-being.

5. Conclusions

This study extends Roback’s model to investigate the effects of natural and locally produced amenities on urban land and housing prices in prefecture and higher level cities across China. Given the segregated residential and industrial land markets in Chinese cities, a set of structural equations are estimated using the 2SLS method and subsequently the implicit prices of various amenities are imputed. The housing price equation estimates show that climatic amenities, coastal location, environmental quality, and some public services are significantly valued by households, while public service such as student-teacher ratio is insignificant due to the fact that the data may not be precisely measuring the value of educational service. The industrial land price equation estimates reveal that intercity transport systems, coastal location, business services, and college education are valued by industrial firms and the values are capitalized in urban industrial land, while intracity bus service and population density are not considered by firms. These results indicate that, although the institutional structure of Chinese urban economies is still in transition, most amenities traditionally valued by consumers and producers in a market economy such as the US are similarly treasured by Chinese households and firms.

Notwithstanding many statistically significant findings in this study, it is necessary to note several caveats. First, this is a cross-sectional study, carried out at a single point in time. We cannot tell how much implicit values of the natural and the publicly provided amenities have changed over time in the past decade. It is expected that any amenity attribute that benefits consumers or producers tends to be better capitalized in urban real property values as the markets develop and urbanization stabilizes and, on the other hand, growing problems of congestion, poor air quality, and overloaded public infrastructure will also be factored in the urban property values by increasing numbers of households and firms. Second, what amenity attributes should be included in the econometric model is more or less a matter of discretion. During the course of the research, we considered more amenity measures. Some of the publicly produced cultural services, such as restaurants, theaters, and aesthetics and urban design, are considered by early studies as consumer amenities but are not included in this study due to lack of adequate data for Chinese cities [33]. Other amenities are important too. For example, Carlino and Saiz demonstrate the importance of leisure amenities for urban development [34]. They validate the number of tourist trips and the number of crowdsourced picturesque locations as measures of consumer revealed preferences for local lifestyle amenities. Their results show that “beautiful cities” attracted highly educated individuals and experienced faster housing price appreciation. We propose to include local lifestyle amenities in our future studies. Hanushek et al. demonstrate that land-use regulation matters in real estate market [35,36]. In the case of China, some cities may preserve specific historical sites and hence restrict the real estate development in certain areas. Such a policy would have at least two effects. First, it decreases the total land supply and lifts the land and housing prices. Second, it increases the city’s amenities, further raising the city’s housing prices (we thank the reviewer for pointing this out). We leave this issue for future exploration. Third, the theoretical framework of the analysis assumes that workers and households are perfectly mobile in order to reach equilibrium. However, population migration and labor mobility across Chinese cities are not of perfect free flow [30]. With mobility across cities further improving, it is expected that amenities will be more fully capitalized in Chinese urban housing and land.