Spatial Structure and Efficiency in Transition-Economy
Housing Markets: Evidence from Matched Location
and Location-Preference Data
Siqi Zheng
Institute of Real Estate Studies, Tsinghua University, Beijing 100084, China
Zhengsq00@mails.tsinghua.edu.cn
Yuming Fu
Department of Real Estate, National University of Singapore, 4 Architecture Drive,
Singapore, 117566, rstfuym@nus.edu.sg
Hongyu Liu
Institute of Real Estate Studies, Tsinghua University, Beijing 100084, China
liuhy@tsinghua.edu.cn
First version: December 2003
This version: February 2005
Running title: Spatial Structure and Efficiency in Transition Economy
Acknowledgement: For their helpful comments, we thank the participants at the 2004 Annual
Rena Sivitanidou Research Symposium at the Lusk Center for Real Estate, University of
Southern California, at the 2004 Summer Urban Economics Symposium at the Centre for
Urban Economics and Real Estate, University of British Columbia, and at the 2005 AREUEA
Conference in Philadelphia.
Spatial Structure and Efficiency in Transition-Economy Housing Markets:
Evidence from Matched Location and Location-Preference Data
Abstract
In cities with a well-functioning land market, spatial equilibrium entails the sorting of their
residents according to individuals’ bid-rent gradient; those with a higher gradient locate nearer
to the urban center. Violation of this sorting condition creates opportunities for Paretoimproving trading of location and can be sustained only if the market is hindered. Applying
this sorting principle to matched location and location-preferences data of individual
households enables us to examine the presence of hindrances to individuals’ housing-cumlocation choices. Using a sample of observations from Chinese cities, where the previous
housing welfare system was recently replaced by housing markets, we are able to identify a
number of population groups whose housing choices are possibly hindered by deficient
property rights in their current home, inadequate access to housing financing, or spatially
mismatched housing supply. Removing these hindrances makes possible a more efficient
spatial equilibrium.
Key Words: Bid-rent gradient; spatial structure; spatial sorting; efficiency; housing markets;
transition economies.
1
I. INTRODUCTION
Understanding the location choice of households and the consequent spatial structure in
cities has always been an important focus of urban economics (excellent recent surveys on this
topic include Mieszkowski and Mills [24], Mills and Lubuele [26], Anas, Arnott and Small [1],
and Glaeser and Kahn [18]).1 The monocentric city model of Alonso, Mills and Muth (AMM)
lays the foundation for urban spatial analysis four decades ago. The AMM model captures the
fundamental tradeoff in residential location choice between central-city oriented commuting
cost and housing consumption (see Fujita [13]). To this, the recent contribution by Brueckner,
Thisse and Zenou [7] adds the demand for urban amenities, whose location pattern is in part
determined by the urban history. A related body of literature on local public finance examines
the location choice of households across communities within metropolitan areas, focusing on
the tradeoff between the housing cost and the local public good provision (e.g. Epple, Filimon
and Romer [12]). Empirical studies of the residential location choice along both lines generally
assume an unhindered housing market so that the spatial equilibrium reveal the location
preferences of the households (e.g. Quigley [32], Gabriel and Rosenthal [17], Nechyba and
Strauss [27], and Bayer, McMillan and Rueben [3]). However, housing market can be hindered
even in developed market economies. Fiscal zoning, for example, restricts the types of home
available in suburban communities (e.g. Gyourko [21]), credit rationing prevents liquidityconstrained households from attaining their long-term optimal housing choices (e.g. Rosenthal,
Duca and Gabriel [33]), and rent control discourages residential mobility (e.g. Ault, Jackson
and Saba [2]); these housing-market restrictions can prevent the spatial equilibrium from fully
reflecting the location preferences of the urban residents. In countries undergoing transition
from planned economy to market economy, housing market can further be hindered by
deficient private property rights in privatized homes. In this paper, we depart from the extant
empirical studies of residential location by incorporating the stated location preferences into
the location choice model. In so doing we seek to separate the determinants of location
preferences from the effects on location choices due to possible hindrances to housing choices.
Our analysis is built on the basic spatial equilibrium principle of the AMM model.
Consider a monocentric city with an unhindered housing market. Residents compete for space
1
Mills [25] define the spatial structure of urban areas as the locations of various sectors within urban areas.
2
at different locations according to their willingness-to-pay for these locations, or their bid-rent
curves. In equilibrium, the location of different population groups in the city must be sorted
according to the gradient of their bid-rent curves; those with a higher gradient (a steeper bidrent curve) locate nearer to the city center (see Fujita [13] chapter 2).2 This spatial sorting
condition must hold in the housing market in equilibrium because at the boundary of the
different residential zones, where the bid rent of the competing population groups equalizes,
the group with a higher bid-rent gradient will out bid the other group for the more central
locations. Once the spatial order of the population groups is determined by the sorting
condition, the types of homes (and hence the residential density) within each zone will be
determined by the housing demand of the population group in the zone.
This spatial sorting condition has been the corner stone of urban spatial structure analysis.
Wheaton [36], for example, examines the income elasticity of demand for land relative to that
of the cost of commuting time—a higher value for the former will imply a declining bid-rent
gradient with income. He finds that the two elasticities are too close for income to have any
significant effect on the bid-rent gradient and hence to account for the postwar suburbanization
of the rich in US. More recently, Glaeser, Kahn and Rappaport [19] show that the different
commuting technologies available to different income groups can account for the differences in
the bid-rent gradients that support the central-city versus suburban segregation between the
poor and the rich. Whereas the poor rely on the cheaper but more time-consuming public
transit services available mostly in central cities, the rich can afford the expensive but timeefficient automobile-based commuting and hence have a relatively lower bid-rent gradient.
Our objective is to examine the spatial structure and efficiency in transition-economy cities,
focusing on the location preferences of different population groups and the possible hindrances
to their housing-cum-location choices. For this purpose, we propose a simple ordered-locationchoice model based on the spatial sorting principle of the AMM model. Absent hindrances to
housing choices, the individuals’ locations preferences alone would determine the relative
locations of these individuals according to the spatial sorting condition. Violation of this
sorting condition creates opportunities for Pareto-improving trading of location and can be
sustained only if the market is hindered. By comparing the observed residential location
2
This result applies also when capital can be used to substitute for land in producing housing space. When the
capital-to-land ratio is chosen optimally to maximize the land value, the gradient of the land bid-rent curve is
increasing in the capital-to-land ratio, which in turn is increasing in the bid rent for space (see, for example, Fu
and Somerville [15]). Note also that the comparison of the bid-rent gradient is independent of the size of housing
consumption; it is the bid rent per unit of space that matters.
3
against the location predicted by the spatial sorting condition, we are able to measure the
importance of the hindrances to housing choices.
Using matched location and location-preference data of individual households in Chinese
cities, we demonstrate how our simple ordered-location-choice model that incorporates stated
location preferences can help us to identify the effects on household location due to hindrances
to housing choices. We present a three-fold analysis. First, we describe the spatial structure of
the Chinese cities as reflected by our household location data. In particular, we find a pattern of
centrally-oriented commuting outside of the old central area of the cities and evidence of
reverse commuting from the old central area, which indicates both the greater concentration of
employment than population in the cities and the importance of urban amenities concentrated
in the old city center (Glaeser, Kolko and Saiz [20]). We also observe that high-income
residents tend to locate more centrally—a pattern more similar to European cities than to
American cities (see, e.g., Brueckner, Thisse and Zenou [7]). Second, we examine how the
location preference in terms of bid-rent gradient varies across individuals. We find that the
gradient generally increases with income, even after controlling for differences in the needs for
job-market access and in lifestyle. The finding indicates that proximity to city center is a
normal good in Chinese cities. Third, combining the location and location-preferences data, we
examine the observed residential location of the individuals against the spatial sorting
condition. Specifically we investigate whether the residents whose housing choices in the
market might be hindered by deficient property rights in their homes, inadequate access to
housing finance, or spatially mismatched housing supply tend to violate the sorting condition.
Our findings suggest that they do.
Our empirical study makes a contribution to the understanding of residential market
transition in the formerly centrally planned economies. Extant studies on transition-economy
urban spatial structure largely focus on the impact of housing market liberalization on the
spatial structure in terms of changes in residential density gradients and land price gradients
(e.g. Bertaud and Renaud [4] and Dale-Johnson and Brzeski [10]; Bertaud and Melpazzi [5]
surveys this literature). By contrast, we attempt to separate the influence of the market force
(the market sorting incentives) and that of the housing-choice hindrances on the spatial
structure.
Compared with the studies on “wasteful” commuting (e.g. Hamilton [22], and Small and
Song [35]), which also examine the spatial sorting of residents among metropolitan areas, our
4
analysis provides clearer policy implications. The “wasteful” commuting studies focus on the
validity of the assumptions underlying the spatial equilibrium model that predicts the necessary
amount of aggregate commuting. Violation of the necessary-commuting condition (the
presence of “wasteful” commuting) refutes the validity of the spatial equilibrium model. Our
analysis, in contrast, aims to measure the violation of the spatial sorting condition in residential
markets for specific population groups whose housing choices might be hindered in various
ways. The evidence of such violation would suggest possible improvements in the land-use
efficiency and in the welfare of the residents when the hindrances to housing choices are
removed.
We organize the rest of the paper in five sections. In the next section, we present the
ordered-residential-location-choice model. The basic ordered-choice model based on the
spatial sorting condition is extended to account for housing-choice hindrances that may prevent
different population groups from attaining their Pareto optimal locations. Section III provides
the institutional background for our empirical analysis, where we briefly review the
development of the urban form and housing reform in China and highlights the presence of
various hindrances to housing choices that may impact on the spatial structure. We describe the
data and the variables in section IV, and in section V we present the analysis of the urban
spatial structure, the location preferences and the impact of housing-choice hindrances on the
spatial structure. Section VI concludes and discusses the policy implications.
II. AN ORDERED RESIDENTIAL-LOCATION CHOICE MODEL
Within the AMM framework, spatial equilibrium in residential markets requires that the
residents in a city be sorted spatially from the city center according to their bid-rent gradient.
Whenever this equilibrium sorting condition is violated, some residents will be able to find
more centrally located counterparties with relatively low bid-rent gradients, and they can trade
the locations at a differential rent that makes both parties better off. Such Pareto-improving
transactions may be forgone when the market is hindered. To isolate the effect on location
choices due to the spatial sorting incentives from the effects due to possible hindrances to
housing choices, we propose a simple ordered-location-choice model. For the purpose of our
analysis, we divide a city into three zones: zone 3 is the most central, followed in turn by zone
2 in the middle and zone 1 in the fringe. The spatial equilibrium requires that residents in the
city be assigned to one of the three zones according to their bid-rent gradient. Let BRGj denote
5
the bid-rent gradient of resident j and g2 and g3 the minimum bid-rent gradient in zone 2 and 3
respectively (g2 < g3); the spatial sorting condition requires that:
Resident j locate in zone 1 iff BRGj < g2;
(1a)
Resident j locate in zone 2 iff g2 ≤ BRGj < g3;
(1b)
Resident j locate in zone 3 iff BRGj ≥ g3.
(1c)
Equation (1) implies an ordered-choice model of residential zones where individuals’ bid-rent
gradient alone is sufficient to determine their relative locations.
When the housing market is interfered by various restrictions, BRG may no longer be
sufficient to determine the location order of individuals within the city. The spatial equilibrium
will then depend on both the location preferences, which determine the spatial sorting
condition, and the restrictions, which compromise the location choice of the individuals
according to their location preferences. Individuals in a transition economy who had obtained
homes at favorable locations in the previous housing welfare system, for instance, might be
discouraged from adjusting their location according to their BRG due to the deficient property
rights that impaired the marketability of their home. These individuals may live in more central
locations than their BRG would justify and can be said to be spatially advantaged. Moreover,
individuals may be spatially disadvantaged and live in less central locations than their BRG
would predict if their housing choice is constrained by their inadequate access to housing
finance or the housing supply in central locations is restricted. To account for the spatial
impact of housing-market restrictions, we allow individuals to have a location advantage or
disadvantage according to their characteristics xj. Let the function f(xj) denote an index of
location advantage for individual j, such that the location assignment of the individual is
determined by Equation (2) below:
Resident j locate in zone 1 iff BRGj + f(xj) < g2;
(2a)
Resident j locate in zone 2 iff g2 ≤ BRGj + f(xj) < g3;
(2b)
Resident j locate in zone 3 iff BRGj + f(xj) ≥ g3.
(2c)
Thus a positive f(xj) value indicates a location advantage, in that the individual would live in
a more central location than his or her BRGj would predict. Equation (2) suggests an orderedchoice model where both BRGj and the individuals’ characteristics xj explain their relative
locations.
6
Our analysis will focus on the estimates of the location advantage index f(xj), which
indicates the impact of the housing-market restrictions on the location equilibrium of different
population groups. The identification of such effects depends crucially on the measure of
individuals’ bid-rent gradient. The measure we have is obtained from a contingent-valuation
(CV) survey. Specifically, the survey asks individuals to indicate how much they would be
willing to pay in terms of percentage of housing price, if they were to buy a new home, to live
15 minutes nearer to their city center. We use the expressed willingness to pay for this
hypothetical choice as our measure of individuals’ BRG.
The CV method is criticized for its potential biases and validity problems when it is applied
to assess the value of public goods, such as environmental damages and the value of public
recreational facilities (see, e.g., Diamond and Hausman [11] for critiques). Individuals’
statement of their willingness to pay regarding such public goods may be unreliable because
they do not usually make active use of these goods to be aware of their willingness to pay.
Individuals may also express their willingness to pay as a political or moral statement rather
than what they are prepared to pay. They can also understate their willingness to pay to enjoy a
free ride. These problems, however, are unlikely to undermine the validity of our BRG
measure. Residential location provides access to urban amenities and job markets and these
accessibilities are private goods. Residents in a booming city would often use and contemplate
these accessibilities to be aware of their willingness to pay for them. Moreover, their
willingness to pay for living in a more accessible location is unlikely to be influenced by their
political or moral persuasion or free-rider incentives. Perez, Martinez and Ortuzar [31], for
example, find individuals’ value of time implied by their sated preferences over residential
locations consistent with the estimates based on the observed transport-mode-choice data.3
Moreover, since the equilibrium spatial order predicted by Equation (1) is invariant to a
monotonic transformation of the observed BRGj, the estimates of f(xj) would be qualitatively
robust to general measurement biases due to, for example, the framing of the CV question
(Boyle [6]). Furthermore, our estimates of f(xj) will be unbiased if the measurement error in the
observed BRGj is uncorrelated with the observed characteristics xj.
3
Even for quasi-public goods, such as outdoor recreation facilities, air and water quality, and work-related health
risks, studies have documented evidence of convergence between stated willingness to pay from CV survey and
the reveal preferences from observed choices (see, e.g. Carson et. al. [8]).
7
III. THE EMERGING URBAN LAND MARKET AND HOUSING REFORM IN CHINA
After forty years of a planned economy, China reinstated the urban land market in the early
1990s as it opened its economy more fully to foreign direct investment. The real estate market
took off, and massive land redevelopment took place in many Chinese cities, especially in the
coastal regions where the economic growth was remarkably strong. Before the reinstatement of
the urban land market, Chinese cities were typically very compact with a predominantly mixed
pattern of residential and non-residential land uses (see Sit [34]). The majority of urban
workforce would commute on foot or on bicycle to work near their home. Such a land-use
pattern, although largely an outcome of central planning, would be consistent with the
prediction of the endogenous urban spatial model of Ogawa and Fujita [30] and Lucas and
Rossi-Hansberg [23] under the conditions of a high commuting cost and low external
economies in production. Such conditions indeed apply to Chinese cities during the planned
economy. However, the old central areas of Chinese cities have always been the commercial,
cultural and administrative hub, even during the period of the planned economy.4 With the
massive investment in the urban transport infrastructure and the rapid growth of the service
sector in Chinese cities since the beginning of the 1990s, a more specialized land-use pattern
has emerged: the central business district (CBD) has greatly expanded and the residential land
use has been extended into suburbs, whereas industrial land use has been pushed towards the
outlying urban locations. At the same time, land-rent profiles sloping downward from the
traditional city centers also emerged in the land market, reflecting the importance of the old
central area for business and consumption.5 This new urban form is consistent with the
prediction of the endogenous urban spatial model under the conditions of a relatively low
commuting cost and large external economies in production. These conditions now generally
characterize the new urban economy of Chinese cities, where the commuting trips increasingly
rely on rapid rail transit and private automobiles and where personal networking and face-toface communications become crucial for private enterprises. This remarkable transformation of
the urban forms at the macro level demonstrates the powerful market forces at work in the
emerging land market in Chinese cities.
Before 1980’s, urban housing in China was allocated to residents as a welfare good by their
employer (the work unit) through the central planning system. Workers enjoyed different
4
This is reflected by the monocentric population density profiles in Chinese cities that decay quickly from the city
center, as documented in Bertaud and Melpazzi [5].
5
Fu et. al. [14] examine the urban form and redevelopment pattern in Shanghai during the early 1990s.
8
levels of housing welfare according to their office ranking, occupational status, working
experience and other merits. Governments and work units were responsible for housing
construction, typically near the work unit, and residential land was allocated through the
central planning. Workers would also receive most of the services, such as child care, child
education and family health care, from their work unit. Large publicly owned enterprises,
including state-owned enterprises, urban collective enterprises and government administrative
units, would provide better housing and other welfare than small ones. Residents had little
opportunity to choose their residential location according to their income and other household
characteristics in the absence of the housing market.
Since the 1980s, most of the work-unit housing units have been privatized. By the end of
the 1990s, housing procurement by work units for their employees had officially ended and
new homes would be built and sold in the market.6 Developable land is supplied and regulated
by the government through long-term leases.7 Large amounts of old homes in central urban
locations were demolished to make way for new transport infrastructure, commercial
developments and up-market housing projects. Urban built-up areas were quickly expanded
and new mass housing projects were largely built in the suburban locations.
Despite the remarkable change in urban forms and the increasing liberalization of the
housing market and the urban land market in the 1990s, the spatial structure in Chinese cities
may not be fully determined by spatial sorting condition according to individuals location
preferences due to impediments to housing resale, credit rationing in the mortgage market, and
spatial mismatches between housing supply and demand. The impediments to housing resale
are reflected by the low turnover of the existing housing stock relative to the new home sales,
which had characterized Chinese housing markets until recently.8 One contributor to the thin
resale market was the deficient private property rights in privatized work-unit housing units—
the new owners may not possess a marketable property title or are required to share the profit
from sale with the work unit. Individuals who purchased their home from the market with
subsidies from their work unit may also be subject to resale restrictions and may not be entitled
to the full profit from resale. In addition, the resale market institutions, including real estate
6
See Fu, Tse and Zhou [16] for a review of the housing reform and housing market development in Chinese cities.
Unofficially, some public enterprises continued to build homes and sold them with partial property rights to their
employees at deep discount.
7
See Fu and Somerville [16] for a review of the emerging land market in Chinese cities.
8
According to the sales record at the central real estate exchanges in Shanghai and Guangzhou, resale of existing
homes accounts for less than half the total home sale volume in the year 2003. In Beijing, resale accounts for less
than 10% of the total home sale volume.
9
listing services, title transfer and brokerage were still under development. These impediments
to resale would prevent the market from re-allocating housing resources according to the
spatial sorting condition.
Although residential mortgage market expanded rapidly since 1997, the total supply of
housing credit is still relatively small. The total mortgage loans outstanding as a percentage of
total domestic bank loans to non-financial sectors increased from 0.49% in 1998 to 7.41% in
2003.9 Buyers of privatized homes in the resale market are often subject to extra transaction
costs in obtaining bank mortgage loans. Mortgage lending has been also unfavorable to elder
home buyers and low-income households and the government support for low-income
households to obtain housing financing is largely undeveloped. At the same time, home prices
are high relative to income in Chinese cities.10 The inadequate supply of housing credit
together with high housing prices creates liquidity constraints for many urban households,
hindering their housing market participation according to their bid-rent gradient. The hindrance
may be more severe for older or less skilled urban workers and for new migrants to the cities,
who are more likely subject to credit rationing.
Finally, the spatial structure in Chinese cities may be distorted due to land supply policies
that contributed to spatial mismatch between housing demand and supply. In the past decade,
public land leases for new mass residential projects, many of which were built for households
displaced by urban redevelopment in old central areas, were mostly located in the fringe of the
cities, where land was more abundant but employment opportunities thinner. The urban
redevelopment projects in the central areas, however, provided little supply of modest homes
for working families.
IV. DATA AND VARIABLES
The data are collected from a survey of urban residents undertaken by the Institute of Real
Estate Studies at Tsinghua University in August 2003. The survey was conducted in five cities,
including Beijing, which is the national capital, Shanghai and Guangzhou, which are major
coastal cities of high income, and Wuhan and Chongqing, which are major interior cities on the
Yangtze River of relatively low income. Table 1 provides selected urban economic
9
People’s Bank of China Statistical Bulletin, 1st quarter of 2004.
10
The ratio of median home price to median household annual income ranged between 7 and 13 among the five
cities in our sample in 2003, according to statistics at www.sofang.com.cn.
10
characteristics of these cities. A total of 1124 completed questionnaires were collected; they
are about equally distributed among the five cities (see Table 2). Given the small sample size,
the sample is by no means an accurate representation of the population in the five cities. To
achieve a reasonable representation, the sampling process combines random sampling with
quota targets, which include gender representation, age group representation and occupational
group representation roughly in accordance to the adult population statistics in these cities.
*** Insert Table 1 about here ***
The variables we use for our analysis include the observed residential locations, the location
preferences, household characteristics, housing types, and the preferences for urban amenities.
A summary of their definition and sample statistics is provided in Appendix for easy reference.
The number of valid observations varies for different variables due to missing observations.
*** Insert Table 2 about here ***
Individuals’ home location, denoted by LOCATION, is indicated by one of the three zones,
identified as the old central area (central zone), and new suburban towns (outer zone) and the
areas in between them (middle zone). Table 2 shows the sample distribution by the three zones.
For all five cities, about half of the respondents lived in the middle zone. The average travel
time to city center reported by the respondents are about 18 minutes, 35 minutes and 50
minutes, respectively, for people living in the central zone, the middle zone and the outer zone.
Individuals’ bid-rent gradient, BRG, is indicated by their willingness-to-pay in terms of
percentage of home price for living 15 minute closer to the center of their city; the 15 minute
distance is about the difference of one zone in travel time to the city center. On average, the
respondents indicated a BRG of 12.5%, which appears consistent with the perceived market
price gradient.11 The range of the observed BRG varies between -30% (only one negative BRG
observation) and 100%. As common in CV-based studies, we trim the BRG observations to
limit the influence of possible gross outliers; observations of negative value or above 40%,
11
We estimated a residential price gradient using a sample of 414 observations from our survey, where the
individuals bought their home from the market after 1990. We regressed the logarithm of the reported purchase
price on the logarithm of total living area, the location dummy variables and the joint fixed effects of city and the
purchase year. We find a statistically significant price differential of 21.1% between the central zone and the
middle zone and a statistically insignificant price differential of 8.8% between the middle zone and the outer zone.
For comparison, Fu and Somerville [15] report a land price (per square meter of buildable area) gradient of about
7% per km in Shanghai in 1993.
11
which account for less than 3.5% of total observations, are excluded from our analysis. The
appendix shows that the average BRG (in the trimmed sample) is the highest in the central zone
and lowest in the outer zone.
The current annual income of the respondents (including the gross income of the respondent
and, if married, that of the spouse), denoted by INCOME, is reported in 5 discrete levels from 1
(less than RMB50,000 yuan, or about USD 6,000) to 5 (more than RMB250,000 yuan or about
USD30,000). About 62% reported an annual income of less than 80,000 yuan and 14% above
150,000 yuan; the mean reported income level for the whole sample is 2.2. We use the monthly
expenditure on the cell phone (or mobile phone), denoted by CELL, as a proxy for permanent
income in our analysis. Nearly all working adults in our sample cities own a cell phone. It is
reported on a scale from 1 (up to RMB300 yuan) to 5 (more than RMB2,000 yuan); the sample
mean level is 1.6.
Two variables represent the household’s demographic and lifecycle characteristics.
Household size, HSIZE, is measured by the number of cohabitating family members; the
average size is slightly over 3 people. AGE is recorded in five age groups: 1 being younger
than 20 years and 5 being 50 years or older. None of the respondents in our sample is below 20
years of age and about 9% of the respondents are 50 years old or older. Additional household
characteristics are measured by binary variables. EDU indicates whether or not the respondent
has college or university education; MARRY, is married; KID, lives with children; and OCCUP,
is employed in an occupation typically located in central urban areas—we classify jobs in
government bureaus, financial industry, and communication industry as centrally located
occupation. Furthermore, LEADER indicates whether or not the respondent is in charge of a
government office or public enterprise and POE, is employed by a publicly owned enterprise.
These last two binary variables are intended to reflect the individuals’ privilege in the previous
work-unit-based housing welfare system. HUKOU indicates whether the individual has official
resident status in the city. Those without such status would be recent migrants to the city and
would enjoy little welfare privileges in the city.
We also observe the housing types and residential location preferences. WORK_UNIT
indicates whether or not the respondent’s home originally belonged to their work unit. Such
dwelling, often built near the work unit and found in the central and middle zones of the city,
was typically sold to the occupant with restricted property rights. PRIVATE indicates that the
respondent lives in commodity housing—dwelling projects recently built for sale in the market,
12
including economy homes built on subsidized land. Majority of the respondents in our sample
occupy this type of home. LAREA measures the total living area of the respondent’s home. The
location preferences are indicated by three variables. ENTMT gauges the preference for
entertainment facilities, more popular ones of which are often found in the central zone, and
PARK, gauges the preference for outdoor recreational parks, often found in more suburban
locations; these preferences are ranked from 1 (not important) to 5 (very important). Another
location preference indicator is ACCEPT, the farthest acceptable residential location from city
center; not surprisingly the appendix shows that those living in more distant zones are
generally willing to live farther. Lastly, we have information on private automobile ownership,
which is indicated by a dummy variable CAR.
V. EMPIRICAL ANALYSIS AND FINDINGS
We present a three-fold analysis. First, we describe the spatial structure of Chinese cities as
reflected by our sample data. Because the present spatial structure of Chinese cities after over a
decade of rapid urban economic transformation has not been widely reported, a few
observations of the important characteristics of the contemporary urban spatial structure is
useful for setting the stage for our analysis of the location incentives and equilibrium. Second,
we examine the variations in location preferences across different population groups in our
sample. We do so both to gain insights to the location incentives of the individuals and to
check the validity of our BRG measure. Third, we apply the ordered-location-choice model to
examine the effects of housing-choice hindrances on the spatial structure.
A. Urban spatial structure
The table in the appendix shows several characteristics of the spatial structure in Chinese
cities. First, we observe that the average household income decreases with distance to the city
center. Such a pattern appears consistent with an amenity-based urban spatial model
(Brueckner, Thisse and Zenou [7]). Major urban amenities, such as major hospitals, good
schools, theatres and museums, and up-market retail, were typically found in the old central
areas in these Chinese cities. Moreover, the transportation-divide effect of Glaeser, Kahn and
Rappaport [19] is not found in these cities, as public transit services are widely available.
Indeed, we observe that the car ownership rate is slightly higher in the central zone.
13
*** Insert Table 3 about here ***
Table 3 shows the average commuting time in different residential zones. With the
exception of Wuhan (a city divided into three parts by rivers), where the average commuting
time varies little across the zones, the commuting time generally increase as one lives farther
from the city center. This spatial pattern of commuting time indicates a greater concentration
of employment than population, which is characteristic of monocentric cities. There also seem
to be significant reverse commuting in the central zone, as the average commuting time in the
zone, 24.8 minutes, notably exceeds the average travel time to the city center of 18 minutes.
Such reverse commuting can be explained by the demand for access to urban amenities located
in the central areas (Glaeser, Kolko and Saiz [20]).
It is interesting to observe from the statistics in the appendix that the average household size
is somewhat larger in the outer zone but the average living area somewhat larger in the central
zone. Moreover, the proportion of people living in newly built PRIVATE homes is greatest in
the outer zone. These statistics reflect the fact that most of the new affordable residential
projects, many of which built for households displaced by urban redevelopment, were located
in the outer zone. We also observe that residential location is correlated with the job-location
indicator OCCUP and with the indicators of housing privileges, i.e. HUKOU and LEADER.
B. The determinants of the bid-rent gradients
We examine the determinants of the stated bid-rent gradients for three purposes. First, we
want to check whether such a stated preference appears consistent with our prior expectation of
its variation with the characteristics of the individuals and with other indicators of the location
preferences. Second, to the extent that the stated bid-rent gradient is predictable, we can check
whether the predicted BRG explains the relative locations of the residents in the city in the
same way as the stated BRG does. Third, we provide evidence on how BRG is affected by
income. The literature has offered little direct evidence about the income effect on BRG and
the knowledge of such effect would help us to assess the contributions of various forces that
shape the urban spatial structure.
We expect individuals’ BRG to be affected by their income, which affects the demand for
urban amenities and the opportunity cost of travel time; by housing consumption, since the
14
AMM model predicts a negative relationship between housing consumption and BRG; by the
individuals’ job location and the need to access a thicker job market; and by the individuals’
lifestyle, which determines their preferences for urban amenities. Table 4 reports the regression
of BRG on various determinants. Before we discuss the income effect, we take a look at the
other effects first. The main findings are reported under the regression equation BRG_1. We
find a negative effect of housing size, LAREA, consistent with the AMM model. Holding the
housing size constant, household size (HSIZE) would influence BRG via the need to access the
thicker job market in the central areas. More working adults in a household means more
diversified job-matching need, which would be better met in a thicker job market.12 We find a
positive HSIZE effect, indicating the benefit of the central areas in providing a thick job market
for larger households. We also find a higher BRG for married couples without kids, represented
by the dummy variable MARRY*(1-KID). These couples would be more career-oriented and
thus value the benefit of the thicker job market in the central area; their lifestyle may also
demand a better access to the variety of urban amenities that the central locations can offer.
Individuals’ education level may affect both the job-market need and the lifestyle; but we find
little difference in BRG due to EDU. Those aged over 50 years (AGE≥50) appear to have a
weaker preference for central locations; the relative tranquility and better outdoor environment
of suburban locations naturally appeal to the senior citizens.
As expected, individuals’ job location would affect their BRG. Those who would work in
central locations, indicated by OCCUP, have a higher BRG, though the effect is weak due to
the imperfect correlation of OCCUP with the actual employment location. In comparison,
individuals in WORK_UNIT housing, likely living near their work unit, have a weaker
preference for moving closer to their city center.
*** Insert Table 4 about here ***
We find the stated BRG highly consistent with other indicators of the respondents’ location
preferences. Those who value proximity to entertainment facilities are willing to pay more for
living near city center, as the positive and highly significant estimate of ENTMT shows; but
those who value proximity to outdoor recreational parks are happy to live more distant from
12
The same argument explains the fact that larger cities tend to attract disproportionately more dual career
families (see Costa and Kahn [9]).
15
the city center, as indicated by the negative estimate of PARK. In regression equation BRG_2
we consider another location preference indicator, the farthest acceptable home location from
the city center (ACCEPT), as an additional explanatory variable, though the causality between
ACCEPT and BRG can go both ways. We find the two location preference indicators are
highly correlated; those whose farthest accepted home location is farther from the city center
also have a significantly lower BRG. In the last column under BRG_3, we examine whether
individuals’ housing privileges, indicated by LEADER and POE, are correlated in BRG; we
find no such correlation.
Holding housing size constant, BRG increases with income, reflecting a positive income
effect either on the commuting cost or on the demand for centrally located urban amenities.
Interestingly, we note that it is not the current income, but the permanent income, as indicated
by the expenditure on cell phone (CELL), that influences the BRG. The positive income effect
is found even when we hold constant the preferences for proximity to different urban amenities,
the differences in employment locations and the different needs for access to the urban labor
market. We further note that, as the estimates under BRG_3 show, the income effect is still
positive, albeit weaker, when we do not hold the housing size (LAREA) constant. Additional
experiments to consider the interactive effects between the income and the job location
indicators show that the positive income effect on BRG is not affected by the individuals’ job
location. Hence, the cost of commuting time does not appear to be the main reason for the
positive income effect; instead, central locations appear to be normal goods in Chinese cities,
offering a diversity of urban amenities. Our finding points to the importance of distinguishing
between the current and the permanent incomes in studying the income effect on the bid-rent
gradient; studies relying on current income measures may underestimate the positive income
effect on the bid-rent gradient. The positive income effect on BRG we observe in these Chinese
cities supports the hypothesis of Brueckner, Thisse and Zenou [7] on the importance of the
spatial distribution of urban amenities in influencing the location pattern of different income
groups.
We further examine how the stated BRG is influenced by the urban characteristics across
the cities. Table 5 shows the correlation between the city fixed effects of BRG, reported in
Table 4 under regression BRG_2 (Beijing is the default city and has a fixed effect of zero), and
the urban economic characteristics reported in Table 1. As the AMM model would predict, the
average BRG in a city decreases with the urban size, measured by either the built-up area or the
16
urban population. The average BRG is not correlated with the per-capita disposable income in
the city. A larger per-capita living area (hence lower residential density) or a larger per-capita
road area in the city (hence less road congestion) lowers the average BRG in the city. A higher
share of tertiary employment in the city (hence greater importance of the job market in the
central area), on the other hand, increases the average BRG in the city. Our analysis thus
indicates that individuals’ stated BRG based on the CV method is overall consistent with the
individuals’ location incentives.
*** Insert Table 5 about here ***
Finally, we compute the predicted values of BRG according to regression equations BRG_1
and BRG_2 respectively, to be used in the subsequent analysis of the effect of housing-choice
hindrances on the spatial structure. The summary statistics for these two predicted variables,
BRG1 and BRG2, are provided in the appendix.
C. Efficiency of the spatial structure
We examine the spatial structure in two respects. First, we examine how the spatial sorting
condition influences the spatial structure in these Chinese cities after a decade of housing
market liberalization. Such influence will be reflected by the explanatory power of BRG in the
ordered-location-choice model described by Equation (2). Second, we examine the effect of
various housing-choice hindrances on the spatial structure. We do so by examining the location
advantage index f(xj) for various population groups that are potentially subject to different
housing-choice hindrances. The characteristics of the individuals, the vector xj, may be
divided into three groups. The first group includes variables LEADER and POE; they relate to
the individuals’ privileges in the previous work-unit-based housing welfare system. Individuals
employed by publicly owned enterprises and government offices, especially those in leadership
positions, would likely have obtained their current home in relatively more central locations
from the previous housing welfare system. These individuals may be discouraged from moving
even though they may actually prefer living farther from the city center, as long as they are
unable to fully internalize the benefit of relocation due to the deficient private property rights
in their homes.
17
The second group of characteristics identifies individuals who may be hindered in making
housing choices in the market due to their inability to obtain adequate housing finance. These
liquidity-constrained individuals would live farther out from the location that their BRG would
support according to the spatial sorting condition. We hypothesize that the ability to obtain
housing financing is affected by the individuals’ current income (though their location
preferences are determined by their permanent income), their age and education level, and their
official residential status in the residing city. We expect those with higher current income to be
less constrained by liquidity but those older or less educated or without the official residential
status in their city to be more likely subject to credit rationing.
The third group of characteristics relates to individuals’ housing needs and is included in the
model to test the spatial mismatch hypothesis. We have noted earlier that new and more
affordable mass residential projects were predominantly built in urban fringe, where the job
market is thinner. New residential projects in old central areas typically targeted overseas
investors and up-market consumers. Consequently, we expect larger households and working
families, who value the central locations more highly for access to a thicker job market, to be
disadvantaged in the housing market due to the short supply of modest homes in the more
central locations. Those who were displaced by urban redevelopment would also be
disadvantaged since they had little choice of homes in the old central areas.
*** Insert Table 6 about here ***
Table 6 reports the estimates of the ordered-location-choice model. The basic results,
reported under equation Ordered_1, are based on the trimmed BRG observations. We find
BRG highly statistically significant in explaining the relative locations of the individuals in the
same city. The finding shows that the market force has shaped the spatial structure in these
Chinese cities since the liberalization of the housing and the urban land market in the early
1990s. However, the continual influence on the spatial structure of the institutional legacies is
also clearly indicated by the positive estimates of LEADER and POE. Not surprisingly, the
leaders enjoy a more significant location advantage. The estimates suggest that the deficient
property rights in the privatized state-provided homes hinder the turnover of these homes in the
market and hence the transition to a more efficient spatial structure according to the spatial
sorting condition.
18
We also find evidence suggestive of housing-choice hindrance due to financing constraints.
We find a highly positive effect of current income (INCOME) on location, although the
permanent income (CELL) has little additional influence once the BRG is held constant. In
other words, between the individuals of equal BRG, those with a higher current income are
able to exercise their BRG more effectively. Similarly, the negative estimate for AGE and the
positive estimates for EDU and HUKOU suggest the weaker ability for the older or less skilled
individuals or those without the official residential status to obtain adequate housing financing
so as to make their housing choices effectively in the market.
Furthermore, we note that larger households (HSIZE), married couples not living with kids
(MARRY*(1-KID)) and households in PRIVATE residential projects suffer location
disadvantages and the effects are statistically significant. Larger households and married
couples not living with kids are earlier found to have higher BRG; yet their home locations fail
to reflect their higher BRG due to the short supply of modest homes in the old central areas.
Similarly, those living in PRIVATE residential projects, most of which locate in the outer zones,
would be willing to pay the higher land rent in more central locations if comparable homes
could be found there.
We check the robustness of the basic results in several ways. In the estimation equation
Ordered_2 we include additional indicators of location preferences and private car ownership.
None of these additional variables affects the location choice. In other words, BRG adequately
represents the individuals’ location preferences and its influence on location choices is
independent of the individuals’ car ownership. We next check the sensitivity of our basic
results to the BRG measure. We re-estimate the ordered-choice model replacing the observed
BRG with the predicted BRG; the results are reported under equations Ordered_3 and
Ordered_4. BRG1 has weaker explaining power but BRG2 has stronger explaining power of the
relative locations than the observed BRG. Using the predicted BRG also allow us to include a
larger number of observations. The basic results largely hold, except that the effects of AGE
and HUKOU are no longer statistically significant. Lastly, we test whether the basic results are
sensitive to the classification of the relative locations by estimating a model of binary choice
between the inside and the outside of the central zone in the five cities. Again, the basic results
are largely unchanged, except that the effects of POE and PRIVATE become statistically
insignificant. It appears that the spatial distortion for POE and PRIVATE households is mostly
between the middle zone and the outer zone.
19
VI. CONCLUSIONS
We have proposed a simple ordered-location-choice model according to the spatial sorting
condition of the Alonso-Mills-Muth (AMM) model, incorporating the stated location
preferences of individuals. This model enables us to separate the determinants of individuals’
location preferences from the effects on spatial structure of various housing-market restrictions.
We demonstrate the application of this model using matched location and location-preference
data from Chinese cities. Our analysis provides insights to the spatial impact of housing-market
transition in Chinese cities. In particular, we find that many who inherited their home from the
previous housing welfare system would be better off trading their current more central
locations with many suburban dwellers in mass housing projects, especially those large
households and couples not living with kids, who are willing to pay higher rents to live in more
central locations. Further liberalization of the housing market by improving the marketability
of the property rights in previously state-provided homes and by increasing the availability of
mortgage credit in the resale housing market can effect a more efficient spatial structure.
Moreover, government support for low-income home buyers and elder home buyers to obtain
adequate housing finance can also promote a more efficient spatial structure.
Our analysis also demonstrates a useful role for the contingent-valuation (CV) measure of
location preferences in urban economic analysis. Despite the limitations of the CV method, our
measure of the bid-rent gradient (BRG) appears to vary across individuals as expected
according to their household characteristics, housing demand, and location preferences. We
find BRG increasing in household permanent income even after accounting for differences in
individuals’ job-market needs and lifestyle. Together with the observation of reverse
commuting in the central urban area, the finding suggests the important influence of urban
amenities on the spatial structure in Chinese cities.
Given the limited sample size we have, the empirical results of this study should be viewed
as tentative. Further studies with more adequate sampling and more careful design of CV
measure of location preferences shall provide more reliable measures of the spatial impact of
housing-market restrictions to guide government policies. Such studies would be of particular
relevance to transition-economy cities.
20
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22
APPENDIX: DESCRIPTION OF THE VARIABLES AND THEIR SAMPLE STATISTICS
Variable
Description
Willingness to pay (% of home price) for
living 15 minutes closer to city center.
Trimmed to exclude one observation of
BRG
-30% and the observations above 40%
Household annual gross earning (thousand
INCOME yuan): 1= 50 or less; 2= 50+ ~80; 3= 80+
~150; 4= 150+ ~250; 5= 250 or above.
Individual monthly expenditure on cell phone
CELL
(yuan): 1=below 300; 2=300~500;
3=500~1000; 4=1000~2000; 5=2000+.
BRG
MARRY
KID
Marital status: 1= married, 0=not married
Living with children: 1=yes, 0=no.
Household size (number of people living in the
same dwelling unit).
Age of the respondent (years): 1= below 20;
AGE
2= 20~29; 3=30~39; 4=40~49; 5=50 or above.
Education level: 1=technical college,
EDU
university or above; 0=otherwise.
Occupation: 1=government office, post &
OCCUP
communication, and commerce; 0=otherwise.
Official residential status in the city:
HUKOU
1= yes, 0= no.
Official position: 1=leaders in government
LEADER
offices or enterprises; 0=otherwise.
Working for publicly owned enterprises:
POE
1=yes, 0=otherwise.
WORK Housing type: 1= former work-unit housing;
_UNIT 0=otherwise.
Housing type: 1= commodity housing,
PRIVATE
including economy homes; 0=otherwise.
HSIZE
LAREA
ENTMT
PARK
ACCEPT
CAR
SH, GZ,
WH, CQ
BRG1
BRG2
Home living area (m2).
Preference for living close to entertainment
facilities: 1=not important…5=very important.
Preference for living close to parks: 1= not
important…5= very important.
The farthest acceptable residential location:
3=central zone, 2=middle zone, 1=outer zone
Private car ownership: 1= yes, 0= no
City dummies for Shanghai, Guangzhou,
Wuhan and Chongqin, respectively.
Predicted BRG according to regression
equation BRG_1
Predicted BRG according to regression
equation BRG_2
Sample mean (s.d.) by home location
All
Central Middle
Outer
Zones
zone
zone
zone
12.54
15.11
10.60
12.77
(12.59) (13.67) (10.59) (15.95)
11.04
13.39
9.75
9.30
(9.36) (10.10) (8.83)
(7.51)
No.
of
obs.
862
832
2.22
(1.16)
2.38
(1.17)
2.17
(1.11)
1.95
(1.07)
1106
1.61
(0.87)
1.69
(0.91)
1.55
(0.83)
1.57
(0.93)
1116
0.68
(0.47)
0.30
(0.46)
3.07
(1.00)
2.95
(0.96)
0.72
(0.45)
0.20
(0.40)
0.80
(0.40)
0.11
(0.31)
0.48
(0.50)
0.33
(0.47)
0.56
(0.50)
93.85
(49.99)
3.63
(0.95)
4.29
(0.83)
1.84
(0.61)
0.18
(0.38)
0.63
(0.48)
0.28
(0.45)
3.04
(0.97)
2.83
(0.87)
0.78
(0.42)
0.23
(0.42)
0.83
(0.38)
0.17
(0.37)
0.46
(0.50)
0.30
(0.46)
0.57
(0.50)
97.36
(48.48)
3.70
(0.94)
4.21
(0.84)
1.99
(0.66)
0.20
(0.40)
0.73
(0.44)
0.33
(0.47)
3.06
(1.02)
3.07
(1.02)
0.69
(0.46)
0.19
(0.39)
0.80
(0.40)
0.08
(0.28)
0.51
(0.50)
0.37
(0.48)
0.54
(0.50)
91.85
(52.56)
3.62
(0.97)
4.37
(0.79)
1.78
(0.52)
0.16
(0.36)
0.57
(0.50)
0.22
(0.41)
3.22
(1.03)
2.80
(0.92)
0.66
(0.47)
0.12
(0.32)
0.70
(0.46)
0.03
(0.16)
0.36
(0.48)
0.25
(0.44)
0.64
(0.48)
90.82
(42.59)
3.48
(0.91)
4.26
(0.83)
1.56
(0.66)
0.17
(0.38)
1116
1116
1082
1110
1116
1116
1116
1116
1116
1116
1116
1104
1086
1105
1090
1116
1116
11.25
(3.18)
11.21
(3.34)
11.87
(3.14)
12.18
(3.32)
10.83
(3.19)
10.64
(3.19)
10.93
(2.89)
10.31
(3.21)
1014
996
23
Table 1: Selected urban economic characteristics (2001)
City
Built-up urban area（km2）
Urban population (thousand）
Per-capita disposabel income
(RMB Yuan）
Tertiary employment share in
urban area (% total employment)
Per-capita living area (m2)
Per-capita road area (m2）
Beijing
780
9,880
11,578
Shanghai Guangzhou Wuhan Chongqing
550
526
212
268
12,620
5,770
7,580
8,960
12,883
14,694
7,305
6,721
63.16
48.88
59.61
54.23
48.42
13.76
6.11
12.5
10.62
13.87
10.22
9.7
2.35
11.47
4.43
Sources: China Statistical Yearbook and China Urban Statistical Yearbook.
Table 2: Sample distribution by city and location
City
Beijing
Shanghai
Guangzhou
Wuhan
Chongqing
All five Cities
LOCATION
3=Central zone 2=Middle zone
28%
26%
44%
52%
42%
38%
1=Outer zone
59%
63%
43%
39%
47%
50%
No. of
obs.
14%
10%
11%
8%
11%
11%
206
248
207
235
220
1116
Table 3: Average commuting time to work (minutes) by city and residential location
City
Beijing
Shanghai
Guangzhou
Wuhan
Chongqing
Average
Central
Zone
25.7
27.0
19.6
30.7
20.4
24.8
Middle
Zone
35.5
36.9
28.9
27.9
24.0
31.5
Outer
Zone
36.0
57.9
29.7
28.9
36.8
38.6
All
locations
32.8
36.6
24.8
29.4
23.7
29.7
24
Table 4. Regression estimates of the determinants of the bid-rent gradient
(The dependent variable is BRG. The estimation is based on the trimmed sample. t statistics are
computed based on White heteroskedasticity-consistent standard errors & covariance. * and ** indicate
statistical significance at 5% level and 1% level respectively)
Regression equations
Variables
Constant
Ln(INCOME)
Ln(CELL)
Ln(LAREA)
HSIZE
MARRY*(1-KID)
EDU
AGE≥50
OCCUP
WORK_UNIT
ENTMT
PARK
ACCEPT
LEADER
POE
SH
GZ
WH
CQ
R squared
No. of observations
BRG_1
Estimates
(t-statistics)
13.092 (3.4)**
0.360 (0.5)
2.336 (2.7)**
-1.740 (2.3)*
0.930 (2.4)*
2.259 (3.3)**
-0.370 (0.5)
-2.469 (2.3)*
1.588 (1.8)
-1.427 (1.9)
1.389 (4.0)**
-1.008 (2.4)*
-0.139 (0.1)
2.116 (1.9)
3.208 (2.8)**
-0.402 (0.4)
0.113
783
BRG_2
Estimates
(t-statistics)
7.893 (2.0)*
0.331 (0.4)
2.092 (2.4)*
-1.416 (1.8)
0.857 (2.3)*
1.928 (2.8)**
-0.239 (0.3)
-2.620 (2.5)*
1.626 (1.8)
-1.415 (1.9)
1.273 (3.7)**
-0.912 (2.1)*
2.309 (4.0)**
-0.398 (0.4)
1.961 (1.8)
3.043 (2.7)**
-0.425 (0.4)
0.127
769
BRG_3
Estimates
(t-statistics)
6.769 (2.7)**
-0.133 (0.2)
2.082 (2.3)*
0.602 (1.7)
2.296 (3.3)**
-0.563 (0.7)
-2.812 (2.6)**
1.434 (1.6)
-1.156 (1.6)
1.454 (4.3)**
-1.006 (2.3)*
0.383 (0.3)
0.340 (0.5)
-0.244 (0.2)
2.058 (1.8)
2.628 (2.4)*
-1.026 (1.0)
0.108
784
Table 5. Pair-wise correlation between the city fixed effects of BRG
and the urban economic characteristics
Urban economic characteristics
(reported in Table 1)
Built-up urban area
Urban population
Per-capita disposabel income
Per-capita living area
Per-capita road area
Tertiary employment share in urban area
Correlation with city
fixed effects of BRG
-0.42
-0.74
-0.06
-0.40
-0.31
0.31
25
Table 6. Ordered-probit estimates of residential location choice
(The dependent variable for the ordered-choice equation is LOCATION (3=central zone, 2=middle zone,
1=outer zone) and that for the binary-choice equation is LOCATION>2. t statistics are based on QML
(Huber/White) standard errors & covariance. * and ** indicate statistical significance at 5% level and
1% level respectively. All equations control for city fixed effects, which, together with the estimates of
the limit points, are not reported.)
Estimation
equation (BRG
measure)
Variables
Ordered_1
(Trimmed
BRG)
Estimates
(t-statistics)
0.022 (4.8)**
BRG
0.519 (3.7)**
LEADER
0.182 (2.1)*
POE
0.164 (3.7)**
INCOME
-0.050 (0.8)
CELL
-0.126 (2.5)*
AGE
0.205 (1.9)
EDU
0.238 (2.1)*
HUKOU
-0.125 (3.0)**
HSIZE
MARRY*(1-KID) -0.232 (2.7)**
-0.223 (2.5)*
PRIVATE
ENTMT
PARK
CAR
Log likelihood
119.8
ratio
(15 df)
No. of obs.
795
Ordered_2
(Trimmed
BRG)
Estimates
(t-statistics)
0.021 (4.4)**
0.529 (3.7)**
0.180 (2.0)
0.165 (3.6)**
-0.046 (0.7)
-0.118 (2.3)*
0.193 (1.8)
0.227 (1.9)
-0.129 (3.0)**
-0.209 (2.4)*
-0.213 (2.4)*
0.039 (0.8)
-0.011 (0.2)
-0.019 (0.2)
117.8
(18 df)
778
Ordered_3
(Predicted
BRG1)
Estimates
(t-statistics)
0.060 (3.1)**
0.526 (4.1)**
0.145 (1.9)
0.139 (3.6)**
-0.124 (2.2)*
-0.056 (1.2)
0.179 (2.0)*
0.131 (1.3)
-0.122 (3.1)**
-0.201 (2.3)*
-0.227 (2.8)**
Ordered_4
(Predicted
BRG2)
Estimates
(t-statistics)
0.117 (6.9)**
0.482 (3.6)**
0.151 (1.9)
0.132 (3.3)**
-0.189 (3.4)**
-0.012 (0.3)
0.218 (2.4)*
0.111 (1.0)
-0.160 (4.1)**
-0.316 (3.7)**
-0.252 (3.1)**
Binary
(Trimmed
BRG)
Estimates
(t-statistics)
0.025 (4.7)**
0.466 (3.0)**
0.115 (1.1)
0.141 (2.8)**
-0.032 (0.5)
-0.172 (2.8)**
0.266 (2.1)*
0.247 (1.9)
-0.122 (2.5)*
-0.331 (3.2)**
-0.145 (1.4)
107.6
(15 df)
1014
145.8
(15 df)
995
122.4
(15 df)
795
26