Housing Price and Fundamentals in A
Transition Economy:
The Case of Beijing Market
Bing Han1 and Lu Han2 and Guozhong Zhu3
2016 Conference on the Chinese Economy
1
Rotman School of Management, University of Toronto,
[email protected]
2
Rotman School of Management, University of Toronto,
[email protected]
3
Alberta School of Business, University of Alberta, [email protected].
Motivation: the Unusual Beijing Market
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Extremely high house price
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price-income ratio ≈ 30
price-rent ratio ≈ 40
price up by 500% in the past decade.
FIGURE
Questions:
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Can the high house price be consistent with economic
fundamentals?
In general, how to understand the link between house price
and economic fundamentals?
Price and Fundamentals
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Tradition approach (Case and Shiller (2003))
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“normal” relation between price and fundamentals in the
data
regression-based, using historical data
Price and Fundamentals
I
Tradition approach (Case and Shiller (2003))
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I
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“normal” relation between price and fundamentals in the
data
regression-based, using historical data
But...
Price and Fundamentals
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Tradition approach (Case and Shiller (2003))
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I
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“normal” relation between price and fundamentals in the
data
regression-based, using historical data
But...
“China is in such a rapid growth period. It is very hard to price
assets when growth is at the high level. The future matters
more. In a stable economy that is not going anywhere, you
have a pretty good idea of what they are worth.”
—– Robert Shiller, April 2014
Price and Fundamentals
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Our approach: rely less on historical data but impose a lot
of structure
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a dynamic rational expectation general equilibrium model
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forward-looking and utility-maximizing households
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a value-maximizing home builder
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endogenous paths of house price and rent
What are the fundamentals?
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income growth rate: high but declining
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large scale immigration FIGURE
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restricted land supply FIGURE
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high household savings rate
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savings rate: 25% (NBS)
80% of urban household wealth in housing (CHFS2012)
Rent is not considered fundamental.
map of Beijing
Key Features
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no aggregate uncertainty, but with idiosyncratic shocks
Key Features
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no aggregate uncertainty, but with idiosyncratic shocks
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an economy that eventually converges to a balanced
growth path (BGP)
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Constant price-income and price-rent ratios
Everything can be re-scaled
Key Features
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no aggregate uncertainty, but with idiosyncratic shocks
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an economy that eventually converges to a balanced
growth path (BGP)
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Constant price-income and price-rent ratios
Everything can be re-scaled
a reference city that operates in a BGP
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to pin down parameters
Hong Kong, DC, SF
Key Features
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no aggregate uncertainty, but with idiosyncratic shocks
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an economy that eventually converges to a balanced
growth path (BGP)
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a reference city that operates in a BGP
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Constant price-income and price-rent ratios
Everything can be re-scaled
to pin down parameters
Hong Kong, DC, SF
During the economic transition, there are changes in
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income growth
birth rate
age distribution
migration
Projection of Population Distribution
Distribution of Population (2013)
0.025
Fertility Rate
0.1
Beijing
Urban China
0.02
0.015
0.06
0.01
0.04
0.005
0.02
0
20
40
60
age
80
0
Mortality Rate
0.8
0.04
0.6
0.03
0.4
0.02
0.2
0.01
40
60
age
30
40
50
60
Distribution of Population
0.05
20
20
age
1
0
Old Rate
New Rate
0.08
80
0
20
2020
2060
2100
40
60
age
80
Projection of Land Supply and Income
Land supply per capita (square meters)
27
23
Income per capita (thousand RMB)
1210
growth = 0.5%
growth = 0%
growth = 1%
970
growth = 30 yrs
growth = 40 yrs
growth = 20 yrs
730
19
490
15
11
2014
250
2034
2054
2074
year
2094
2114
10
2014
2034
2054
2074
year
2094
2114
Model Elements
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A representative firm (developer)
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Over-lapping generations of households
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Own s share of the firm ⇒ housing investment
Rent h unit of housing from the firm ⇒ housing
consumption
Let d=down payment, s ≥ d × h ⇒ owner
The Representative Firm
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Production technology:
Ht = ZLθt Kt1−θ
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L: land
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K: capital
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Z: scaling parameter
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θ: land share in housing production
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considered labor/construction cost ⇒ similar results
Firm’s Optimization Problem
capital
purchase
land
purchase
z
}|
{ z
}|
{
1
rt Ht − [Kt − (1 − δ)Kt−1 ] − qt (Lt − Lt−1 ) +
pt+1 Ht
Rt+1
max
Kt ,Lt
s.t. Ht = ZKt1−θ Lθt
where
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r = housing rental rate
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q = land price
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p = house price
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R = firm’s financing cost (household’s investment return)
Housing Supply Function
Ht = Z
1/θ
(1 − θ)rt
1 − (1 − δ)/Rt+1
Housing supply increases with
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land provision (Lt )
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rental rate of houses (rt )
Housing supply decreases with
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financing cost of the firm (Rt+1 )
(1−θ)/θ
Lt
Households
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overlapping generations of households
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Works for J years, then retires
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Lives up to T years. Before age T, death probability is
taken from the data
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Two decisions
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inter-temporal allocation: save/dis-save
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intra-temporal allocation: housing vs non-housing
Equilibrium
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Need to find the trajectories of price and rent to clear two
markets:
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rental market
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equity market
Efficient numerical solution strategy
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Need to solve paths of price and rent, each has 100 years!
Results
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baseline results
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Hong Kong as reference city
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using income per capita as reported
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exogenous migration
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robustness
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results with endogenous migration
Results: Prices and Rent
2
Growth rate of hous
House price (thousand RMB per m )
147
0.11
113
0.06
79
0.01
45
11
2005
2025
2045
2065
2085
2105
−0.04
2005
2
Rental rate (thousand RMB per m )
738
3.3
558
2.3
378
1.3
198
2025
2045
2065
year
2085
2105
18
2005
2025
Price in 2014 = 14,920 RMB per square meter (30,000 in
the data)
I Annual rent in 2014 = 459 RMB per square meter (700 in the
data)
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2045
2065
Land price (thousand R
4.3
0.3
2005
2025
2045
2065
year
Results: Ratios
Ann
Price−income ratio
22
6.2
19
5
16
3.8
13
2.6
10
2005
2025
2045
2065
2085
2105
1.4
2005
Price−rent ratio
Ret
40.8
0.084
37.8
0.071
34.8
0.058
31.8
2005
2025
2045
2065
2025
2085
Land price / House price
2105
0.045
2005
2025
Regression Results
Dependent Variable: growth of price and rent
Dependent variable:
2005-2040
2041-2080
2081-2114
log(Gp )
income
land
0.710 -0.797
1.161 -3.020
0.807
0.140
log(Gr )
income
land
0.670
0.321
0.761 -1.135
0.856 -0.916
Sensitivity
(1)
(2)
(3)
(4)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
Baseline
Growth of land supply = 1%
Growth of land supply = 0.0%
Income stabilizes in 20 years
Income stabilizes in 40 years
Initial Fin’l wealth = 2 M
FAR ≤ 3
Mortgage rate = 3%
Down payment = 30%
Minimum housing size = 20
Minimum housing size = 40
DC calibration
DC calibration (more land)
SF calibration
Less income risk
Less medical expense risk
Price
2014
2114
19.41 153.54
18.10 86.40
22.33 207.21
18.55 128.87
20.06 183.81
20.01 161.07
21.43 289.87
21.96 176.41
24.62 179.96
19.41 148.06
18.89 153.36
14.87 122.81
23.69 105.34
18.12 150.07
18.83 144.32
19.37 151.79
Rent
2014 2114
0.56 4.31
0.57 2.72
0.62 5.90
0.54 3.64
0.60 5.32
0.59 4.42
0.61 7.94
0.62 4.65
0.63 4.66
0.56 4.19
0.57 4.36
0.53 3.95
0.81 3.39
0.50 3.33
0.57 4.39
0.57 4.31
What have we found?
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Price-income ratio declines over time as the economy
converges. Housing becomes more affordable.
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The equilibrium house price in Beijing that can be justified
by the fundamentals is around 19,410 RMB per square
meter in 2014, much lower than 30,000 RMB in the data.
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Alternative assumptions on land supply, income growth
and population structure do not help in narrowing the gap
between the model-implied price and the observed price.
detail
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However · · ·
What might explain the gap between the model and
the data?
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Measurement error of fundamental variables
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Endogenous inflow of rich immigrants
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Features not captured by the current model
Extension 1: Underreported Income
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Evidence of officers’ “grey incomes” from housing
purchase behavior (Deng, Wei and Wu, 2016):
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The higher the rank of government officials, the larger the
percentage of unreported income:
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FU-KE: 29.5%
ZHENG-KE: 55.8%
FU-CHU: 63.2%
ZHENG-CHU: 151.1%
FU-JU: 218.7%
ZHENG-JU: 694.7%
Price and Rent Given Higher Income
Baseline
Income = 2/3 times Hong Kong
Income = Hong Kong
Price
2014
2114
19.41 153.54
32.40 252.47
42.40 369.02
Rent
2014 2114
0.56 4.31
0.97 7.18
1.30 9.95
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High price in Beijing can be rationalized if the Beijing
resident income is about 70% higher than reported.
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Actual income of government officials is 60% higher than
reported income on average (Deng, Wei and Wu 2016)
Who bought houses in Beijing?
Extension 2: Migration of Rich Households
Extension 2: Migration of Rich Households
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Migrants: Households in second and third tier cities
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roughly 200 millions people in these cities
Benefits:
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higher utility (amenity)
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benefit of migration ≈ 25% increase in consumption
equivalence
potentially higher return to housing investment
Costs:
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high savings rate needed to afford down payment
higher living cost (rent)
Endogenous Migration: Price and Rent
Baseline
Endogenous Migration
Price
2014
2114
19.41 153.54
33.19 243.26
Rent
2014 2114
0.56
4.31
0.702 6.685
Features We Have Not Captured Yet
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Cyclical variations in fundamentals
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Search frictions
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Aggregate uncertainty
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Illiquidity
Conclusions
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Link house price and rent to fundamentals in a transition
economy
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For Beijing market, we show
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Price is too high unless...
General lessons
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Historical relation between price and fundamentals is
unlikely to repeat itself during the transition periods
High price/income and price/rent may be consistent with
the fundamentals.
Underreported income or migration of rich households can
drive up house price a lot. (a lesson for Toronto?)
THANK YOU!
北京大学——林肯研究院城市发展与土地政策研究中心
清华大学恒隆房地产研究中心
House Price Indices: Beijing, Shanghai,
Shenzhen,
Tianjian,Wuhan, Chengdu, Dalian and Xi’an
500
CQCHPI新建商品住房中心城区同质价格指数
（2006Q1-2014Q3）
2006Q1=100
450
400
350
300
250
200
150
50
2006Q1
2006Q2
2006Q3
2006Q4
2007Q1
2007Q2
2007Q3
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
2009Q4
2010Q1
2010Q2
2010Q3
2010Q4
2011Q1
2011Q2
2011Q3
2011Q4
2012Q1
2012Q2
2012Q3
2012Q4
2013Q1
2013Q2
2013Q3
2013Q4
2014Q1
2014Q2
2014Q3
100
北京
大连
RETURN
上海
天津
深圳
武汉
西安
8个城市综合
成都
City of Beijing
RETURN
Population of Beijing (millions)
Population of Beijing
21
20
19
18
17
16
15
14
2002
RETURN
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
Land Supply in Beijing
New supply of residential land (hectares)
2500
2000
1500
1000
500
0
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2009
2010
2011
2012
2
Residential land (m ) per person
24
23
22
21
20
19
2002
RETURN
2003
2004
2005
2006
2007
year
2008
Young home buyers badly need help from parents
RETURN
A rich coal-mine owner owns 99 houses in Beijing,
plus some commercial real estate(June 14, 2014,
People’s Daily Online).
RETURN