Uncertainty and New Apartment Price Setting: a real options approach
Song Shi
School of Economics and Finance, Massey University, Palmerston North, New Zealand
Email: [email protected]
Zan Yang*
Tsinghua Hang Lung Center for Real Estate, Institute of Real Estate Studies, Department of
Construction Management, Tsinghua University, Beijing, China
Email: [email protected]
David Tripe
School of Economics and Finance, Massey University, Palmerston North, New Zealand
Email: [email protected]
Huan Zhang
Tsinghua Hang Lung Center for Real Estate, Institute of Real Estate Studies, Department of
Construction Management, Tsinghua University, Beijing, China
Email: [email protected]
February 2015
*corresponding author
Abstract
This paper investigates real estate development firms’ pricing behaviours in Beijing, China during the period
2006-2008. New apartment prices are set by real estate development firms at the presale stage with widely
observed price rigidity. Home buyers are often price takers without much power of negotiation in the price
setting process. We find that real estate development firms apply real options theory for new apartment price
setting at the presale stage, having regard also to apartments’ physical attributes, firms’ financial position and
other economic conditions. Our results shed lights on the nature of residential real estate development
market, in particular how changes in the market uncertainty will affect firms’ price setting behaviours.
JEL classification: D40, G30, R30
Keywords: new apartment price setting, real options theory, uncertainty
2
1. Introduction
Price setting is among the most challenging decisions for firms. Economic theory on firms’ price setting
in imperfect competition is modelled on profit-maximising where firms can use all available information to set
their product prices. Cost to produce, competitors’ prices and expectations of the future are all relevant in the
process. Very few studies, however, test the price setting behaviour of firms in the real estate development
business where products are heterogeneous and location specific, and firms often operate in a less efficient
and sometimes oligopolistic market.1 Given the important role of the real estate market in the economy,
understanding real estate developers’ price setting behaviour is of particular interest, especially for any policy
intervention in the housing market.
One feature in the newly-built or under construction residential apartment market is price rigidity.
Once apartments are priced to sell, their initial pricing provides benchmarks for subsequent sales. There are a
number of competing theories of nominal price stickiness. Research shows that property buyers identify an
anchoring effect of opening prices (Bucchianeri and Minson, 2013; Leung and Tsang, 2013), and are ‘angered’
at price increases, even though subsequent price increases may be less than market price movements
(Rotemberg, 2005). Compared to the effect of price increases, a subsequent price reduction or discount may
be even more harmful to the firm’s reputation, especially if other firms in the sector have yet to lower prices.
Ball and Romer (1990) show that firms benefit from “strategic complementarity” in price setting: a firm’s
desired price depends positively on others’ prices. Strategic complementarity strengthens price rigidity. In
addition to market effects, regulatory requirements could be another reason for the price stickiness as, in the
highly regulated Chinese market, developers are required to register their apartments in advance with the
local authority and stick with their registered apartment sale prices in the ongoing sale process.
1
Real estate development is capital intensive and market is highly regulated with the typical “kinked” supply function, i.e. the supply
of built space is fixed in the short run. See Geltner et al. (2007) for more discussions.
3
Developers otherwise have an option to defer putting apartments on the market for sale, with the
choice of when to list them being a strategic decision by management. Although regulatory rules and
procedures are complicated, developers can generally start presales well before the project is completed.
However, starting presales according to the precept the earlier the better is not necessarily optimal for profitmaximising. In the corporate finance literature, a firm is inclined to consider option values attached to future
higher prices, particularly if an investment is capital intensive and irreversible under high regulation and
uncertainty (Myers, 1977; Trigeorgis, 1996). Under this theoretical framework, the developer is in fact selling
an option contract for a newly-built apartment.
The real options approach has previously been documented in the real estate literature. Most studies
are focused on land development, where real options are used to explain vacant urban land (Capozza and Li,
2001; Cunningham, 2006; Geltner, 1989; Geltner et al., 1996; Grovenstein et al., 2011). Others are primarily
interested in examining uncertainty in investment decision making (Bulan et al., 2009; Holland et al., 2000;
Williams, 1991). The theory has recently been tested in property valuations, where real options are captured
by non-negative option values to represent redevelopment possibility in a hedonic price model (e.g. Clapp and
Salavei (2010), Clapp, Jou and Lee (2012), Clapp, Eichholtz and Lindenthal (2013)). No studies have been
carried out to examine the option value at real estate firm level of their pricing behaviours.
In this article, using a real options model, we show that real estate development firms have
incorporated a forward view into their price setting, an approach which has not been followed in prior
research. Market uncertainty will increase firms’ pricing, but encourage them to defer selling of apartments;
by contrast, government subsidies (another characteristic of the Chinese market) have the counter effect of
reducing market uncertainty on firms’ pricing behaviour, even though they are not intended to do so. Our
focus is on the market in Beijing, for which we have detailed data, and where the large numbers of
transactions mean that we can have a higher degree of confidence in our results. Beijing is the one of the
4
largest and fast growing apartment development markets in the world. According to statistics from the
MacroChina Industries database, the area of new residential construction in Beijing has been maintained at
about 18 million square meters per annum in the past ten years, with an annual residential development
investment of 120 billion RMB. This means that, despite some price regulation, lessons from Beijing, the
capital city of the world’s second biggest economy, could apply in other cities around the world.
In the next section we look at the Chinese market for newly built apartments and other market
characteristics in more detail. Section 3 presents the theoretical framework. Section 4 describes the data while
Section 5 reports the empirical results. Section 6 outlines policy recommendations and concludes.
2. Optionality and other characteristics of the Beijing property market
New housing construction dominates the Chinese real estate market. As in many other countries, real
estate developers in China are allowed to presell apartments under construction to purchasers who pay a
deposit or the building cost, and it is a common practice for people to buy new apartments off a plan. The
deposit, the payment made by apartment purchasers to secure their options to buy, is normally between 2030% of the total purchase price for first home buyers and can be increased to 40-60% for non-first home
buyers. However, few people pay by instalments when buying new apartments in China. This is because the
total payment by instalments is usually more expensive than paying a lump sum at once. According to
statistics from the National Bureau of Statistics of China, 81% of new apartment purchasers paid the asking
price in one-off lump sum payments between 2002 and 2009. Once a sales and purchase agreement is signed,
it can be legally enforced in court. The standard contracts provide clauses in the case of default by either party.
If it is the developer fault causes the contract to fail, i.e. the apartment cannot be completed or differs from
the original plan and specifications, the buyers can cancel the contract and get their money back plus interest
5
costs and additional compensation. On the other hand, purchasers are required to pay extra penalties if they
do not make instalments on time and the contract can be cancelled by the developer. Since the Beijing market
has been characterised by an undersupply of property during the period of the study, there has been very
little likelihood that purchasers would fail to exercise their options. Moreover, because purchasers are
normally required to pay a large amount of deposit for the purchase, and encouraged to pay the total price at
purchase, they would expect to complete the contract even in an environment where prices might have fallen.
The presale process is referenced from Hong Kong and was formally introduced to the Chinese
property market by the Ministry of Housing of Urban and Rural Development (MOHURD) in 1994. 2 Under the
MOHURD regulations, real estate development firms must apply for a presale permit first before they can
start presales. A proposed presale price for all apartments must be entered at the time of application. The
“registered” prices can be adjusted later, but approval needs to be obtained from the local authorities to reset
prices. 3 Developers can choose to sell apartments in a single development or in a number of stages, applying
for presale permits for each stage.
Once apartments are listed on the market for sale, they become fixed price offerings. Increases or falls
in prices are likely to be obstructed because of tacit collusion and the anchor effect in China (Leung and Tsang,
2013; Wu et al., 2014). Under regional oligopoly market structures in China, tacit collusion commonly occurs
among major property market participants, preventing a competitive equilibrium from being reached.
Purchasers who have paid earlier for apartments are generally opposed to later lowering of spot prices, and
because individuals’ subsequent quantitative judgments assimilate to the “anchor”, housing sellers prefer a
fixed selling price. Reflecting all these regulations and other effects, the asking price is generally equal to the
transaction price in the Chinese property market (Wu et al., 2014).
2
See Urban Real Estate Management Act 1994 and its specific provisions for Unban Management Practices: Pre-sale of Commercial
Housing.
3
For the attempt of reining in high housing prices (i.e. inflation targeting), local governments are sometimes unwilling to give
permission for reregistering of higher prices.
6
This indicates that presale apartment prices represent an options contract, where the price largely
depends on the apartment’s expected future value. Apartments’ prices are determined by the firm at presale
stage, based on construction cost subject to uncertainty about the future. This uncertainty relates not only to
market dynamics impacted by demand and policy, but also to the timing of sales. Given the rather limited
scope to adjust listed prices in the Chinese case, uncertainty is important in developer’s price setting.
An important feature in China’s property market is that local governments are deeply involved in land
development. Real estate development companies are the main contributors to local infrastructure projects
and public housing, and their sustained profitability and growth are crucial to local economies. Thus, real
estate development firms often obtain financial support from local governments through fiscal transfers or
subsidies. In 1994, only about 5% of all listed companies in the Chinese stock market obtained fiscal transfers,
but the percentage increased to about 35% by 2001 (Chen et al., 2008). One reason for the increase in
government subsidies is that the Chinese government targets listed companies, especially to boost their
return on equity. This reflects unique transition economy characteristics of the Chinese stock market, where
essentially all listed companies were transformed from State Owned Enterprises (SOE), which included local
government as a major shareholder and symbiotic partner of listed companies (Chen et al., 2008; Lee et al.,
2014). Under the rules of the China Securities Regulatory Commission, any Chinese stock market listed firm
with two successive years of losses or with an asset value per share less than the stock’s face value is
designated as a Specially Treated (ST) firm, and faces trading and financial restrictions. Governments at
various levels are thus willing to provide subsidies to help their listed firms to overcome capital constraints or
financial difficulties (Claro, 2006). The subsidies can be cash or non-cash assistance (i.e. tax rebates) and are
additional to the capital invested by the government as the partial owner of the enterprise. According to the
7
RESSET Financial Research database, 4 the subsidised enterprise ratio rose from 35% in 2001 to 48% in 2011,
with the average subsidised amount per enterprise increasing from 4.6 to 18.7 million RMB.
3. Empirical Estimation Strategy
3.1 Options theory
According to real options theory, uncertainty as to future housing market price movements will cause
the firm to delay putting newly-built apartments on the market, and increase their prices. In contrast,
government subsidies for real estate development should have a counter-effect of reducing uncertainty on
new apartment pricings. The theoretical framework in this study is based on real options theory to decompose
factors which might affect new apartment listing prices and listing speeds into three groups: an apartment’s
physical attributes, the firm’s financial characteristics and market conditions. The results will shed light on the
developers’ pricing behaviour and the impact of market uncertainty and government subsidies. The main
estimation equations are
For pricing – hedonic model at apartment level
𝑝𝑖𝑖𝑖 = 𝛼 + 𝑔𝑖𝑖 + 𝑔𝑖𝑖 ∗ 𝐸𝑡 [𝜎# ] + 𝐸𝑡 [𝜎# ] + 𝑋𝑖𝑖′ 𝛽 + 𝑌𝑗𝑗′ 𝛾 + 𝑍𝑖𝑖′ 𝛿 + 𝑓𝑗 + 𝐷𝑖 + 𝑆𝑖𝑖 + 𝑇𝑖𝑖 + 𝜀𝑖𝑖𝑖
(1)
where 𝑝𝑖𝑖𝑖 is the log listing price for apartment i by developer j at time t. The subsidy variable 𝑔𝑖𝑖
equals to 1 when the firm receives a subsidy, and otherwise 0. 𝐸𝑡 [𝜎# ] represents the expected market
uncertainty, # =d or c, to be explained later. The term 𝑋𝑖𝑖 is a vector of property attributes comprising
apartment area, apartment floor, presale building area, presale building floor, distance to CBD and distance to
local amenities (school and hospital). The term 𝑌𝑗𝑗 is a vector of the firm’s financial characteristics including
4
A research database on financial and economic dataset in China, jointly developed by Tsinghua University, Peking University and
London School of Economics.
8
size, price-to-earnings ratio, debt-to-assets ratio, interest cover, return on assets, and EBIT to total revenue.
The term 𝑍𝑖𝑖 is a vector of market conditions including interest rate changes and district level real GDP
growth. 𝑓𝑗 is the fixed effect for firm j and 𝐷𝑖 is the district (sub-market) in which the property is located. The
vectors 𝑆𝑖𝑖 and 𝑇𝑖𝑖 are dummy variables for seasonal and year effects, respectively. 𝜀𝑖𝑖𝑖 is the error term.
For timing – hazard models at apartment level
(2)
λ(t; Η) = 𝜆0 (𝑡)𝜅(Η)
where 𝜆0 (𝑡) is the baseline hazard and 𝜅(Η) is a positive function of observed covariates H. The model
indicates that the hazard function of apartment’s timing λ(t; Η), the time length from the presale permit to
the time of developers to put apartments on the market for sale, depends on the baseline hazard model
assumption 𝜆0 (𝑡) and a vector of covariates 𝜅(Η).
let 𝜅(H) = exp(Hβ), where β is a vector of parameters. Then
log λ(t; H) = log 𝜆0 (𝑡) + Hβ ; and
Hβ = 𝐸𝑡 [𝑝# ] + 𝑔𝑖𝑖 + 𝑔𝑖𝑖 ∗ 𝐸𝑡 [𝜎# ] + 𝐸𝑡 [𝜎# ] + 𝑋𝑖𝑖′ 𝛽 + 𝑌𝑗𝑗′ 𝛾 + 𝑍𝑖𝑖′ 𝛿 + 𝑓𝑗 + 𝐷𝑖 + 𝜑𝑖𝑖
(3)
(4)
where 𝐸𝑡 [𝑝# ] is the log of expected market price movement, # =d or c, to be explained later and 𝜑𝑖𝑖 is
the white noise. Definitions for other variables are the same as in Eq (1).
This study applies a proportional-hazard Cox (1972) model to the above duration test. The strength of
the Cox method is that it does not require estimating the baseline hazard function 𝜆0 (𝑡), provided that people
are interested only in the effects of the covariates X in Eq (2). For a robustness check, the results of Cox model
are compared to the parametric Weibull model. In the Weibull model, the baseline hazard function is specified
as 𝜆0 (𝑡) = 𝛾𝛾𝑡 𝛼−1 . When α = 1, the Weibull hazard function reduces to a constant model. If α > 1, the
hazard is monotonically increasing; For α < 1, the hazard is monotonically decreasing.
9
We test the following hypotheses:
H1. The coefficient for market volatility, 𝐸𝑡 [𝜎# ], will have a positive sign in Eq (1) and negative sign in
Eq (4), if the real options theory is followed in firms’ price setting.
H2. The coefficient for subsidy, 𝑔𝑖𝑖 , will have a negative sign in Eq (1) and positive sign in Eq (4), if the
government subsidy has a counter effect on reducing market uncertainty on firms’ price setting.
H3. The coefficient for the interaction term 𝑔𝑖𝑖 ∗ 𝐸𝑡 [𝜎# ] will have a negative sign in Eq (1) and positive
sign in Eq (4), if the counter effect of government subsidy is increased with market volatility.
3.2 Quality adjusted market price indices
We are interested in the district level price movements as spatial and economic heterogeneities could
be significant within a big city like Beijing. For achieving this, a standard hedonic regression model is utilized
for each district over time, as follows:
′
𝛽 + 𝜇𝑖𝑖𝑖
𝑝𝑖𝑖𝑖 = 𝛼𝑑𝑑 + 𝑋𝑖𝑖𝑖
(5)
where 𝑝𝑖𝑖𝑖 is the log sale price for apartment i in district d at calendar quarter t. The term 𝑋𝑖𝑖 is a
vector of property attributes comprising apartment area, apartment floor, presale building area, presale
building floor, distance to CBD and average distance to local amenities (school and hospital), while 𝜇𝑖𝑖𝑖 is
white noise.
The coefficients obtained in Eq (5) are then used to calculate the quarterly house price level in district
d, denoted 𝑝𝑑,𝑡 , using the average property attributes in the district over the whole period studied. The
advantage of this estimation procedure is that the regression coefficients can change in each quarter, allowing
estimated quarterly house prices to reflect changing market tastes and preferences, particularly in a rapidly
10
changing market. A similar hedonic method is used by Arbel et al. (2010) to estimate quality adjusted house
price movements in their study of terrorism effects on local house prices.
3.3 Market volatilities
Market volatility is measured as the difference between the forecast and actual market prices. A
straightforward method to approximate future prices is to use their past values. Case and Shiller (1989)
studied the efficiency of housing market in the USA. They showed that house prices are somewhat predicable
on an annual basis. To quantify the perceived market price and volatility based on different forecasting
horizons, we create two forecasting estimates, denoted 𝐸𝑡 [𝑝# ] and 𝐸𝑡 [𝜎# ], to take into account the price and
volatility at district and city levels respectively. 𝐸𝑡 [𝑝𝑑 ] is based on 2-quarter-ahead forecasting at each district
level and is computed as
𝐸𝑡 [𝑝𝑑 ] = 𝑝𝑑,𝑡−2 + 𝜔𝑑,𝑡
(6a)
where 𝑝𝑑,𝑡−2 is the district apartment price at time t-2 and 𝜔𝑑,𝑡 is the district level forecasting error.
The second estimate, denoted 𝐸𝑡 [𝑝𝑐 ], is based on 4-quarter-ahead forecasting at city level. The intuition is
that firms may seek city level indicators to estimate uncertainty over an extended forecasting period, when
local submarkets are too volatile to be accurately measured. The estimation equation is written as follows:
𝐸𝑡 [𝑝𝑐 ] = 𝜌0 + 𝜌1 𝑝𝑐,𝑡−4 + 𝜌2 𝑝𝑐,𝑡−5 + 𝜌3 𝑝𝑐,𝑡−6 + 𝜌4 𝑝𝑐,𝑡−7 + 𝐵𝑐,𝑡−4 + 𝑒𝑐,𝑡
(6b)
where 𝑝𝑐,𝑡−4 is the city level new apartment price at time t-4, 𝐵𝑐,𝑡−4 is the potential structural break as
indicated from the Zivot-Andrews (1992) unit root tests and 𝑒𝑐,𝑡 is the city level forecasting error.
Under rational expectations (Lucas and Sargent, 1981) firms will use all past information to
approximate future apartment price movements. Following this strategy, we first estimate Eq (6b) using all
11
past information up to time t-4, then use the estimated coefficients to forecast the apartment price at time t.
In this process, rational expectations of apartment prices are developed from a dynamic information update,
i.e. for each time period t, the firm will re-estimate Eq (6b) based on newly arrived information up to t-4.
Similar estimation strategies were used by Cunningham (2006) to forecast a quality adjusted house price. He
estimated the one-year-ahead quality adjusted price of housing as a function of the current quality-adjusted
price without using any past price information.
An empirical issue is how many lags should be included in the estimation. In this study, the selection of
lags is guided by the general-to-specific model selection procedures (Campos et al., 2005). The structural
break is taken at June 2006, which can be related to a major policy change in new apartment development
market in China. 5
The estimated forecasting errors are then calculated in a relative measure as follow:
𝑓𝑑,𝑡 = 𝜔
�𝑑,𝑡 /𝑝𝑑,𝑡
(7a)
𝑓𝑐,𝑡 = 𝑒̂𝑐,𝑡 /𝑝𝑐,𝑡
(7b)
where 𝑓𝑑,𝑡 and 𝑓𝑐,𝑡 are calculated relative forecasting errors at district and city levels, respectively.
The expected price volatilities are then calculated as the standard deviation of moving average of
relative forecasting errors from Eqs (7a) and (7b), respectively:
2
̅ � /2
𝐸𝑡 [𝜎𝑑 ] = �∑2𝑛=1�𝑓𝑑,𝑡−𝑛 − 𝑓𝑑,𝑡
(8a)
5
The Zivot-Andrews unit root test indicate that the structural break occurred at June 2006 based on the city level real new
apartment price index from 2000 to 2008. On May 2006, the general office of the State Council in China issued “opinions on
adjusting housing supply structure to stabilise housing prices” which is also called “Guo Liu Tiao”. This document aims to curb overrapid housing prices by adjusting housing supply and demand through an increase in the weight of medium and small-sized
commercial residential housing and affordable housing construction.
12
̅ �2 /4
𝐸𝑡 [𝜎𝑐 ] = �∑4𝑛=1�𝑓𝑐,𝑡−𝑛 − 𝑓𝑐,𝑡
(8b)
Where 𝐸𝑡 [𝜎𝑑 ] and 𝐸𝑡 [𝜎𝑐 ] are the forecast market price volatilities at district and city levels,
respectively; and
1
(9a)
1
(9b)
̅ = ∑2𝑛=1 𝑓𝑑,𝑡−𝑛
𝑓𝑑,𝑡
2
̅ = ∑4𝑛=1 𝑓𝑐,𝑡−𝑛
𝑓𝑐,𝑡
4
4. Data
The data used in the paper covers newly-built apartments in Beijing between 2006 and 2008. The data
can be further classified into three groups: the first is property transaction data for all newly-built apartments
in Beijing. This is used to control for the heterogeneity of physical characteristics between apartments, and to
calculate district level quality adjusted apartment price indices. The second is financial data on real estate
development firms in Beijing over the period studied, which is then linked to property transaction data to
control for heterogeneity between each real estate development firm. The third is macroeconomic data for
Beijing which will help control for general market conditions. All variables are defined in Appendix A.
There are 281,405 apartments included in this study.6 Information on attributes of those apartments
are collected from the “Real Estate Market Information System” of Beijing, covering 18 districts and the
Yizhuang specialized development area. Figure 1 shows administrative districts in Beijing Metropolitan area.
This system is established by the local authority to electronically record each apartment transaction and
6
Any erroneous data was identified and removed. This included the apartment area is restricted between 30 and 360 square meter
and apartment price is confined between 3,000 and 30,000 per square meter. Transactions with a project area less than 5,000
square meters were also removed from our analysis. Following the initial data clean-up, we further restricted the permit-to-listing
time beyond 18 months. In total, we removed about 5.9% of data in our analysis.
13
related attributes according to central government requirements. Based on GIS information collected by the
Institute of Real Estate Study of Tsinghua University, we can further identify public facilities around the
apartments including distance to CBD, railway station, hospital and primary schools. The transaction data is
then utilized in calculating new apartment price indices at district level. Among all new apartments, about 40%
are developed and sold by listed firms. Moreover, there is no obvious difference in apartments sold between
listed and non-listed firms. As a result, the price indices using all sales are adequate for listed firms to analyse
market uncertainty. The property characteristics of all newly-built apartments in Beijing between 2006 and
2008 are detailed in Appendix B.
<Insert Figure 1 about here>
Information on pre-sale registration, such as names of real estate firms, date of registration,
development projects and respective apartments are obtained from the Beijing Municipal Commission of
Housing, Urban and Rural Development (BMCHURD) which is responsible for administration and management
of housing and urban-rural development in the city. Project companies are identified by their parent firms. In
total, there are 503 real estate development enterprises identified through the BMCHURD presale registration
database over the study period. Amongst these 503 firms, 65 are identified as listed firms trading either on the
Shanghai or Shenzhen Stock market. 7 Financial data for listed companies are obtained from RESSET Financial
Research database. The financial data includes the firms’ yearly market value, price-to-earnings ratio, interest
cover, debt-to-assets ratio, return on assets, EBIT to total revenue, and information on subsidies received.
Among the 65 listed firms, more than 50% received subsidies. The year-by-year summary statistics for the
financial characteristics of the 65 listed firms used in this study are detailed in Appendix C.
7
There are total 90 listed firms in the dataset. 65 firms are traded either on the Shanghai or Shenzhen Stock market, and 25 firms
are traded in Hong Kong or Singapore Stock market. Financial information for non-listed firms is unavailable and we restrict our
study to those 65 firms traded in China in the analysis.
14
Macroeconomic data such as the city level Consumer Price Index (CPI) and district level Gross Domestic
Production (GDP) are obtained from the National Bureau of Statistics of China. We use the linear interpolation
method to turn the annual data series into quarterly series if required. Interest rates are from the People’s
Bank of China (the central bank) benchmark lending rates. Apartment prices, indices, GDP and interest rate
are all in real terms, deflated by the CPI over the studied period.
To calculate the time period from the presale permit to the time developers put apartments on the
market (permit-to-listings), we use the first apartment sale date as an indicator for the presale open date (also
called project open date) for all apartments. In other words, all apartments under the same permit will have
the same open date. 8 Accordingly, we readjust properties’ sale dates to the project open date in the following
analysis. The reason for using the project open date in the listing price and listing time models is because the
apartment sale prices are set by the firm at the time of listing, rather than when the apartments are actually
sold. The average time length of permit-to-listings for all listed and non-listed firms is 4.7 months by presale
permits, 3.1 months by apartments and 5.2 months by firms, respectively. Overall, permit-to-listings are pretty
much similar between the listed firms and non-listed firms. Summary statistics are shown in Table 1.
<Insert Table 1 here>
5. Empirical results
5.1 Estimated new apartment price indices and market volatilities
8
Multiple listings are strictly prohibited under the presale registration system.
15
We first calculate district level quality-adjusted new apartment price indices of 𝑝𝑑,𝑡 using the property
transaction data for the study period. 9 The results show that Chaoyang and Haidan districts have the highest
prices among all districts. New apartment prices in Fengtai district are close to the average price levels in the
city, while prices in Changping district are generally low except for a surge during 2007 and 2008. The results
are in line with the Beijing new apartment market, where Chaoyang district is generally regarded as the most
sought-after living area due to its closeness to the city centre, while Haidain is famous for the research and
development (R&D) facilities and universities in the district. On the other hand, Changping is located in a
suburban area with generally low apartment prices, although these have increased rapidly due to population
growth. Relative price movements for new apartments in Beijing are shown in Figure 2.
<Insert Figure 2 about here>
The district level new apartment price volatilities of 𝐸𝑡 [𝜎𝑑 ] are then estimated and reported in Figure 3.
It shows that district level volatilities for new apartments in Beijing are high. Among districts, Haidan,
Changping and Fengtai tend to have high price volatilities, and Chaoyang district has the smallest price
volatility. This could be due to the relatively solid housing demand in the center of city, as compared to
changing patterns of demand in other districts. The average quarterly price volatilities are 2.2% in Chaoyang,
8.8% in Haidian, 7.5% in Fengtai and 7.1% in Changping. For the rest of city, the aggregate volatility is about 3%
over the study period.10
<Insert Figure 3 about here>
The city level new apartment prices and volatilities are presented in Figure 4. It shows that the forecast
𝐸𝑡 [𝑝𝑐 ] and actual prices 𝑝𝑐,𝑡 generally tracked each other until the Global Financial Crisis (GFC) in 2007. The
9
Chaoyang, Haidian, Fengtai and Changping are identified as the four main districts. Other districts and area are classified as rest of
city due to insufficient data for analysis. The combined sales in the main four districts are about 60% of all new apartments sold
during the studied period.
10
Detailed statistics are available from the authors on request.
16
expected price volatility of 𝐸𝑡 [𝜎𝑐 ] is generally small at about 1.2% on average prior to the GFC and increased
to 7.7% in 2008.11 Overall, using the city level price index we record substantially lower price volatility
compared to district level price indices.
<Insert Figure 4 about here>
5.2 factors influenced firm’s price setting
Table 2 shows the firms’ listing prices having regard to factors such as the effect of market uncertainty
and government subsidies. Panel A shows the results when expected uncertainty is measured by 𝐸𝑡 [𝜎𝑑 ], while
panel B shows the results when expected uncertainty is measured by 𝐸𝑡 [𝜎𝑐 ]. Overall, results from Panels A
and B are consistent with each other. The difference in estimates is due to the different measurements of
expected uncertainty, with expected uncertainty in Panel A more volatile than in Panel B.
Model (1) shows that market volatility has a positive effect on the real listing price. A one percentage
point change of price volatility will increase listing prices by about 7.5%. 12 In the meantime, government
subsidies have a negative effect by reducing listing prices by about 5.5%. Both price uncertainty and subsidies
are statistically significant at the 1% level. The results are in line with our hypothesis that uncertainty will
positively influence listing prices while government subsidies will have a counter effect to reduce firms’ listing
prices.
<Insert Table 2 about here >
The effect of physical property characteristics on new apartment listing prices is that large presale
building areas have a positive effect on firms’ prices, while a high rise project will lead to lower listing prices.
11
12
Forecast prices and volatilities are available from the authors on request.
The percentage of price change is calculated as exp(2.137)-1.
17
For individual apartments, large floor area and higher altitude (within the building) will increase listing prices.
Distance to CBD and local amenities such as schools and hospitals all have the expected signs. The closer to
CBD and those amenities the higher listing price is.
Apart from the physical attributes of apartments, firms’ financial characteristics also play an important
role in setting the new apartment prices. Large and profitable firms, as indicated by the firms’ market
capitalization (lyrmc) and return on assets (ROA), tend to set lower listing prices; while growth firms with high
price-earnings ratios (PeRatio) and high debt-to-asset ratios (DaRatio) tend to set prices higher. Firms with
high EBIT to total revenue (EBITTOR) and lower financial leverage, as indicated by higher interest cover (Intcvr),
tend to set their prices higher.
Finally, real GDP and interest rate growth have positive impacts on firms’ listing prices, which could
indicate favourable market conditions for housing. The positive effect of interest rates on housing prices,
particularly during the bubble period prior to the GFC are found in the literature. In their study of how interest
rates affected real housing prices in New Zealand during the period 1999-2009, Shi et al (2014) find that real
interest rates are significantly and positively related to real housing prices, indicating that increases in the
policy rate may not be effective in depressing real housing prices. Similar findings are also seen for the
Australia housing market, e.g. see Leung et al. (2013) among others.
The interaction term between price uncertainty and subsidies, shown in panel A model (2) is negative
and statistically significant at the 1% level. The results imply that the counter effect of government subsidy on
firms’ listing prices is increasing with market volatility. All the variables in model (2) have similar estimates and
expected signs as in model (1).
5.3 The likelihood of firms to list their apartments on the market
18
When to list apartments on the market is a strategic decision by the firm. The results of factors which
could influence the firm’s listing decision are estimated from the Cox proportional hazards model and
reported in Table 3. Results from both Panel A and Panel B are consistent with real options theory, with
market uncertainty delaying listings and subsidies having a counter effect to increase the likelihood of listings.
Moreover, future apartment prices have a positive effect on listings. For example, model (1) shows that future
forecast apartment prices will increase the likelihood of listing by 47%; while future price uncertainty will
deter firms from listing by 56%. Subsidies themselves will increase the likelihood of listing by 77%. Again, the
degrees of difference in the estimates between Panels A and B are because of the different measurements in
volatility.
<Insert Table 3 about here>
Besides market volatility and government subsidies, property attributes also influence the firm’s
decision as to when to list apartments for sale. Large presale areas tend to encourage the firm to list
apartments sooner and large individual apartment areas tend to delay the listings. Firms with projects located
close to CBD tend to delay listings while those whose projects are close to local amenities tend to list sooner.
Among firms’ financial characteristics, firm size (l_yrmc) has the largest impact on the likelihood of listings,
followed by firms’ return on assets (ROA) and debt-to-asset ratios (dbastrt). Other financial variables have
contributed little to determining listing time. For general market conditions, real interest rate increases tend
to encourage firms to list sooner to reduce interest rate risk. In contrast, GDP growth tends to encourage firms
to hold apartments longer.
5.4 Testing interaction effects between uncertainty and subsidy
19
The interaction effects of price uncertainty and subsidies on apartments’ listing prices and listing
speeds are presented in Figure 5. In this figure, non-subsidised firms are compared with subsidised firms,
controlling for all other variables except the interaction term. Panel A shows the joint effects of uncertainty
and subsidy on apartment listing prices, with these increasing with uncertainty. Firms which receive
government subsidies will reduce their apartment listing prices compared to firms which do not receive them.
The extent of price discount from subsidised firms is about 4-26% for 𝐸𝑡 [𝜎𝑑 ] and 10-15% when the forecast
volatility is estimated by 𝐸𝑡 [𝜎𝑐 ].
Panel B shows their joint effects on apartments’ listing speeds. We find that firms’ apartment listing
speed increases with uncertainty 𝐸𝑡 [𝜎𝑑 ] for subsidised firms but decreases for non-subsidised firms. In
contrast 𝐸𝑡 [𝜎𝑐 ] has almost no impact on non-subsidised firms’ apartment listing speed; and positively affect
subsidised firms’ apartment listing speed at a decreasing rate.
<Insert Figure 5 about here>
5.5 Robustness check
The proportionality assumption in the Cox model has been checked through comparing the KaplanMeier observed survivor curves against Cox predicted curves. The results show that the predicted curves
closely follow the observed curves after the early period. Therefore, the proportional hazard assumption is
less likely violated in the Cox model analysis. Allison (1995) argues that including all the relevant covariates in
a Cox model is more important than the assumption of proportionality itself; whenever time-varying
covariates are included in the Cox model, the proportionality assumption is violated. In addition, the
likelihood-ratio test statistic of homogeneity between the subsidised and non-subsidised firms cannot be
20
rejected, which indicates the two groups of firms have similar survivor functions. Our results support using the
subsidies dummy in our empirical analysis to separate the subsidies effect. 13
To validate other hazard functions, we compute a log-survivor plot and log-log survivor plot to
determine the suitability of other parametric models. The idea is that if the empirical data shows an
exponential distribution, the log-survivor plot should yield a straight line. If the empirical data follows a
Weibull distribution, the log-log survivor plot should become a straight line. The plots are presented in
Appendix D. It shows that the hazard rate is definitely not constant but could follow a Weibull distribution. As
a result, we include the Weibull model for comparisons in Table 4.
<Insert Table 4 about here>
This shows that the hazard of listing is monotonically increasing over time as α (log p) is more than one
in all Weibull models. The estimates of uncertainty and subsidies in the Weibull models show even stronger
effects on the timing of listings when compared to the Cox model. Overall, the results from the Weibull model
support our previous finding that uncertainty will decrease the likelihood of listing and government subsidies
will encourage listing. All variables have the expected signs and are consistent with the Cox model results.
Finally, we used the city level land price index to replace the apartment price index in our analysis. This
had little effect on our main findings. 14
6. Policy implications and Conclusions
Correct price setting is crucial for project success in the real estate development business. It requires
the developer to think ahead about future market price movements as there is a trade-off between property
13
14
Statistical results are available from the authors on request.
Estimation results are available from the authors on request.
21
marketing prices and their time-on-market, especially in the presale market for properties under construction.
We find that market volatility has positively affected firms in pricing their products but negatively affected
them for putting apartments on the market. The results suggest that real estate development firms apply real
options theory in pricing their products. Other factors which could affect firm’s pricing behaviours include the
projects’ physical characteristics, firms’ financial position and general market conditions.
We also find that the government subsidies can be influential in firms’ pricing behaviours. Firms which
receive subsidies tend to lower their apartment prices and shorten the period before they put them on sale.
The housing market has become the central focus for many countries in the 21st century. Various monetary
policies and government subsidies have been seen in housing markets both prior to and post the Global
Financial Crisis (GFC) in 2007/2008, for reasons such as vote trading, remedying market imperfections and
social policy objectives. Despite these conditions, their effect on real estate development firm’s pricing
behaviours is in line with the options theory.
22
Acknowledgements
The authors would like to thank Jianguo Chen and Oscar Lau for comments and suggestions. The authors also
thank Wei Zhang from Tsinghua University for her excellent research assistance.
23
References
Allison, P.D., 1995. Survival analysis using the SAS system. SAS Institute, Cary, NC.
Arbel, Y., Ben-Shahar, D., Gabriel, S., Tobol, Y., 2010. The local cost of terror: effects of the second Palestinian intifada on
Jerusalem house prices. Regional Science and Urban Economics 40, 415-426.
Ball, L., Romer, D., 1990. Real Rigidities and the Non-Neutrality of Money. The Review of Economic Studies 57, 183-203.
Bucchianeri, G.W., Minson, J.A., 2013. A homeowner's dilemma: Anchoring in residential real estate transactions.
Journal of Economic Behavior & Organization 89, 76-92.
Bulan, L., Mayer, C., Somerville, C.T., 2009. Irreversible investment, real options, and competition: Evidence from real
estate development. Journal of Urban Economics 65, 237-251.
Campos, J., Ericsson, N.R., Hendry, D.F., 2005. General-to-specific modelling: an overview and selected bibliography.
Board of Governors of the Federal Reserve System, International Finance Discussion Papers #838.
Capozza, D.R., Li, Y., 2001. Residential Investment and Interest Rates: An Empirical Test of Land Development as a Real
Option. Real Estate Economics 29, 503-519.
Case, K.E., Shiller, R.J., 1989. The efficiency of the market for single-family homes. The American Economic Review 79,
125-137.
Chen, X., Lee, C.-W.J., Li, J., 2008. Government assisted earnings management in China. Journal of Accounting and Public
Policy 27, 262-274.
Clapp, J.M., Eichholtz, P., Lindenthal, T., 2013. Real option value over a housing market cycle. Regional Science & Urban
Economics 43, 862-874.
Clapp, J.M., Jou, J.-B., Lee, T., 2012. Hedonic Models with Redevelopment Options under Uncertainty. Real Estate
Economics 40, 197-216.
Clapp, J.M., Salavei, K., 2010. Hedonic pricing with redevelopment options: A new approach to estimating depreciation
effects. Journal of Urban Economics 67, 362-377.
Claro, S., 2006. Supporting inefficient firms with capital subsidies: China and Germany in the 1990s. Journal of
Comparative Economics 34, 377-401.
Cox, D.R., 1972. Regression Models and Life-Tables. Journal of the Royal Statistical Society. Series B (Methodological) 34,
187-220.
Cunningham, C.R., 2006. House price uncertainty, timing of development, and vacant land prices: evidence for real
options in Seattle. Journal of Urban Economics 59, 1-31.
Geltner, D., 1989. On the use of the Financial Option Price Model to Value and Explain Vacant Urban Land. Real Estate
Economics 17, 142-158.
Geltner, D., Miller, N., Clayton, J., Eichholtz, P., 2007. Commercial real estate analysis & investments, 2nd ed. Thomson
South-Western, Mason.
24
Geltner, D., Riddiough, T., Stojanovic, S., 1996. Insights on the Effect of Land Use Choice: The Perpetual Option on the
Best of Two Underlying Assets. Journal of Urban Economics 39, 20-50.
Grovenstein, R., Kau, J., Munneke, H., 2011. Development Value: A Real Options Approach Using Empirical Data. The
Journal of Real Estate Finance and Economics 43, 321-335.
Holland, A.S., Ott, S.H., Riddiough, T.J., 2000. The Role of Uncertainty in Investment: An Examination of Competing
Investment Models Using Commercial Real Estate Data. Real Estate Economics 28, 33-64.
Lee, E., Walker, M., Zeng, C., 2014. Do Chinese government subsidies affect firm value? Accounting, Organizations and
Society 39, 149-169.
Leung, C.K.Y., Shi, S., Tang, E.H., 2013. Commodity house prices. Regional Science and Urban Economics 43, 875-887.
Leung, T.C., Tsang, K.P., 2013. Anchoring and loss aversion in the housing market: Implications on price dynamics. China
Economic Review 24, 42-54.
Lucas, R.E., Jr., Sargent, T., J., 1981. Rational expectations and econometric practice. The University of Minnesota Press,
Minneapolis.
Myers, S.C., 1977. Determinants of corporate borrowing. Journal of Financial Economics 5, 147-175.
Rotemberg, J.J., 2005. Customer anger at price increases, changes in the frequency of price adjustment and monetary
policy. Journal of Monetary Economics 52, 829-852.
Shi, S., Jou, J.-B., Tripe, D., 2014. Can interest rates really control house prices? Effectiveness and implications for
macroprudential policy. J Bank Financ 47, 15-28.
Trigeorgis, L., 1996. Real options. The MIT Press.
Williams, J., 1991. Real estate development as an option. The Journal of Real Estate Finance and Economics 4, 191-208.
Wu, J., Deng, Y., Liu, H., 2014. House price index construction in the nascent housing market: the case of China. Journal
of Real Estate Finance and Economics 48, 522-545.
Zivot, E., Andrews, D.W.K., 1992. Further evidence on the great crash, the oil-price shock and the unit-root hypothesis.
Journal of Business and Economic Statistics 10, 251-270.
25
Appendix A: Variable definitions
Variable
Description
Data Source
A. Apartment units and their
attributes
Apartment listing price
lrprice
Log of real apartment sale price, denominated in RMB
Apartment floor area
lunit_area
Log of the apartment floor area, denominated in square meter
Apartment floor number
lunit_floor
Log of the apartment floor number
Presale building area
lpre_area
Log of total project building area specified in the presale permit, denominated in square meter
Presale building floor
lpre_floor
Log of average total number of floors of the project
Distance to CBD
ld_cbd
Log of the direct distance of the apartment to CBD, denominated in meter
Distance to local
amenities
Permit-to-listing
ld_amenity
Log of the average direct distance to the nearest subway station, 3A hospital and key primary
school, denominated in meter
The time interval of a apartment from getting pre-sale permit to list on the market, denominated
in months
The physical properties and the
location information of the residence
are from the online signing up data
of newly built commercial housing
in Beijing, collected by the
MOHURD; the GIS coordinates of
residence and the corresponding
distance are calculated by Real
Estate Institution, Tsinghua
University
Acronym
ptl
B. Firm level variables
Firm size
lyrmc
Log of firm's yearly market capitalisation, denominated in RMB
Price-to-earnings ratio
PeRatio
The current closing price / the sum of last four quarters' earnings per share
Debt-to-asset ratio
DaRatio
Total liabilities / total assets × 100
Interest cover
Intcvr
Earnings before interest and tax / ( financial expense + capitalized interest expense)
Return on asset
ROA
Net profit / average total assets
EBIT to total revenue
EBITTOR
Earnings before interest and tax / total operating revenue
C. Market level
variables
Interest rate growth
rint_growth
GDP growth
rgdp_growth
Real quarterly interest rate growth of average People Bank of China (PBOC) benchmark lending
rate of one to three years (including 3 years)
Real quarterly district GDP growth rate in Beijing
Consumers price index
CPI
Quarterly Consumer Price Index in Beijing
26
RESSET Financial Research
Database
National Bureau of Statistics of
China
Appendix B: New apartment sales in Beijing, 2006Q1 – 2008Q4
Variable
Observations
Mean
STD
Min
Median
Max
lrprice
111379
13.822
0.624
11.983
13.742
16.113
lunit_area
111379
4.701
0.418
3.402
4.696
5.886
lunit_floor
111379
1.871
0.841
0
1.946
3.466
Panel A: Apartments sold by listed firms
lpre_area
111379
10.929
0.715
8.546
10.964
12.575
lpre_floor
111379
2.684
0.547
0
2.833
3.466
ld_cbd
111379
9.323
0.727
7.152
9.437
11.299
ld_amenity
111379
8.304
0.916
6.181
8.163
11.073
lrprice
170026
13.530
0.620
11.463
13.464
16.087
lunit_area
170026
4.623
0.397
3.413
4.604
5.885
lunit_floor
170026
1.819
0.844
0
1.946
3.807
Panel B: Apartments sold by non-listed firms
lpre_area
170026
10.617
0.694
8.527
10.654
12.460
lpre_floor
170026
2.613
0.562
0
2.708
4.007
ld_cbd
170026
9.553
0.675
6.715
9.559
11.422
ld_amenity
170026
8.448
0.951
5.744
8.318
11.205
lrprice
281405
13.646
0.638
11.463
13.572
16.113
lunit_area
281405
4.654
0.407
3.402
4.634
5.886
lunit_floor
281405
1.840
0.843
0
1.946
3.807
Panel C: Apartments sold by all firms
lpre_area
281405
10.740
0.719
8.527
10.762
12.575
lpre_floor
281405
2.641
0.557
0
2.773
4.007
ld_cbd
281405
9.462
0.705
6.715
9.517
11.422
ld_amenity
281405
8.391
0.940
5.744
8.277
11.205
This table summarises property characteristics of all new apartment sales in Beijing over the 2006 to 2008 sample period. Panel A
reports apartments sold by listed firms, Panel B is apartments sold by non-listed firms and Panel C is apartments sold by all firms.
27
Appendix C: Financial characteristics of listed real estate development firms in Beijing, 2006 - 2008
Variable
Observations
Mean
STD
Min
Median
Max
lyrmc
58
21.223
1.014
19.622
21.019
23.898
PeRatio
58
30.840
108.989
-474.212
29.945
363.662
DaRatio
64
77.138
73.636
7.677
63.886
511.728
Intcvr
64
17.062
70.042
-94.909
2.609
465.354
ROA
64
0.009
0.039
-0.165
0.012
0.175
EBITTOR
64
0.020
0.575
-4.159
0.062
0.717
22.361
29.325
69.428
608.146
64.313
290.422
4.069
5315.246
Year=2006
Year=2007
lyrmc
60
22.544
1.683
PeRatio
60
74.740
273.714
DaRatio
65
69.136
43.305
19.714
1495.504
19.461
Intcvr
65
90.942
686.478
-629.470
ROA
64
0.025
0.043
-0.070
0.020
0.265
EBITTOR
65
-0.013
0.877
-6.328
0.127
1.128
Year=2008
lyrmc
61
22.375
1.626
19.714
22.107
28.619
PeRatio
61
65.014
253.045
-429.426
26.225
1861.363
DaRatio
65
63.455
25.778
9.929
60.697
179.820
Intcvr
65
20.566
143.303
-250.722
5.321
1096.603
ROA
64
0.034
0.132
-0.233
0.016
0.964
EBITTOR
65
0.004
1.304
-10.185
0.149
0.952
This table summarises the financial characteristics of 65 listed real estate development firms in Beijing, trading either on the Shanghai
or Shenzhen Stock market over the 2006 to 2008 sample period.
28
Appendix D: Log-survivor and log-log survivor plots based on the empirical data
Log-Survivor Plot
1.8
1.6
-logS(t)
1.4
1.2
1.0
0.8
0.6
0.4
0
1
2
3
4
5
6
7
Months (t)
Log-log Survivor Plot
.3
.2
Log(-logS(t))
.1
.0
-.1
-.2
-.3
-.4
.0
.1
.2
.3
.4
.5
.6
.7
.8
Log of months (t)
This figure plots the relationship between apartments’ survivor function and their listing time (in months), based on the listed firms
over the 2006 to 2008 sample period. The figure is used for determining the suitability of applying certain parametric hazard models,
such as exponential and Weibull models.
29
Table 1: Summary statistics
Variable
Observations
Mean
STD
Min
Median
Panel A: Apartments sold by 65 listed firms
13.880
0.660
12.248
13.802
Max
lrprice
56970
lunit_area
56970
4.706
0.433
3.414
4.697
5.886
lunit_floor
56970
1.847
0.834
0.000
1.946
3.466
lpre_area
56970
10.936
0.727
8.546
11.017
12.460
lpre_floor
56970
2.656
0.542
0.000
2.773
3.466
ld_cbd
56970
9.413
0.750
7.262
9.502
11.024
ld_amenity
56970
8.278
1.031
5.842
8.106
10.774
Panel B:Financial characteristics of 65 listed firms
22.162
1.652
19.708
21.852
51.303
56.836
71.909
167.083
69.952
44.202
24.348
63.518
3.743
42.788
241.055
200.186
0.021
0.061
-0.165
0.020
lyrmc
61
PeRatio
61
DaRatio
65
Intcvr
65
ROA
65
EBITTOR
65
0.004
rint_growth
12
0.004
rgdp_growth
228
0.029
0.022
CPI
12
1.073
0.029
all
1,513
0.650
-4.136
16.094
28.972
313.762
269.724
1846.202
0.406
0.125
0.615
0.010
0.074
-0.025
0.028
0.132
1.042
1.065
1.129
Panel C: Market conditions
0.054
-0.143
Panel D: Permit-to-listing by presale permits (months)
4.697
4.664
1
2
18
Listed*
522
4.268
4.342
1
2
18
Non-listed
991
4.923
4.811
1
2
18
Panel E: Permit-to-listing by apartments (months)
3.084
3.313
1
2
all
281,405
Listed*
111,379
3.010
3.233
1
2
18
Non-listed
170,026
3.132
3.364
1
2
18
Panel F: Permit-to-listing by firms (months)
5.199
4.167
1
4
18
4.745
17
all
Listed*
503
90
3.429
1
4
18
413
5.297
4.309
1
4
18
Non-listed
* There are 90 listed companies in the property transaction dataset, but only 65 listed companies are used in the
study due to the available financial data of the company. The sample is for new apartments sold in Beijing between
2006 and 2008. Panel A reports the physical characteristics of apartments sold by the listed 65 firms. Panel B reports
the financial characteristics of the 65 listed firms. Panel C reports the market conditions. Real GDP growth
(rgdp_growth) is reported at district levels. There are 19 districts in Beijing, and total observations are calculated as
19x12=228. Panels D, E and F report the time length from permit to listing in months. All the variables are defined
in Appendix A.
30
Table 2: The effect of uncertainty and government subsidy on new apartment listing prices
Panel A:Market volatility estimates
based on 𝐸𝑡 [𝜎𝑑 ]
(1)
(2)
Dependant variable: Log of apartment real listing price
2.137 ***
forecast price volatility
(0.078)
2.563
***
-0.087
forecast volatility*subsidy
-0.664
Panel B: Market volatility estimates
based on 𝐸𝑡 [𝜎𝑐 ]
(3)
(4)
2.200
***
(0.212)
-0.057
***
(0.006)
lpre_floor
-0.197
***
-0.349**
***
0.024
1.059
***
0.020
***
-0.040
-0.267
-0.073
**
0.000
***
0.000
***
0.005
-1.186
0.056
3.756
constant
0.615
***
0.000
***
0.005
***
-1.213
***
0.062
***
3.757
***
0.373
0.021
-0.149
-0.173
-0.132
0.000
***
***
***
***
***
***
1.087
0.020
***
-0.149
***
-0.176
***
-0.131
***
0.000
*
-0.001
***
-0.603
0.005
0.002
(0.006)
(0.006)
***
2.915
(0.103)
(0.114)
0.033
-0.239
(0.177)
12.760
12.730
14.270
14.270
(587.1)
(.)
(.)
(349.3)
District fixed effect
yes
yes
yes
yes
Firm fixed effect
yes
yes
yes
yes
31
***
***
*
(0.001)
(0.151)
(0.132)
***
(0.000)
(0.149)
(0.115)
***
(0.007)
0.000
(0.116)
***
(0.006)
(0.000)
2.859
***
(0.008)
0.000
-0.604
***
(0.001)
(0.001)
***
-0.031
(0.000)
-0.001
***
(0.003)
(0.000)
(0.069)
***
***
(0.007)
(0.005)
***
1.087
-0.072
(0.003)
(0.006)
(0.064)
***
***
(0.008)
(0.000)
***
-0.032
***
(0.004)
(0.001)
(0.000)
(0.069)
rgdp_growth
0.000
***
(0.005)
rint_growth
-0.071
***
(0.003)
(0.000)
(0.063)
ebittor
-0.274
***
(0.000)
roa
***
(0.008)
(0.000)
dbastrt
-0.036
-0.072
-0.089
(0.005)
(0.003)
(0.008)
(0.000)
intcvr
***
(0.011)
(0.008)
pe_ratio
0.019
***
(0.004)
(0.001)
(0.008)
l_yrmc
1.060
***
(0.011)
ld_amenity
***
(0.004)
(0.001)
ld_cbd
0.023
-0.097
(0.004)
(0.003)
(0.004)
lunit_floor
***
(0.005)
(0.003)
lunit_area
-0.196
**
(0.146)
(0.006)
(0.005)
lpre_area
-0.039
***
(0.264)
(0.106)
subsidy
2.436
***
***
Year fixed effect
yes
yes
yes
yes
Season fixed effect
yes
yes
yes
yes
36,474
36,474
52,516
52,516
Number of obs
0.939
0.940
0.913
0.913
AdjRsq
This table presents OLS regression of a apartment listing price (lrprice) on market uncertainty and government
subsidy, controlled for apartment characteristics (X), firm’s financial characteristics (Y) and other economic
conditions (Z) as well as unreported district, firm, year and season fixed effects on the samples sold by the 65 listed
firms. Panel A reports the results when the market uncertainty is measured at district levels based on two-quarterahead forecast of Et [σd ]. Panel B reports the results when the market uncertainty is measured at city level based on
four-quarter-ahead forecast of Et [σc ]. The regression model is pijt = α + g it + g it ∗ Et [σ# ] + Et [σ# ] + Xit′ β +
Yjt′ γ + Zit′ δ + fj + Di + Sit + Tit + εijt , where pijt is the log listing price for apartment i by developer j at time t. The
subsidy variable g it equals to 1 when the firm receives a subsidy, and otherwise 0. Et [σ# ] represents the expected
market uncertainty, # =d or c. The term Xit is a vector of property attributes comprising apartment area, apartment
floor, presale building area, presale building floor, distance to CBD and distance to local amenities (school and
hospital). The term Yjt is a vector of the firm’s financial characteristics including size, price-to-earnings ratio, debtto-assets ratio, interest cover, return on assets, and EBIT to total revenue. The term Zit is a vector of market
conditions including interest rate changes and district level real GDP growth. fj is the fixed effect for firm j and Di is
the district (sub-market) in which the property is located. The vectors Sit and Tit are dummy variables for seasonal
and year effects, respectively. εijt is the error term. Standard errors shown in parentheses are based on standard
errors adjusted for heteroskedasticity. Obs denotes the number of apartments and AdjRsq is adjusted R2. The sample
period is from 2006 to 2008. Statistical significance: *<0.10, **<0.05, ***<0.01.
32
Table 3: The effect of uncertainty and government subsidy on new apartment listing speed
Panel A: Market volatility estimates
based on 𝐸𝑡 [𝜎𝑑 ]
(1)
(2)
Dependant variable: the hazard rate at time t for property i
0.382 ***
0.450
forecast apartment price
(0.050)
(0.051)
forecast volatility
-0.830
***
(0.244)
-6.413
***
11.130
0.699
***
(0.059)
***
(0.332)
forecast volatility*subsidy
Panel B: Market volatility estimates
based on 𝐸𝑡 [𝜎𝑐 ]
(3)
(4)
-3.107
***
(0.426)
0.573
(0.070)
lpre_floor
-0.124
***
0.059
lunit_floor
ld_cbd
-0.144
***
District dummy
0.084
***
(0.013)
***
-0.184
0.105
***
-0.169
(0.008)
(0.008)
(0.007)
(0.007)
-0.724
***
0.377
-0.302
0.000
0.001
-0.031
0.040
-0.004
0.544
-5.285
-0.815
***
(0.046)
0.467
***
-0.312
***
0.000
***
0.001
***
-0.027
***
0.040
***
-0.001
***
0.514
***
-1.710
0.001
-0.018
0.036
0.001
***
*
0.181
-0.290
0.000
***
0.001
***
-0.019
***
***
***
(0.002)
***
0.027
***
(0.007)
***
0.001
***
(0.000)
0.287
0.851
(0.218)
***
-12.030
(0.896)
(0.883)
(0.889)
(0.972)
yes
yes
yes
yes
33
***
(0.000)
(0.214)
-7.419
***
(0.000)
(0.000)
(0.181)
***
***
(0.006)
(0.001)
***
0.000
***
(0.018)
(0.002)
(0.007)
***
***
(0.000)
(0.003)
***
-0.290
-0.549
***
(0.027)
(0.000)
(0.000)
***
***
(0.018)
(0.000)
***
0.282
***
(0.039)
(0.026)
(0.020)
***
***
(0.039)
(0.030)
***
-0.607
***
(0.013)
0.000
(0.183)
rgdp_growth
***
-0.164
(0.017)
0.002
(0.001)
rint_growth
***
0.007
(0.007)
ebittor
-0.164
(0.017)
0.000
(0.003)
roa
***
***
(0.064)
(0.016)
(0.000)
dbastrt
(0.063)
0.807
(0.016)
(0.000)
intcvr
***
(0.018)
(0.020)
pe_ratio
-0.195
0.608
(0.018)
(0.030)
l_yrmc
***
(0.012)
(0.046)
ld_amenity
0.073
***
***
(0.559)
(0.018)
(0.012)
lunit_area
-0.126
-0.165
-7.480
***
(0.070)
(0.019)
lpre_area
0.248
***
***
(0.483)
(0.426)
subsidy
0.768
(0.060)
***
***
Firm fixed effects
Year dummy
yes
yes
yes
yes
no
no
no
no
Season dummy
no
no
no
no
Number of obs
54,672
54,672
63,801
63,801
9,985
10,244
12,047
12,227
LR Chi-square
This table presents the proportional-hazard Cox regression of an apartment listing time on market uncertainty and
government subsidy, controlled for apartment characteristics (X), firm’s financial characteristics (Y) and other
economic conditions (Z) as well as unreported district and firm fixed effects on the samples sold by the 65 listed
firms. Panel A reports the results when the market uncertainty is measured at district levels based on two-quarterahead forecast. Panel B reports the results when the market uncertainty is measured at city level based on fourquarter-ahead forecast. The Cox regression model is log λ(t; H) = log 𝜆0 (𝑡) + Hβ; and Hβ = 𝐸𝑡 [𝑝# ] + 𝑔𝑖𝑖 + 𝑔𝑖𝑖 ∗
𝐸𝑡 [𝜎# ] + 𝐸𝑡 [𝜎# ] + 𝑋𝑖𝑖′ 𝛽 + 𝑌𝑗𝑗′ 𝛾 + 𝑍𝑖𝑖′ 𝛿 + 𝑓𝑗 + 𝐷𝑖 + 𝜑𝑖𝑖 , where λ(t; Η) is the apartment’s hazard function of listing,
λ0 (t) is the baseline hazard, H is a vector of covariates and β is a vector of parameters. Et [p# ] is the log of expected
market price movement, # =d or c. The subsidy variable 𝑔𝑖𝑖 equals to 1 when the firm receives a subsidy, and
otherwise 0. Et [σ# ] represents the expected market uncertainty, # =d or c. The term Xit is a vector of property
attributes comprising apartment area, apartment floor, presale building area, presale building floor, distance to CBD
and distance to local amenities (school and hospital). The term 𝑋𝑖𝑖 is a vector of property attributes comprising
apartment area, apartment floor, presale building area, presale building floor, distance to CBD and distance to local
amenities (school and hospital). The term 𝑌𝑗𝑗 is a vector of the firm’s financial characteristics including size, priceto-earnings ratio, debt-to-assets ratio, interest cover, return on assets, and EBIT to total revenue. The term 𝑍𝑖𝑖 is a
vector of market conditions including interest rate changes and district level real GDP growth. 𝑓𝑗 is the fixed effect
for firm j, 𝐷𝑖 is the district in which the property is located and d 𝜑𝑖𝑖 is the white noise. Standard errors are reported
in parentheses. Breslow method is used for control ties. Obs denotes the number of apartment-month and LR is
likelihood ratio. The sample period is from 2006 to 2008. Statistical significance: *<0.10, **<0.05, ***<0.01.
34
Table 4: Model comparisons
Panel A: Market volatility estimates based on 𝐸𝑡 [𝜎𝑑 ]
(1)
(2)
Cox
Weibull
Dependant variable: the hazard rate at time t for property
i
0.382
0.231
forecast apartment price
forecast volatility
(4)
(5)
(6)
(7)
(8)
Cox
Weibull
Cox
Weibull
Cox
Weibull
0.450
0.655
0.699
0.434
0.768
0.506
(0.05)
(0.05)
(0.05)
(0.06)
(0.06)
(0.07)
(0.06)
(0.07)
-0.830
-3.429
-6.413
-12.430
-3.107
-7.730
-0.165
-0.854
(0.24)
(0.29)
(0.33)
(0.36)
(0.43)
(0.48)
(0.48)
(0.55)
11.130
24.470
-7.480
-15.720
(0.43)
(0.50)
(0.56)
(0.57)
forecast volatility*subsidy
subsidy
(3)
Panel B: Market volatility estimates based on 𝐸𝑡 [𝜎𝑐 ]
0.573
2.262
0.248
1.097
0.608
2.519
0.807
3.069
(0.07)
(0.07)
(0.07)
(0.07)
(0.06)
(0.06)
(0.06)
(0.07)
constant
log p
24.600
24.110
17.490
16.240
(0.54)
(0.56)
(0.67)
(0.67)
1.450
1.465
1.472
1.477
(0.00)
(0.00)
(0.00)
(0.00)
Property characteristics
yes
yes
yes
yes
yes
yes
yes
yes
Firm's financial characteristics
yes
yes
yes
yes
yes
yes
yes
yes
Market conditions
yes
yes
yes
yes
yes
yes
yes
yes
District dummy
Firm fixed effects
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
no
no
no
no
no
no
no
no
Year dummy
Season dummy
no
no
no
no
no
no
no
no
Number of obs
54,480
54,480
54,480
54,480
63,801
63,801
63,801
63,801
9,909
54,168
10,557
56,209
12,047
63,111
12,228
63,873
LR Chi-square
This table compares the results of Cox model with the parametric Weibull model for an apartment listing time on market uncertainty and government subsidy, controlled for
apartment characteristics (X), firm’s financial characteristics (Y) and other economic conditions (Z) as well as unreported district and firm fixed effects on the samples sold by the
65 listed firms. Panel A reports the results when the market uncertainty is measured at district levels based on two-quarter-ahead forecast. Panel B reports the results when the
market uncertainty is measured at city level based on four-quarter-ahead forecast. The Cox regression model is log λ(t; H) = log 𝜆0 (𝑡) + Hβ; and Hβ = 𝐸𝑡 [𝑝# ] + 𝑔𝑖𝑖 + 𝑔𝑖𝑖 ∗
𝐸𝑡 [𝜎# ] + 𝐸𝑡 [𝜎# ] + 𝑋𝑖𝑖′ 𝛽 + 𝑌𝑗𝑗′ 𝛾 + 𝑍𝑖𝑖′ 𝛿 + 𝑓𝑗 + 𝐷𝑖 + 𝜑𝑖𝑖 , where λ(t; Η) is the apartment’s hazard function of listing, λ0 (t) is the baseline hazard, H is a vector of covariates and β is a
vector of parameters. 𝐸𝑡 [p# ] is the log of expected new apartment price movement, # =c or d. The subsidy variable 𝑔𝑖𝑖 equals to 1 when the firm receives a subsidy, and otherwise
0. 𝐸𝑡 [𝜎# ] represents the expected new apartment price volatility, # =c or d. The term 𝑋𝑖𝑖 is a vector of property attributes comprising apartment area, apartment floor, presale
35
building area, presale building floor, distance to CBD and distance to local amenities (school and hospital). The term 𝑌𝑗𝑗 is a vector of the firm’s financial characteristics including
size, price-to-earnings ratio, debt-to-assets ratio, interest cover, return on assets, and EBIT to total revenue. The term 𝑍𝑖𝑖 is a vector of market conditions including interest rate
changes and district level real GDP growth. 𝑓𝑗 is the fixed effect for firm j, 𝐷𝑖 is the district in which the property is located and d 𝜑𝑖𝑖 is the white noise. In the Weibull model, the
baseline hazard function is specified as 𝜆0 (𝑡) = 𝛾𝛾𝑡 𝛼−1 . When α = 1, the Weibull hazard function reduces to a constant model. If α > 1, the hazard is monotonically increasing;
For α < 1, the hazard is monotonically decreasing. Standard errors are reported in parentheses. Breslow method is used for control ties. Obs denotes the number of apartmentmonth and LR is likelihood ratio. The sample period is from 2006 to 2008.
36
Figure 1: Administrative districts of Beijing metropolitan area
37
Figure 2: Estimated district level real price indices of newly-built apartment market, 2006Q12008Q4
4,000
Beijing Districts
3,600
3,200
2,800
2,400
2,000
1,600
1,200
800
Q1
Q2
Q3
2006
Q4
Q1
Q2
Q3
Q4
Q1
Q2
2007
Q3
Q4
2008
CHANGPING
FENGTAI
REST OF CITY
CHAOYANG
HAIDIAN
This figure plots the calculated new apartment price indices for main districts in Beijing, based on all new apartment
transactions between 2006 and 2008. Price indices are estimated based on the hedonic regression model as follows:
pidt = αdt + X ′idt β + µidt , where pidt is the log sale price for apartment i in district d at calendar quarter t. The term
Xit is a vector of property attributes comprising apartment area, apartment floor, presale building area, presale
building floor, distance to CBD and average distance to local amenities (school and hospital), while µidt is white
noise. Property attributes are held constant in calculating district price movements over the studied period.
38
Figure 3: Estimated district level real price volatility of newly-built apartment market, 2006Q42008Q4
30%
Beijing Districts
25%
20%
15%
10%
5%
0%
Q4
2006
Q1
Q2
Q3
Q4
Q1
2007
CHANGPING
FENGTAI
RESTOFCITY
Q2
Q3
Q4
2008
CHAOYANG
HAIDIAN
This figure plots the forecasted two-quarter-ahead new apartment price volatilities for main districts in Beijing,
based on the district level new apartment price indices between 2006 and 2008. Price volatilities are estimated based
2
̅ � /2;
�𝑑,𝑡 /𝑝𝑑,𝑡 ; 𝐸𝑡 [𝜎𝑑 ] = �∑2𝑛=1�𝑓𝑑,𝑡−𝑛 − 𝑓𝑑,𝑡
on a set of equations as follows: 𝐸𝑡 [𝑝𝑑 ] = 𝑝𝑑,𝑡−2 + 𝜔𝑑,𝑡 ; 𝑓𝑑,𝑡 = 𝜔
1
̅ = ∑2𝑛=1 𝑓𝑑,𝑡−𝑛 , where 𝐸𝑡 [𝑝𝑑 ] is the two-quarter-ahead forecast new apartment price for the district d, 𝑝𝑑,𝑡 is the
𝑓𝑑,𝑡
2
district apartment price at time t, 𝑝𝑑,𝑡−2 is the district apartment price at time t-2 and 𝜔𝑑,𝑡 is the district level
̅ is the average forecasting error and 𝐸𝑡 [𝜎𝑑 ] is the
forecasting error. 𝑓𝑑,𝑡 is the relative district forecasting errors, 𝑓𝑑,𝑡
forecast district price volatilities.
39
Figure 4: Forecast city level real price and volatility of newly-built apartment market, 2004Q12008Q4
12%
Beijing City
14,000
10%
12,000
8%
10,000
6%
4%
8,000
2%
6,000
0%
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4
2004
2005
2006
2007
2008
Real new apartment price index
Four quarters ahead forecasted price index
Four quarters ahead forecasted price volatility
This figure plots the city level new apartment price index and forecasted four-quarter-ahead new apartment prices
and volatilities. Forecast apartment prices are based on the regression model: 𝐸𝑡 [𝑝𝑐 ] = 𝜌0 + 𝜌1 𝑝𝑐,𝑡−4 + 𝜌2 𝑝𝑐,𝑡−5 +
𝜌3 𝑝𝑐,𝑡−6 + 𝜌4 𝑝𝑐,𝑡−7 + 𝐵𝑐,𝑡−4 + 𝑒𝑐,𝑡 , where 𝐸𝑡 [𝑝𝑐 ] is the expected city level new apartment price at time t, 𝑝𝑐,𝑡−4 is
the city level new apartment price at time t-4, so on for others. 𝐵𝑐,𝑡−4 is the potential structural break as indicated
from the Zivot-Andrews (1992) unit root tests and 𝑒𝑐,𝑡 is the city level forecasting error. General-to-specific
approach is used for model selection and the structural break is taken at June 2006 in the model. Price volatilities are
̅ �2 /4; 𝑓𝑐,𝑡
̅ =
estimated based on a set of following equations: 𝑓𝑐,𝑡 = 𝑒̂𝑐,𝑡 /𝑝𝑐,𝑡 ; 𝐸𝑡 [𝜎𝑐 ] = �∑4𝑛=1�𝑓𝑐,𝑡−𝑛 − 𝑓𝑐,𝑡
1
∑4𝑛=1 𝑓𝑐,𝑡−𝑛 , where 𝑓𝑐,𝑡 is the relative city level forecasting errors, 𝑒̂𝑐,𝑡 is the calculated city level forecasting error
̅ is the average forecasting error and
from above price regression and 𝑝𝑐,𝑡 is the actual city level price at time t. 𝑓𝑐,𝑡
𝐸𝑡 [𝜎𝑐 ] is the forecast city level price volatilities.
4
40
Figure 5: Interaction effects
Panel A: Interaction effects on apartment listing price
District level two-quarter forecast
City level four-quarter forecast
2.2
1.30
No subsidy
Subsidy
No subsidy
Subsidy
1.25
1.20
1.8
Apartment listing price
Apartment listing price
2.0
1.6
1.4
1.2
1.15
1.10
1.05
1.00
1.0
0.95
0.90
0.8
.00
.04
.08
.12
.16
.20
.24
.28
.32
.00
.01
.02
.03
.04
Expected price uncertainty
.05
.06
.07
.08
.09
.10
.11
.08
.09
.10
.11
Expected price uncertainty
Panel B: Interaction effects on apartmetn listing speed
City level four-quarter forecast
District level two-quarter forecast
2.4
6
No subsidy
Subsidy
No subsidy
subsidy
2.2
Apartment listing speed
Apartment listing speed
5
4
3
2
1
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0
.00
.04
.08
.12
.16
.20
Expected price uncertainty
.24
.28
.32
.00
.01
.02
.03
.04
.05
.06
.07
Expected price uncertainty
This figure plots the interactive relationship between market uncertainty and government subsidy on apartment listing price in Panel A and on apartment listing speed in Panel B,
controlled for all other variables except the interaction term in the respective models. Apartment listing price and listing speed are set at one for non-subsidised firms and compared
with subsidised firms.
41