Discussion Paper No. 990

WHAT ACCOUNTFOR THE DIFFERENCESIN RENT-PRICE RATIOAND TURNOVER RATE?
A SEARCH-AND-MATCHING APPROACH
Daisy J. Huang
Charles Ka Yui Leung
Chung-Yi Tse

February 2017

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Title: What account for the differences in rent-price ratio and turnoverrate? A search-and-matching approach
Author: Daisy J. Huang, Charles Ka Yui Leung and Chung-Yi TseThis version: February, 2017
Abstract
We build an on-the-house-search model and show analytically that the rent-to-price ratio(or rental yield) and turnover rate, which are frequently used metrics for the housing
market, are jointly determined in equilibrium. We therefore adopt a simultaneous equation
approach on matched sale-rental pairs in our empirical investigation, as a housing unit
cannot be owner-occupied and renter-occupied at the same time. Our empirical results
confirm a higher turnover rate is associated with a lower rent-to-price ratio, as predicted by
the model. Furthermore, our results suggest a form of “dichotomy” in the empiricaldeterminants of rental yield and turnover at the real-estate-development (RED) level: thedemographic structure, and past return performance affect its turnover rate, while
popularity, human capital environment, mortgage burden, and long run rent growthdetermine the rental yield. No evidence of “thick market effect” is found. The robustness of
our results are established through a series of tests. In addition to these findings, ourtractable search-theoretic model, a ranking of more than 130 RED in Hong Kong based on
the popularity index we construct, and the estimated brand-premium for different major
real estate developers may also carry independent research and practical interests.
Keywords: housing rental yield, turnover rate, bootstrap, leave-one-out cross validation(LOOCV), matching estimator, 3 stages least squares (3SLS)JEL Classification Numbers: D10, G10, R21

Acknowledgement: We are grateful to Been-Lon Chen, Nan-Kuang Chen, Man Cho,
Gangzhi Fan, Shihe Fu, Richard Green, Cheuk Yin Ho, Mingming Jiang, Kamhon Kan,
Yuichiro Kawaguchi, Shian-Yu Liao, Steve Malpezzi, Masao Ogaki, Tim Riddiough, Jay SaAadu, Jim Shilling, Jingjing Tang, Wei Xiao, Haijian Zeng, seminar participants at the
Asia-Pacific Real Estate Research Symposium (2015, Cheng Du), Global Real Estate
Submit (2015, Washington, D.C.), Taiwan Economic Association meeting (2016, Taipei),
City University of Hong Kong, Guangxi University, anonymous referees for helpfulcomments. Financial support from the City University of Hong Kong and University ofHong Kong are gratefully acknowledged. Part of this research is conducted when Leung is avisiting scholar of ISER, Osaka University, whose hospitality is gratefully acknowledged.
Tommy Chan provides capable research assistance. The usual disclaimer applies.
Correspondence: Huang: Institute of Economics and Finance, Nanjing Audit University,
No.86 Yushan Rd(W), Pukou, Nanjing, P.R.China, 211815, daisy@nau.edu.cn ; Leung,
Department of Economics and Finance, City University of Hong Kong, Kowloon Tong, Hong
Kong, kycleung@cityu.edu.hk ; Tse, School of Economics and Finance, University of Hong
Kong, Pokfulam, Hong Kong, tsechung@econ.hku.hk .

1Introduction

Rent-to-price ratio and turnover are both key elements in discussions of the housing
market. One example is how the rent-to-price ratio, also known as the (gross) rental
yield, is often used in the media and in the academic literature as a metric of the possibility that a “bubble” has formed.1 Similarly, turnover, also known as the trading ortransaction volume, is a commonly used metric for the “status” of the housing market.2 However, the equilibrium determination of rent-to-price ratio is under-exploredin empirical works and policy discussion, making it diﬃcult to assess whether theobserved rent-to-price ratio and turnover rate are “reasonable.” To put it diﬀerently,
what levels of the rent-to-price ratio and turnover rate are more likely to be associated with housing market mispricing?3 This study uses a straightforward method toanswer this question. First, we propose a simple equilibrium search-theoretic model,
in which the rent-to-price ratio and the turnover rate are endogenously determined.
1

Examples of using rent-to-price ratio as a measurement of the housing market abound in the
media. For instance, in a widely used website, Global Property Guide (2010) states that “In thestock market a very popular rule of thumb involves the price-earnings ratio, which measures howhigh the company’s net earnings are, in relation to the price of the stock. . . . It’s the same in the
housing market. What’s generally viewed as reasonable is similar to what’s considered reasonable
in the stock market, although houses tend to be expected to yield slightly less, perhaps because ahouse’s value depreciates less over time than the assets of a typical company. The price/rent ratio(or gross rental yield) is the housing parallel to the price/earnings ratio.” (Italic added).
The rent-to-price ratio is also widely used in the academic literature. For example, in theirinvestigation of possible mis-pricing of housing markets in China, Wu et al. (2012, p.533) statesthat “. . . The data show that price-to-rent ratios not only are high in these places, but they haveincreased sharply in the past few years. The price-to-rent ratio in Beijing increased by almost
three-quarters just in the last three years, rising from 26.4 in 2007(1) to 45.9 in 2010(1). Hangzhou,
Shanghai, and Shenzhen also have seen their price-to-rent ratios rise sharply to over 40. . . . Given
what we think are reasonable assumptions about the other parameters determining user costs, itappears that home buyers are assuming quite large capital gains on their homes. . . . However, homeprices do not always rise and certainly not consistently at the high rates recently experienced in
China. . . one can conclude that house prices in major Chinese markets are quite risky, even though
the data are too limited to make a blanket claim of mis-pricing.” (Italic added). Similarly, in a
research report by the staﬀ of the Reserve Bank of Australia, Fox and Tulip (2014) also use aconstant-quality measure of rental yield to measure the degree of over-valuation.
More recently, Green (2015) acknowledges that in the evaluation of whether a “bubble” exists or
not, it is not enough to consider the price only; the rent should also be taken into consideration.
2
For example, Financial Times (2015) reports that as the global transaction volume of commercial
real estate hits a record in the last quarter of 2014, “fear of bubble” arises among analysts. Similarstatements can be found in the academic literature as well. For example, in their survey of diﬀerent
classes of “bubble models”, Brunnermeier and Oehmke (2013) write that “. . . heterogeneous-belief
models generate the prediction that bubbles are associated with high trading volume, something thatis often observed in practice.. . . ” (Italic added). In the book coauthored by S. Gjerstad and Nobel
laureate Vermon Smith (2014, p.21), it is written that “. . . before an asset bubble collapses, trading
volume typically declines substantially. This occurred in the housing market. . . ” (Italic added).
3
Clearly, there are exceptions, such as Kashiwagi (2014). More discussion is to be followed.

2

We find, unsurprisingly, that the two variables are jointly determined at the equilibrium. This motivates us to take a simultaneous equations approach to identify
the empirical determinants of both the rent-to-price ratio and turnover rate, taking
into considerations that the two variables would interact in equilibrium. Our empirical framework can hence provide a benchmark for an estimate of “reasonable”
rent-to-price ratio and turnover rate given the empirical determinants, which in turnconstitute a yardstick for potential housing market mispricing. The details will be
provided in later sections.
The search-theoretic approach to the study of real estate markets and urban
economic issues has recently been the subject of much research (for example, Anglin,
2006; Anglin and Gao, 2011; Albrecht et al., 2007; Diaz and Jerez, 2013; Fisher etal., 2003; Genesove and Han, 2012; Krainer, 2001; Novy-Marx, 2009; Piazzesi andSchneider, 2009; Tse, 2011; Wheaton, 1990; Yavas, 1992a, 1992b). Many studies haveexamined equilibrium transaction price and trading volume, but the rental segmentof the residential real estate market appears to be under-explored.4 We take an initial
step in this regard by developing a search and matching model that enables landlords
to choose whether to sell or to rent their properties. Thus, the equilibrium rental
yield and the turnover can then be derived endogenously. Changes in real estatedevelopment (RED) level variables are demonstrated to induce a negative correlation
between rental yield and normed transaction. Our simple framework is tractable andcan be further extended for other research projects. Hence, it may carry independent
research interest.
Our second contribution is to propose a simultaneous equations system to accountfor endogenously correlated rental yield and turnover rate, instead of the usual ordinary least squares estimation.5 We employ the Hong Kong data for our empiricaltesting based on the following reasons. First, Hong Kong provides a housing market
in which the owner-occupied and rental segments are “integrated,” in the sense thatthe same unit can be used for both types of housing. Owners can hence arbitrage
for diﬀerent opportunities and so the rent-to-price ratio is maintained at a level thatreflects a “no-arbitrage” situation. The population density of Hong Kong is high andmost people live in units in high-rise condominiums, which are for sale and for rental.6
In contrast, the for-sale housing in the United States is typically detached houses,
while rental housing is concentrated in the apartment buildings, many of which are
owned by institutional investors. Thus, the two housing markets are virtually segregated, hence limiting the arbitrage opportunities for individual house owners. The
standard rent-to-price ratio may therefore not be as informative (Glaeser and Gy4

Xiao (2014), Sato and Xiao (2015) explore the relationship between house rent and labor market.
Their models do not have housing price though.
5
More specifically, we implement three-stage least squares estimation on a two equation systemwith rental yield and turnover rate treated as endogenous variables and on the same footing.
6
Among others, see Leung and Tang (2015) for more discussion on the Hong Kong housing
market.

3

ourko, 2007, Malpezzi, 2014, among others). We have access to RED level data in
Hong Kong, which helps us to mitigate the potential aggregation bias.7 More specifically, our sample covers 130 major private REDs in Hong Kong during the period
from November 2011 to October 2012. This choice of sampling period enables us toinclude corresponding information about demographics, household income, and housing related expenditure from the oﬃcial census.8 The rent-to-price ratio and normed
transactions are constructed out of the micro-transaction data. We also construct a“popularity” index based on a formative measurement model, and attempt to makeit as composite as possible.9 This index may therefore independently be of interest
for academic research and practical business investment.
In addition to constructing the popularity index, we have several other major findings. First, our three-stage least squares (3SLS) estimation confirms our theoreticalmodel and suggests significantly negative eﬀects of turnover and popularity on therent-price ratio. If the normalized transaction increases by one standard deviation,other things being equal, the associated rental yield would be 048 standard deviations
lower. If the popularity index increases by one standard deviation, its rent-to-priceratio would be lower by almost 016 standard deviations, holding other variables constant. On the other hand, neither the estimate coeﬃcient of the popularity index
nor that of the rent-to-price ratio of the RED, is statistically significant in explaining
the turnover rate.10 Second, we identify some (potential) empirical determinants of
the rent-to-price ratio and the turnover rate, controlling for the popularity index andthe endogenous variables. As a demand shifter, increases in income should stimulate
sales volume, but a higher income also means a higher opportunity cost of moving.
Ex ante, it is not clear which will be the dominant force, but our empirical finding
suggests it will be the latter. Third, we identify a form of empirical “dichotomy”
in the housing market. The demographic structure, and past return performance ofa real estate development tend to aﬀect its turnover rate, while popularity, humancapital environment, mortgage burden, and long-run rent growth have more influence
on rental yield. Last, we obtain direct evidence on the brand value ranking of nine
main developers in Hong Kong residential property development market. We alsofind occupational exposure to real estate has significant and positive impacts on thevaluation ratio of rental yield, but not on trading intensity, which is consistent withthe confirmed moral hazard eﬀect in real estate brokerage.11
7

See Hanushek et al. (1996) for more discussion, among others.
The Census and Statistics Department of the Hong Kong government has published, the firsttime in Hong Kong history, RED level statistics for free public access after the 2011 Census.
9
It takes into account all factors that are accessible to us and potentially relevant in housingpurchase decision, such as aﬀordability, location appeal, access to public transportation, developer
reputation, architectural design, surrounding environment, school zone, building age, facility, etc.
10
On the other hand, we do identify other variables that are significant in explaining the RED
level turnover rate. Please see below.
11
It is beyond the scope of this paper to discuss this literature. Among others, see Levitt andSyverson (2008), Rutherford et al. (2005).
8

4

Our paper can also be broadly considered as a study of the asset market liquidity (e.g. Amihud et al. 2013), as real estate is an asset traded with significant
frictions. There are recent studies of the rent-to-price ratio that also use a searchtheoretic framework. For instance, Kashiwagi (2014) considers a search theoretic
model with two sub-markets (“locations”). Homeowners in a location receiving “separation shocks” are forced to sell their houses immediately, move to another location
and become renters in the next period. Renters who do not receive separation shocks
would attempt to purchase a house. In that sense, Kashiwagi’s model may be closer
to the inter-regional mobility discussed in the literature, i.e. a situation when economic agents are relocated among diﬀerent states or cities that are far from eachother. Hence, it is natural for Kashiwagi (2014) to calibrate his model to matchthe aggregate data of the US. In terms of modelling strategy, the assumption that
homeowners need to sell their houses immediately and move to another location is
analogous to the “job destruction model” developed in the seminal work of Mortensen
and Pissarides (1994), where workers need to search for new jobs once they receive
the separation shocks, because their jobs are “destroyed.” Kashiwage also proves theexistence and uniqueness of a symmetric steady state. Our model instead assumes
that mismatched households can stay in their original homes until they find newones, as houses are not “destroyed” after the separation shocks. It may therefore
be applicable to the situation of intra-regional mobility or intra-metropolitan mobility
discussed in the literature, which is also consistent with our empirical implementationof using micro-data from a single city.12 In terms of modelling strategy, as agents in
our model are allowed to stay in the houses even after receiving separation shock, ourmodel has some parallel to the “on-the-job search” model in the labor market search
literature. In those models, workers who are not satisfied with the current job-wage
package would nevertheless stay in the current jobs until they find “better ones”(Burdett and Mortensen, 1998; Pissarides 1994). We also prove that a unique steadystate exists in that environment. Halket and Pignatti (2013) also study the rent-toprice ratio in a search-theoretic housing market model. Their focus is whether rental
housing is available in the local market and how the rent-to-price ratio will relate
to the homeownership rate in equilibrium. They do not elaborate the relationshipbetween the rent-to-price ratio and trading volume, which is one of the focuses ofthis paper. They also propose a competitive search model (CSM) while we adopt a
random search model (RSM),13 and it is well known that CSM and RSM can deliver
very diﬀerent conclusions on similar issues.14 The data sets in these previous studies
12

The literature on intra-regional or intra-metropolitan mobility has a long history. Among others,
see Quigley and Weinberg (1977) for a review of the earlier literature, and Zax (1994) for a recent
analysis. See also Green and Malpezzi (2003).
13
For another example of CSM in real estate, see Leung and Zhang (2011), among others.
14
For instance, see Moen and Rosen (2004), and the reference therein.
In the context of a housing market, a CSM envisions the situation where there are many diﬀerent
prices oﬀered for identical for-sale units, and many diﬀerent rents oﬀered for identical rental units.
It follows that there will be a distribution of rent-price ratios at the equilibrium. It may create5are from the United States, while ours is from an Asian city, and we adopt a 3SLS
estimation methodology. Our work should therefore be considered complementary tothat in these other studies.
Recently, the liquidity of the housing market is studied empirically. For instance,
Kwok and Tse (2006) investigate the price premia for easy-to-sell condominiums in
one administrative district of Hong Kong in 2005. Using data from 24 major oﬃce
markets in the U.S. from 1995 to 2010, Liu and Qian (2012) find a bust period driven
illiquidity premium in the real estate expected returns. We complement these studies
by adopting the simultaneous equations approach and by combining housing market
data with household data (in this case, the 2011 Census of Hong Kong). The trade-oﬀ
is that we are unable to examine the time series variations of the rent-to-price ratio,as the 2011 Census is a cross-sectional survey by nature. We leave this to future
research.
Our findings are also connected to the literature on real estate capitalization rates,
which focuses on four categories of cap rate determinants: macroeconomy (Ambroseand Nourse 1993; Evans 1990; Jud and Winkler 1995), property attributes (Peng2013), investor characteristics, as well as regional market conditions including expected returns and rent growth rate (An and Deng 2009; Campbell et al., 2009;
Plazzi et al., 2010), vacancy rate (Sivitanidou and Sivitanides 1999), investor sentiment (Clayton et al., 2009), and credit availability (Chervachidze and Wheaton2013). We demonstrate in the context of the Hong Kong market that the property’s
physical attractiveness, earnings potential, and household characteristics all matterin the determination of housing rent to price ratio. However, short-term housing priceappreciation rate does not seem to be significant.
The organization of the remainder of this paper is straightforward. The next section presents a simple theoretical model. We then describe our empirical methodology,
which is followed by a discussion of the data. Empirical results are then presented,
and the concluding remarks are given in the last section.

2

Theoretical Analysis

2.1

Model setup

2.1.1

Basic Environment

In our theoretical model, time runs continuously from zero to infinity. The populationof households is normalized to unity, of which a fraction  demand to reside in for-salean issue as our dataset only has one rent-price ratio for each RED. The theoretical model and theempirical part would not match. See also Leung et al. (2006) for a related study.

6housing and the remaining fraction (1 − ) demand rental housing.15 The housing
stock is exogenously given at some value  assumed to exceed the population ofhouseholds at unity, each unit of which can be used for either for-sale or rental
housing.16
A household in either for-sale or rental housing who finds their current dwellingsuited to their needs is referred to as a matched household as opposed to a mismatchedhousehold — one who desires to move because the current dwelling no longer meetsthe household’s needs. We model the distinction between matched and mismatchedhouseholds by assuming that the former, but not the latter, receive a flow utility  0 per time unit. Matched households are subjected to periodic moving shocks,
after which they become mismatched with their current dwellings. The shocks aremeant to model events such as job relocation, separation, the loss of family members,
etc., that necessitate the need to change housing. Because such shocks typicallyoccur independent of the state of the housing market, it is natural to treat themas exogenous to the market. Formally, we model the occurrence of the shocks as
Poisson processes with an arrival rate equal to some value we denote as 17 An
intuitive interpretation is that a given household would be hit by a moving shock at
an instantaneous probability  over each unit of time.
When an owner-occupier is mismatched, the household remains in the old house
while searching for a new house to buy. The household vacates the old house once thehousehold finds a new house to move into, but not before.18 Similarly, when a rental
household is mismatched, the household remains in the old house while searching for
a new house to rent. Once a new house is found, the household breaks the leaseand leaves the old house. An owner of a vacant house chooses between oﬀering his
property for sale and for rent — whichever option oﬀers the higher expected discounted
returns.
15

In this paper, we assume that renters and owner-occupiers would not change their identities.
This assumption has two major merits. First, Jovanovic and Rosenthal (1988) show that in ananonymous game (of which market equilibrium is a special case) where agents are not allowed tochange their identities, the existence and certain properties of equilibrium are guaranteed. Second,endogenizing the tenure choice (i.e., rent or own) in a frictional housing market is by no meansa simple problem. For a flavor of the complexity involved, see Chambers et al. (2009) whichstudy households’ tenure choices, with price and rent endogenously determined, in a life-cycle model
without search friction. We believe that the goal of the theoretical analysis in this paper — toconstruct the simplest model possible in which the transaction volume and the rent-to-price ratio
are determined simultaneously in equilibrium — is better served with a model in which tenure choices
are exogenously given.
16
See also Leung and Tse (2016), in which the stock of owner-occupied houses is assumed to be lessthan the population of households demanding such housing whereby a fraction of those households
must stay in rental housing temporarily at each moment in time.
17
The assumption of exogenous separation shock is the “standard” assumption in the labor market
search literature, which can be traced back to Mortensen and Pissarides (1994), among others.
18
See also Leung and Tse (2015) for the case where mismatched households need to sell theirhouses before they can search for new houses.

72.1.2

Matching rate and Market Tightness

The model housing market is a decentralized market in which imperfectly informed
buyers and sellers engage in time-consuming search for trading partners, the outcomeof which, as in Pissarides (2000), is modeled by a matching function. In particular,e
we assume that
³ if there´are  would-be buyers and  vacant houses for sale, theree   bilateral meetings between pairs of buyers and sellers over awould be  unit of time, where  ( ) is an increasing, concave, and constant returns function.19
For an individual³´buyer, a meeting with a seller comes about at the Poisson arrivale   e , whereas the arrival rate of meetings for an individual seller
rate  

³
´
³
´
³
´
e    . Now,  e   =     1 , given that  ( )is  is constant returns
toscale.
Then,
we
can
write
the
meeting rate for sellers as³´
e    =  (  1), where  ≡ e  denotes the ratio of ( ) ≡  

the measures of buyers to sellers, or what is known as the market
tightness,in the³´eefor-sale market. The meeting rate for buyers  ( ) ≡      can beshown to be equal to  ( )  . With the matching function increasing and concave
in both arguments, ( ) 0 2  ( )
 0
2

 ( ) 0 2  ( )
 0
2

(1)

The upshot of all this is that the meeting rates for buyers and sellers are functionsof the tightness of the market only, independent of the scale of the market due tothe constant-returns assumption on the matching function. Intuitively, in a tighter
market as manifested by a larger  , there are more buyers for each seller and as aresult, it would be easier for an individual seller to meet a potential buyer and theconverse holds for an individual buyer.
A bilateral meeting does not guarantee that the house in question is a good
match for the would-be buyer though. We assume that the would-be buyer indeed
finds the house a good match with probability  ∈ (0 1).20 Then, the instantaneous
probability (Poisson arrival rate) at which a buyer finds a suitable house to buy is
19

For instance, Blanchard and Diamond (1990) show that the aggregate matching function in thelabor market in the U.S. is indeed subject to constant returns to scale. A few subsequent studies
have substantiated the finding in various diﬀerent contexts. See Petrongolo and Pissardes (2001),
among others, for a review of the literature.
20
Here we assume that the “match quality” is either 1 or 0, with respective probabilities  and1 − . A more general approach is to assume that the match quality is a continuous random variable
having positive support over a range of values as in Pissardies (2000, chapter 6). In this case,there will be a reservation match quality above which the would-be buyer would find acceptablein equilibrium. The generalization would add the new endogenous variable — reservation match
quality — to be determined in equilibrium, which is the counterpart to the reservation job matchingquality in the labor market search literature. This generalization is useful in the latter literature in
studying how the reservation match quality changes over the business cycle and how the changes

8 ( ), whereas the instantaneous probability (Poisson arrival rate) at which a seller
successfully sells is   ( ).
21
The same search and matching framework is imposedon the³´ rental market.
e   bilateral meetings
In particular, over a unit of time, there would be  between pairs of individuals from the two sides of the market, where  ( ) is ane andincreasing, concave, and constant returns to scale matching function and  the respective measures of rental households who are on the market and owners
of for-rent vacant houses. Then, the instantaneous probability (Poisson arrival rate)
at which a landlord successfully finds a tenant is  ( ) and the instantaneous
probability (Poisson arrival rate) at which a rental household successfully finds a housee 
is  ( ), where  ( ) ≡  (  1),  ( ) =  ( )  , and  = is the tightness of the rental market. Given the assumptions on  ( ), we have,analogous to  ( ) and  ( ) for the for-sale market,
  ( )
 0

2.1.3

 2  ( )
 0
2

 ( ) 0 2  ( )
 0
2

(2)

Expected Discounted Payoﬀ, Price, and Market Rental

A key element of our model is how owners of vacant houses decide between oﬀering
their properties for sale and for rent. To proceed, we first assume that all actors in
the housing market are risk neutral. Second, we should restrict attentions to studying
steady-state equilibrium of the housing market in which the measures of households
in various states are unchanging through time.
Consider first a matched household in an owner-occupied house. Over a unit
a time, the household enjoys the flow utility  while staying in a matched house.
But then, the match can be broken at each moment in time at an instantaneous
probability , after which the given household becomes a mismatched household. A
forward-looking risk-neutral matched household then has expected discounted payoﬀ
 satisfying,
³
´
f− 
 =  +  (3)f the expected discounted payoﬀ ofwhere  is the household’s discount rate and 
f −  can be interpreted as the capital lossa mismatched household, and that 
the household suﬀers at the moment of becoming mismatched. Had we not assumed
that the market is in a steady state,  could vary over time, in which case wehelp amplify the eﬀects of technology shocks on employment and output. In the present analysis, westudy the steady state of a housing market not subjected to any random shocks. Adding “stochastic
matching” to the present model complicates the analysis while not helping bring out any additional
insights.
21
The virtue of imposing similar search and matching frameworks for the two markets is that wecan be certain that the theoretical results to follow are not due to any possible diﬀerence in themeeting technologies assumed for the two markets.

9·need to append the time derivative term  ≡  to the RHS of (3) for any
possible expected capital gains or losses. The same caveat applies to all “assetpricing” equations to be defined in the following.
A mismatched household in an owner-occupied house no longer enjoys any positive
flow utility and is now on the market, searching for a new house to buy. The household
meets a seller and finds the house for sale a suitable match at the instantaneous
probability  ( ), after which a trade between the buyer and the seller takes place
at a price we denote as , the determination of which will be spelled out in thefollowing. Thereafter, the household moves into the new house, while becoming amatched household, and vacates the old house. In all, the expected discounted payoﬀ
f satisfies,of a mismatched household ³´ff =  ( )  −  −  +  (4)where  is the expected discounted payoﬀ the household earns from the vacant housethat they just leave behind.
The respective expected discounted payoﬀs of matched and mismatched rental
households can be defined analogously as follows,³´e =  −  +   −  (5)³´
e = − +  ( )  − 
e 


(6)

where  is the endogenously determined flow rental payment. Notice that the mismatched rental household is obliged to continue paying the same rent for the houseeven though the house no longer matches their needs as we assume that recontracting
between the landlord and the tenant is not feasible.
An important assumption in the above is that the matched owner-occupier and therenter derive the same flow utility  from staying in a matched house. The assumption
ensures that the equilibrium rent-to-price ratio would be free of any eﬀects due toany assumed diﬀerence in utility households enjoy from the two types of housing.
Thus far, we have described the expected discounted payoﬀs of households on the“demand side.” of the two markets. We next turn to the “supply side.” Consider firstthe expected discounted returns of putting up a vacant house for sale. Before thehouse is sold, it does not generate any flow payoﬀ for the owner. The reward comesin the form of the sale price  at the time of sale, which takes place at each momentin time at the instantaneous probability  ( ). The expected discounted returnsof holding a vacant house for sale  thus satisfies, =   ( ) ( −  ) (7)where  −  can be interpreted as the “capital gain” accruing to the owner froma successful sale. The expected discounted returns of putting up a vacant house for10

rent  can be defined similarly, =   ( ) ( −  ) (8)where  denotes the expected discounted returns of having a house rented to amatched rental household. To complete the definition, we next turn to the determination of . While the house is occupied by the rental household, the owner collects
the flow rental  per time unit. And then, at the instantaneous probability , thetenant is hit by a moving shock, after which it will be on the market searching for a
new house to rent. Hence,
³
´
e− 
 =  +  (9)e denotes the expected discounted returns of having a house rented to awhere mismatched household who will break the lease as soon as the household succeeds infinding a new house to move into. At this point then, the house becomes vacant andthe owner begins collecting the expected discounted returns of such a house. Thus,e satisfies,22

³
´
e
e
 =  +  ( )  −  (10)We have yet to specify how the sale price  and the market rental  are determined.
In a perfectly competitive market with fully informed participants on both sides of themarket, the market price should be at the level that clears the market. In a frictional
market with imperfectly informed buyers and sellers, the market need not and usuallywould not be cleared at any given moment. Moreover, unlike the buyers and sellers
in a perfectly competitive market who can trade with just anyone in the market atany moment in time, when a pair of potential trading partners meet each other in theenvironment that a search and matching model describes, they may only trade witheach another as search frictions prevent them from contacting others. There is thena “bilateral monopoly,” so to speak, in which the terms of trade may be determinedby either the seller committing to some sale price beforehand, the buyer committing
to some purchase price beforehand, or by the two bargaining over the surplus of the
trade. Assuming commitment by either the buyer or the seller is ad hoc and thetheoretically more appealing approach is that the terms of trade are reached via thetwo sides bargaining over the trade surplus. In Nash bargaining in game theory,23
each side earns one-half of the surplus of trade. In the context of the present model,
 and  satisfy the following two conditions, respectively,f −  +  =  −  
 −

(11)

e depends on  , given that once a mismatched tenant finds a new house, he/she
Insofar as 
would move out and the landlord would be left with a vacant house, whose value is   ultimately
also depends on  . In this regard, our model diﬀers significantly from the models in Xiao (2014)
and Sato and Xiao (2015), where the search friction is only present in the labor market but not in
the rental housing market.
23
See Rubinstein (1990) for example.
22

11

e
 −  =  − 

(12)In (11), the LHS gives the surplus the buyer earns from becoming a matched household, whereas the RHS gives the surplus the owner of the for-sale vacant house earns
in selling the house. The bargaining concludes with the sale price  set at the levelthat equates the surpluses. A similar interpretation applies to (12).
The final step is to analyze how an owner of a vacant house chooses between
putting up the house for sale and for rent. In maximizing expected discounted returns,
the owner chooses putting up the house for sale instead of for rent if and only if   . Then, the value of a vacant house is given by, = max {   } Now, if    , all vacant houses will be for sale, whereas if the inequality holds
in reverse, all vacant houses will be for rent. Either scenario cannot be equilibriumwith a fixed fraction of households demanding for-sale and the rest demanding rental
housing. This means that =  = (13)must hold in equilibrium.
At this point, we can solve (3)-(13) for all the expected discounted returns, thee ,  — in terms of thef, , ,e  ,  , , ,sale price, and the market rental —  , 
two market tightness  and  . The equation which is of particular interest in thisexercise is the solution of (13), given by =  ⇒ ( ) ( )=
2 ( + ) +  ( ) +  +  ( )(A)

which is simply a no-arbitrage condition for how the two market tightness should
be related to ensure that owners of vacant houses earn the same expected returns
between putting up their properties for sale and for rent.
2.1.4

Stock-flow Equations

We next turn to restrictions on the measures of matched and mismatched households
and the stock of vacant houses in the two markets that should hold in market equilibrium. First, with a fraction of the population  demanding for-sale housing, any
member of which must either be staying in a matched or a mismatched house at each
moment in time,e = 
 + 
(14)e the measure of mismatched housewhere  denotes the measure of matched and 
holds in for-sale housing. A similar relation holds in the rental market,e = 1 −  + 
12(15)

e are the respective counterparts to  and e for the rental market.
where  and 
Since each household must stay in one and only one house at each moment in
time, the measure of occupied houses is simply equal to the population of households
at unity. With the market endowed with a stock of   1 houses, the stock of vacanthouses is then just equal to  − 1. Write  and  , respectively, for the measuresof vacant houses for sale and for rent. Then, +  =  − 1

(16)The last set of conditions describe how the measures of matched households inthe two market evolve over time. In particular, over a unit of time, the measureof matched households in for-sale housing falls by the measure of those who are
hit by moving shocks but increases by the measure of the successful buyers amongmismatched households in the interim. Then,·e −  
 =  ( ) A similar equation holds for the rental market,·e −  
 =  ( ) In this paper, we shall restrict the analysis to steady-state equilibrium in which themeasures of matched households in each market are unchanging over time, whereby·· =  = 0.24 The two equations above then specialize to, respectively,e  =  ( ) 

(17)

e 
 =  ( ) (18)e  ,  = e  ,  ( ) =Now, together with the definitions  = e ,  , e , ( )  , and  ( ) =  ( )  , we can solve (14)-(18) for  ,  and  as functions of  and  . Of particular interest in this exercise is thesolution of (16), given as +  =  − 1 ⇒24 (1 − )+=  − 1  ( ) +   ( ) + (E)

The steady-state equilibrium can be interpreted as the long-run equilibrium that the market·

should approach over time from any initial state. Take the equation for  for example. Supposee should decline asthat the RHS is positive initially. Then,  should increase over time while more and more mismatched households find new houses to buy. Eventually, the two flows that makeup the RHS of the equation should be equalized, at which point the market reaches the steady state.
We did not explore the transition dynamics as we believe that the major lessons that concern us
hold both in and oﬀ the steady state. Also, since our dataset is cross-sectional and as such is notsuited to test the implications from the transition dynamics.

13

which describes how the two market tightness have to be related to equate the sumof the vacancies in the two markets to the stock of vacant houses in existence. If wethink of  and  as the respective “demand for vacancies” in the two marketsand  − 1 as the “supply of vacancies”, () can be interpreted as the counterpart tothe market clearing condition in a model of a frictionless market.

2.2

Equilibrium

We now have two equations, () and (), in two unknowns,  and  , the solutionof which constitutes the equilibrium of the model housing market.
Proposition 1 A unique equilibrium exists.
Equation () defines an implicit function for  in terms of  that begins at theorigin and then is increasing everywhere as depicted in Figure 1. Intuitively, when
the for-sale market is tighter, vacant houses are sold faster on average. Putting up
a house for sale then should yield greater expected discounted returns. For the noarbitrage condition to continue to hold, the expected discounted returns of putting
up a house for rent have to increase in tandem, which comes about when the rental
market is tighter too. Equation () defines another implicit function for  in termsof  which is everywhere decreasing, as depicted in Figure 1. The interpretation isthat in a tighter for-sale market, there will be faster sale on average, leaving behind
fewer vacant houses for sale. In this case, there have to be more vacant houses forrent for the supply of vacant houses to be just equal to  − 1. There can be more
rental vacant houses on the market only if the houses are rented out more slowly on
average due to a smaller instantaneous probability of lease as in a slower market witha smaller  .
It should be clear from Figure 1 that the two functions () and () must intersect
once and only once, meaning that there is a unique pair of { ,  } that solves the two
equations.25 Once the two market tightness are pinned down, the various equilibrium
expected returns, the sale price, the market rental, and the measures of households
and vacancies in the two markets are known given that they can all be shown to befunctions of { ,  }.
Before proceeding further, we would like to argue that the two equilibrium conditions () and () are both rather compelling. If condition () fails to hold, then no
vacant houses would be made available for sale or for rent, depending on whether 25

It is well known that even a simple search and matching model can display instability and indeterminacy, such as in Krause and Lubik (2010). The Proposition here shows that the equilibriumis unique and hence rules out indeterminacy. The empirical analysis to follow is by and large motivated by the model’s predictions on how the sale volume and the rent-to-price ratio are determined
simultaneously and vary in response to changes in the environment. A model having multiple equilibria, as a rule, has no definite predictions about how the endogenous variables may vary when theenvironment changes. Among others, see Jovanovic (1989) for more discussion.

14

Figure 1: Existence and uniqueness of equilibrium
falls below or exceeds  . In particular, suppose    initially; then the tightnessof the for-sale market should reach infinity as all owners of vacant houses shun themarket. But then if the market were that tight, the sale price  and then the expected discounted returns of putting up a house for sale  should rise significantly toovertake the initially greater expected returns  . This kind of oscillation, if it evertakes place at all, should eventually settle down when  =  just holds. Condition() which stipulates that the sum of the vacancies in the two market  +  isequal to the stock of vacant houses  − 1 is a straightforward adding-up constraint,
the violation of which gives rise to a logical inconsistency of the first order.

2.3

Empirical Implications

Our main goal in studying a model of a frictional housing market is to analyze how thetransaction volume in the for-sale market and the rent-to-price ratio are determined
simultaneously and how the two may be correlated in the time series and in the
cross section. At this point, it helps to simplify to assume that  () =   ();i.e., there is the same matching function for the for-sale and the rental markets.
This is a reasonable assumption, as there should not be any reason to believe thematching technologies in the for-sale market and the rental market should diﬀer inany fundamental manners given that real estate agencies and their online platforms
almost always serve both markets.

15

2.3.1

Transaction Volume

In the for-sale market, there is a stock of  vacant houses on the market at each
moment in time, each one of which is sold at the instantaneous probability  ( ).
Then, over a unit of time, there would be =   ( )  (19)

houses sold in the market.
Proposition 2 The transaction volume in the for-sale market  is increasing in , and .
Proof. Solving (14)-(18) for  and then substituting into (19), =  ( ) ( ) + (20)

which is increasing in  and  but decreasing in  .
First note that () holds only if    for   () =  (). Then, an increasein  lowers the LHS of (), which must be followed by decreases in  and/or  forthe condition to be restored. An increase in  must similarly be met by decreasesin  and/or  for () to continue to hold. By (), the two market tightness goesup and down together. Then an increase in  or  must be met by a decline in  .
Thus,  is increasing in  by the direct eﬀect of a larger  and the indirect eﬀect ofa smaller  , whereas  is increasing in  by the indirect eﬀect of a smaller  .
An increase in  lowers the LHS of (), meaning that there has be to a smaller for each  for the condition to hold, as depicted in Figure 2. It is straightforward
to verify that with a larger , there is a larger  for each  for () as depicted in
Figure 2, given that    in equilibrium. Now, either tendency gives rise to asmaller  as can be seen in Figure 2.  , as given in (20)  then increases by the
direct eﬀect of a larger  and the indirect eﬀect of a smaller  
That there should be a greater volume of sales in a market with a larger housing
stock and where a larger fraction of households demand for-sale housing is perhaps not
surprising. Holding  and  constant, the Proposition says that there would also be
a greater sale volume when there is a higher matching probability  with which moremeetings between pairs of buyers and sellers result in successful sales. But notice thatwhen houses are sold more quickly, there can only be fewer vacant houses left behind,other things equal. Yet, with the housing stock  given, there must be the same
stock of vacant houses on the market. The apparent contradiction is resolved once itis recognized that when mismatched households spend less time finding suitable newmatches, they also vacate their old houses at a faster rate, refurbishing the market
with vacant houses at a similarly faster rate to help maintain the same stock of vacant16Figure 2: Comparative steady states of 
houses on the market. In all, with a greater matching probability , more houses are
put on the market for sale and more such houses are sold at each moment in time.
An empirically more relevant question is how the normed transaction volume
  may vary with the environment rather than how  itself varies. Of course, if is increasing in  and ,   is increasing in the two exogenous variables too.
However,   need not be increasing in  even if  is increasing in . Intuitively,
with the same population of households demanding for-sale housing but a greater
housing supply, there should be fewer houses sold per unit of the housing stock.
Conjecture 3 The normed transaction volume in the for-sale market   is decreasing in .
In a wide variety of quantitative analyses that we undertake, we find the Conjecture indeed always holds.26
2.3.2

Sale Price and Market Rental

We next turn to the determination of the sale price and market rental. Solving(3)-(13), we find that +  ( )
=

(21)
(2 + 2 +  ( )) The analyzes assume  () =  () =  for some   0 and  ∈ (0 1). The computer codes
for all quantitative analyzes to follow are available upon request.
26

17

=

( +  +  ( )) ( +  ( )) +  ( )( +  +  ( ))2(22)

Proposition 4 The sale price  is decreasing in  and . The market rental  isdecreasing in  and  if   .
Proof. The sale price , as given in (21), is increasing in  . The market rental
 as given in (22), is guaranteed increasing in  if   . The two market tightness
is decreasing in  and , as shown in the proof of Proposition 2.
With a larger housing stock, there would more for-sale vacant houses on the market
and a more sluggish market follows. Sale price  then falls as the market slows down.
The reason for how  should be decreasing in  too is as follows. First observe that   in equilibrium from (), which results from the diﬀerence in the bargaining
environment facing agents in the two markets. In the for-sale market, the surplus
f, independent of the sale price  and the value of a
of a match is equal to  − vacant unit  . That the sale price — a transfer between the buyer and the seller — is
not part of the surplus is not surprising. More subtle is that the value of a vacantunit  is also not a factor, which is the result of the eﬀect of the seller forgoing avacant unit and the eﬀect of the buyer becoming an owner of one cancelling out. Ine the latterthe rental market, the surplus of a match is  −  in addition to  − ,f in that the gains to both the rental household
roughly equal in value to  − 
and the owner-occupier by becoming matched are equal to the PV of the flow payoﬀ
. Apparently, there tends to be a larger surplus in the rental market than in thefor-sale market, other things equal. In the rental market, when a match takes place,the owner of the previous units occupied by the rental household suﬀers a capital losse This loss can be thought of as an externality as it is not taken into account − .
in the bargaining between the rental household and his new landlord. Had it been
considered by the agents, the loss would have canceled out the gain  −  . All thisthen tends to cause  to exceed  for the same market tightness. The no-arbitrage
condition thus requires a tighter for-sale market to equalize  and  . In this case,given  and  , transferring one household from the less tight rental market to thetighter for-sale market raises the overall market tightness and therefore lowers theoverall measure of vacant houses  +  from the previous level. To restore theequality in () requires a decline in market tightness in one or both markets. But
since, by the no-arbitrage condition (), the tightness in the two markets must movein the same direction,  and  decline in tandem, where the decline in the former
causes  to go down.
In the meantime, in a slower market, there will not just be more houses for sale,
but also more houses for rent as well. Then, perhaps the market rental should also
go down too in response to either a decline in  or . Surprisingly, it does not seem
possible to ascertain such a tendency without further assumptions. The present setup
assumes that the renter continues to stay in the old house and pay the same rent 18

after the match between the household and house is broken while the household issearching for a new house. In a slower market, on average, a new match is foundsooner. This raises the renter’s surplus from entering into the lease in the first place,knowing that on average he/she is only obliged to continue paying the same rent fora shorter period of time after the newly found house no longer matches his/her need.
It cannot be ruled out in general that this eﬀect dominates the direct negative eﬀectof a slower market on equilibrium rental unless   . In some extensive quantitative
analyses, however, we have not uncovered a single instance where indeed  becomesincreasing in  or  even for ridiculously large . In all, it seems safe to conclude
that an increase in the two variables should also lower , in addition to lowering  forany practical values of .
We next move to check how  and  should vary with . First, notice thatby (21), holding constant  and therefore the instantaneous meeting probabilities ( ) and  ( ), the sale price  is increasing in  — other things equal, a higher
matching probability means that mismatched houses, when they can be sold fasteron average, are more liquid assets commanding a higher sale price. In the meantime
though, a higher matching probability would be followed by a decline in  to meetthe restrictions in (), which tends to lengthen the time mismatched houses can besold, turning them into less liquid and therefore less valuable assets. Our quantitative
analyses indicate that the direct positive eﬀect dominates for small  but the indirect
negative eﬀect dominates for large ; i.e.,  is initially increasing but eventually
decreasing in . Intuitively, when  is large to begin with, there tends to be a relatively
small initial  . With   a concave function, for the relatively small initial  , a given
decline in  results in a large decline in  ( ). In this way, the instantaneous saleprobability   ( ) tends to be decreasing in  for large .
Not unexpectedly, a similar initially positive and eventually negative eﬀect of  isalso found on market rental  in our quantitative analyses.
Conjecture 5 The sale price  and the market rental  are both initially increasing
but eventually decreasing in .
2.3.3

Rent-to-Price Ratio

Dividing (22) by (21) and making use of (),¶µ +  ( )  ( ) ( )


=
+

 +  ( )  ( ) ( +  +  ( )) ( +   ( )) (23)

Other things equal, owners should require a rental yield above the discount rate towillingly oﬀer his/her property for rent instead of for sale given that a rental unit
would earn no rental income every now and then when the unit becomes vacant. The
above equation indeed says that    is guaranteed to hold if   ( ) =  ( ) as
in where vacant houses are sold and rented out at the same instantaneous probability.
19

By Proposition 4, increases in  or  cause  to decline for sure and should also
lead to a smaller . How the rent-to-price ratio should behave then depends on how
the elasticities of  compare against the elasticities of  with respect to  and . Ourconjecture is that the first set of elasticities should be greater than the second set. A
larger  or  causes  and  to vary through the changes in the respective market
tightness in the two markets. In the rental market, as we argue above, an increasein  has both a usual positive and an indirect negative eﬀects on , whereas in thefor-sale market, there is just the usual positive direct eﬀect of  on . If indeed decreases proportionately more than  does in response to a given increase in  or ,
to follow is a larger . The conjecture holds up always in our quantitative analyses.
The ratio , given in (23), is guaranteed to be decreasing in  for small 
and/or , holding constant the two market tightness, meaning that an increase in thematching probability, other things equal, tends to exert stronger positive eﬀects on
the sale price than on the market rental. This is reasonable in that an improvement
in asset liquidity should mainly help raise the sale price, whereas the market rental
should not directly benefit from the improvement.
The rent-to-price ratio can also vary in response to the given increase in  tothe extent that the increase in  impacts on the two market tightness, on which and  depend. By Conjecture 5, an increase in  should cause both  and  to go
up initially but to fall eventually as the two market tightness decline. Along theincreasing phase,  should increase proportionately more than  does, just as  rises
faster than  in response to a given decline in  or  In this case then,  should
fall. Along the decreasing phase,  should decrease proportionately more than  does,
to which a larger  should follow. In our quantitative analyzes, however, we findthat  is everywhere decreasing in . Apparently, any tendency for  to increase
with  arising from the changes in market tightness is more than oﬀset by the direct
negative eﬀect of  on .
Conjecture 6 The rent-to-price ratio  is increasing in  and  but decreasingin .
In sum,  varies in the way it does as described in the Conjecture is due to thetendency that the sale price should be more sensitive to changes in market tightness
arising from changes in supply  and demand composition  and that improvements
in market liquidity should help raise the sale price more than the market rental.
2.3.4

Correlation between the Transaction Volume and Rent-to-Price ratio

Proposition 2 and Conjecture 6 together imply that:
Corollary 7 Variations in  induce a positive correlation between   and ,i.e., (  )  0
(24)
20

Variations in  induce a negative correlation between   and , i.e., (  )  0

(25)

Conjectures 3 and 6 together imply that:
Corollary 8 Variations in  induce a negative correlation between   and , (  )  0(26)

By construction, the housing units in the model are observationally identical andas such the model has no cross-sectional implications. But then, if we imagine,instead of there being one unified housing market, that there are numerous segmented
markets, each of which is as described in the model above. The theoretical results
can then be interpreted as cross-sectional implications. The last two Corollaries
suggest that across the segmented markets, transaction volumes and the rental yields
can exhibit negative correlations or positive correlations. Our empirical analyses in
the following are in the main motivated to resolve this ambiguity of the theoreticalmodel.27

3

Our Econometric Framework

In this section, we describe our econometric framework for testing the predictions of
the theoretical model with a cross-sectional data set. In particular, we test whether achange in the fraction of owner-occupants , or in the probability of good match  orin the housing stock  would induce the rent-to-price ratio () and the transaction
ratio in the sale market ( ) to move in the same or opposite directions. Twoissues need addressing to achieve these goals. First, in the model, housing units arehomogeneous, while in practice they are heterogeneous. Second, we must also obtaina measure of the probability of good match  which would vary across diﬀerent submarkets (which are REDs in the current context). One possible method is to adopt
a hedonic-type regression in order to control for the heterogeneity among housing
units. Unfortunately,  is not directly observable. In addition, as our sample size isrelatively small (132 RED), listing all the control variables on the right hand sideof the regression equation would exhaust our degree of freedom, and adversely aﬀect
subsequent analysis. Therefore, a hedonic-type regression approach is not practical.
27

Notice also that our model is an on-the-house-search model, meaning that mismatched households would stay in the house, even when it generates zero utility flow to the households, until theyfind new ones. Since utility flows to households are not directly observable, the total number of“house seekers” may not be directly observable neither. Hence, important variables such as market tightness may not be observable. In this sense, the empirical focus of this paper, namely, theturnover rate and the rent-to-price ratios may very well be the only variables that can be observed
and measured without controversy in the model.

21Another common approach is to use principal component (PC) analysis, which “combines” diﬀerent variables into a few “factors” or PCs. We can then use those PCs
as the right hand side variables to control for diﬀerences across RED. However, aprerequisite of adopting the PC analysis is that those variables are significantly correlated, and that a few variables can summarize most of the total variations (Jolliﬀe,2005). Unfortunately, this is not the case in our sample. It takes six PCs to accountfor 80% of the total variations, as shown in the appendix, and hence adopting the PC
analysis would not be helpful in our context. Furthermore, neither the hedonic nor
PC approach provides an empirical proxy for  An alternative approach is required.
The starting point of our approach is the observation that variations in the fractionof owner-occupants, in the probability of good match and in housing attributes can beinterpreted as changes in particular popularity measures. For instance, a RED thatis more popular (i.e. has some good features) would attract more owner-occupants.
Since owners tend to stay longer than renters, we would observe less turnover on
average. On the other hand, a RED with a high matching probability means that,
other things being equal, the housing units are more liquid. This attracts investors
and increases the popularity of the RED. Similarly, as the number of households
targeting each submarket is normalized to unity,  can be interpreted as the relative
demand for housing in a certain submarket. Thus, the smaller  is, the stronger
the relative demand for residence in a particular submarket. Obviously, the moredesirable the structural and neighborhood attributes are, the greater the demand
for the RED, and hence a smaller  and a higher popularity. Accordingly, we cansummarize the major implications of the search and matching model (from (24) to(26)) as follows: () ( )≷ 0,
≷ 0.
( )( )(27)

As the theoretical analysis does not help us to dictate the relationship, we switch
to the empirical analysis. Thus, our next step is to build a composite popularity index
based on housing aﬀordability and a bundle of structural, neighborhood, and location
characteristics. A significant advantage of this approach is that we consolidate theinformation that are contained in the structural and neighborhood characteristics of a
RED into one variable, hence we can increase the degree of freedom in our regression.
Thus, the “popularity” index can be interpreted as a “summary statistics” of many
housing characteristics as well as a “proxy” for the matching probabilities which we
do not observe directly, and therefore it needs to be inclusive. Our choice of the“ingredients” of the popularity index is influenced by the hedonic pricing literature,
motivated by exploratory interviews with market practitioners,28 and constrained by
28

The two major real estate agencies in Hong Kong are Centaline Property and Midland Realty.
One of the authors personally visited one branch of each. Questions like “What kind of condominiums is more popular among home buyers?”, “What characteristics are most valued in homepurchase decision?” are explicitly asked.

22

data availability. Following a large literature on index construction, our popularity
index is a linear sum of equally weighted selected indicators.29 We provide moredetails about the construction of the index in a later section and in the Appendix.
It is clearly an imperfect proxy of the conceptual “popularity” in the model. Even if
we were able to include all of the characteristics of a RED in the index, it is unlikely
it could address all the concerns surrounding relative demand and the likelihood of a
successful match, which result from the interactions of consumers with the housing
market (Griliches 1971).
If we take the existence of a popularity proxy for granted, a natural formulationreflecting the simultaneous relationship between the rent-to-price ratio () andthe transaction rate ( ) on one side, and how both variables may relate to the
Popularity index on the other is:




µ

¶

+  + 1 µ ¶
=  0 +  1 ( ) +  2+  + 2 
=  0 +  1 ( ) +  2
(28)

where  and  are row vectors of other controls, whose detailed contents will be
discussed later.  ,   ,  = 0 1 2 are all scalars, while  and  are column vectors.
1 and 2 are residual terms. In line with the model implications, we should expect 1  0,  1  0,  2 ,  2  0 In words, it means that we expect more frequent
trading in popular REDs. And the rental yield must be lower to compensate forhigher popularity. Clearly, this simple simultaneous equations system (28) can berearranged asµ ¶=  00 +  01 ( ) + ( +  2 ) + (1 + 2 2 ) 


µ ¶


(29)
=  00 +  01 ( ) + ( 2  + ) + ( 2 1 + 2 ) where  = (1 −  2  2 ),  00 = 0 + 2  0 ,  01 = 1 + 2  1 ,  00 =  0 + 0  2 ,  01 =  1 +1  2 
Several issues emerge. Clearly, ( ) is correlated with 1 , and () is correlatedwith 2 . Thus, there are “cross-equation restrictions” implicitly imposed in (28),30
and if we estimate each equation in (28) separately, the ordinary least squares (OLS)
estimates are inconsistent. Similarly, even though 1 and 2 in (28) can be assumed
to be independent error terms, (1 + 2 2 ) and ( 2 1 + 2 ) in (29) are clearly not
29

Notice that while some of our indicators are continuous variables, some are dummy variables.
And without any prior knowledge of the detailed preference of the households, we consider the choiceof using an equal-weighted linear sum of diﬀerent indicators to be both sensible and consistent withthe practice of the literature on index construction.
30
For more discussion of “cross-equation restrictions,” see Sims (1980), among others.

23independent. Again, it is a kind of “cross-equation restriction.” Thus, ignoring sucha restriction and estimating the two equations in (29) separately with OLS may not
deliver eﬃcient estimates, as the covariance between (1 +  2 2 ) and ( 2 1 + 2 ) are
not properly taken into considerations. In this case, structural estimators should be
preferred. More specifically, we use 3SLS, which is a full information estimator, andestimate the two equations as a system.31 The procedure is as follows:Stage 1µ ¶= 0 + 1 ( ) +  +  +  1 µ ¶=  0 +  1 ( ) +  +  +  2 
where 0 , 1 ,  0 ,  1 are scalars, and , , ,  are vectors. We obtain the OLS³d´¡  ¢
projections of the endogenous variables,  and [Stage 2
µ ¶
µ
¶
\


=  0 +  1 ( ) + 2
+  + 1 


µd¶
µ ¶


=  0 +  1 ( ) +  2+  + 2 



(30)
(31)

where ,  are vectors. We retain the residuals to form a consistent estimate of thecovariance matrix of the disturbances.
Stage 3
Perform Generalized Least Squares (GLS) estimation on (30), (31)with the covariance matrix in Stage 2 as the optimal weighting matrix.
For the future reference, (30) would be labelled as the rent-to-price equation, and(31) as the turnover equation.

4

Data and Popularity Index construction

In this paper, we use data from three diﬀerent sources. First, we retrieve microtransaction records from EPRC, a commercial Hong Kong real estate database. Second, we obtain demographic and socioeconomic data from the 2011 Hong Kong Census. We also use online resources, including real estate brokers’ and government websites, geographic information system, and popular local internet discussion forums,
31

Among others, see Wooldridge (2010) for more discussion of 3SLS.

24

which provide us with complementary information on structural, neighborhood, andlocational characteristics.
The EPRC data set has been employed by several previous studies.32 We therefore
first discuss the oﬃcial census. To gain a better understanding of the socioeconomic
environment, the Hong Kong government conducts a census of all households in Hong
Kong every decade, and a by-census for a selected sub-sample between the main censuses. Previous censuses and by-censuses published at most the district level data for
public reference.33 In the 2011 Census, the Census and Statistics Department (CSD)of the Hong Kong government provides publicly accessible statistics of “major housing estates,” (i.e. REDs) “with at least 3,000 residents or 1,000 domestic households”
at the time of survey.34 Information is readily available for a total of 487 REDs (or“estates”), of which 163 are private residential REDs. We exclude all public housing,as the allocation of these units is not decided by the market and the corresponding
rents and prices are highly subsidized. This collection of private residential RED isfar from being ideal, but it does provide information on demographics, income andhousing related expenditure disaggregated at the RED level. Hong Kong has no zip
code system, but as most of the Hong Kong population lives in high-rise buildings, theRED level analysis in Hong Kong can be comparable to those zip code-level analysesof the US. We include variables for the total population, the young population aged
from 25 to 44 years, the percentage of residents’ with a college education, the household monthly median income, the median monthly mortgage payment, and residents
working in real estate consulting industry.
The 2011 Census was conducted from June 30 to August 2, 2011. Correspondingly,
we extract rental contracts, as well as “purchase and sale agreements” (i.e. contractsof for-sale housing units) from EPRC that occurred in the 163 private REDs in thesubsequent period. Typically, a transaction is completed in two months; hence werestrict the time horizon to range from November 2011 to October 2012.35 For eachRED, we are able to observe the actual transaction volume. With some data cleaning
eﬀorts, we collect 3,616 transactions in the rental market and 29,671 transactions in
the for-sale counterpart.36 Notice that in any given period of time, a housing unit iseither transacted in the sale market or the rental market, but not both. Therefore, tofind the rent-to-price ratio while holding the quality of the housing unit constant, we
32

Among others, see Leung et al. (2002).
There are eighteen administrative districts in Hong Kong. For a list of these districts, please
visit the District Council homepage http://www.districtcouncils.gov.hk/index.html .
34
The oﬃcial webpage is http://www.census2011.gov.hk/en/major-housing-estates.html.
35
Notice that the data set is constructed in a manner that the potential simultaneous bias is
mitigated. According to Leung, Leong and Chan (2002), most housing transactions in Hong Kong are
finished within two months. Therefore, when we collected housing transactions between November
2011 to October 2012, even the initial sale agreements were signed after the 2011 Census was finished,and hence we can take the variables from the household survey as “pre-determined” variables. For
more justifications on using pre-determined as exogenous variables, see Greene (2008), Sims (2010).
36
See the Appendix for the details of our construction of the data set.
33

25

need to match each transaction from the rental market with one in the sale market
with “similar characteristics.”37 Following Huang and Leung (2014), we require theunit for-sale and the unit for rental both to be transacted in the sampling periods,
and to have the same estate code, floor level, living room orientation, the gross square
footage to diﬀer by not more than ten feet, the net gross ratio to diﬀer by less than
one percent, and to have a building age disparity of less than three years. This
data-matching methodology ensures that each rental unit is “matched” with a forsale unit that is similar in observable attributes, and inevitably implies that someREDs will not qualify. For instance, during our sampling period, some estates have
only sale transactions but no lease transactions. Some have new leases signed but
no sale transaction, or they have both but the units transacted in the for-sale andrental markets are so diﬀerent that we cannot “match” them. From this, a totalof 132 REDs remain in our sample.38 As it is very likely to have more than one
transaction in the rental market in each of these REDs, we would therefore obtainseveral rent-to-price ratios. For the estimation purpose, we take the mean value ofthese rent-to-price ratios in each RED.
To further enrich our empirical analysis, we compute the RED level rent growthrate and housing price appreciation rate before our sampling period begins.39 We
collect six years of rental records for each RED, and transform the nominal rent
into real values.40 To control for the possible quality diﬀerence, we match the rental
units transacted with those transacted in previous years, based on the same matching
criteria applied to the for-sale units and their rental counterpart. We therefore obtain
five consecutive yearly growth rates of rent in a rolling fashion. The historical house
price appreciation rate is constructed in the same manner, but with only two yearsof data.41
37

According to the literature review by Todd (2006), matching estimators have a long history in
the literature. See McMillen (2012), Rivkin et al. (2005), among others, for some recent applications.
38
Clearly, this data-matching methodology is like a sample-screening process and the final results
could be aﬀected. We provide more discussion on this in a later section.
39
Notice that our sampling period is somehow constrained by the period the 2011 Census was
conducted, which is itself an administrative decision. Using the data before the sampling period
would enrich our analysis and help us to capture the potentially diﬀerent “initial conditions” of theREDs.
40
We have consulted market practitioners, and we are told that in Hong Kong, most rental contracts last for one to two years. Hence, six years of rental contract collection should be suﬃcient forour purpose to control for “rental market conditions before the sampling period”.
41
Notice that the growth rate of rent exhibits cyclical behavior. Reverse chronologically, theaverage rent growth rate across our sampled REDs is 19.83% in 2010, -11.6% in 2009, 10.58% in
2008, 7.967% in 2007, and -1.267% in 2006. Such pattern suggests a longer horizon would be morereasonable.
In terms of the data conversion, Year 2005 is used as the benchmark. The CPI data comes from
IFS (International Financial Statistics), which is maintained by the IMF.
A drawback of the inclusion of this additional variable is that it further reduces the number of
estates to 130, as some RED might not have very active rental markets.
Notice also that what we report in the following is based on the geometric mean in the past five26

Next we examine the construction of the popularity index. According to Diamantopoulos and Winklhofer (2001), constructing an index demands a proper set offormative indicators, which must include all facets of the determinants involved; anyomission can lead to an incomplete index. It is obvious what domains should be
captured in our context, as we need to account for both physical attributes and affordability. After considering a combination of hedonic pricing literature, interviews
with real estate brokers, and data availability, we include the following variables: theaﬀordability, the RED-level average net gross ratio, swimming pool and club houseavailability, developer brand, distance to a MTR station,42 distance to CBD, distanceto the waterfront, and the school zone. Table 1a provides the summary statistics.
We use the transaction price as a proxy of the aﬀordability. EPRC provides certain
housing characteristics, including the building age, net gross ratio, and housing estate
facilities, such as swimming pool, club house, etc. We take the mean of the net grossratios of all transacted units in a RED as the average net gross ratio of the RED,and the mean age of all buildings in a RED as the average age of the RED. Other“ingredients” for the popularity index are derived from various online resources. For
instance, we determine the distances in meters from an estate to the nearest subway
stations and to the central business district (CBD) with data from the government
geographic information system.43 We also measure the distance from an estate toits nearby waterfront. Hong Kong has a long and sinuous coastline, so proximity
to the waterfront means possible sea view from home, and accessibility to a nearby
waterfront park or promenade.

(Table 1a about here)
The access to quality schools is also included in our popularity index.44 Most Hong
Kong students at the end of Secondary Grade Six take the Hong Kong Diploma of
Secondary Education (HKDSE) examination, which is the benchmark assessment
for local higher education admission. Competition is high for the enrollment ingovernment-funded degree-granting institutions in Hong Kong, we therefore focus
years. Replacing it with the arithmetic mean would make little diﬀerence to the final results.
42
MTR is the train company which operates the train, the subway and the light-train system inHong Kong.
43
There is an online system. Its website is http://www1.map.gov.hk/gih3/view/index.jsp.
44
The justifications are clear. First, the hedonic pricing literature, which is surveyed by Malpezzi(2008), among others, indicates that access to quality schools is an important determinant of house
price. Studies such as Black (1999), Dhar and Ross (2012), Figlio and Lucas (2004), Hanushek andYilmaz (2007, 2013), Nguyen-Hoang and Yinger (2011) also confirm the relationship between school
quality and property value.
The recent literature seems to confirm that quality of education matters. Among others, see
Hanushek et al. (2008), Hanushek and Woessmann (2012).

27

on the quality of secondary schools in our study.45 There is no oﬃcial ranking ofhigh schools in Hong Kong, but parents do exchange information and rank schools
on internet discussion forum, such as “Book of School.” This website lists the top
100 out of 490 local secondary schools, based on parents’ ratings on the campus, theteachers, students’ academic performance, and non-academic attainment in music
and sports.46 We group the top 100 secondary schools by their physical locations,and consider their distributions in diﬀerent districts.
Finally, we include information on nearby land auctions and the developer brand,
as the former is related to the quantity dimension of housing supply and the latterto the quality dimension of housing supply. Clearly, land auctions in adjacent areas
signify increases in the local housing supply, which tend to encourage prospective
home buyers to exercise the option of waiting (i.e. to delay their purchases until,
say, the new housing units come to the market). We retrieve land area, in termsof square meters auctioned for residential development, from the Lands Departmentof the Hong Kong government.47 To match with our sample, we restrict ourselvesto the auction records occurred between November 2011 and October 2012, and to
those sites within 2 kilometers radius around any of our 132 REDs.48 We combine
the location and lot number in the land sale files, land surveyors’ plan maps, and thestreet index and the lot address cross-reference table to ascertain the exact positionof a site.49
We have clear reasons for including the developer brand in the popularity index.
The primary residential real estate market in Hong Kong is dominated by a few developers; for example, in 2010, over seventy percent of new home sales come from45

The following figures may illustrate the keen competition for the enrollment in the 8 governmentfunded degree-granting institutions in Hong Kong. For instance, in the year 2014 HKDSE, the total
number of participants is about 79,572 and only 20,089 of them (25.25%) are admitted by the 8 local
UGC funded institutions. For more details, see http://cdcf.ugc.edu.hk/cdcf/indepthAnalysis.do
46

Hong Kong has a rather complicated primary and secondary education system consistingof seven types of schools according to their funding source including government establishedschools, aided schools, caput schools, schools under direct subsidy scheme (DSS), private schools,
international schools, and schools operated by English schools foundation (ESF). Other thaninternational and ESF schools catering the need of foreigners, other schools mainly accommodate
local children. A more detailed description of various types of schools in Hong Kong can befound in a public document provided by the Hong Kong University of Science and Technology
athttps://www.ab.ust.hk/hro/PubDoc/new_staﬀ_guide/resources/school_types_in_hk.pdf.
The
top
100
secondaryschools
listedon
Bookof
Schoolat
http://www.bookofschool.com/school/controller/schoolSearch?reporttype=secondaryranking&schoolcategory=2
are either government schools, or aided schools, or DSS schools. The former two kinds are publicsector schools, which are fully subsidized by the government and provide local children with freeeducation. DSS schools are private schools receiving government subsidies.
47
The web link for download is http://www.landsd.gov.hk/en/landsale/records.htm.
48
See Lam and Cheung (2000) for more discussion on the 2km radius.
49
These information can be found on http://www.landsd.gov.hk/mapping/en/landsale/2011/ls_t.htm
and http://www.landreg.gov.hk/tc/public/pu-si_agree.htm.

28

Cheung Kong Holdings and Sun Hung Kai Properties, two of the largest property
developers in Hong Kong.50 Other years are not as extreme, but the oligopolistic
structure remains. In our sample, nine developers, alone or in joint venture, participate in the developments of 119 projects.51 All other developers account for thedesign and construction of only thirteen projects.52 Severe information asymmetry
could potentially aﬀect the housing market, as unlike buyers, the developers possess the full knowledge regarding the development quality. Home owners may only
discover the true quality of the housing units after moving in, or even after years of occupation. This clearly discourages market transactions. In this market environment,
some firms put more eﬀorts into reputation building than others, such as providing
high-quality units more consistently, to signal their quality.53 The major developers
are therefore not equally favored by the market. Sung Hung Kai Properties appears
to be the most valued, and Cheung Kong Holdings the least valued. We carried out
a Factiva keywords search to investigate this.54 A search for “Sung Hung Kai” and“award”, retrieved 163 news articles reporting numerous accolades.55 Sung Hung Kai
50

See Vivian Kwok (2010 August 12), Two developers tower over market, South China Morning
Post.
In this paper, the real estate developer information are extracted from real estate broker’s websites.
We also obtain the information about the RED scale, which will be further discussed later, from thesewebsites. For instance, the website of Centaline Property is http://hk.centanet.com/eng/ehome.htm,
and the link for Midland Realty is http://www.midland.com.hk/en/.
51
These nine property developers are Cheung Kong Holdings, Chinachem Group, Hang Lung Properties, Henderson Land Development, MTR Properties, Nan Fung Group, New World Development,
Sino Group, and Sun Hung Kai Properties.
Notice that Cheung Kong Holdings belongs to Hong Kong’s most famous multi-national conglomerate, Cheung Kong Group. The group has another company called Hutchison Whampoa Limited,which also actively participated in the real estate market. In this paper, we consider REDs developedby Hutchison Whampoa Limited as if they were developed by Cheung Kong Holdings.
52
There are economic reasons suggested for such oligopolistic market structure, despite the factthat a significant amount of land sale is conducted through open auction. For instance, due to the
population density, high-rise buildings are needed as the dominant form of residential housing in
Hong Kong. The development of high-rise buildings, however, demands specialists and a large sunkcost. Thus, it is unlike that such buildings will be provided by a continuum of small developers, assome textbooks would assert. Among others, see Leung and Tang (2015) for more discussion for the
institutional details of the Hong Kong market.
53
Among others, see Mas-Colell et al. (1995) for more discussion of the signalling theory andreputation.
54
Factiva.com is a global news database with wide coverage in Chinese publications as well. We
initiate the search in the language of traditional Chinese.
WiseNews, a local news database more focused on Chinese newspapers and magazines, may fulfill
the same goal. However, it does not allow for subject classification. Searching with a combination of
keywords listed above generates too many noises. Factiva.com enables us to restrict ourselves to themore relevant “Corporate Awards” subject. As a subsidary of the Dow Jones & Reuters Company,
it is the industry leader and arguably has more advanced technology. So we mainly use Factiva.com
for news search.
55
In particular, two honors stand out. For both 2012 and 2013, four REDs of Sung Hung Kai
Properties have been awarded the annual “Best REDs” by the Hong Kong Professional Build-29

won the most awards between March 8, 2006 and the time of the search on March
11, 2014. In contrast, a similar search for Cheung Kong Holdings from November 30,
2005 to the same ending date returned only 88 pieces of news on corporate awards,
many of which are not for its contribution to the real estate development, but forthe company’s investment value as a multi-national conglomerate, its corporate social
responsibility, or for the lifetime achievement of Li Ka Shing, the founder and leaderof the company. In fact, by a keyword search for “estate” and “quality,” we findin four articles documenting consumer complaints and even lawsuits concerning thepoor quality of buildings designed and built by Cheung Kong Holdings in Beijing,
Guangzhou, Hong Kong, and Vancouver.56
As economists, we believe that if there is a consensus of quality diﬀerence, it should
be priced in the market. We verify this by evaluating the developer brands in a hedonic pricing framework with our underlying purchase and sale data. We introduce
nine dummy variables for the nine major developers, and the control group includes
all other developers. In addition, we control housing structural characteristics including gross square footage, net gross ratio, floor level, condominium orientation, andbuilding age, neighborhood characteristics including estate scale, RED facilities, andthe number of quality schools in the district, and locational characteristics including distance to subway stations and to the central business district, and proximity
to the waterfront. We also add district dummies, in an attempt to capture some
unobservable district-specific eﬀects. Considering the possible intraclass correlationof prices within the same RED, we use the clustered standard errors for reference.
The regression results are reported in Table 1b. In line with the previous discussions,
Sung Hung Kai Properties is the only developer with a significantly positive coeﬃcient, implying its developments sell at a premium even after controlling for diﬀerent
characteristics. The price discounts (i.e., negative price premium) of both Cheung
Kong Holdings and Chinachem Group are about 5%. Thus, this regression suggeststhat the reputation of the developers matters, even after controlling for other factors.
[Table 1b about here.]ing Inspection Academy, which is founded by a well-known local engineer Tsim Chai Nam in the
middle of 2012. This academy aims to provide consultancy for locals with respect to quality inspections and oversights of construction, decoration, remodeling, as well as maintenance. The
other two estates awarded this accolade are of Sino Group. See http://ps.hket.com/content/48406/
and http://www.hkcd.com.hk/content/2013-05/31/content_3201810.htm. Besides, Sung Hung Kai
Properties has been awarded “Prestigious Corporate Brand Awards” each year ever since 2007
when the program was initiated. This brand recognition award is jointly presented by Ming Pao,
one of the most credible local newspapers, and Department of Marketing of The Chinese Universityof Hong Kong. See http://pcbaward.com/cfm/other.cfm?html=13result for a complete list of allaward winning brands for 2013, and http://www.shkp.com/en-US/Pages/awards-and-recognition/
for the accolades wined by Sung Hung Kai in each year.
56
The articles are in traditional Chinese as well.

30Based on the discussion above, our popularity index combines nine indicators,
which are sorted in ascending order of desirability. As a reference point, a condominium is deemed to be the more desirable if it has a higher net gross ratio, is ina RED with both swimming pool and club house, is closer to a subway station,
the CBD, and the waterfront, has good schools in the district, and is sold at a low
price. Some formative indicators, namely, the proximity to the waterfront and subway, swimming pool and club house availability, are dummy variables, being scoredas either zero or one. Each of the six continuous variables, aﬀordability, net grossratio, building age, estate scale, distance to the CBD, and the number of top one
hundred secondary schools, are divided into ten equal groups. We then score thegroups from 0.1 to 1 from the least to the most desirable, with increments of 0.1.
With regard to the developer brand, we assign a value of one to Sung Hung Kai
properties, one-third to condominiums of Cheung Kong Holdings and the Chinachem
Group, and two-thirds to all the other units to represent market’s valuations of thesedevelopers. This scoring system ensures that all the formative indicators range fromzero to one, and no indicator carries more weight than another. For each RED, wetake the mean of the nine scores to be our final RED (or estate)-level popularity index, with a mean of 6249, a standard deviation of 1277, a sample minimum of 2948,
and a sample maximum of 9018. A complete list of ranked REDs in our sample ispresented in the Table 1c. Figure 3 relates the popularity index to the housing pricein the past five years at the RED level, with each RED represented by one dot. Figure
3a shows no notable relation between the popularity index and mean price growthrate of REDs once three outliers are removed, but Figure 3b clearly demonstrates
a negative correlation between the index and the associated price growth volatility.
The more popular an estate is, the lower the price growth volatility it displays.
[Table 1c, Figure 3a, Figure 3b about here.]
We attempt to make our popularity index all-inclusive, but it does have someshortcomings. It only considers the physical characteristics of a condominium, which
are more objectively measured. Nevertheless, without integrating the market forcesof supply and demand, our constructed “popularity” can only serve as an imperfectmeasure of the “popularity” in the theoretical model. To illustrate this we can compare two REDs, The Belcher’s and Kingswood Villas. The former is more appealing
than the latter in almost every aspect. The Belcher’s was developed by Sung Hung
Kai Properties, and is situated just 2 500 meters away from the CBD, 310 meters
away from the beautiful waterfront of Victoria Harbor. In contrast, Kingswood Villas
is a Cheung Kong Holdings development, and is situated over 25 000 meters awayfrom the CBD, and nowhere near the seaside. Kingswood Villas is six years older
than The Belcher’s, and has only seven high-quality secondary schools in the vicinity,
whereas The Belcher’s has nine. Under our construction, other things being equal,
31

The Belcher’s should be ranked higher.57 However, other things are not equal. During
the sampling period, the mean selling price is more than 13 000 Hong Kong Dollars(HKD) per square feet for The Belcher’s, but under 3 500 HKD per square feet forKingswood Villas.58 The Belcher’s residents have a median monthly household income of 93 580 HKD, while the residents of Kingswood Villas merely have 26 000
HKD, according to the census.59 Kingswood Villas is obviously more attractive toordinary people in Hong Kong.

5

Empirical Findings

The previous sections provide detailed discussions on the data set used, the construction of the popularity index and the econometric framework. This section reports
how the theoretical model proposed is verified empirically, and what the empiricalfindings are. Existing literature has suggested four types of empirical determinants of
the rent-to-price ratio, which are the macroeconomic variables, regional market conditions, property attributes, and investor characteristics.60 This paper complements
the literature by exploring the linkage between rental yields on the one hand, andproperty attributes and the characteristics of the owner-occupiers, which can also beinterpreted as the “investors” of the housing market, on the other hand. To achieve
this goal, we estimate the empirical model (28) with a dataset compiled by a crosssectional data set of household survey and a panel of housing transactions. We havediscussed in details how the rent-to-price ratio, the turnover rate and the popularity
index are constructed. We now provide more explanations about how the vectors
 and  in (28) are constructed. The choice ingredients in vector  can be easily
justified. They include the average rent growth rate and house price appreciation in
the previous years at the RED level. As property attributes do not change significantly over time, especially for condominium, those previous year rent and price data
enable us to have a good control of the “initial conditions.”61 The vector  set also
57

Belcher’s is ranked the sixth, and Kingswood Villas is ranked the 37th out of 132 REDs in our
sample.
58
The oﬃcial exchange rate is 7.8 HKD for one US dollar. And one square meter is roughly equal
to ten square feet.
59
Alternatively, we could use hedonic estimates as weights. But then we will not be able to dictate
the “aﬀordability” because price is the dependent variable in the hedonic regression.
60
While earlier studies focus predominantly on the eﬀects of macroeconomic variables, such as
interest rates, expected inflation, and stock market risk and return (Ambrose and Nourse 1993;
Evans 1990; Jud and Winkler 1995; Peng, 2013), more recent research extends this to regional
market conditions, most importantly rent growth rates and the expected returns of real estate (Anand Deng 2009; Campbell et al. 2009; Plazzi et al. 2010). Other relevant local market factors
include vacancy rate (Sivitanidou and Sivitanides 1999), investor sentiment (Clayton et al. 2009),
and credit availability (Chervachidze and Wheaton 2013).
61
In the literature, some authors use the historical returns of the RED as proxies for the corresponding expected values.

32contains information of the owner-occupiers, such as the median household monthly
income, mortgage payment-to-income ratio, percent of residents with college degrees,
and the percent of residents working in real estate consultation industry, as well assome physical conditions of the RED, such as the RED scale, nearby land auctions
representing local market conditions, which have been argued as important determinants of the rent-to-price ratio in the discussions on diﬀerent media. Here, we simply
put them in an unifying framework and assess these discussions more rigorously.
Since asset quantities and trading have “received far less attention” in the literature (Lo and Wang, 2009), our choice of control variable vector  in the empiricalmodel (28) is based on simple economic reasoning. First, expected returns and earnings (rents) potential are obvious candidates. Partly as an investment vehicle, returnrelated variables must aﬀect the trading activity of residential properties. Second, areal-estate-related occupation may also provide the advantage of being able to invest
in property.62 REDs housing more residents working in the real estate profession may
therefore display more frequent trading. Third, the role of household income is more
complicated in ex ante terms so that research is needed. Increases in income may
influence housing demand, resulting in a higher sales volume, but a higher incomemeans a higher opportunity cost of moving, which will dampen trading volume. Being agnostic of which eﬀect would dominate, we include the variable in the regression
and allow the data to inform us. Fourth, because early works on search models emphasize the existence of thick market eﬀect (TME) (Diamond, 1982a, 1982b; Ngai
and Tenreyro 2014), RED size is incorporated as a simple proxy for TME to allow
for such possibility. The RED scale is extracted from real estate broker’s websites.63
Fifth, land auction is controlled as well for the justification in the following. Landauctions in adjacent areas suggest more housing supply in the near future. Hence,
potential buyers may demand a deeper discount in transaction price (which usuallylead to a longer bargaining process and less transactions in the short run), or simply
delay their purchases. Finally, the young population proportion and building age aretaken into account too, but the reasons for such inclusion will be elaborated in thenext paragraph.
Notice that the variables in vector  and  overlap, but not completely. Clayton et al. (2009) use mortgage payment as an indicator of investor sentiment andfind that it is negatively associated with property capitalization rate. Following theirapproach, we control mortgage income ratio in the rent-to-price regression. Thismeasure, however, is an average of many households who are at diﬀerent phases ofmortgage cycle. Some mortgages were signed a long time ago. There is no reason
to believe mortgage income ratio will impact current trading activity, and thus is
excluded from the turnover regression. As previously mentioned, housing is an investment vehicle. But it is also a consumption good, of which hedonic attributes
62

For instance, see Munneke et al. (2012) and the reference therein.
The website of Centaline Property is http://hk.centanet.com/eng/ehome.htm, and the link for
Midland Realty is http://www.midland.com.hk/en/.
63

33

are important pricing components. For example, Shapiro (2006) demonstrates thathuman capital, as an indicator of local amenity, has a causal eﬀect on rents and house
prices. Motivated by his work, we incorporate the human capital environment of acommunity in the rental yield regression using percent of college degree holders in a
RED as a proxy. Again we do not expect more college degree holders will necessarily
be more or less active in trading properties, hence this variable does not show up in
the turnover regression. To put it diﬀerently, mortgage income ratio and percent ofresidents with college degrees are our instruments to identify the turnover equation.
Similarly, percent of young population and building age appear in vector  but
not , hence help us to identify the rent-to-price equation. Young population ispresumably more mobile. Higher mobility in the 25 to 44 age-group could lead tohigher turnover rates in REDs with relatively higher concentrations of young households. Our discussions with the market practitioners confirm the observation that newREDs tend to be more actively traded. Thus, the age of the buildings is includedin the turnover equation. RED size and household income enter both equations innatural logs to capture some nonlinearity.

5.1

Main Results

Our theoretical model has shown that both rent-to-price ratio and turnover rate areendogenous and they are simultaneously determined in the equilibrium. In that case,ordinary least squares (OLS) estimation of system (28) suﬀers from simultaneous
equations bias (SEB). As Greene (2008, chapter 13) once remarked, “Although we
can say with certainty that  (ordinary least squares estimator) is inconsistent (inthe context of simultaneous-equations estimation), we cannot state how serious thisproblem is.” In other words, we need to assess the magnitude of the SEB in the current
context. To proceed, we show the OLS estimates in Column (1) and their corresponding standardized coeﬃcients in Column (4) of Table 2. While the turnover rate in
the rent-to-price equation is confirmed to be endogenous by a formal Hausman test,
the endogeneity (or, exogeneity) of the rent-to-price ratio in the turnover equation
is a borderline case.64 Concerned with the power of the test, it is not clear whether
the rental yield is truly exogenous. Notice also that while the theory is ambiguouson the sign of the correlations between the turnover rate and the rent-to-price ratio(see from (24) to (26)), OLS estimates deliver positive coeﬃcients in both turnoverratio equation and rent-to-price ratio equation.
64

The Hausman test is implemented equation by equation in four steps: (1) run a reduced-form
regression of the potential endogenous variable on all exogenous variables (both X and Z) using
the OLS estimator, (2) predict the residuals from the above regression, (3) estimate the structural
equation with residuals from last step as an extra control, (4) test if the coeﬃcient of the residual
variable is zero. The -statistic is 2.9 for the significance test of turnover’s residual and 1.4 for thatof rent-to-price ratio’s residual. The critical value for 10% relative bias toleration is about 1.6.

34

[Table 2 about here.]

Given these results, we consider it appropriate to proceed with a consistent, full
information estimator, which is the three-stage least squares (3SLS). But before that,
we need to verify that our system of equations is identifiable. The order condition,
which requires the number of exogenous variables excluded from one equation to beat least as large as the number of endogenous variables included in the equation, isclearly satisfied in the current context. And our system passes the rank condition
test (Baum 2007) as well. A final specification test, the Hansen-Sargan test of overidentifying restrictions (Baum 2006),65 confirms our instruments are all valid.
Since we have validated our approach, we now present more detailed results. Column (3) of Table 2 reports the 3SLS estimates with small sample adjustment on thecovariance matrix of the regression residuals. Column (6), a list of corresponding
standardized coeﬃcients, gives the economic magnitude of our results. Consistent
with the prediction of our theoretical model, investors of the less popular REDs arecompensated with higher rental yields, probably in the form of a lower purchasing price. With an increase in the popularity index by one standard deviation, therent-to-price ratio would decrease by 0.158 standard deviations. This is statisticallysignificant at the 10% significance level. We also find a negative relationship between
the rent-to-price ratio and the turnover rate. Other variables held constant, if theturnover rate increases by one standard deviation, the rent-to-price ratio will decline
by 0.475 standard deviations. The estimate is statistically diﬀerent from zero at the
5% significance level. However, we fail to find any significant eﬀects on turnover rateof rental yield and popularity index in the lower panel of Table 2. Such disappointing result may be due to imperfections of our popularity index, our small sample
size, and our still limited understanding or imperfect modeling of the house trading
process.66 Alternatively, the insignificant empirical result may reflect the theoreticalresult, which is ambiguous. More research is needed on this topic.
On top of providing an empirical verification of the theoretical model, our econometric model also identifies the empirical determinants of the RED-level rent-to-priceratio and the turnover rate. The coeﬃcients of Ln(Income) in both equations are negative and highly significant (both economically and statistically). The upper panel ofTable 2 shows that the rent-to-price ratio will fall by 0.794% for every unit increasein Ln(Income) in the RED. An interpretation of this result is that there exist someamenities which attract people with higher income and at the same time unobservableto econometricians (for instance, the “harmony” and the degree of “quietness” of the65

The Hansen-Sargan statistic is 2.008, which is distributed as Chi-squared with two degrees of
freedom.
66
For instance, housing transaction taxation (HTT) is assumed away in the model. In practice,
HTT is nonlinear and might be important. Among others, see Leung et al. (2015) for a recent study.

35

environment). Hence, a RED with a higher level of “econometrician-unobservableamenities” would have a higher level of (average) income. As higher income residents
are more reluctant to move (i.e. the opportunity cost of moving eﬀect dominates thedemand eﬀect), REDs with higher income residents are likely to have more homeowners, which tends to drive up the house price more than the rent, resulting in alower rent-to-price ratio. The turnover rate of a RED would be 3.693% lower with aunit increase in the median household income. Real-estate work experience does notseem to trigger more trading. Yet despite that, the occupational advantage does havea significant positive impact on the valuation, as reflected by the positive and significant coeﬃcient of the “Work in Real Estate Consulting” variable. This is consistent
with the finding in the literature that real estate agents may have informational advantages over their clients (Levitt and Syverson 2008). While the previous year’s
housing price appreciation rate has no significant influence on the rent-to-price ratio,
it has a significantly negative eﬀect on the turnover rate. Transaction volume typically co-moves with property price.67 A higher price appreciation rate in last year
is probably associated with a higher turnover. If the new owners keep their units inthe portfolio, turnover rate in the current period would decrease. Quantitatively, if
the housing price growth rate of a particular RED was 10% higher than the meanacross all estates last year, then the current normalized transaction would decline by
1%. In contrast, the average rent growth rate in past five years, which can be interpreted as a measure of the potential for the housing units to generate income flow,
significantly aﬀects the rent-to-price ratio (at 5% level) but not the turnover rate.
RED scale, the proposed measure of “thick market eﬀect” (TME), is not significant
in either regression, holding other variables constant. While it is still premature to
reject the existence of TME with our relatively small sample size and relatively shortsampling period, it is fair to say that its empirical relevance in the housing market
remains to be proven. To conclude the paragraph, we find that nearby land auctions,which proxies for future substitutes in the neighborhood have a dampening eﬀect on
current sales volume, although the impact may only be marginally significant, witha p-value of 0.189. Potential home owners may indeed keep their option to buy laterin the face of nearby land auction.
The last set of results from the 3SLS is about the four instruments. In line with
Clayton et al. (2009), we also find a significantly negative association between themortgage burden and rental yield, holding other things constant. Thus, investors arewilling to take out a heavier mortgage, even with a lower rental yield at the moment,
perhaps expecting a larger capital gain in the future. However, since we do not havedirect measure of the expected house price changes from the household survey, we
can only leave the full explanation of this empirical finding to future research. We
also find that communities with a higher level of human capital, measured by the per67

The literature on the house price-transaction volume correlation is too large to be reviewed here.
Among others, see Leung et al. (2002) for a study of such correlation in the Hong Kong housing
market.

36

centage of college-educated residents, tend to have higher rent-to-price ratio. Finally,
properties that are build more recently and REDs with a larger young population,
who are considered more mobile, are more actively traded. All these four estimates
are significant at least at the 10% significance level.

5.2

Robustness

In the previous section, we report our findings on the co-determination of the rentto-price ratio and the turnover rate, as well as the empirical determinants of thetwo variables. In this section, we would address some statistical concerns and showthat our results are indeed robust. First, we would address the issue of econometricmethod. As we have explained before, our theoretical model shows that the rentto-price ratio and the turnover rate are jointly determined. To faithfully verify thistheoretical conclusion, we need an econometric method for a system of simultaneous
equations. In this regard, 3SLS is a natural candidate as it estimates our equations,(30) and (31), jointly. Another consistent but less eﬃcient estimator for simultaneous
equations models is two-stage least squares (2SLS). Methodologically, it is essentiallythe first two steps of 3SLS. However, treating the disturbances of equations as independent, it is a limited information estimator and hence less eﬃcient. 2SLS forgoes
some eﬃciency for the benefit of a less stringent data requirement. Therefore, it canserve a useful robustness check. As shown in Column (2) and (5) of Table 4, despite
being less significant, the results are very similar to those in Column (3) and (6).
The second issue is the small sample size of this paper. We bootstrap and crossvalidate the data.68 The resampling operation applied here involves bootstrapping the
3SLS regression coeﬃcients in a thousand replications. Visualizations of the resulting
1000 bootstrapped coeﬃcients are provided by their density distributions in Figure 4
and the appendix. The vertical lines in the figures stand for the coeﬃcient estimatesfrom the actual data, i.e. those in Column (3) of Table 2. Since they are almost
always in the middle of the distribution, there should be no substantial bias in ourestimates. In Figure 4a, more than 94% of the bootstrapped coeﬃcients for turnover
fall in the range between -1.5 and zero. In both Figure 4b and 4d, the vast majorityof the estimated coeﬃcients for popularity index have the same negative signs as inColumn (3) of Table 2. The estimated range of the coeﬃcient of rental yield in theturnover equation is however too wide to be informative, as in the case of the actual
sample. Coeﬃcient distributions of other covariates from the bootstrapping exercises
can be found in the appendix. Based on these findings, it seems that the small sample
size is not issue.

68

Both the bootstrap method and cross-validation are widely used in the literature. Among others,
see Diebold (2016), Efron and Tibshirani (1993), Moore (2016).

37

[Figure 4 about here]
It is well known that the existence of outliers could potentially aﬀect the empiricalresults, especially in a relatively small sample. To address this issue, we employ theleave-one-out cross validation (LOOCV) to detect influential outliers. The idea issimple. We repeatedly re-run the same regression model with all but one observations.
We iterate this process throughout our sample. Visual representations of the resulting
130 vectors of coeﬃcients are in Figure 5 and the appendix. Although leaving certain
observations out does lead to some deviations from the full-sample estimates, there
is no qualitative change in results. Thus, outlier does not seem to be an issue either.
[Figure 5 about here]
We also receive some feedback about our popularity index and hence we feel obligated to provide more discussion here. This research attempts to build a novel
popularity index for housing. According to the literature (Diamantopoulos and Winklhofer 2001; Jarvis et al. 2003), measurement models are of two types, refective andformative. What the former does is to look for some latent variable which causes theobservable eﬀect indicators such as economic growth and poverty reduction. Multiple eﬀect indicators could be traced back to a common latent variable. In contrast,
the objective of a formative model is to summarize a set of causal indicators into acomposite outcome index. Socioeconomic status, combining income, education, andoccupation, is a typical example. Conceptually, a formative model fit our purpose
better. So we form the popularity index as a linear combination of nine causal indicators with equal weights. Clearly, such a simple approach may raise concerns about
how it might aﬀect the robustness of our findings. In order to alleviate such concerns,in the spirit of LOOCV we remove one sub-indicator at a time, reformulate the index
based on the remaining eight sub-indicators, and re-run the 3SLS regression. This
process is repeated nine times for every sub-indicator and results in several extra coeﬃcient estimates for every control variable of the regression. In Figure 6 and theappendix, these point estimates are plotted around the coeﬃcients (the horizontalline) from regressions with default popularity index. Again the deviations are very
mild, suggesting our results are robust to diﬀerent weighting schemes on the subindicators. As an alternative index construction method, we also try the principal
component analysis on our data in the appendix. However, we need to retain as
many as six principal components to capture less than 80% of variances in our nine
indicators, which does not seem to be a promising approach given our small sample
size and 3SLS procedure. Last but not the least, we also incorporate some districtlevel information in an extended specification and the results, which are reported in
the appendix, do not significantly change.
38

[Figure 6 about here]

6

Concluding Remarks

Research in real estate has been growing since the Great Recession. Search models
endogenize vacancy and trading volume and are therefore investigated more heavily
in the theoretical literature.69 On the other hand, empirical investigations on therental yield and normalized transaction, and the interactions among them in theresidential property market, are surprisingly scarce.70 Previous studies focus on how
the macroeconomic environment, regional market conditions, property attributes,
and investor characteristics would aﬀect the rent-to-price ratio. However, few studies
examine how the rental yields are related to the characteristics of the household livingin those housing units. Empirical works typically treat the rent-to-price ratio as the
housing market counterpart of the earning-to-price ratio in the stock market, but
few consider how the ratio is determined in equilibrium, and how it can be related toeconomic fundamentals. This paper attempts to complement the existing literatureby providing a search-theoretic model and applying it to a unique RED-level data set
in Asia, where housing units are (relatively) frequently traded.
Our theoretical model shows that both the rent-to-price ratio and the turnoverrate can be related to each other, and to the level of popularity. Building on previous
literature, our empirical work attempts to construct a popularity index as a proxy forthe underlying good-match probability or the desire for owner-occupants on a RED
that econometricians may not observe directly. Second, as housing units are eithertransacted in the sale market or rental market but not both, we adopt a matching estimator to create sale-rental pairs, where both units have the same “quality.” Third,
we adopt a 3SLS approach to solve the simultaneity issue. Our empirical results dosuggest that the OLS estimates are very likely to be biased, which justifies our 3SLS
estimation approach. We confirm a significantly negative eﬀect of the turnover rateon the rent-to-price ratio. If the trading activities are more intensive, measured by aone-standard-deviation increase in the turnover rate, the associated rental yield would
be 0475 standard deviations lower. The two-stage least squares analysis reports similar results. These findings provide supportive evidence of a liquidity eﬀect in theproperty market, which has been widely reported in the financial market research.
69

Among others, see Wheaton (1990), Yavas, (1992a, 1992b), Krainer (2001), Albrecht et al.
(2007), Genesove and Han (2012), Diaz and Jerez (2013), Anglin (2006), Anglin and Gao (2011),
Lin and Vandell (2007), Lin and Liu (2008), and Tse (2011).
70
Exceptions include Kwok and Tse (2006), which test the price premium for condominiums
easier to sell in a submarket of Hong Kong, and Liu and Qian (2012), which confirm an illiquidity
compensation in property returns based on a sample of 24 oﬃce markets in the U.S.

39

Our constructed popularity index is also important in explaining the rental yield.
A RED with a popularity index one standard deviation higher has its rent-to-priceratio 0158 standard deviations lower. This eﬀect is also in line with our theoretical model. Our on-the-house-search model, which can be considered as the housing
market counterpart of the on-the-job-search model, the popularity index, and ourempirical estimates of brand premium for diﬀerent developers, may independently beof interest for market practitioners and academics.
In addition, we identify the empirical determinants of the rental yield or theturnover rate. We find that income has a dampening eﬀect on both the rental yieldand the turnover rate. In our sample, the opportunity cost of moving appears todominate the wealth eﬀect. We also find evidence of a “dichotomous structure” inthe housing market: the demographic structure, and lagged price appreciation of a
RED tend to aﬀect its turnover rate, while popularity, human capital environment,
mortgage burden, and long run rent growth have more influence on the rental yield.
We employed several statistical methods to establish the robustness of our results.
We believe our results have both academic and practical value.
This study provides a search-theoretic model which endogenizes both the rentto-price ratio and the transaction volume. The rent-to-price equation is empiricallyconfirmed and we make some additional empirical observations. Nevertheless, there
is room for further improvement. While we can identify the empirical determinantsof the cross-sectional diﬀerences in turnover rates among diﬀerent REDs, we fail tofind any evidence that the popularity index or the rent-to-price ratio play a rolein explaining the turnover rate diﬀerence. Future research, therefore, can improveon the popularity index. In fact, there may exist two diﬀerent indices, one is more
relevant for the cross-sectional rental yield diﬀerence and the other for the turnoverrate diﬀerence. In theoretical terms, a more sophisticated model of the housing market
could also be constructed.71

71

For instance, see Leung and Tse (2016), Luo (2014).

40

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47

Table 1a. Summary Statistics
Variables
count
mean
Mean R/P of the RED (%)
132
3.772
Median R/P of the RED (%)
132
3.681
Turnover Rate in Sample Period (%)
132
7.181
Average Rent Growth Rate in Past 5 YRs (%)
130
4.294
Last Year HP Growth Rate (%)
132
21.564
Population Resided in the RED (Persons)1327640.803
Young Population (%)
132
40.139Middle Age Population (%)
132
29.314
Median Age of the Residents (Years)
132
39.008Married Population (%)
132
56.921
Mandarin Speaker (%)
132
3.933
College Education Level (%)
132
46.477
Household Monthly Median Income (2005 HKD)
132
37907.360
Median Monthly Mortgage Payment (2005 HKD)
132
8875.867
Mortgage Income Ratio (%)
132
20.345Home Ownership Rate in the RED (%)
132
76.314
RED Popularity
132
6.249
Average Net Gross Ratio (%)
132
78.090
Average Building Age (Years)
132
19.214
Estate Scale
132
2899.932
Distance to CBD (Meters)
132
12168.281
Distance to MTR (Meters)
132
380.302
Distance to Waterfront (Meters)
132
381.629# Top 100 Secondary School in the Same District
132
5.742
Nearby Land Auction (Square Meters)
132
6140.515

sd
0.476
0.464
3.160
4.022
5.889
6978.537
7.994
5.451
2.390
3.220
2.620
11.42917274.432
4691.953
2.647
10.111
1.277
4.710
8.701
2474.556
6775.361
151.925158.259
2.995
15539.870

min
2.629
2.596
0.484
-13.0962.231
2263
23.05512.90334.10048.1170.500
20.90013090.000
3400.000
14.90041.3002.948
63.9532.933
900.000
1152.10052.28434.000
0
0

max
5.631
5.308
18.97220.62635.80339361
62.21842.32846.10065.09612.90075.500133450.000
30132.500
28.50094.0009.018
88.65441.12115836.000
25431.000
500.000
500.000
13
76167

Table 1b. Hedonic Pricing: Developers' Ranking
VARIABLES

Ln(Price)

Cheung Kong Holdings-0.050**[0.038]-0.055**[0.013]-0.037[0.182]-0.008[0.710]-0.035[0.257]0.011[0.725]0.021[0.381]
0.043[0.314]0.053***[0.008]12.843***[0.000]Chinachem Group
Hang Lung Properties
Henderson Land Development
MTR Properties
Nan Fung GroupNew World Development
Sino GroupSun Hung Kai Properties
Constant

Housing Structural Characteristics
Neighborhood Characteristics
Location Characteristics

YES
YES
YES

Observations
29,647
Adjusted R-squared
0.813
District FE
YES
Clustered Std Errors
YES
F
124.2
pval in brackets*** p<0.01, ** p<0.05, * p<0.1

Table 1c. Popularity Ranking of Real Estate Development (RED)
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41

EstateHARBOUR PLACE
HARBOUR GREEN
OCEAN SHORESHENG FA CHUENPARK AVE
BELCHER'SLAGUNA CITYSORRENTOLOHAS PARKGRAND PROMENADE
ISLAND HARBOURVIEWTIERRA VERDECITY GDNWATERFRONTVILLA ESPLANADAROYAL PENINSULAVILLA ATHENATAIKOO SHINGGRAND WATERFRONTLAKE SILVER
MERTONGREENFIELD GDNSUNSHINE CITYTELFORD GDNPARK CENTRALISLAND RESORTLAGUNA VERDEMETRO HARBOUR VIEW
EAST POINT CITY
COASTAL SKYLINEYOHO TOWNVISTA PARADISORESIDENCE BEL-AIR
LIBERTEPARK ISLANDMETRO CITYKINGSWOOD VILLASTUNG CHUNG CRESCENTMETRO TOWNGRANDIOSE
GRAND HORIZON

Popularity Index
9.018
8.814
8.640
8.611
8.248
8.211
8.209
8.191
8.189
8.138
8.115
8.101
8.085
7.961
7.905
7.663
7.646
7.645
7.588
7.584
7.553
7.551
7.543
7.492
7.454
7.430
7.427
7.418
7.366
7.344
7.324
7.312
7.302
7.268
7.265
7.263
7.046
7.021
7.019
7.001
6.984

District
Kowloon City
Yau Tsim Mong
Sai Kung
Eastern
Yau Tsim Mong
Central and Western
Kwun Tong
Yau Tsim Mong
Sai Kung
Eastern
Yau Tsim Mong
Kwai Tsing
Eastern
Yau Tsim Mong
Kwai Tsing
Kowloon City
Sha TinEastern
Kowloon City
Sha TinCentral and Western
Kwai Tsing
Sha Tin
Kwun Tong
Sai Kung
Eastern
Kowloon City
Yau Tsim Mong
Sai Kung
Islands
Yuen Long
Sha TinSouthern
Sham Shui Po
Tsuen Wan
Sai Kung
Yuen Long
Islands
Sai Kung
Sai Kung
Kwai Tsing

42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85

MANHATTAN HILLDISCOVERY PARK
SOUTH HORIZONSPARCVILLE
CENTRAL PARKRESIDENCE OASISSEAVIEW CRESCENTSEA CREST VILLAPROVIDENT CTR
SCENEWAY GDNLA CITE NOBLE
PACIFICAAQUAMARINEAEGEAN COASTNAN FUNG PLAZABANYAN GDNBELLAGIO
CENTRAL PARK TWRS
TSING YI GDN
HANFORD GDNRAMBLER CREST
SKY TWR
PALAZZO
HONG KONG GOLD COAST
LEI KING WAN
VISION CITYROYAL ASCOTMIAMI BEACH TWRSPARKLAND VILLASRIVIERA GDN
SERENITY PLACESUMMIT TERRSERENITY PARKCITY ONE SHATIN
NERINE COVERHINE GDN
DIS. BAY
WHAMPOA GDNSUN YUEN LONG CTRCHELSEA COURTRAVANA GDNQUEEN'S TERRCASTELLOTAI HING GDNS

6.965
6.896
6.842
6.830
6.829
6.819
6.805
6.775
6.755
6.724
6.703
6.693
6.679
6.666
6.638
6.633
6.589
6.587
6.554
6.490
6.454
6.425
6.413
6.354
6.344
6.301
6.289
6.274
6.115
6.107
6.104
6.053
6.048
5.998
5.907
5.901
5.890
5.890
5.863
5.849
5.797
5.787
5.771
5.705

Sham Shui Po
Tsuen Wan
Southern
Yuen Long
Yau Tsim Mong
Sai Kung
Islands
Tsuen Wan
Eastern
Kwun Tong
Sai Kung
Sham Shui Po
Sham Shui Po
Tuen Mun
Sai Kung
Sham Shui Po
Tsuen Wan
Yuen Long
Kwai Tsing
Tuen Mun
Kwai Tsing
Kowloon City
Sha Tin
Tuen Mun
Eastern
Tsuen Wan
Sha Tin
Tuen Mun
Tuen Mun
Tsuen Wan
Sai Kung
Tsuen Wan
Tai PoSha Tin
Tuen Mun
Tsuen Wan
Islands
Kowloon City
Yuen Long
Tsuen Wan
Sha TinCentral and Western
Sha Tin
Tuen Mun

86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129

GRAND DEL SOLBELVEDERE GDNUPTOWN PLAZA
TAK BO GDNCHELSEA HTSWELL ON GDNSERENO VERDESHA TIN CTR
VIANNI COVEBAGUIO VILLACHI FU FA YUENWONDERLAND VILLASDAWNING VIEWSJUBILEE GDNSUN TUEN MUN CTRSHERWOOD
PIERHEAD GDNLIDO GDNCARIBBEAN COAST
MAYFAIR GDNSAVON PARKGARDEN RIVERAFLORA PLAZAAMOY GDNMEI FOO SUN CHUENFANLING CTR
WHAMPOA ESTTSUEN KING GDNTUEN MUN TOWN PLAZALUK YEUNG SUN CHUENBELAIR MONTEALLWAY GDNABERDEEN CTR
BRAEMAR HILL MANSTAI PO CTRJUBILANT PLACEBELAIR GDNSFANLING TOWN CTRGOODVIEW GDNGOLDEN LION GDNGOLDEN LION GDNPICTORIAL GDN
NEW KWAI FONG GDNLUCKY PLAZA

5.686
5.658
5.621
5.620
5.577
5.576
5.540
5.536
5.502
5.404
5.370
5.315
5.286
5.258
5.256
5.233
5.220
5.211
5.191
5.183
5.154
5.144
5.105
5.073
5.027
5.014
5.006
4.964
4.863
4.800
4.780
4.752
4.721
4.490
4.447
4.380
4.314
4.304
4.170
4.100
4.013
4.005
3.932
3.902

Yuen Long
Tsuen Wan
Tai PoKwun Tong
Tuen Mun
Sai Kung
Yuen Long
Sha TinYuen LongSouthern
Southern
Kwai TsingNorth
Sha Tin
Tuen Mun
Tuen Mun
Tuen Mun
Tsuen Wan
Islands
Kwai TsingNorth
Sha TinNorth
Kwun Tong
Sham Shui Po
North
Kowloon City
Tsuen Wan
Tuen Mun
Tsuen Wan
North
Tsuen Wan
Southern
Eastern
Tai PoKowloon City
Sha Tin
North
Tuen Mun
Sha TinSha TinSha Tin
Kwai Tsing
Sha Tin

130
131
132

TSUEN WAN CTR
HONG KONG GDNWALDORF GDN

3.853
3.373
2.948

Tsuen Wan
Tsuen Wan
Tuen Mun

Equation: R/P
Turnover Rate %Popularity of the RED
College Education Level %Ln(Income)Mortgage Income Ratio %Work in Real Estate Consulting %Last Year HP Growth Rate %Rent Growth Rate in Past 5 YRs
Ln(RED Scale)Land Auction
Observations
RMSE
F/Chi-squared
R-squared
Equation: Turnover
Mean R/P of the RED
Popularity of the RED
Young Population %Ln(Income)Work in Real Estate Consulting %Last Year HP Growth Rate %Rent Growth Rate in Past 5 YRs
Average Building Age
Ln(RED Scale)Land Auction
Observations
RMSE
F/Chi-squared
R-squared

Table 2: Main Results
Coef.
OLS
2SLS
3SLS
(1)
(2)
(3)
0.016
-0.075*0.003-0.450***-0.046***0.028*
0.001
0.012
0.106*-0.007
130
0.351
14.42
0.479

-0.064*-0.0620.004-0.724***-0.040***0.044**-0.0120.020*
0.080-0.014*130
0.401
121.420.258

1.540*-0.172
0.093**-2.141***0.090-0.089**0.077-0.103***0.102-0.060
130
2.579
6.10
0.389

-1.525-0.3300.098**-3.578**0.198-0.113**0.115-0.0590.342-0.097
130
2.681
75.59
0.278

OLS
(4)

Beta Coef.
2SLS
(5)

3SLS
(6)

-0.072**-0.068*0.007*-0.794***-0.037**0.044**-0.0120.020**
0.078-0.015
130
0.413
80.24
0.213

0.106
-0.174*0.070-0.378***-0.256***0.118*
0.008
0.097
0.135*-0.061
130
0.737
14.42
0.479

-0.427*-0.1440.093-0.609***-0.221***0.182**-0.1480.165*
0.102-0.120*130
0.842
121.420.258-0.475**-0.158*0.161*-0.668***-0.207**0.182**-0.1480.171**
0.100-0.123
130
0.867
80.24
0.213

-1.188-0.2960.070**-3.693**0.211-0.102**0.114-0.093**0.285-0.092
130
2.644
61.56
0.298

0.232*-0.0600.234**-0.271***
0.057-0.166**0.098-0.284***0.020-0.076
130
0.816
6.10
0.389

-0.230-0.1150.247**-0.454**0.125-0.210**0.147-0.1620.066-0.122
130
0.849
75.59
0.278

-0.179-0.1030.178**-0.468**0.133-0.191**0.145-0.257**0.055-0.115
130
0.837
61.56
0.298

Note: OLS and 2SLS estimations are performed equation by equation. Estimates of standard errors are adjusted to
be robust to misspecifications arising from neglecting heteroscedasticity. 3SLS estimates the two structural
equations simultaneously. Small sample adjustment is made on the covariance matrix of the regression residuals.
Standard errors and intercepts are suppressed to save space. The stars *, **, and *** indicate the significance levelat 10%, 5%, and 1% respectively.

-20

Mean Price Growth in Past 5 Years %
-10
0
10
20

30

Figure 3a Popularity Index and Housing Price Growth2

4

6
Popularity Index

8

10Volatility of Price Growth Rate in Past 5 Years
10
20
30
40

Figure 3b Popularity Index and Housing Price Volatility

2

46Popularity Index

810Figure 4 Bootstrap Replications
Figure 4a Coefficient Distribution of Turnover Rate

0

2

4

Density
6

8

10

from 1000 boostrap replications of the rent-to-price regression

-.3

-.2

-.1
Coefficient0.1kernel = epanechnikov, bandwidth = 0.0086

Figure 4b Coefficient Distribution of Popularity Index

02

Density
4

6

8

from 1000 boostrap replications of the rent-to-price regression

-.3

-.2

-.1
Coefficientkernel = epanechnikov, bandwidth = 0.0113

0.1Figure 4c Coefficient Distribution of Rent-to-Price Ratio

0.05

Density
.1

.15

.2

from 1000 boostrap replications of the turnover regression

-20

-10

0

10

Coefficientkernel = epanechnikov, bandwidth = 0.5041

Figure 4d Coefficient Distribution of Popularity Index Ratio

0.5

Density1

1.5

from 1000 boostrap replications of the turnover regression

-2

-1

0
Coefficientkernel = epanechnikov, bandwidth = 0.0758

1

Figure 5 Leave-one-out Cross Validations
Figure 5a Coefficient Distribution of Turnover Rate

0

10

20

%

30

40

50

from leave-one-out cross validations of the rent-to-price regression

-.09

-.08

-.07

-.06

Coefficient

Figure 5b Coefficient Distribution of Popularity Index

0

20

%
40

60

80

from leave-one-out cross validations of the rent-to-price regression

-.08

-.06
Coefficient

-.04

-.02

Figure 5c Coefficient Distribution of Rent-to-Price Ratio

0

10

20

%

30

40

50

from leave-one-out cross validations of the turnover regression

-2

-1.5

-1

-.5

Coefficient

Figure 5d Coefficient Distribution of Popularity Index

0

20

%
40

60

80

from leave-one-out cross validations of the turnover regression

-.5

-.4

-.3
Coefficient-.2Figure 6 Different Popularity IndicesFigure 6a Coefficients of Turnover Rate-.06

from rent-to-price regressions with different popularity indices3

Coefficient
-.08
-.07

9

1

8
5

6

4

-.09

2

7

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

8

Alternative Estimate

Figure 6b Coefficients of Population Index-.02

from rent-to-price regressions with different popularity indices

Coefficient
-.06
-.04

4

7

6

2
3

-.08

5
8

-.1

1
9

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

8Figure 6c Coefficients of Rent-to-Price Ratio-1from turnover regressions with different popularity indices
7
6

4

9

Coefficient
-1.4
-1.2

2
3

5

8

-1.6

1

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

8

Alternative Estimate

Figure 6d Coefficients of Population Index
from turnover regressions with different popularity indices
-.1

4

-.2

6
7

Coefficient
-.4
-.3

2

9

3
8

-.5

5

-.6

1

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

8Description
Symbol
1
2
3
4
5
6
7
8
9

Indicator Removed
Swimming PoolClub House
Average Net Gross Ratio
Distance to Metro
Developer Brand
Distance to CBD
School Zone
Affordability
Distance to Waterfront

Appendix
This appendix provides some supplementary materials to the main text.
Appendix A provides the proof of proposition 1.
Appendix B provides the results of our bootstrap replications for each of our
explanatory variable and show that our results are indeed robust.
Appendix C provides the results of our Leave-one-out Cross Validations (LOOCV)
for each of our explanatory variable and show that our results are indeed robust.
Appendix D compares the point estimate for each potential empirical determinantin (28) with alternatively constructed popularity index and show that our results areindeed robust.
Appendix E provides correlation tables among diﬀerent variables and discusses
the construction of the popularity index.
Appendix F contains the 3SLS estimation with additional district level data.
Appendix G provides a robustness check for altering the variable choices in  and.
Appendix H provides a discussion of the possible interactions between the laborand housing markets.

48Appendix B: Bootstrap Replications
Figure B1 Coefficient Distribution of College-Educated Residents

020

Density
40

60

80

from 1000 boostrap replications of the rent-to-price regression

-.01

0

.01
Coefficient

.02

.03

kernel = epanechnikov, bandwidth = 0.0013

Figure B2 Coefficient Distribution of Household Income

0.5

Density1

1.5

2

from 1000 boostrap replications of the rent-to-price regression

-1.5

-1

-.5
Coefficientkernel = epanechnikov, bandwidth = 0.04720Figure B3 Coefficient Distribution of Mortgage

010Density

20

30

from 1000 boostrap replications of the rent-to-price regression

-.1

-.05

0

.05

Coefficientkernel = epanechnikov, bandwidth = 0.0032

Figure B4 Coefficient Distribution of Real Estate Work Experience

05

Density
10

15

20

from 1000 boostrap replications of the rent-to-price regression

-.05

0

.05
Coefficientkernel = epanechnikov, bandwidth = 0.0051

.1

.15

Figure B5 Coefficient Distribution of House Price Growth Rate

010

Density
20
30

40

50

from 1000 boostrap replications of the rent-to-price regression

-.06

-.04

-.02
Coefficient

0.02

kernel = epanechnikov, bandwidth = 0.0018

Figure B6 Coefficient Distribution of Rent Growth Rate

010

Density
20

30

40

from 1000 boostrap replications of the rent-to-price regression

-.05

0

.05
Coefficientkernel = epanechnikov, bandwidth = 0.0026.1

Figure B7 Coefficient Distribution of RED Size

02

Density4

6from 1000 boostrap replications of the rent-to-price regression

-.2

0

.2

.4

Coefficientkernel = epanechnikov, bandwidth = 0.0155

Figure B8 Coefficient Distribution of Land Auction

0

10

Density
20

30

40

from 1000 boostrap replications of the rent-to-price regression

-.08

-.06

-.04
-.02
Coefficientkernel = epanechnikov, bandwidth = 0.0021

0.02Figure B9 Coefficient Distribution of Young Population

02

Density
4

6

8

from 1000 boostrap replications of the turnover regression

-.1

0

.1
Coefficient.2.3kernel = epanechnikov, bandwidth = 0.0096

Figure B10 Coefficient Distribution of Household Income

0.05

Density
.1
.15

.2

.25

from 1000 boostrap replications of the turnover regression

-15

-10

-5
Coefficientkernel = epanechnikov, bandwidth = 0.3362

05

Figure B11 Coefficient Distribution of Real Estate Work Experience01

Density2

3from 1000 boostrap replications of the turnover regression

-.5

0

.5

1

Coefficientkernel = epanechnikov, bandwidth = 0.0347

Figure B12 Coefficient Distribution of House Price Growth Rate

02

Density
4

6

8

from 1000 boostrap replications of the turnover regression

-.3

-.2

-.1
Coefficientkernel = epanechnikov, bandwidth = 0.0107

0.1

Figure B13 Coefficient Distribution of Rent Growth Rate

01

Density2
3

4

5

from 1000 boostrap replications of the turnover regression

-.2

0

.2
Coefficient.4.6kernel = epanechnikov, bandwidth = 0.0190

Figure B14 Coefficient Distribution of Building Age

02

Density
4
6

8

10

from 1000 boostrap replications of the turnover regression

-.3

-.2

-.1
Coefficientkernel = epanechnikov, bandwidth = 0.0092

0.1

Figure B15 Coefficient Distribution of RED Size

0.2

Density.4.6.8

from 1000 boostrap replications of the turnover regression

-2

-1

0

1

2

3

Coefficientkernel = epanechnikov, bandwidth = 0.0990

Figure B16 Coefficient Distribution of Land Auction

02

Density4

6from 1000 boostrap replications of the turnover regression

-.6

-.4

-.2
Coefficientkernel = epanechnikov, bandwidth = 0.0148

0.2

Appendix C: Leave-one-out Cross Validations
Figure C1 Coefficient Distribution of College-Educated Residents

0

20

%
40

60

80

from leave-one-out cross validations of the rent-to-price regression

.003

.004

.005

.006
Coefficient

.007

.008

Figure C2 Coefficient Distribution of Household Income

0

20

%

40

60

from leave-one-out cross validations of the rent-to-price regression

-.95

-.9

-.85
Coefficient

-.8

-.75

Figure C3 Coefficient Distribution of Mortgage

0

10

20

%

30

40

50

from leave-one-out cross validations of the rent-to-price regression

-.044

-.042

-.04

-.038
Coefficient

-.036

-.034

Figure C4 Coefficient Distribution of Real Estate Work Experience

0

10

20

%

30

40

50

from leave-one-out cross validations of the rent-to-price regression

.025

.03

.035

.04
Coefficient

.045

.05

Figure C5 Coefficient Distribution of House Price Growth Rate

0

10

%
20

30

40

from leave-one-out cross validations of the rent-to-price regression

-.014

-.013

-.012
Coefficient

-.011

-.01

Figure C6 Coefficient Distribution of Rent Growth Rate

0

20

%
40

60

80

from leave-one-out cross validations of the rent-to-price regression

.016

.018

.02
Coefficient

.022

.024

Figure C7 Coefficient Distribution of RED Size

0

20

%

40

60

from leave-one-out cross validations of the rent-to-price regression

.04

.06

.08

.1

Coefficient

Figure C8 Coefficient Distribution of Land Auction

0

10

%
20

30

40

from leave-one-out cross validations of the rent-to-price regression

-.018

-.016

-.014
Coefficient-.012

Figure C9 Coefficient Distribution of Young Population

0

20

%

40

60

from leave-one-out cross validations of the turnover regression

.05

.06

.07
Coefficient

.08

.09

Figure C10 Coefficient Distribution of Household Income

0

10

20

%
30

40

50

from leave-one-out cross validations of the turnover regression

-4.2

-4

-3.8

-3.6
Coefficient

-3.4

-3.2

Figure C11 Coefficient Distribution of Real Estate Work Experience

0

10

%
20

30

40

from leave-one-out cross validations of the turnover regression.15.2
Coefficient.25

Figure C12 Coefficient Distribution of House Price Growth Rate

0

10

20

%

30

40

50

from leave-one-out cross validations of the turnover regression

-.12

-.11

-.1
Coefficient

-.09

-.08

Figure C13 Coefficient Distribution of Rent Growth Rate

0

20

%
40

60

80

from leave-one-out cross validations of the turnover regression.05.1
Coefficient.15

Figure C14 Coefficient Distribution of Building Age

0

20

%

40

60

from leave-one-out cross validations of the turnover regression

-.11

-.1

-.09
Coefficient-.08Figure C15 Coefficient Distribution of RED Size

0

10

20

%

30

40

50

from leave-one-out cross validations of the turnover regression

.1

.2

.3
Coefficient.4.5

Figure C16 Coefficient Distribution of Land Auction

0

20

%

40

60

from leave-one-out cross validations of the turnover regression

-.12

-.1

-.08
Coefficient

-.06

-.04

Appendix D: Population Index
Figure D1 Coefficients of College-Educated Residents.007

from rent-to-price regressions with different popularity indices
3

8

9

.006

Coefficient.0062 .0064 .0066 .0068

1

2

1

2

4

3

5

6

4
5
6
Alternative Population Index
Original Estimate

7

7

8

Alternative Estimate

Figure D2 Coefficients of Household Income
from rent-to-price regressions with different popularity indices
-.75

8

3

1

9

Coefficient
-.85
-.8

5

7
6
2

-.9

4

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

8Figure D3 Coefficients of Mortgage-.035

from rent-to-price regressions with different popularity indices

-.036

1

Coefficient-.038 -.037

5

2

8

4

6

7

-.04

-.039

3

9

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

8

Alternative Estimate

Figure D4 Coefficients of Real Estate Work Experience.05

from rent-to-price regressions with different popularity indices

Coefficient
.046
.048

2
4

.044

7
3

9

6
5

.042

1

8

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

8Figure D5 Coefficients of House Price Growth Rate-.011

from rent-to-price regressions with different popularity indices

Coefficient
-.013
-.012

3

1

5

6

-.014

2

8

9

7

4

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

8

Alternative Estimate

Figure D6 Coefficients of Rent Growth Rate.023

from rent-to-price regressions with different popularity indices

Coefficient
.021
.022

4

2

7

.02

6

.019

3

9

5

1

1

8

2

3

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

8Figure D7 Coefficients of RED Size.085

from rent-to-price regressions with different popularity indices1

8

Coefficient
.07
.075

.08

5

9
3
2

7

.065

6

.06

4

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

8

Alternative Estimate

Figure D8 Coefficients of Land Auction-.013

from rent-to-price regressions with different popularity indices

Coefficient
-.015
-.014

9

3

5

-.016

1

8

-.017

6

2

1

2

7

4

3

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

8Figure D9 Coefficients of Young Population.075

from turnover regressions with different popularity indices1
3

Coefficient
.065
.07

8
5

7
9
6

4

.06

2

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

8

Alternative Estimate

Figure D10 Coefficients of Household Income-3.5

from turnover regressions with different popularity indices

Coefficient
-3.7
-3.6

8

1

7
5

-3.8

3

9

2

-3.9

6

4

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

8Figure D11 Coefficients of Real Estate Work Experiencefrom turnover regressions with different popularity indices
.22

2
3

Coefficient
.21
.215

9
1
8
4

.205

5

6

.2

7

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

8

Alternative Estimate

Figure D12 Coefficients of House Price Growth Rate-.101

from turnover regressions with different popularity indices7

Coefficient
-.103
-.102

2

4

6

-.104

3

-.105

9

1

1

5

2

3

8

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

8Figure D13 Coefficients of Rent Growth Rate
.118

from turnover regressions with different popularity indices

Coefficient
.114
.116

9

2

3

4

6
7

8

.112

5

.11

1

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

8

Alternative Estimate

Figure D14 Coefficients of Building Age-.088

from turnover regressions with different popularity indices

Coefficient
-.092
-.09

4
2
6
1
7

8

-.094

5

9

-.096

3

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

8Figure D15 Coefficients of RED Size
.4

from turnover regressions with different popularity indices.35

1

Coefficient
.3

5

8

.25

3

7

2

9

.2

6
4

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

8

Alternative Estimate

Figure D16 Coefficients of Land Auction-.09

from turnover regressions with different popularity indices

Coefficient
-.094
-.092

5

8

1

2

3

6

-.096

7

4

1

2

3

4
5
6
Alternative Population Index
Original Estimate

7

Alternative Estimate

89Appendix E: More on our popularity index

This appendix provides a correlation table among different variables and some discussion of
the construction of our popularity index, and provides a complete list of that index on 132
major RED in Hong Kong.
We first provide the correlation table, Table E1, which is also known as the correlation
matrix. Notice that not all variables are highly correlated. It should not be surprising, as Table
E1 mixes variables which represent housing characteristics and variables which represent
household characteristics. A more sensible comparison would be to focus on the correlations
among housing characteristics, which is provided by Table E2. It shows that housing
characteristics are indeed statistically correlated. One might therefore be tempted to constructprincipal components (PC) to summarize the co-variations of the variables. Unfortunately,
statistically significance does not always translate to economic significance and our sample
provides a good illustration for this principle. As shown by Table E3, the first principal
component explains only 20% of the total variations. We need to include from the first to thesixth principal components to explain 80% of the total variations. However, we only have asmall sample of RED and we cannot afford to 6 PC into the regression and at the same time
be able to identify different effects given the 3SLS framework. Therefore, the formative index
approach may be constrained optima in terms of the econometric strategy.

Table E1: Correlation Matrix
Number

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

1
2

0.25

3

0.11

-0.12

4

-0.14

0.40

-0.32

5

0.17

-0.33

0.22

-0.89

6

0.17

-0.36

0.37

-0.79

0.81

7

-0.43

-0.08

-0.02

0.33

-0.29

8

-0.53

-0.32

-0.06

-0.06

0.03

-0.02

0.61

9

-0.60

-0.34

0.02

-0.13

0.08

0.07

0.54

0.93

10

-0.44

-0.03

-0.07

0.12

-0.14

-0.13

0.38

0.34

0.45

-0.20

11

0.13

-0.21

0.03

-0.33

0.24

0.23

-0.35

-0.21

-0.25

-0.42

12

-0.43

-0.09

0.07

0.28

-0.29

-0.21

0.55

0.40

0.41

0.28

-0.28

13

-0.08

-0.36

0.33

-0.49

0.41

0.47

-0.03

0.20

0.25

-0.05

0.17

0.15

14

0.47

-0.25

0.25

-0.57

0.56

0.65

-0.50

-0.29

-0.20

-0.33

0.23

-0.41

0.42

15

0.13

-0.06

0.97

-0.26

0.20

0.34

-0.01

-0.09

-0.02

-0.04

-0.07

0.06

0.24

0.21

16

0.23

0.22

-0.15

-0.02

0.14

-0.04

-0.33

-0.40

-0.47

-0.25

0.28

-0.36

-0.14

-0.05

-0.10

17

0.14

0.17

-0.06

0.05

-0.03

-0.06

-0.17

-0.23

-0.23

-0.15

0.05

-0.42

-0.25

0.10

-0.03

0.15

18

-0.26

-0.08

0.01

0.07

-0.18

-0.16

0.21

0.15

0.22

0.25

-0.19

0.35

-0.09

-0.12

-0.01

-0.41

Note: Variables with correlations lower than 0.4 to other variables are left out to save space.

0.03

Key:
Number

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

Variables
Mean R/P of the RED
Turnover rate %Population Resided in the RED
Young population %Middle Age Population %Median Age of the Residents
College education level %Monthly Median Income of Residents HKD
Median Monthly Mortgage Payment HKD
Mortgage income ratio %Home Ownership Rate in the RED %Popularity of the RED
Average Net Gross Ratio %Average building age
Estate Scale
Distance to CBD M
Distance to Seafront M# Top 100 Middle School

Table E2: Correlations among Housing Characteristics
1
2
3
4
5
6
7
8
9

Variables
Affordability
Access to MTR within 500 Meters
Distance to the CBD
Net Gross Ratio# of Top 100 Middle Schools
Developer Reputation
Access to Waterfront within 500 Meters
RED Has Club House
RED Has Swimming Pool

* p<0.05; ** p<0.01; *** p<0.001

1

2

3

4

5

6

7

8

0.01*
‐0.32***
0.16***
0.11***
0.00
0.23***
0.13***
0.03***‐0.02***‐0.02***
0.25***‐0.09***‐0.22***
0.05***
0.05***‐0.19***‐0.33***‐0.02***‐0.24***
0.09***
0.24***‐0.06***
0.02***
0.20***‐0.24***‐0.19***‐0.14***
0.05***
0.12***‐0.01*‐0.07***‐0.03***
0.05***

0.14***
0.04***

0.49***

9

Table E3: Principal Component Analysis
Measures

Comp1

Comp2

Comp3

Comp4

Comp5

Comp6

Affordability-0.347

0.369

0.156

0.215

0.236

-0.719

Access to MTR within 500 Meters

0.057

0.160

-0.610

0.201

0.508

0.080

Distance to the CBD

0.548-0.1960.117-0.1930.295-0.016Net Gross Ratio-0.429-0.149

0.167

0.025

0.644

0.389

# of Top 100 Middle Schools-0.2100.381-0.4860.012-0.3140.331

Developer Reputation

0.046-0.122

0.260

0.877

-0.1700.236

Access to Waterfront within 500 Meters-0.322

0.291

0.439

-0.311-0.0550.343

RED Has Club House

0.285

0.582

0.150

0.004

-0.0040.038

RED Has Swimming Pool

0.401

0.440

0.204

0.102

0.233

0.200

Cumulative proportion of variance

0.204

0.388

0.540

0.653

0.752

0.833

Now we need to discuss our “popularity index.” While it is beyond the scope of this paper toreview the literature, it may nevertheless be instructive to highlight some of the key findings.
Measurement models can be divided into two types, reflective, where the term of “scale
development” is usually used, and formative, where the phrase of “index construction” ismore often employed. Many scholars have discussed that, including Diamantopoulos and
Winklhofer (2001) and Jarvis, MacKenzie, and Podsakoff (2003), among others.
In reflective models, the composite variable is cause, and indicators composing it are effects.
The reflective measurement model is essentially seeking common information among
realized results. Since all effects stem from a common cause, there must be collinearity
among them. It follows that data dimension reduction technique such as principal component
or factor analysis best applies to the context. In contrast, cause and effect are reversed in aformative model, i.e. indicators produce the composite variable they compose. Researchersattempt to summarize an outcome considering all possible causes. In fact, formative
measurement models have been applied in economics and other social sciences. Daly andCobb (1994) develop the sustainable economic welfare index. United Nations Development
Program builds the human development index in 1990. Johnston (1988) constructs thequality-of-life index. In the case of real estate studies, Griliches (1971) builds the hedonic
price indices. More examples can be found in Horn (1993).
Clearly, different causes are not necessarily highly correlated. For such reasons, principal
component kind of analysis may not be practical. As a matter of fact, we try the principal
component analysis on our data. As we have shown, we need to retain as many as six PCs tocapture less than 80% of variances in our eleven indicators, which does not seem to be a
promising approach given our small sample size and 3SLS procedure.
A simple alternative is the linear combination of formative indicators. In our case, popularity
is obviously a consequence variable determined by underlying items, suggesting developing
the popularity index as a formative measurement model may be more promising. Specifically,
our popularity is a linear sum of equally weighted indicators selected.

Appendix F: 3SLS estimation with district level data
This appendix tries to incorporate some district level data in the 3SLS regression toaccount for the district specific effect. Such data come from the 2011 Census and 2006 bycensus. At first, we attempt to include a number of variables in the specification, such as
population and income growth rates between two census periods, population density, average
household size, percent of college degree holders, the median rent and median mortgage
payment, as well as proportion of foreign population in 2011. We even use four measures toproxy for possible foreigners’ effect: new immigrants from mainland China with duration ofresidence less than seven years, population born outside of Hong Kong, population whose placeof domicile is not Hong Kong, and population whose first language is not Cantonese. Yet after
experimenting with different subsets of these variables, we find that at district level only the
population density and income growth rate have explanatory power over property level rental
yield. Therefore, only these two variables are introduced in the regression and the results arereported in Table F.1.
We first discuss the rental yield regression results. Comparing the RMSE statistics inthe tables in the main text and other appendices, the goodness-of-fit of the rent-price ratio
regression slightly improves. The new results are that both higher population density and higher
income growth in the district will predict a lower RED-level rent-to-price ratio. On the other
hand, the inclusion of the district data tempers both the economic magnitude and the statisticalsignificance of normed transaction and popularity index estimates. Other variables remain
significant as well. The numerical values of estimates do not change much.
The goodness-of-fit of the turnover rate equation even degenerates. The statisticalsignificance of other variables also diminishes. The population density and the income growthrate are merely marginally significant. The rent growth rate becomes insignificant as well,which is supportive evidence of our finding that long run rent growth influences rent to priceratio while trading volume is more affected by short-term return in price. Only the income,young population proportion, and lagged price appreciation, are statistically significantly
different from zero.

Table F1: Results of 3SLS with District Data
Coef.
Beta Coef.
Std. err.
Equation: R/P
Turnover Rate %Popularity of the RED
College Education Level %Ln(Income)Mortgage Income Ratio %Work in Real Estate Consulting %Last Year HP Growth Rate %Rent Growth Rate in Past 5 YRs
RED ScaleLand Auction
District Population Density
District Income Growth
Constant
Observations
RMSE
Chi-squared
P valueEquation: Turnover
Mean R/P of the RED
Popularity of the RED
Young Population %Ln(Income)Work in Real Estate Consulting %Last Year HP Growth Rate %Rent Growth Rate in Past 5 YRs
Average Building Age
RED ScaleLand Auction
District Population Density
District Income Growth
Constant
Observations
RMSE
Chi-squared
P valuepval.

-0.047-0.0430.006*-0.635***-0.031**
0.046**-0.0070.017*
0.104*-0.014-0.107**-0.021*
11. 543***
130
0.367
111.600.000-0.315-0.1160.147*-0.534***-0.170**0.193**-0.0910.143*
0.133*-0.113-0.247**-0.150*-0.014130
0.771
111.60
0.000

0.031
0.040
0.003
0.137
0.014
0.018
0.007
0.009
0.059
0.009
0.046
0.013
1.796

0.122
0.282
0.066
0.000
0.028
0.012
0.310
0.051
0.077
0.136
0.019
0.095
0.000

-2.735-0.1920.082*-3.776**0.319-0.095*0.127-0.0930.569-0.109-0.855-0.19161.300**130
2.785
65. 530.000-0.412-0.0770.206*-0.479**0.201-0.177*0.161-0.2560.110-0.137-0.297-0.202
0.003
130
0.881
65. 53
0.000

3.656
0.332
0.044
1.618
0.197
0.054
0.080
0.071
0.611
0.086
0.554
0.126
29.953

0.454
0.564
0.063
0.020
0.105
0.079
0.112
0.191
0.352
0.208
0.122
0.129
0.041

Appendix G: Robustness of the variable choices on X and Z.
In the main text of the paper, we put “Mortgage Income ratio” among the R/P equation
control variables, and “Young Population %” among the turnover equation control variables.
It has been suggested to us that the mortgage-income ratio could also matter for turnover. The
idea is that a higher value of the mortgage-income ratio might imply that people are lessmobile. To check for the robustness of our results, we move that variable to the turnoverequation. To apply 3SLS methodology, we move the young population percentage variable to
the R/P equation. Results indicate that both variables become insignificant after switching.
Moreover, the overall performances of both equations deteriorate significantly. We therefore
maintain our original variable choices in the text.
Table G1: Results of 3SLS with control variable changes
Coef.
Beta Coef.
Equation: R/P
Turnover Rate %Popularity of the RED
College Education Level %Ln(Income)Average Building Age
Young Population %Work in Real Estate Consulting %Last Year HP Growth Rate %Rent Growth Rate in Past 5 YRs
RED ScaleLand Auction
Constant
Observations
RMSE
Chi-squared
P-valueEquation: Turnover
Mean R/P of the RED
Popularity of the RED
Mortgage Income Ratio %Ln(Income)
Last Year HP Growth Rate %Rent Growth Rate in Past 5 YRs
Work in Real Estate Consulting %RED ScaleLand Auction
Constant
Observations
RMSE
Chi-squared
P-value

Std. err.

pval.

-0.820-0.103-0.035-2.500-0.0690.051
0.198-0.1050.095
0.221-0.08136.849
130
2.173
5.79
0.887

-5.442-0.276-0.851-2.104-1.2700.849
0.827-1.2950.801
0.283-0.675
0.075
130
4.565
5.79
0.887

2.259
0.533
0.096
4.806
0.195
0.257
0.372
0.260
0.222
0.939
0.197
64.116

0.717
0.847
0.711
0.603
0.722
0.844
0.594
0.687
0.670
0.814
0.681
0.565

-11.107*-0.489-0.385-8.299***-0.202**0.246*
0.570*
0.959-0.194140.648**
130
4.934
17.13
0.047

-1.673*-0.198-0.323-1.052***0.358*-0.376**0.314*
0.185-0.243-0.004
130
1.562
17.13
0.047

6.174
0.645
0.312
2.964
0.081
0.135
0.301
1.114
0.124
54.318

0.072
0.448
0.216
0.005
0.012
0.068
0.058
0.389
0.119
0.010

Appendix H: Possible interactions possible interactions between the labor and housing
markets

It has been suggested to us that there may be non-trivial interactions between the labor andhousing markets. While we agree with this conjecture theoretically, the current manuscript
provides limited coverage on that. Here are the reasons. First, our focus is on the interactions
between the rent-to-price ratio and the turnover rate. It is not clear to us how the interactions
between these two variables would affect the labor market and then feed back to the housing
market. Second, we have a data issue. Since our empirical works mainly focus on crosssectional comparison across different real estate developments (RED), it is natural to seek for
RED level unemployment rate data. However, in the case of Hong Kong, we do not evenhave district level unemployment rate data. Even if we had the district level unemployment
rate data, we may not be able to rule out the possibility that different REDs within the same
district exhibit different unemployment rates. Hence, it is difficult for us to conduct muchcross-sectional analysis on the unemployment rate and property market rent-price ratio (orproperty yield). All we have from the official data is a wage index constructed for the whole
Hong Kong. We nevertheless explore whether such wage index is correlated to the housing
market yield in time series. Recent works such as Chang et al. (2013), Leung et al. (2013)
suggest that Hong Kong macroeconomic data may display regime-switching and structuralchange. If this is indeed the case, full sample correlation coefficient could be mis-leading.
Following the literature, we conduct rolling window estimation instead. Figure H1 shows the
subsample correlations between the unemployment rate and property yield evolve over time(please see the following pages). Notice that the correlation between the two variables does
not seem to be stable. It can exceed well above 0.5 in some periods and drops below -0.5 insome other periods. To model the relationship between these variables may not be easy.
Similarly, the subsample correlations between the real wage and the property yield also varyover time. As shown in Figure H2, while the correlations are mostly positive, we do observe
several subsamples exhibiting negative correlations. Among the positive correlations, someare small in magnitude and not statistically significant.

Figure H1: Rolling Window Correlation Coefficients of Unemployment Rate and Property Yields

-1

-.5

Correlation Coefficients
0.5

1(Rolling Window: 24 Months)

1998m1

2000m1

2002m1

2004m1

2006m1

Property: 40-69.9 Sq m

2008m1

2010m1

2012m1

2014m1

Property: 70-99.9 Sq m

2016m1

Figure H2: Rolling Window Correlation Coefficients of Real Wage and Property Yields-.5

Correlation Coefficients
0.5

1(Rolling Window: 20 Quarters)

1990q1

1995q1

2000q1

Property: 40-69.9 Sq m

2005q1

2010q1

2015q1

Property: 70-99.9 Sq m

Note:
While the unemployment rate data is in monthly frequency, the wage data is in quarterly frequency.
We therefore shrink the rolling window to 20 periods (i.e. 20 quarters) instead of 24. Otherwise, thenumber of sub‐samples will be too small for any meaningful inference.

Moreover, the progress of Hong Kong labor market research in terms of search-theoretic
approach may be limited. For instance, based on Krause and Lubik (2007), Krause et al.
(2008a, b), Lubik (2009), among others, Lubik (2012) estimates a new Keynesian model withfrictional labor market with Hong Kong data. It is found that some parameters may not be
identified very well. For instance, the range of the posterior estimate of the bargaining power
is not very precise (please see Table 3 of Lubik, 2012). Given such imprecision, it may noteven be practical to assess whether the interaction between the labor market and housing
market is statistically significant.
Clearly, all these findings do not rule out the possibility that there are economically andstatistically significant interactions between the labor market and housing market. They dosuggest that the relationship may be more complicated than we thought and can only reservethat to future research.