Residential Mobility Decisions in Japan: Effects of Housing Equity Constraints and Income Shocks Under the Recourse Loan System

Abstract

This paper draws on six waves of Japanese household longitudinal data (Keio Household Panel Survey, KHPS) and estimates a
conditional fixed effects logit model to investigate the effects of housing equity constraints and income shocks on own-to-own
residential moves in Japan. By looking at contemporaneous extended Loan-to-Value (ELTV) and extended Debt-to-Income (EDTI)
ratios under the recourse loan system, we examine whether housing equity constraints and negative income shocks have any impact
on own-to-own residential moves. Taking account of the specific nature of the recourse loan system in Japan, we further investigate
whether these effects are different between positive and negative equity households. The estimation results show that housing
equity constraints and negative income shocks significantly deter own-to-own residential moves for positive equity households.

KeywordsResidential mobility–Housing equity constraint–Conditional fixed effects logit model–Loan-to-value ratio–Debt-to-income ratio–Negative equity–Japan–Recourse loan

Full text

Electronic copy available at: http://ssrn.com/abstract=1662231
Residential Mobility Decisions in Japan:
Effects of Housing Equity Constraints and Income Shocks
under the Recourse Loan System*
First draft: November 19, 2009
This version: July 25, 2010
Miki Sekoa,†, Kazuto Sumitab and Michio Naoic
a. Faculty of Economics, Keio University (seko@econ.keio.ac.jp)
b. Department of Economics, Kanazawa Seiryo University (sumita@seiryo-u.ac.jp)
c. Faculty of Economics, Keio University (naoi@2001.jukuin.keio.ac.jp)
Abstract
This paper draws on six waves of Japanese household longitudinal data (Keio Household
Panel Survey, KHPS) and estimates a conditional fixed effects logit model to investigate the
effects of housing equity constraints and income shocks on own-to-own residential moves in
Japan. By looking at contemporaneous extended Loan-to-Value (ELTV) and extended
Debt-to-Income (EDTI) ratios under the recourse loan system, we examine whether housing
equity constraints and negative income shocks have any impact on own-to-own residential
moves. Taking account of the specific nature of the recourse loan system in Japan, we fur-
ther investigate whether these effects are different between positive and negative equity
households. The estimation results show that housing equity constraints and negative in-
come shocks significantly deter own-to-own residential moves for positive equity house-
holds.
JEL classification: R21, C51, G21
Keywords: Residential mobility, housing equity constraint, conditional fixed effects logit
model, loan-to-value ratio, debt-to-income ratio, negative equity, Japan, recourse loan.
* An earlier version of this paper (Seko, Sumita, and Naoi, 2009) was presented at the Asian Real Estate
Society-American Real Estate and Urban Economics Association Joint International Conference, the
University of California, Los Angeles, July 11-14, 2009, and received the Best Paper Award (the Maury
Seldin Advanced Studies Institute Award). It was also presented at the Asia Pacific Real Estate Research
Symposium at the University of Southern California, July 10-11, 2009 and at the 2009 Fall Annual
Meeting of the Japan Economic Association at Senshu University, October 10-11, 2009. We are grateful
for Danny Ben-Shahar, Peng Liu, Seow Eng Ong, Gary Painter, Chihiro Shimizu, Fukuju Yamazaki,
participants of the conferences for their helpful comments.
† Corresponding author. Professor, Faculty of Economics, Keio University: 2-15-45 Mita, Minato-ku,
Tokyo 108-8345, Japan.
1

Electronic copy available at: http://ssrn.com/abstract=1662231
1. Introduction
The purpose of this paper is to examine whether housing equity constraints and negative income
shocks deter own-to-own residential mobility and to identify the effect of housing equity con-
straints taking account of the specific nature of the recourse loan system in Japan.
The degree of residential mobility varies across countries1 and Japan is known as a low
residential mobility society. Relatively high residential mobility rates are common in the U.S.
and Canada; the residential mobility rate between 1995 and 2000 in the U.S. is 50.4 percent
while that between 2001 and 2006 in Canada is 40.9 percent.2 In contrast, the Japanese residen-
tial mobility rate between 2003 and 2008 is 20.8 percent, less than half of that in the U.S., and
this rate has been decreasing.3
Well-functioning housing markets allocate housing, and determine housing equity, a very
important component of household wealth. Residential mobility is an equilibrating factor in this
allocating function of housing markets. When institutional constraints or other barriers impede
residential mobility, this allocating role of housing markets is disrupted. Countries with low
rates of residential mobility tend to suffer from high price volatility (Englund and Ioannides,
1993). Due to high transaction costs, most households cannot immediately react to price
changes by changing their residences, causing market disequilibrium and price volatility. In ad-
dition, low rates of residential mobility make labor markets less efficient, and hence can ad-
versely affect economic growth (Hardman and Ioannides, 1999). To address these problems,
government policies are devised to promote residential mobility (Englund and Ioannides, 1993;
Long, 1991).
The implosion of real estate prices after Japan’s asset Bubble burst began in 1991. From
the late 1980s, Japan witnessed a rise and fall in land and housing values that rivals that of any
period in modern history anywhere. The sharp downturn in the 1990s left many Japanese
homeowners with low or negative housing equity that constrained residential mobility.
The negative effects of the housing equity constraint on residential mobility are certainly
amplified by the mortgage loan system. Housing loans for residential houses in Japan are based
1 Long (1991) analyzed residential mobility differences among developed countries. Strassmann (1991)
made an international comparison of housing market interventions and mobility. Angel (2000), Table A.25
(p.372) shows annual residential mobility rates as of 1990 among 53 major cities in 53 countries. Hars-
man and Quigley (1991), Table 1-5 shows annual residential mobility rates among European countries
and the U.S.
2 U.S. data is from the Social Science Data Analysis Network (http://www.censusscope.org/us/s48/
chart_migration.html, accessed on November 17, 2009). Canadian data is from Statistics Canada released
2006 census mobility data (http://www12.statcan.gc.ca/census-recensement/2006/dp-pd/index-eng.cfm,
accessed on November 17, 2009).
3 This figure is based on the 2008 Housing and Land Survey of Japan. The annual residential mobility
rate was 8.1% between 1968-1973, 7.5% between 1973-1978, 6.8% between 1978-1982, 6.2% between
1982-1988, 6.1% between 1988-1993, 5.8% between 1993-1998, 5.1% between 1998-2003, and 4.4%
between 2003-2008.
2

on a recourse loan contract system. Under this system, when the value of the mortgage (housing
loans) exceeds the value of the housing, and the borrower is unable to service the loan, borrow-
ers have to surrender any unencumbered assets to cover the loan outstanding. On the other hand,
under a non-recourse loan system, even if the value of the mortgage exceeds the value of the
housing, and the borrower is unable to service the loan, they do not need to surrender unen-
cumbered assets. Therefore, under a non-recourse loan system, borrowers may default and re-
tain their other assets. As a result, the negative effects of housing equity constraints on residen-
tial mobility should be much more severe under a recourse loan system than under a
non-recourse system.
The mortgage loan system also has a significant impact on the maintenance and the overall
quality of the housing. In Japan financial institutions (lenders) determine the loan amount based
mostly on the value of the land pledged as collateral and also on the apparent reliability of the
applicant (income, job status, etc.). Since Japanese land prices kept increasing in the post-WWII
era, at least until the bubble burst in the early 1990s, and the land value exceeds that of the
housing, lenders typically have not factored in the value of the housing even though it is part of
the property asset being used as collateral. As a result, borrowers are not interested in maintain-
ing and investing in their housing. In contrast, in the United States and other countries under the
non-recourse system, financial institutions determine the amount to lend taking into considera-
tion the value of the housing. As a result, there are strong incentives to maintain the quality of
housing and better maintenance helps create a more robust second-hand housing market in those
countries.
This is a rigorous econometric analysis based on household longitudinal data that investi-
gates the effects, under the recourse loan system, of housing equity constraints and income
shocks on residential mobility in Japan, focusing on the owner-occupied housing market. It is
essential to understand the impact of recourse loan housing systems on residential mobility to
formulate more effective housing policy and housing loan systems so that Japanese housing
markets can function more effectively. The distinctive characteristics of the Japanese owned
housing market detailed above, together with the availability of the recent, large-scale house-
hold longitudinal data, enable us to assess the potential effect of housing loan systems on resi-
dential mobility in Japan. Our micro-data is based on the “Keio Household Panel Survey”
(KHPS) covering all Japan. In this research, the conditional fixed effects logit model is used to
investigate those effects on residential moves. We carefully constructed the Extended
Loan-to-Value (ELTV) and the Extended Debt-to-Income (EDTI) ratios incorporating the cha-
racteristics of the recourse loan system.
The organization of the remainder of this paper is as follows: in Section 2, we briefly re-
view the characteristics of the Japanese economy and the Japanese housing markets; in Section
3, we briefly review the related research; in Section 4, we present a theoretical model about res-
3

idential mobility under the recourse loan system; in Section 5, we discuss the econometric mod-
el; in Section 6 we discuss the data and variables; in Section 7, we present the estimation results
of the conditional fixed effects logit model for residential moves under the recourse loan system,
and; Section 8 offers some concluding remarks.
2. Overview of the Japanese economy and the Japanese housing market
Since 1986, Japan has experienced a sharp rise and fall in land and housing values that rivals
that of any period in modern history. Figure 1 shows the trend in land prices, nominal GDP and
stock prices between 1965 and 2009 and Figure 2 shows the actual housing price and the house
price of 75 square meters in the Tokyo Metropolitan Area between 1975 and 2008. Asset prices
began increasing in 1983, and it was around 1986 when the rise began accelerating rapidly. The
rise in land prices spread from Tokyo to major cities such as Osaka and Nagoya, and then to
other cities.
(Figure 1 around here)
(Figure 2 around here)
Many Japanese households that bought housing during the Bubble era have a low or nega-
tive net equity due to subsequent asset price deflation. Due to the high price of housing in Japan,
many households carry large mortgages and for those that bought housing during the Bubble era,
in many cases loans outstanding exceed the current value of the housing. In periods of asset
deflation, borrowers assume all risks stemming from any decline in real estate collateral values
because they cannot move to a different residence without fully repaying the borrowed amount
(i.e. principal plus interest).
Furthermore, many Japanese households are suffering from negative income shocks during
the post-bubble era. Figure 3 depicts the decline in the real wage index from 1990 to 2009. Over
the past decade alone, average household income dropped by 20%. For homeowners holding a
mortgage loan, decreasing income makes their existing mortgage increasingly unaffordable, as
indicated in a rising Debt-to-Income (DTI) ratio, and gives them an incentive to refinance their
mortgage.4
(Figure 3 around here)
4 Seko and Sumita (forthcoming) surveyed trends and prospects in Japan’s Mortgage Market.
4

In the following analysis, we will identify equity effects from the run-up and declines in
housing prices that occurred in the late 2000’s using the 2004-2009 panel data.
3. Literature review
There are several theoretical studies focusing on the role of the equity constraint hypothesis re-
lated to the movements of prices and transaction volumes in the housing market. Stein (1995)
presented a static model and demonstrated how extreme credit constraint distress may result in
lower housing prices and fewer transactions because negative equity prevents some households
from moving. Ortalo-Magne and Rady (2006) developed a life-cycle model of the housing
market with a property ladder and a credit constraint.5
Empirical studies about the impact of equity constraints on residential moves are based on
mainly Western owner-occupied samples. For example, a recent paper by Ferreira et al. (2010)
reports that the (2-year) mobility rate of negative equity households is 8% while the average
mobility rate is about 12%. Henley (1998) investigated the impact of negative housing equity on
residential moves using a single and competing risk discrete time duration model of residence
duration based on a U.K. owner-occupied sample. He also analyzed whether a stagnant housing
market impairs labor market flexibility. Chan (1996, 2001) empirically analyzed the impact of
equity constraints on residential moves based on U.S. owner-occupied samples. Engelhardt
(2003) examined the effect of equity constraints and nominal loss aversion on household mobil-
ity based on US data.6 Seslen (2003) examined the role of housing price dynamics in mobility
decisions, asking whether households respond to prices in a forward- or backward-looking
manner, and the extent to which high levels of leverage constrain moving behavior using PSID
(the Panel Study of Income Dynamics). Lee and Ong (2005) empirically analyzed the impact of
equity constraints on residential moves based on Singapore owner-occupied samples using the
probit model. Although those studies investigate the impact of housing equity constraints on
residential moves, none of them explicitly examine the effects of government policies aimed at
easing equity constraints on residential moves. Seko and Sumita (2007) investigated the effect
of the tax deduction policy on residential mobility in Japan based on an owned-housing panel
sample in Japan using a proportional hazard model. They found that the tax deduction policy
devised to cope with severe equity constraints has a strong impact on owners’ residential mobil-
ity.
There are several studies examining the recent relationship between the housing and mort-
5 Leung (2004) surveyed research focusing on the relationship between housing price cyclicality, volatil-
ity and the structure of the residential lending market.
6 Genesove and Mayer (1997; 2001) find that nominal loss aversion also affects seller behavior (i.e.
higher asking prices) in the housing market, and as a result causes a longer time on the market.
5

gage markets under the non-recourse loan system. Leece (2004) analyzes the microeconomics
of the mortgage market under the non-recourse system. Rosenthal and Strange ( 2008) focus on
the linkages between mortgages and housing markets in the United States while Green, Sanders
and Wachter (2008) focus on the importance of the housing and mortgage markets to the econ-
omy and analyze the root causes of the “sub-prime crisis” in the United States.
Our present study attempts to shed light on the role of equity constraints and negative in-
come shocks under the recourse loan system using the conditional fixed effects logit model. The
reason why we adopt the conditional fixed effects logit model is that the fixed effects specifica-
tion captures the selection of a housing tenure and the timing of the move into it (see
Börsch-Supan, 1990).7 This is the first rigorous econometric study to analyze the effects of
housing equity constraints under the recourse loan system on the own-to-own residential moves
in Japan based on the conditional logit panel data estimation method.
4. A Simple Model of Residential Mobility under the Recourse Loan Sys-
tem
This section presents a simple theoretical model to illustrate the residential mobility decision of
homeowners and a “lock-in” effect due to housing equity constraints. The purpose of our theo-
retical analysis is to present an empirically testable hypothesis pertaining to the housing equity
constraints under the recourse loan system.
Our main theoretical results are as follows. First, it can be shown that housing equity con-
straints, represented by the Loan-to-Value ratio, has a “lock-in” effect on residential moves –
LTV is negatively associated with the propensity to move. This finding is not new in the litera-
ture. For example, Stein (1995) and Ortalo-Magné and Rady (2006) present the negative rela-
tionship between housing equity and residential mobility under the non-recourse loan system.
Hence our first result confirms that the same relationship also holds for the recourse loan system.
Second, and more importantly, the effect of LTV crucially depends on the household’s equity
position: while the higher LTV reduces the residential mobility of positive equity households
(i.e. LTV < 1), it does not have any impact for the negative equity households (i.e. LTV > 1). To
the best of our knowledge, no previous studies have directly examined the asymmetric impact of
LTV depending on the household’s equity position. Our analysis provides an empirical basis for
identifying the effect of the housing equity constraint under the recourse loan system.
Our argument can be summarized as follows. Consider a homeowner who wants to buy a
new home. A situation of higher LTV means that there is less net equity that can be used for a
7 Börsch-Supan (1987, 1990) employed this model to analyze the choice of housing tenure and size using
five waves of PSID. Andrew (2004) used this model to explain why home ownership rates among young
adults fell in the early 1990s even as various indicators suggested it had become more affordable.
6

down payment on a new home, and hence this reduces the propensity to move. For negative
equity households, however, the above argument is not completely true under the recourse loan
system. Under the recourse loan system, for homeowners with negative housing equity, stra-
tegic default is virtually impossible or prohibitively costly. They cannot make any down pay-
ment for a new house even after selling their current house; hence a marginal change in the
LTV does not matter for such households. On the other hand, under the non-recourse loan sys-
tem, people can walk away from a mortgage with a certain cost (e.g. the increased cost of fu-
ture credit due to a reduction in credit rating) and buy a new (possibly smaller) home with a
new mortgage. Under the non-recourse system, thus, it is important to take account of the
possible simultaneity between residential mobility of negative equity households and strategic
defaults. In comparison, the recourse loan system in Japan provides a much simpler case to
identify the potential impact of housing equity constraints on the own-to-own residential
moves.
4.1 The Model
The setting of the model is similar to that of Stein (1995). The model has three time periods,
0, 1, and 2. At time 0 each household owns their home with one unit of housing stock. They are
also endowed with a fixed amount of mortgage outstanding K and non-housing asset .
At time 1 households can move to another owner-occupied housing with housing price ,
so that the cost of buying a new house of size  is . Two assumptions are made for this
transaction process. First, when a household sells their old house, they must repay the outstand-
ing mortgage at that point, leaving them with net wealth of –. Second, the purchase of
their new house requires a down payment of 100 % of the purchase price, i.e., if the new
house costs , a minimum down payment would be  with 01. At time 2
households get labor income . We assume that household income is sufficient for repaying all
the outstanding mortgages, and that the rest is used for numeraire goods consumption.
A household’s utility is g ar form: iven as the following log line
ln 1ln

where  is housing stock and  is numeraire goods consumption.  is a binary indicator
variable that takes the value of one if a household moves at time 1, and  is the gain from
housing adjustment that can be achieved by the residential moves.
(1)
Consider first the case without any down payment requirement. Clearly, without a down
payment requirement, every household will change their residence at time 1, since this will in-
crease utility by . On the other hand, if there is a minimum down payment requirement, some
households would be compelled to stay in their old house due to the financial constraint. The
7

down payment requirement can b t se wri ten a :
. (2)
Therefore, households facing a down p int would consume housing stock of ayment constra

 (3)
if they decide to move at time 1. Their mobility decision will be determined by comparing the
utility from moving  to the utility from not moving . These two scenarios are
represented respectively as follows:
ln ,and
1ln
1ln,
(4)
where numeraire goods consumption is determined by the household’s lifetime budget con-
straint, . The household will move if Δ0. With
some tedious but easy m ation, Δ can be writteanipul n as:
Δln1
1ln1 1
1
1, (5)
where,

and 1

are defined as the loan-to-value (LTV) and debt-to-income (DTI) ratio. Note that under the re-
course loan system not only housing but also non-housing asset is regarded as collateral. Hence
the numerator of  should be the net value of the mortgage (i.e. mortgage outstanding minus
non-housing asset).8
In order to show that the effect of LTV on residential moves crucially depends on the
household’s equity position, the comparative static results for both positive and negative equity
households are examined. From equation (5), it can be shown that, for positive equity house-
holds (i.e. 01), when 1, Δ0 regardless of the value of . This implies that
the higher LTV reduces the residential mobility of positive equity households. On the other hand,
negative equity households (i.e. 1) are always forced to remain in the current housing,
hence not moving, due to the down payment constraint (see equation (2)). Therefore, our model
also predicts that the level of LTV does not have any impact on the propensity of negative equi-
8 An empirical counterpart of this variable is discussed in further detail in Section 6.2.
8

ty households to move.9
5. Conditional Fixed Effects Logit Model
We adopt a discrete dependent variable panel model for the estimation. In particular, we consid-
er the following und y o erl ing latent m del:


, 1,…,, 1,…,, (6)
where 
 is a continuous but unobserved index of residential mobility of owner-occupied
household  in period ,  is a vector of explanatory variables, and  is a fixed effect
which accounts for inter-household differences in the factors affecting residential mobility and
unobserved explanatory variables, as long as these differences are constant over time.  is the
stochastic error term.
Rather than observing 
 we observe:
 1i
f

0
0otherwise
. (7)
We assume that  follows in d that is: depen ently logistic distribution,
P 1|,exp

1exp
. (8)
Chamberlain (1980) shows that such a fixed effects logit model can be estimated by condi-
tional maximum likelihood. This depends on the probability f a particular sequence: o
,…,,conditionalon 


 ,
P,…,|,…,,,∏exp



∑∏exp 


 


 (9)
where  is the set of all possible combinations of  ones and  zeros, and is indepen-
dent of . The estimator obtained by this estimation method is called the conditional fixed ef-
fect logit estimator and denoted as . Use of this conditional fixed effect panel data logit
model provides the opportunity to properly distinguish dynamic effects from selection effects in
the context of dynamic housing adjustments—typically achieved by residential moves
(Börsch-Supan, 1990). Our goal in this paper is to identify the time-varying dynamic effects of
housing equity constraints and income shocks on the mobility decision. However, these
9
9 It should be noted that, compared with our model based on the recourse loan system, non-recourse loan
contracts can yield somewhat different results. Under the non-recourse contract, the down payment con-
straint for a defaulting household would be  instead of equation (2). Because non-housing
asset  can be positive even for negative equity households, under the non-recourse loan contract they
can rationally default and move to a new house (with a certain cost for defaulting).

time-varying characteristics are likely to be correlated with unobserved heterogeneity of prefe-
rences among consumers (i.e., selection effects). For example, households with a strong inclina-
tion toward mobility are likely to avoid large mortgages because the loan outstanding combined
with collateral risk would impose a substantial transaction cost when they want to purchase (and
move to) a new house. Hence, without controlling for time-invariant selection effects due to
housing preferences or omitted characteristics, we cannot identify time-varying dynamic effects
of housing price changes or income shocks.
In order to test for the fixed individual household effect, one can perform a Hausman-type
test based on the difference between the above conditional MLE and the other logit MLE, de-
noted as . The ist test-stat ic:










 

is asymptotically  distributed with  degrees of freedom, where  is the number of para-
meters except for constant terms.
(10)
6. Data
6.1 Keio Household Panel Survey
The KHPS started to collect data from 2004. The survey is conducted every January on an an-
nual basis, and currently six waves are available until now. The details of the KHPS are as fol-
lows: The KHPS is collected by Keio University (the Faculties of Economics, and Business and
Commerce). Respondents for the first wave were limited to men and women aged between 20
and 69 as of January 31, 2004 from the whole of Japan. The first wave (2004) has data on 4,005
households, the second wave (2005) has data on 3,314 of the 4,005 households in the first wave,
the third wave (2006) has data on 2,884 households and the fourth wave (2007) has data on
2,643 households, meaning an attrition rate between the first and fourth waves of about 34%. In
addition to these samples, in the fourth wave, a new sample of 1,419 households is added. The
fifth wave (2008) has data on 3,691 households and the sixth wave (2009) has data on 3,422
households.
A little over 70% of the surveyed households are married couples. We collect information
related to household characteristics, and detailed information on labor market and housing
choices. Although the respondents to the survey were restricted to the 20-69 age group at the
time of the first survey in early 2004, all other demographic characteristics are representative of
Japanese households.
Theoretically, residential moves are determined by life-cycle factors over the duration of
households. In addition, there exist several institutional barriers to residential moves. Residen-
tial moves are determined by socioeconomic factors at the time of the move, past histories, fu-
10

ture expectations, financial asset position, changing liquidity constraints, price of each tenure,
rate of change of housing prices for each tenure, and government policies and/or systems. In the
following section, we examine determinants that influence residential moves in Japan such as
household attributes, housing attributes, labor market conditions, ability to borrow, and regional
characteristics.
6.2 Determinants of residential moves in Japan
In each survey conducted in January every year, household information concerning the previous
year was asked. For example, the first wave (2004) contains household information for 2003. In
order to assess household mobility, we use the previous year’s information as determinants of
residential moves. That is, if the household answered that they moved house in the 2005 survey,
household information from the 2004 survey is used in assessing this residential move.
As for household and housing attributes, we use the following variables: The number of
household members and dummy variable for any child(ren) in the household represent basic
household characteristics that determine housing demand and need for mobility. The number of
rooms (excluding bathrooms) in the current residence is used for the housing attribute.
In addition to the basic household and housing attributes discussed above, we hypothesize
that there are two principal determinants of the mobility decision: the borrower’s current equity
position in the mortgaged property, measured by the loan-to-value (LTV) ratio, and the size of
the borrower’s mortgage payment obligation relative to his disposable income, measured by the
debt-to-income (DTI) ratio. As for the former, we construct the Extended Loan-to-Value ratio
(ELTV) to reflect the characteristics of the recourse loan system. Ordinary LTV is the ratio of
loans outstanding to value of the house (i.e. selling price) because homeowners with an existing
mortgage for the current h wn payment on a new home: ouse would use their net equity for a do

 .
In the extended version of the LTV, the numerator of the above definition is replaced by the net
value of the mortgage (i.e. loan outstanding minus saving and securities):

 .
Because the Japanese mortgage system is based on the recourse loan system, not only the hous-
ing value, but also the value of other assets, is regarded as collateral. The ELTV reflects the
characteristics of the Japanese mortgage system.10
10 Our ELTV is similar to Chan’s (2001, p.578) extended LTV. However, our ELTV is devised explicitly
taking into consideration the characteristics of the recourse loan system. Moreover, Chan did not conduct
11

For the denominator, Value of house, we use the owner’s self-reported current value of the
house reported in the survey.11 The first part of the numerator, Mortgage loan outstanding, is
calculated as follows. The total amount of the housing loan at the end of the last year  is
reported in the questionnaire. Ideally, we should use the LTV just before the move, which de-
pends on  rather than , to predict residential moves. However, for households that expe-
rienced residential mobility between 1 and ,  reported in the questionnaire is likely to
be the mortgage outstanding after the residential move, not before the move. To circumvent this
problem, the predicted Mortgage loan outstanding, 
, is calculated by extracting the annual
housing loan payment (excluding the interest payments), , from the total amount of the
housing loan outstanding at the end f ear, . o the previous y

. (11)
The annual housing loan payment excluding the interest payment, , is calculated as
follows. From the questionnaire, we can obtain total loan payment (including interest payments)
between 2 and 1. Let  denote this total loan payment reported in the question-
naire. Assuming equal payments including interest, total payment between 2 and 1
should be a good proxy for the payment between 1 and , i.e. .12 Based on this
assumption,  is calculated by excluding interest payments, which is determined by multip-
lying the total amount of the housing loan at the end of the previous year, , by the interest
rate, , from .13 These relationships are specified as follows:
 (12)
For the second and third parts of the numerator, we use the figures for saving and securities re-
ported in the questionnaire.
Together with the LTV, debt-to-income ratio is often considered when lenders (financial in-
stitutions) decide how much money they lend in the case of a residential mortgage. DTI is often
defined as the ratio of the housing loan payment to income:
empirical analysis using the extended LTV. We have also devised another variant of LTV, i.e. adding sav-
ing and securities into the denominator (Seko, Sumita, and Naoi, 2009). Both variants of LTV exhibit
qualitatively similar results.
11 For those households that did not provide the self-reported value, we impute (using hedonic regres-
sion) the missing self-reported value. In doing so, we first estimate the hedonic regression with fixed ef-
fects by using the existing (non-missing) self-reported value and housing attributes information available
from the questionnaire. The estimation result is reported in Table A. Using the regression result, we then
compute the truncated predictor to impute the missing house value. This is the predictor that uses the
coefficient estimates of the hedonic model without the fixed effects in order to make up for the missing
observations (Ballie and Baltagi, 1999). For households that provided the self-reported house value data,
we compute the fixed effects predictor.
12 Equal monthly payments including interest are the most widespread repayment method in Japan.
13 For the mortgage interest rate, we use the base interest rate (kijun kinri) of the Japan Housing Finance
Agency. (http://www.jhf.go.jp/customer/yushi/kinri/suji_kikouyushi.html, accessed on November 9,
2009)
12





 .
We defined the extended DTI (EDTI) as follows:




 .
In this EDTI, in addition to the annual housing loan payment, other loan payments are also in-
cluded in order to assess the household’s overall debt burden and ability to service this debt.
We also include the residential spell, i.e. duration of living in the current housing, as a de-
terminant of residential moves. This variable has two, potentially different, interpretations. As-
suming that the mortgage repayment starts at the time of moving into the current housing, this
variable would represent the duration that the sample household has repaid their existing mort-
gage. Previous studies on mortgage termination suggest that mortgage default—and therefore
subsequent residential mobility—is significantly associated with duration of residence (Deng et
al., 2000). Hence, for mortgage holders, such duration dependence can be controlled for by the
residential spell, although we cannot explicitly observe mortgage defaults from our data. Even
for households with no loans, residential spell is an important determinant for residential moves
since it represents the barrier to residential moves, i.e. transaction costs.
In addition to household-level characteristics, we also use the real prefectural-level housing
price change to capture the expected future price change. The data is taken from the Annual
Report on the Borrowers Survey of the House for Installment Sale issued by the former Gov-
ernment Housing Loan Corporation (GHLC) and its successor organization, the Japan Housing
Finance Agency (JHFA). This price data reflects the prefectural average purchase price for
ready-built houses purchased by those who borrow funds from the GHLC and JHFA. This data
is converted to real terms by using the CPI such that the average value throughout Japan in 2000
is unity. This variable is considered to represent the expected future housing price change based
on rational expectations. Furthermore, region dummy variables for 8 regions in Japan, and city
size dummy variables for households living in a large city, a medium-sized city, and a small city
are included to control for possible geographic differences in mobility behavior.
6.3 Descriptive statistics of the sample
In this section, we discuss the descriptive statistics of the variables. In the following analysis,
we examine how housing equity constraints and income shocks affect subsequent own-to-own
residential moves for homeowners in 2005.
Table 1 provides the descriptive statistics for the whole sample (i.e. homeowners in 2005
survey) and for two sub-samples, classified as “stayers” who continue living in the same hous-
13

ing during 2005-2009, and “own-to-own movers” who experienced moving at least once within
the observation period (2005-2009). As for the whole sample, the average (annual) mobility rate
is about 2.6%. Note that, since we have panel data, there are multiple observations for the same
household. This leads to a lower percentage of observations with residential mobility. If we cal-
culate the household-level average, about 5.8% of the households experience own-to-own
moves at least once during our sample period, which is slightly higher than the nationwide av-
erage own-to-own mobility rate (3.4%) between 2004 and 2008 obtained from the 2008 Hous-
ing and Land Survey of Japan.
The average age of the household heads in the whole sample is about 53.6 years old. The
age of the household head that experienced a residential move is about 43 years old; 77% of the
household heads are working as regular employees and 79% of them are married; about 68% of
the families have children. The average number of household members is about four in each
sample. Stayers are living in 6 room houses and mover households are living in 5 room houses.
Regarding the regional dummies, we can see that over half of the households are living in the
Kanto and Kinki regions: about 33% of the households in the whole sample are living in the
Kanto region, and 22% of the households in the same sample are living in the Kinki region.
Regarding housing loan variables, 34% of the households in the whole sample have a
housing mortgage compared to 37% of mover households. The mean of the LTV for the whole
sample is 31%. The mean of the ELTV has a negative value, -32%, for the whole sample since
the amount of the housing loan is smaller than most households’ financial assets. As for the DTI,
the mean of this value for the whole sample is 5.5%. EDTI, in general, is larger than DTI, as
expected. For the full sample, the average EDTI is 9.5%.
In Table 2, descriptive statistics of the LTV related variables are tabulated by the classifica-
tion of the values of ELTV and LTV. For the mover sample, the ratio of households that have
negative equity, i.e., ELTV is larger than 1, is about 11.5%, and is larger than the corresponding
ratio for stayer households (9.3%). Furthermore, the ratio of households that have positive equi-
ty, i.e., ELTV is less than 1, is about 20.2%, and is not so different for the corresponding ratio
for stayer households (19.3%). From the definition of the variable, LTV is larger than the ELTV,
but produces similar results. Given these figures, it is worth examining whether mort-
gage-related lock-in effects of ELTV and EDTI are different between positive and negative eq-
uity households using econometric analysis.
(Table 1 around here)
(Table 2 around here)
14

7. Estimation results
7.1 Estimation results
Estimation results of the logit models are presented in Table 3. Model (1) is our benchmark es-
timation based on the conditional fixed effects logit model. Model (2) is the estimation based on
the random effects logit model. Model (3) is also based on the random effects specification, but
restricts the sample to movers during our sample period (i.e. we use the same sample as in
Model (1)).
From the conditional fixed effects estimate of Model (1), the estimated coefficients have
the expected signs in general. It is found that the negative equity dummy has a negative impact
on own-to-own moves. Although the estimated coefficient itself is not significant, the result
suggests that negative equity constraints exist among Japanese households. In terms of contem-
poraneous ELTV, we find a significantly negative effect on residential mobility only for positive
equity households. This result indicates that net housing equity—housing and other assets minus
mortgage outstanding—matters only when households have positive net equity, which is con-
sistent with our theoretical result.
Our argument goes as follows. Consider a prospective mover who has sufficient net equity
to make a down payment for a new house.14 With higher housing prices, which coincide with
lower ELTV, the household can still purchase a new house even though housing is more expen-
sive, because now it has more housing equity in its’ current housing. With a decline in prices,
however, the household has less housing equity for a down payment. Although housing is now
cheaper, the household cannot afford the down payment and thus can’t move. Hence, for posi-
tive equity households, the contemporaneous ELTV may have a negative effect on the probabil-
ity of moving, especially in periods of asset deflation.
Consider now, in contrast, an equity constrained household with a larger mortgage out-
standing than housing and other assets. For such negative equity households, a marginal in-
crease in housing prices would not have any impact on the probability of moving because so
long as their net housing equity is negative, the down payment required for a new house forces
them to remain in the current residence. Therefore, changes in housing prices, and the corres-
ponding ELTV variable, have a discontinuous effect at the boundary, i.e., at ELTV = 1. For
households at the boundary, a small increase in housing prices would produce positive housing
equity thus making a down payment feasible, but a decline in prices has absolutely no effect. In
other words, contemporaneous ELTV can have asymmetric effects on mobility depending on the
household’s equity position: they have significant effects for positive equity households, but
have no effect for negative equity households. We can also say that the down payment require-
14 There is no standard rule, but in Japan down payments range from 10 to 20% of the purchase price.
15

ment leads to a discontinuous effect of the negative equity constraint, i.e. a “jump” at the boun-
dary of these two types of households. Figure 4 illustrates the above argument based on our
benchmark estimates of Model (1). We plot the predicted probability of moving for the average
household at various ELTV levels. Figure 4 clearly shows that ELTV has a significantly nega-
tive impact for positive equity households (ELTV < 1), but has virtually no effect on negative
equity households (ELTV ≥ 1). It also shows that the average probability becomes discontinuous
at the boundary (ELTV = 1), reflecting the negative equity constraint associated with the down
payment requirement.
(Figure 4 around here)
The contemporaneous debt-to-income ratio also has a significantly negative impact on mo-
bility, but again only for positive equity households. As long as the DTI for the existing mort-
gage represents the potential repayment capacity of the household, those with high DTI cannot
afford a mortgage for the new house as well.15 But this effect can be observed only for house-
holds who can actually move—i.e., positive equity households. For negative equity households,
equity constraints force them to stay in the current residence, and therefore the EDTI has no
impact on the probability of own-to-own moves. When we look at the marginal effects, the
magnitude of the effect is larger for EDTI than for ELTV. We consider that these results reflect
the fact that bankers are now paying more attention to the (extended) debt-to-income ratio rather
than the (extended) loan-to-value ratio under the recourse loan system.16 Under the recourse
loan system financial institutions determine the loan amount based mostly on the apparent relia-
bility of the applicant.
For the other variables, we find the following results: Residential size in terms of the num-
ber of rooms shows a clear U-shaped relationship with the probability of moving. This implies
that households living in smaller or larger homes than they required would adjust their residen-
tial size. The number of household members increases the probability of moving, possibly re-
flecting the need for the adjustment of residential size. As for the residential spell, we find a
significantly positive coefficient. As discussed in Section 6.2, for households with a mortgage,
residential spell represents the length of the repayment period for the mortgage that should be
negatively associated with transaction costs. Even for households without any mortgage loan,
the residential spell would represent the need for housing adjustment due to various reasons
such as marriage, childbearing, and job turnover. These two factors justify the positive relation-
15 Note that, at the same time, a greater burden of repayment gives an incentive to move to a smaller
home. Therefore EDTI may have a positive effect on residential mobility. Our estimate here is net of
these two effects.
16 Orui and Rating and Investment Information, Inc. (2006, p. 31).
16

ship between residential spell and the probability of moving.17
As discussed in Section 5, the conditional fixed effects logit models can be useful because
it allows for household-specific effects that have an arbitrary correlation with explanatory va-
riables. The relevance of the fixed effects specification can be tested by comparing the fixed
effects model (Model (1)), and the random effects model (Model (2)). A comparison between
the fixed and random effects logit models leads to the following conclusions. Estimated coeffi-
cients for several variables are considerably different between these two models. For example,
the coefficient for the positiveequitydummyELTV has a completely different sign and is
insignificant in the random effects model. Although the Hausman test on the overall parameter
vector cannot reject the null hypothesis that fixed effects and random effects specifications have
identical parameters, the test on this single variable indicates that two models yield different
coefficient estimates (χ115.32 with p-value 0.000).18 Hence we use the fixed effects
model as our preferred specification.
When looking at the regression results, one has to keep in mind that the fixed effects esti-
mator does not use information provided by stayers. As a consequence, identification is based
on individuals who change their residence during the period. In fact, in the fixed effects logit
model all households with unchanged residences drop out of the conditional likelihood function.
In our sample, we observe 227 households who changed their residence once during the
2005-2009 period. One may think that excluding stayers from the sample and focusing only on
recent movers would yield sample selection bias on the fixed effects estimates, and the differ-
ence between fixed and random effects estimates is due to sample selection, not due to incon-
sistency of random effects specification. To see whether this matters, we re-estimate the model
with the random effects logit, but only use recent movers in our estimation. The results are pre-
sented in Model (3). Since now we use the same sample as in Model (1), any difference in pa-
rameter estimates can be attributed to the inappropriateness of the random effects specification,
not to sample selection bias. As a result, we still find a significant difference in parameter esti-
mates between the two models (χ16.89 with p-value 0.008). Thus we believe that the
random effects model yields biased parameter estimates.
(Table 3 around here)
17 When looking at results for the random effects logit model (Model (2)), we have a completely opposite
result for the effect of residential spell—it is significantly and negatively associated with mobility. This
should be interpreted in light of the fact that the random effects specification ignores unobserved house-
hold-specific effects that are positively correlated with residential spells. For example, households that,
for some reason, are unwilling to move, have a lower probability to move during our particular sample
period. These households will also have a longer residential spell, implying that there would be a spurious
negative correlation between residential spell and mobility without a fixed effects specification.
18 See Cameron and Trivedi (2005, p.273) for detail.
17

7.2 Measurement Error and Endogeneity
Our key variables related to housing equity constraints (ELTV and negative equity dummy) rely
on self-reported house values. It is often pointed out that the measurement error due to
self-reporting biases the estimation results. Furthermore the extended LTV also relies on
household wealth measures (saving and securities) that are likely to be endogenous to expected
mobility. The standard solution to this problem is to use an instrumental variables approach.
Our estimation strategy is to use an alternative measure of housing equity constraint that is
based on regional housing market conditions. A similar approach is developed in Ferreira et al.
(2010). This alternative measure of housing equity is constructed using prefecture-level average
purchase price of housing and the associated price appreciation obtained from the survey con-
ducted by the GHLC. In addition, the prefecture-level average mortgage outstanding for house-
holds with a given residential spell is also available from this survey. Using these two variables,
we construct the prefecture-level LTV variable—average mortgage outstanding divided by the
prefecture-level average housing price—and use it as an instrument for individual-level ELTV.
Our intuition is that regional housing prices and mortgage outstanding should be correlated with
the self-reported values, while they are uncorrelated with individual reporting errors. As a result,
prefecture-level LTV measure should be a valid instrument for the individual-level ELTV. It
should be noted that our alternative measure of housing equity has sufficient variation: it takes
different values for each prefecture-year-residential spell combination. Figure 5 shows the dis-
tribution of our alternative LTV measure during our sample period where dots represent the ob-
served regional LTV for different prefectures and residential spells.19 The figure makes clear
that there is considerable cross-sectional variation across region and households with different
residential duration. Furthermore, it is found that the average value of this variable is about 0.30,
which is comparable to that of the observed (ordinary) LTV (average = 0.31).
The estimation result based on the instrumental variables approach is summarized as fol-
lows. Estimated coefficients of the ELTV are –2.76 for positive equity households (with p-value
= 0.013) and 11.45 for negative equity household (not significant with p-value = 0.412). The
estimated coefficients are somewhat larger in an absolute sense, which is consistent with the
well-known result that measurement errors are likely to cause attenuation bias (Ferreira et al.,
2010). Still, however, our robustness check indicates that the instrumental variables approach
does not change the general result obtained in our benchmark regression (Table 3), i.e., the
ELTV measure has a significantly negative effect on residential mobility only when households
have positive net equity. Hence this gives us confidence that our key variables related to housing
equity constraints are capturing what we think they should.
19 Observations with regional LTV = 0 or LTV > 2 are excluded from Figure 5. Households with zero
regional LTV ranges from 26.3 to 29.4% during our sample period.
18

(Figure 5 around here)
8. Conclusion
Japan is known as a low residential mobility society. The contemporary Japanese economic en-
vironment of severe asset price deflation reinforces this tendency. This paper draws on six
waves of household longitudinal data (Keio Household Panel Survey, KHPS) and estimates a
conditional fixed effects logit model to investigate the effects of housing equity constraints and
income shocks on own-to-own residential moves in Japan. By looking at contemporaneous ex-
tended Loan-to-Value (ELTV) and extended Debt-to-Income (EDTI) ratios under the recourse
loan system, we have examined whether housing equity constraints and negative income shocks
have any impact on own-to-own residential mobility. Taking account of the specific nature of
the recourse loan system in Japan, we have further investigated whether these effects are differ-
ent between positive and negative equity households. We find that housing equity constraints
and income shocks deter residential moves, especially for positive equity households. As dis-
cussed earlier, the mortgage loan system influences the degree of the impact of the housing eq-
uity constraint on residential mobility. Therefore our findings suggest that the recourse loan
system is a contributing factor to the remarkably low rate of residential mobility in Japan.
In order to address regulatory-related disequilibrium in the housing market it is important
to lessen regulatory barriers to residential mobility such as the severe equity constraint of nega-
tive net equity in housing. Since the asset Bubble burst in the early 1990s this is a widespread
phenomenon in Japan and a significant impediment to mobility. A non-recourse loan system
would facilitate greater mobility by lessening equity constraints and thus would help limit
housing price volatility in Japan by encouraging adjustments in the pricing and supply of hous-
ing. We therefore believe that introducing non-recourse loans, while curtailing strategic defaults,
is warranted.
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Strassmann, W.P., 1991. Housing Market Interventions and Mobility: An International Compar-
ison. Urban Studies 28, 759-771.

0
5
10
15
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30
1965
1970
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2008
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Figure 1: Trends in land prices, GDP, and stock prices in Japan, 1965-2009
Lan d pr ice ind ex (6 ma jor cit ies) Lan d pr ice ind ex (nat ion wide aver age)
Nominal GDP Nik kei St ock Av erage
Note: All indices are normalized to 1 in 1965.
Source: “Real Est ate S tatis tics,” Mits ui Fud osan Co., Ltd.
22
Source: "Housing Economy Databook", Housing Industry Newspaper Company
Figure 2: Housing prices, 1975-2008(Tokyo metropolitan area)
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
unit: 10,000 JPY
Actual H ousing Price Housing Price(75㎡)

23
Source: "Montyly La b or S ur v e y", Bur e a u of S ta tistic s o f J a pan
Figure 3: Real wage index in Japan, 1990-2009
94
96
98
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102
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106
1990
1991
1992
1993
1994
1995
1996
1997
1998
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Real Wa ge Index (2005 = 100)
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 0.1 0.2 0 .3 0.4 0.5 0 .6 0.7 0.8 0 .9 1 1.1 1.2 1 .3 1.4 1 .5
Pr(Own-to-Own Move)
Extende d LTV
Figure 4: Extended LTV and Predicted Probability of Own-to-Own Mobility
Note: Exp lanatory variables o ther than negative equ ity dummy and ELTV are set a t the sample means o f Model (1) in Table 3.

24
Figure 5: Distribution of the alternative LTV measure
1.51 2
prefecture-level LTV
.50
2004 2005 2006 2007 2008
year
Note: Observations with LTV = 0 or LTV > 2 are excluded.

25
Table 1: Descriptive statistics of the variables
Variables Mean Std. Dev. Mean Std. Dev. Mean Std. Dev.
Housing Mobilit
y
Own-to-own mover
#
0.026 0.16 0.000 0.00 0.234 0.42
House hold and Housing Characte ristics
Age of hous ehold head 53.62 12.22
a
54.93 11.59
d
43.02 12.02
g
Head working as a regular
employee 0.666 0. 47 0.654 0.48 0.765 0.42
Married
#
0.806 0.40 0.808 0.39 0.787 0.41
Numbe r of rooms 5.973 2.04 6.159 2.01 4.458 1. 56
Numbe r of house hold membe rs 3.587 1.45 3. 600 1.46 3.478 1. 33
Any child(ren) in the house hold
#
0.653 0.48 0.649 0.48 0.679 0.47
Donation or inheritance of the house
#
0.105 0.31 0.116 0.32 0.015 0.12
Real house price c ha nge r at e ( %) -0.082 8.26 -0.087 8.41 -0.035 6.93
Residential spell (in years) 19.62 13.45 20.86 13.30 9.48 9.94
Mortgage-related Variables
Housing mortgage
#
0.343 0. 47
b
0.340 0.47
e
0.367 0.48
Extended Loan-to-value ratio: ELTV -0.321 3.03 -0.368 3.19 0.057 0.91
Loan-to-value ratio: LTV 0.312 0.70
c
0.312 0.72
f
0.306 0.50
Exte nded debt-to-income ratio: EDTI 0.095 0.25 0.094 0.23 0.109 0.37
Debt-to-income ra tio: DTI 0.055 0.17 0.055 0. 17 0.053 0.16
Negative e quity (ELTV ≥ 1)
#
0.096 0.29 0.093 0.29 0.115 0.32
Region Dummies
Hokkaido are a
#
0.042 0.20 0.043 0.20 0.033 0.18
Tohoku a re a
#
0.069 0.25 0.075 0.26 0.020 0.14
Kanto area
#
0.332 0.47 0.322 0.47 0.410 0.49
Chubu area
#
0.155 0.36 0.162 0.37 0.097 0.30
Kinki area
#
0.218 0.41 0.216 0.41 0.234 0.42
Chugoku area
#
0.053 0.22 0.054 0.23 0.040 0.20
Shikoku are a
#
0.036 0.19 0.033 0.18 0.053 0.22
Kyushuu a re a
#
0.096 0.29 0.094 0.29 0.112 0.32
Survey Year Dummies
200
4
#
0.171 0.38 0.169 0.38 0.183 0.39
2005
#
0.182 0.39 0.180 0.38 0.195 0.40
2006
#
0.183 0.39 0.182 0.39 0.193 0.39
2007
#
0.231 0.42 0.233 0.42 0.217 0.41
2008
#
0.233 0.42 0.236 0.42 0.213 0.41
Numbe r of Obs ervations 9,081 8,089 992
Note: Nu mb er of o bse rvat ions : a = 8,954, b = 9,076, c = 9,070, d =7,971, e = 8,084, f=8,078 a nd g =983. # ind icate s th e du mmy va riable.
Stayer household sample Mover household sampleWhole sample

26
Table 2: Descriptive statistics of the LTV related variables
N Mean Std. Dev. N Mean Std. Dev. N Mean Std. Dev.
Extended Loan-to-Value Ratio: ELTV
ELTV 9,081 -0.321 3.026 8,089 -0.368 3.188 992 0.057 0.915
( 100.0 %) ( 100.0 %) ( 100.0 % )
ELTV ≤ 0 6,455 -0.809 3. 423 5,777 -0.869 3.602 678 -0.302 0.847
( 71.1 %) ( 71.4 %) ( 68.3 %)
0< ELTV <1 1,758 0.501 0.286 1,558 0.494 0.285 200 0.558 0.287
( 19.4 %) ( 19.3 %) ( 20.2 %)
ELTV ≥ 1 868 1.644 1.230 754 1.694 1.308 114 1. 316 0.292
( 9.6 %) ( 9.3 % ) ( 11.5 % )
Loan-to-Value Ratio: LTV
LTV 9,070 0.312 0.699 8,078 0.312 0.719 992 0.306 0.504
( 100.0 %) ( 100.0 %) ( 100.0 % )
LTV =0 6,003 0.000 0.000 5,349 0.000 0.000 654 0.000 0.000
( 66.2 %) ( 66.2 %) ( 65.9 %)
0< LTV <1 1,933 0.507 0.284 1,740 0.500 0.285 193 0.574 0.267
( 21.3 %) ( 21.5 %) ( 19.5 %)
LTV ≥ 1 1,134 1.628 1.208 989 1.672 1.283 145 1.326 0.291
( 12.5 %) ( 12.2 %) ( 14.6 %)
Note: Numbers in the parentheses are percent of the total s ample .
Whole s a mple S taye r s a mple Mover sample

27
Table 3: Logit Regre ssion Results for Binary Re sidential Mobility V ariable: Two Models
Explanatory variables
Coef. (S.E.) Marginal
Effect Coef. (S.E.) Marginal
Effect Coef. (S.E.) Marginal
Effect
Household and Housing Cha racteristics
Number of rooms -1.72 ( 0.39 )
***
-5.19 -1.10 ( 0.16 )
***
-0.99 -0.813 ( 0.19 )
***
-12.62
Number of rooms
2
0.10 ( 0.03 )
***
0.29 0.04 ( 0.02 )
***
0.04 0.050 ( 0.02 )
***
0.78
Number of hous ehold members 1.07 ( 0.55 )
*
3.23 0.54 ( 0.25 )
***
0.49 0.314 ( 0.27 ) 4.88
Number of hous ehold members
2
-0.09 ( 0.06 ) -0.27 -0.06 ( 0.03 )
**
-0.05 -0.030 ( 0.03 ) -0. 47
Any child(ren) in the house hold 1.35 ( 0.55 )
**
3.46 0.29 ( 0.21 ) 0.25 0.596 ( 0.24 )
**
8.66
Res idential spe ll (in years ) 0. 17 ( 0.04 )
***
0.50 -0. 05 ( 0.01 )
***
-0.04 0. 033 ( 0.01 )
***
0.52
Real house price change ra te (% ) -0.02 ( 0.01 )
*
-0.07 -0.02 ( 0. 01 )
**
-0.02 -0.029 ( 0.01 )
**
-0.46
Mortgage-Related Variables
Negative equity dummy (1 if ELTV ≥ 1) -4.96 ( 3.04 ) -5.32 -2. 41 ( 1.18 )
**
-1.04 -4.192 ( 1.80 )
**
-27.20
Pos itive equity dummy × ELTV -0.60 ( 0. 20 )
***
-1.79 0.10 ( 0.08 ) 0.09 -0.144 ( 0. 10 ) -2. 24
Negative equity dummy × ELTV 1.43 ( 2.23 ) 4.30 -0.24 ( 0.73 ) -0. 21 1.522 ( 1.19 ) 23.62
Pos itive equity dummy × ED TI -2.45 ( 1.15 )
**
-7.37 -3.45 ( 0. 87 )
***
-3.10 -1.804 ( 0.78 )
**
-27.99
Negative equity dummy × EDTI 0.36 ( 1.15 ) 1.10 0. 80 ( 0.74 ) 0.72 0.432 ( 0.69 ) 6. 71
Region dummie s Yes Yes Yes
City-size dummies Yes Yes Yes
Log likelihood -235.22 -859.21 -485.01
Number of obser vations 992 9,081 992
Number of households 227 2,227 227
Notes: ***, ** and * indic ate that the estimate d coe fficient is s ignificant a t 1% , 5%, and 10% levels, res pectively. Marginal effec ts are multiplie d by 100.
(1) Fixed effects logit model (2) Random e ffec ts logit model (3) Random e ffec ts logit model
(restricted sample)

Table A: Estimation results of purchase price model and owner a ssessed value model
Explained variable
Explanatory variables Coef. (S.E.)
Age of the building (years since built) -0.0196 (0.0016)
***
Number of rooms 0.0348 (0.0098)
***
Detached house (1 = yes) 0.5433 (0.0938)
***
Constant 7.2032 (0.1625)
***
Regional dummies
Survey year dummies
Individual fixed effects
S
u
0.9004
S
e
0.4328
F test [F(3661, 8324)] for all u
i
= 0 8.79
[P-value] [0.0000]
R
2
0.8332
Number of observations
Number of households 3,662
Notes: *** indicates that the es timated coefficient is significant at 1% level. R
2
is calculated from
the square of the correlation between the actual dependent variable and its fitted value. S
u
and S
e
are panel-level standard deviation and standard deviation of error term, respectively.
Yes
Yes
ln(Owner assessed value)
Yes
11,998
28