Panel Data Research Center, Keio University
PDRC Discussion Paper Series

住宅相続と金銭的援助の互恵的依存関係
岩田真一郎、行武憲史

2019 年 2 月 18 日
DP2018-001
https://www.pdrc.keio.ac.jp/publications/dp/4990/

Panel Data Research Center, Keio University
2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
info@pdrc.keio.ac.jp
18 February, 2019

住宅相続と金銭的援助の互恵的依存関係
岩田真一郎、行武憲史
PDRC Keio DP2018-001
2019 年 2 月 18 日
JEL Classification: D10; J14; R21
キーワード: 世代間移転;遺産動機;住宅;暗黙的年金契約;日本【要旨】
日本では、高齢者が子に住宅を遺産として残し、その礼として生前に子から金銭的な援助を受け取るという互恵的依存関係の存在がしばしば指摘される。高齢者が世代間住宅資産移転を通じて、子から金銭的な支援を受け取り、生活を維持しようとする試みは、親子間リバース・モーゲージが暗黙的に契約されていることを意味すると考えられる。そこで本稿では、この親子間リバース・モーゲージの存在を理論的・実証的に検証した。シュタッケルベルグ・モデルを応用した理論分析から、子から親への援助額は親が決定する住宅相続確率の増加関数であることを導いた。そして、「日本家計パネル調査」を用いた実証分析の結果から、相続確率が上昇
すると、援助額が増加することを確認した。これは、親子間リバース・モーゲージの存在を支持する結果である。しかし、十分な援助額を引き出すには、親は子に対して高い相続期待を持たせる必要があることも同時に確認した。

岩田真一郎
富山大学経済学部〒930-8555
富山県富山市五福3190
iwata@eco.u-toyama.ac.jp
行武憲史
日本大学経済学部〒101-8360
東京都千代田区神田三崎町1－3－2
yukutake.norifumi@nihon-u.ac.jp

謝辞：本研究は科研費基盤研究（C）（16K03616）による研究成果である。ここに記して謝意を表したい。

Housing inheritance, …nancial assistance, andreciprocal interdependence
Shinichiro Iwata
Faculty of Economics, University of Toyama,3190 Gofuku, Toyama, 930-8555, Japan
iwata@eco.u-toyama.ac.jp

Norifumi Yukutake
College of Economics, Nihon University,
1-3-2 Kanda-Misakicho, Chiyoda, Tokyo 101-8360, Japan
yukutake.norifumi@nihon-u.ac.jp

February 18, 2019

Abstract
When adult children expect that their parents will bequeath residential property tothem, they may show their appreciation by providing their parents with …nancial support.
This paper theoretically and empirically examines this possibility. We adopt a simple
noncooperative game framework with a Stackelberg equilibrium to examine the reciprocal interdependence between the propensity of housing inheritance and …nancial assistancewhen formal care a¤ects decision-making. We use data from Japanese households to test
this interaction. After considering both the censoring of …nancial transfers and the speci…cation of inheritance propensity, which we control for using information on formal care, ourempirical results suggest that the propensity to inherit the parental home has a signi…cantly
positive impact on the amount of transfers from children to their parents. Consequently,
an implicit annuity contract in the form of an intrafamily reverse mortgage appears to exist
in Japanese society. However, parents should ensure they convey to their children a highexpectation of future housing inheritance to extract su¢ cient …nancial assistance for theircurrent consumption needs.
Keywords: Intergenerational transfers; Bequest motives; Housing; Implicit annuity
contracts; JapanJEL classi…cation: D10, J14, R21

Corresponding author1

1Introduction

There has been growing pressure worldwide to cut expenditure on medical bene…ts and insurance payments for the elderly in aging societies. The elderly therefore increasingly expect touse their accumulated assets for welfare needs rather than relying as heavily on governmental
transfers (Toussaint and Elsinga, 2009; Doling and Ronald, 2010). In turn, housing can play
an important role in addressing this issue because it is the primary asset held by most elderly
households, so …nancial instruments such as reverse mortgages may allow elderly homeowners
to remain in their own home and provide a supplemental income until death. In this manner,a reverse mortgage functions like an annuity. However, reverse mortgages are still quite uncommon because of their potentially high cost, small amount of potential proceeds, and thelimited product knowledge of the elderly (Davido¤ et al., 2017; Moulton et al., 2017). As analternative, in some countries, elderly homeowners tend to leave residential property as a future
bequest to derive current …nancial provision from their adult children (see, e.g., Toussaint andElsinga, 2009 on Europe; Ronald and Doling, 2012 on East Asia).1 The purpose of this paper
is to examine this reciprocal interdependence: whether the anticipation of parental housing
inheritance a¤ects the …nancial assistance behavior of adult children.
Our paper is thus associated with testing a bequest motive related to an implicit annuity
contract (Kotliko¤ and Spivak, 1981). According to theory, the elderly choose to insure against
the longevity risk by creating an implicit annuity contract with their children, whereby parents
receive an annuity from their children while they live in exchange for a future bequest. Horioka(2002) suggested that one variant of this type of contract is an intrafamily reverse mortgage,
whereby children agree to support their parents …nancially in exchange for inheriting theparental home (Farnham and Sevak, 2016). Children may also provide nonmonetary assistancerather than monetary support, especially in advanced countries. Indeed, the literature has
accumulated evidence for a strategic bequest (exchange) motive by examining whether adultchildren provide in-kind transfers to their parents in return for receiving bequests (inter vivos
1
In some cases, the elderly are more likely to leave their home because inheritance taxes give preferential
treatment to real estate assets. This paper, however, is not concerned with tax issues.

2gifts).
For instance, Bernheim et al. (1985) found that children’s attention to their parents,
as measured by visits and phone calls, is positively a¤ected by parental bequests. Norton
and Van Houtven (2006) revealed that children who provide informal care appear to receive
larger inter vivos transfers, while Fu (2019) showed that inter vivos transfers are dependent onchildren’s current residential proximity, which may facilitate future informal care. Ciani and
Deiana (2018) suggested that past downstream housing transfers, such as a real estate donationor down payment, tend to increase current informal elderly care. Tomassini et al. (2003)
and Yamada (2006) indicated that past parental housing assistance has e¤ects on current
children’s geographic proximity. Yin (2010) and Horioka et al. (2018) demonstrated thatbequest expectations encourage intergenerational co-residence, while Yamada (2006) reported
that children who expect to inherit a parental home in the future are more likely to co-residewith their parents. Turning to studies of upstream monetary support, Ohtake (1991) showedthat …nancial transfers provided by children tend to increase when parents possess a large
amount of inheritable assets, where …nancial and real estate assets are considered separately.
The amount of housing assets, however, may not always be positively correlated with housing
inheritance.2 Therefore, to our knowledge, little is known about implicit annuity contracts inthe form of intrafamily reverse mortgages. The main contribution of this paper is testing forthe existence of such contracts.
A Stackelberg model of reciprocal interdependence leads to an empirical model where …nancial assistance is a function of the probability of housing inheritance, which depends onthe cost of formal care. That is, the cost of formal care is assumed to in‡uence the bequest
behavior of elderly parents. Our theory suggests that the probability of housing inheritance encourages upstream …nancial support. To test this hypothesis, we used microdata on Japanesehouseholds. Such evidence may provide particularly interesting insights because Japan is very
close to the situation described in the beginning of this paper. Japan is at the forefront of2

Begley (2017), while providing empirical evidence that an increase in housing wealth, driven by unanticipatedshocks to house prices, exerts a positive e¤ect on the probability of elderly homeowners leaving a bequest, did
not focus in particular on the probability of bequesting residential property.

3population aging. Expenditure on social security is at a record level, with 70 percent of allsocial security expenditure being on the elderly in the form of public pensions and medical
bene…ts. At the same time, approximately 90 percent of the Japanese elderly aged 65 years orover own residential property, and this accounts for 60 percent of their total wealth.3 Using thevalue of residential real estate holdings of the Japanese elderly, Suzuki (2007) calculated thatan 810,000 yen annual annuity could be potentially obtained through reverse mortgages perhousehold.4 This would more than cover the di¤erence between average yearly consumption
expenditure and income of approximately 432,000 yen for a nonworking elderly single-personhousehold and 660,000 yen for a nonworking elderly couple household.5
Nonetheless, it is quite di¢ cult for elderly homeowners to release cash from housing assets
because the …nancial sector does not readily provide reverse mortgage loans against property(Kojima, 2013).6 In general, Japanese reverse mortgage loans are recourse loans. Therefore,both the collateral and other assets can be seized by lenders when borrowers default on theirloan. Additionally, income support cannot be guaranteed for life; therefore, the support may
end even while borrowers are living, and repayment may be required during the loan term when
the assessed value falls because of falling land prices.7 On this basis, institutional innovationsin Japan appear to lag far behind those in most Western countries (Mitchell and Piggott, 2004).
Under these circumstances, the elderly may instead leave their housing assets to children to3

According to the 2014 National Survey of Family Income and Expenditure (Table 69. Estimated value of
assets per household by age group of household head), 88.2 percent of households whose household head is 65
years or older own their own home. In terms of net (gross) value, their total assets are valued at 44,196,000(66,746,000) yen, while their total housing and land assets are valued at 25,924,000 (45,231,000) yen.
4
Simulations by Green and Zhu (2018) suggested that converting home equity into annuity income rather
than a lump sum tends to increase the feasibility of reverse mortgages in Japan under circumstances such as
decreasing land prices and increasing life expectancy.
5
Summary Results of the 2016 Family Income and Expenditure Survey reported that the disposable incomeof no-occupation one-person households with a household head aged 60 years or older is 107,648 yen per month,while their monthly consumption expenditure is 143,959 yen. They, thus, need an additional 36,311 yen permonth to cover their living costs. For no-occupation aged-couple households, composed of a husband aged 65
years or older and a wife aged 60 years or older, the monthly disposable income is 180,958 yen, while theirmonthly consumption expenditure is 235,477 yen. Therefore, the shortfall is approximately 54,519 yen.
6
In his analysis, Suzuki (2007) considered various restrictions on contracting reverse mortgages.
7
The 2016 Japan Household Panel Survey (JHPS) asked respondents (N = 4; 993) to report their intention touse a reverse mortgage based on the following question: “How likely is it that you will use a reverse mortgage? ”
1 = have used; 2 = very likely; 3 = likely; 4 = unlikely; 5 = very unlikely; 6 = do not know. On average, about
1.4 and 10.3 percent of respondents selected the second or third response, respectively, but less than 0.1 percent
selected the …rst response.

4

draw monetary support while living. Similarly to other Asian societies, it is quite common in
Japan for adult children to support their elderly parents, and inherit their parents’property
assets (Ronald and Doling, 2012). This is becoming increasingly common because the low
fertility rate in Japan implies fewer siblings (Hirayama, 2010).
Two considerations are examined empirically. First, a speci…cation issue may exist associated with the expectation of housing inheritance, which arises from the potential for measurement error inherent in a discrete dichotomous response to a question about housing inheritance
expectation and the speci…cation of a dummy variable (Yamada, 2006). Some respondents may
be confused by having to select one of two polar responses: they might have to respond with
0 even if they have a low positive propensity to inherit, while others might have to respondwith 1 even if they do not expect a 100 percent probability of inheritance. To address this, we
specify proxy variables for formal care that appear to a¤ect the bequest behavior of parents,and employ a probit model in our estimation. In fact, our empirical results indicate that theprobability of housing inheritance is signi…cantly a¤ected by one of these formal care variables.
The probit model is ideal for understanding how elderly parents respond to incentives. Second,
we must also account for the censoring of transfers from adult children to aging parents because our transfer observations are limited to values greater than or equal to zero. To examine
this, we estimate a Tobit model, which can consider the intensive margin of upstream …nancial
support (Cox, 1987). In light of both issues, our empirical results demonstrate that the expectation of inheriting housing wealth in the future has a signi…cantly positive e¤ect on current
support payments. This suggests that an implicit annuity contract is a motive to consider
regarding the reciprocal interdependence between housing inheritance and …nancial assistance.
However, our empirical results also indicate that upstream …nancial transfers appear to be too
small to cover the consumption needs of aging parents. To correct this, parents should provide
their children with a substantially high expectation of inheriting the parental home.
The remainder of the paper is organized as follows. In Section 2, we present a theoreticalmodel of reciprocal interdependence between housing inheritance and …nancial assistance. Section 3 discusses the data and empirical model used, along with the empirical results. Section

5

4 summarizes the main …ndings of the paper.

2

Model

The purpose of this section is to construct a simple theoretical model that considers the observable characteristics in our empirical study. The theory adopted within the model leads totestable hypotheses and informs the empirical analysis. There are two players in the model: aparent and a child. The parent is assumed to be imperfectly altruistic: the parent cares for theutility of the child, but the parent also cares about monetary transfers t that the child may provide. In contrast, the child is assumed to be nonaltruistic. The following two-stage frameworkis adopted: the parent …rst decides the propensity

to leave their own house valued at h as aninheritance to the child, and an amount of formal care m in the market. If the parent plans tobequest the house, then

= 1, whereas if the parent does not, then

= 0. Because we treat

as the propensity, which is reasonable for parents who will choose an interior solution,

rangesfrom zero to one. This also allows us to di¤erentiate the transfer function, as shown later. The
child then decides consumption c and the size of transfers t, expecting to consume inherited
housing h. Our model applies a simple noncooperative game framework with a Stackelberg
equilibrium that can examine a reciprocal interdependence between t and . As discussed in
Section 1, one reason why housing is left by the parent is the bequest motive arising from theimplicit annuity contract: the parent receives …nancial assistance from the child upon leaving
the child the home.
Assume that the (expected) utility function of the child is u(c)+ , where h is normalized to
one because we cannot observe it from the data, and uc > 0 and ucc < 0, where the subscripts
indicate the …rst and second derivatives. The child will inherit the parental home whenever
the utility obtained is not less than the reservation utility u that the child obtains from notinheriting the home.
u(c) +u(1)

The budget constraint of the child becomes:yt = c;
6(2)

where y is the income of the child.
The rational parent ensures that the child receives the reservation utility in order to bewilling to supply …nancial support. Hereafter, we only consider the case where Eq. (1) isbinding. Substituting the budget constraint Eq. (2) into the utility function Eq. (1) yields
u(yt) + = u. The amount of transfers must satisfy this relationship. The transfers function

then becomes:t = t( ; y; u):(3)

Conversely, the child refuses the inheritance and chooses t = 0 when Eq. (1) does not hold.
The primary variable of interest is . Di¤erentiating the transfer function with respect to agiven value of , we obtain: @t=@ > 0. The positive sign indicates that the child can increase
monetary support instead of reducing consumption expenditure if the parent is more willingto leave their own home because housing inheritance substitutes for consumption.
We now consider parental behavior. Assume that the private utility function of the parent
depends on t and m. That is, …nancial transfers from the child to the parent directly gratify
the parent’s utility. For example, assisting the parent with money can be regarded as a formof child attention, so receiving money from one’s own children appears to di¤er from receiving
wages or pensions. Because the income of the parent is not observed from the data, private
utility is assumed to be quasilinear: v(t) + m, where vt > 0 and vtt < 0. The imperfectly
altruistic parent’s utility function can be assumed to be:v(t) + m + u(c) + :(4)

The parent uses both the housing asset and …nancial transfers to purchase m. As mentioned,
it is di¢ cult for elderly homeowners to release part of their housing wealth as cash through the…nancial sector, particularly in Japan. For simplicity, however, we neglect this issue. Namely,
the parent can theoretically convert the housing asset into cash. Note that the value of housing
is normalized to one and the parent holds the housing asset with propensity (1). The budget

constraint of the parent is then:(1) + t = pm;
7(5)

where p is the price of care services.
The parent maximizes Eq. (4) subject to the following four constraints: the child’s budget
constraint Eq. (2), the transfer function Eq. (3), the parent’s budget constraint Eq. (5), and
0

(

1).

Substituting Eqs. (2), (3), and (5) into the utility function Eq. (4) yields the result thatthe choice variables are reduced to only one variable:. Suppose the second-order condition ofa maximum and @t=@ < 1. The latter assumption implies that the increment of …nancial help
is less than the value of housing, which is normalized to one. Then, the optimal propensity ofinheritance satis…es:
vt
The optimal value of

1
@t
+
@
p

@t
@

1

0:

(6)

is zero when Eq. (6) holds with inequality, while it is positive when

Eq. (6) holds with equality. The inheritance propensity function then becomes:= (p; y; u):(7)

Eqs. (6) and (7) imply that the cost of formal care a¤ects the bequeathing behavior ofelderly homeowners. Under our assumptions, the partial derivative of the price of care services
p is positive: @ =@p > 0. Because care services are assumed to be a substitute for the child’s
support, the parent is more willing to leave their own home to the child when the price of careservices rises.

3

Empirical analysis

3.1

Empirical model

Our data, which are introduced later, are based on a survey of children’s households i. We
consider the following linear form of the …nancial transfer function:ti =C i + X C + "Ci ;where ti is an observed value measuring the transfer paid,(8)
i is the probability of inheriting theparental home, which is the primary variable of interest, X is a vector of explanatory variables,8

C andC are coe¢ cients, and "Ci is an error term.

Theory suggests that the sign of

C islikely to be positive. Explanatory variables include household income (yi ), which is presented
in Eq. (3). We also control for reservation utility u using household characteristics, regionspeci…c e¤ects (using regional dummy variables), and time-speci…c e¤ects (using year dummy
variables). Eq. (8) may still include unobserved heterogeneity. Panel data allow us to estimate
a …xed e¤ects model, in which we can remove the unobserved e¤ect prior to estimation. We,
however, apply pooled ordinary least squares (OLS) in the empirical stage, because we focus
on dummy variables related to siblings of adult children, which are generally constant overtime.8We must account for the fact that optimizing behavior leads to a corner solution response
for some signi…cant portion of adult children. That is, observations of monetary support arelimited to values greater than or equal to zero. Suppose that children with low chances ofinheriting tend to receive monetary transfers from parents rather than give to them. Then, theC coe¢ cient estimated in Eq.

(8) is likely to be biased downward because of the censoring.

To address this, we replace ti in Eq. (8) as an unobserved latent variable t#
i , and estimate a
Tobit model. Namely, we estimate the upstream …nancial transfers on the intensive margin as
in Cox (1987). The nonnegative value ti is de…ned as follows:#ti = t#i ; if ti > 0= 0; otherwise.
Unfortunately, we cannot observe the probability of housing inheritanceobserve a dummy variable

i . Instead, we candi measuring whether households have a probability of inheriting

the parental home from the dichotomous response to the question. Yamada (2006) also cautioned that the measurement error of the dummy variable for future inheritance expectations
may cause attenuation bias, although he did not examine this issue in his empirical analysis.
To correct this speci…cation, we obtain a predicted value of the inheritance propensity as a
generated regressor from the following linear form of the inheritance propensity function using
8

The …xed e¤ects model does not fundamentally change our main results (results not shown).

9the probit model:
#
i =

where

P pi + X P + " P i ;(9)#i is an unobserved latent variable measuring the inheritance propensity, pi is the priceof formal care,

P

and

P

are coe¢ cients, and "P i is the error term. The latent variable

determines the outcome observed for the zero–one dummydi as follows:

#
i >0

d
i = 1; if= 0; otherwise.
We then replace#
i in Eq. (8) as the probability based on the generated regressor ^i , andestimate a second-stage Tobit model. Consistent with the theoretical analysis, this procedureallows the generated regressor of inheritance propensity in Eq. (8) to become a continuous
variable ranging from zero to one. Given that the probabilities of inheritance calculated in the…rst-stage probit estimation provide the generated regressor, we use bootstrap standard errors
for signi…cance tests of each coe¢ cient in the second-stage Tobit estimation.
Yamada (2006) assumed that future downstream housing transfers may be exogenous in his
empirical analysis. Eq. (8), however, is a structural form model. The
is likely biased because of the endogeneity of

C estimated coe¢ cienti , which arises from the possibility of omitted

variables. For example, unobservable characteristics of the value of the parental home may
have an impact on the bequest behavior of parents (Begley, 2017). The variables also have atendency to impact on the transfer decisions of children. Our empirical model, however, canconsider not only the speci…cation of

i but also the endogeneity ofi.

Estimating Eq. (9)is useful, because we can interpret how the housing transfer decisions of elderly parents arealtered by incentives.

3.2

Data

Our empirical analysis draws on the Japan Household Panel Survey (JHPS) to examine therelationship between heritability and the monetary transfer decisions of adult children. The
JHPS, sponsored by the Japan Society for the Promotion of Science (JSPS), is a nationally10representative and large-scale survey of Japanese households. The JHPS comprises two setsof population surveys: one commenced in 2004 (originally called the Keio Household Panel
Survey, KHPS) and the other in 2009 (the initial JHPS sample), both of which had an initialsample of approximately 4,000 households.9 The KHPS was integrated into the current JHPS
in 2014. In the following analysis, we use the 12 years of the JHPS from 2005 to 2016.
The JHPS is particularly suited to addressing the research questions in this paper because it
contains detailed information on housing inheritance, …nancial support, and includes a rich set
of family background characteristics. In our analysis, we use the questionnaire completed fromthe perspective of the adult child. The JHPS asks these respondents to report the total amountof …nancial assistance to their parents in the last year if their parents were alive (i.e., “howmuch …nancial assistance did you give to your parents last year?”). The possibility of inheriting
the parental home in the future is evaluated using a dichotomous question on inheritance (i.e.,“is there a possibility that you will inherit the parent’s home in the future?”). We therefore
obtain a binary variable indicating whether adult children believe they will inherit the parental
home in the future.
The housing assets of the Japanese elderly generally go to their eldest male child because
patriarchy has traditionally been a common practice in Japanese society (Izuhara, 2010). Filial
piety, where adult children have an obligation to look after and support their aging parents,
also appears to be considered a virtue in Japanese society (Taniguchi and Kaufman, 2017).
Housing asset transmission and intergenerational …nancial assistance then potentially have apositive correlation in Japan given existing social norms. To control for this e¤ect, we specify
a dummy variable for the respondent being the eldest son. Under patriarchy, primogeniture,
whereby the …rstborn son inherits the parental home, is considered as an appropriate form ofinheritance. We also include a binary variable indicating whether a respondent has no siblings(an only child). If Japanese seniors are considering succession, an only child is then more likely
to inherit the family home. In addition to these variables, we gather data on a number ofimportant economic and demographic characteristics of adult children from the JHPS. These9

In addition, there were random refreshment samples of approximately 1,400 and 1,000 new respondents in2007 and 2012, respectively.

11

include the age of the householder, household income, employment status, and the number ofhouseholds. Child’s income is measured by the total annual income of all household members.
Nonworker is a binary variable indicating that a householder is not employed. The dummy
variables for region, city size, and the survey year serve as controls in all of our estimations.
The JHPS categorizes a respondent’s location of residence across seven regions (Hokkaido,
Tohoku, Kanto, Chubu, Kinki, Chugoku/Shikoku, and Kyushu) and three city sizes (20 major
cities, other smaller cities, and towns/villages). All monetary variables are converted to 2005
prices using the consumer price index.
The price of formal care in the vicinity will in‡uence aging parent behavior. In this paper,
we consider the long-term care (LTC) services provided by the market. However, we cannot
obtain a market price for LTC because it is government controlled. Instead, we use the capacityof LTC institutions in each prefecture, which is obtained from the Survey of Institutions andEstablishments for Long-term Care (Ministry of Health, Labour and Welfare). Izuhara (2006)
noted that LTC institutions are unevenly distributed across the country, which results ina shortage of such institutions in some regions. Therefore, LTC institutions may providesu¢ cient variation in the data. To construct this variable, we divide the number of hospitalbeds, which re‡ects the supply side of institutional care, by the elderly population, whichre‡ects the demand side. LTC capacity thus likely proxies the accessibility of formal care.
Contrary to the expected sign of the price of formal care, the expected sign of LTC capacity is
negative. In addition to LTC capacity, we consider professional care services for the home ineach prefecture, data for which are also obtained from the above survey, and specify a homehelper variable that equals the number of home helpers divided by the elderly population.
The number of observations is 63,097. The JHPS asks respondents to answer whether theirparents are alive or not. As we examine …nancial transfers from adult children to living parents
in our empirical analysis, we remove respondents whose parents passed away from this question,
resulting in 35,298 observations. In addition, we remove respondents with a missing value for
upstream transfers, resulting in 33,494 remaining observations. We also focus on respondents
who respond to the question concerning the propensity to inherit the parental home, resulting12

in 33,094 observations. Unfortunately, we cannot obtain the parents’residential location fromthe data prior to 2016. However, the JHPS asks respondents about the residential proximity totheir parents or parents-in-law (respondents are asked to respond about whichever of these live
closest to them). From this question, we can observe whether respondents and their parents
reside in the same region. As data for LTC capacity and home helpers are only observed at
the prefecture level, we restrict the sample to only those respondents whose parents residein the same prefecture. However, because we cannot obtain data on the parents’ residential
location when the closest living parents are not parents of the respondent but the parents of
their spouse, this reduced the number of observations to 11,671. We thus supplement our datawith information on parents’residential location using the 2016 JHPS. From this question, we
can use observations of respondents whose parents have resided in the same prefecture since2016. We also add observations by assuming that these same parents have remained in thesame prefecture since before 2016. This assumption is somewhat valid because Japan is known
as a low-residential-mobility society (Seko and Sumita, 2007). This increased the sample by
9,564 observations; consequently, there are now 21,235 observations. Finally, restricting thesample to those where all necessary information was available, our estimation is based on a
total of 14,204 observations.
Table 1 provides descriptive statistics for our variables. On average, the annual …nancial
support from adult children to their parents is approximately 81,700 yen, equivalent to about$742.7 ($1 = 110 yen). About one in seven respondents provide positive transfers to theirparents. However, approximately half of all respondents expect to inherit the parental home.
This disparity suggests that not all parents receive …nancial support from their children in
exchange for leaving them the family home.
Table 2 presents the di¤erence in summary statistics for annual …nancial transfers between
respondents who expect to inherit the parental home and those who do not. On average, adultchildren who expect to inherit the parental home provide a larger amount of …nancial support
than those who do not. The proportion of adult children who provide a positive transfer toparents is also higher for children who expect to inherit the parental home than for those who

13do not.

3.3

Estimation results

Table 3 reports the estimation results of the …rst-stage probit model, which are used to obtain
the predicted value of inheritance propensity as the generated regressor. The coe¢ cient ofeldest son has a positive and signi…cant sign. This indicates that the eldest son tends to plan
to inherit the parental home, and this seems to correspond with the longstanding practice ofprimogeniture in Japan (Horioka, 2002; Ishino et al., 2017). As expected, respondents who are
an only child are more likely to inherit the family home than their counterparts with siblings.
The estimated coe¢ cient of income is signi…cantly positive, which is inconsistent with parents
behaving in an altruistic way; that is, adult children with low incomes tend to inherit theparental home. The coe¢ cient of household size has a positive sign and is signi…cant, indicatingthat children are more likely to receive the parental home when they have a large family. As
expected, the coe¢ cient of home helper has a negative and signi…cant sign, indicating thatchildren are less likely to inherit the parental home when access to professional care services
by seniors increases. In contrast, the coe¢ cient of LTC capacity has an unexpected sign andis statistically insigni…cant.
Figure 1 represents the kernel densities of the predicted value of the inheritance propensitywith and without heritability, which we obtain from the …rst-stage probit model. Figure 1
indeed demonstrates that children with heritability are more likely to inherit the parental
home.
Table 4 provides the OLS and Tobit estimation results for monetary support from children
to parents. In the second-stage OLS estimation in Table 4, the coe¢ cient of the generated regressor measuring the propensity of inheriting the parental home has a positive and signi…cantsign. This appears to con…rm the hypothesis of an implicit annuity contract in the form of
an intrafamily reverse mortgage between adult children and their parents. However, while thesecond-stage OLS estimation in Table 4 considers the speci…cation issue of inheritance propensity, it does not control for the censoring of …nancial transfers. The second-stage Tobit model14

in Table 4 considers both concerns. Again, the inheritance probabilities have a signi…cantly
positive e¤ect on …nancial assistance from children to parents, which is consistent with our
expectation. The coe¢ cient of housing inheritance in the Tobit model is larger in magnitude
than in the OLS estimation, as expected. From the estimated results of the Tobit model inTable 4, we can compute a marginal e¤ect of housing inheritance probabilities on …nancial
assistance by setting the values of all covariates to their means. The marginal e¤ect is 86.55
and its bootstrap standard error is 38.63.
In terms of the other explanatory variables, the Tobit model in Table 4 shows as follows.
The coe¢ cients indicating the eldest son and an only child have negative and signi…cant signs.
These results seem somewhat inconsistent with social norms. One possible interpretation isthat these children are more likely to give their parents nonmonetary rather than monetaryassistance. Household size also has a negative and signi…cant sign. This indicates that children
cannot a¤ord the expense of supporting their parents when they themselves have a large family
to support.
Figure 2 plots the kernel densities of the predicted value of housing inheritance obtained
from the …rst-stage probit model in Table 3 using all observations. Figure 2 also depicts therelationship between the inheritance propensity and …nancial assistance from the second-stage
Tobit model in Table 4. The average predicted value of inheritance propensity is approximately
47.6 percent and at this propensity the predicted value of …nancial assistance is 141,800 yen
per year, which is 60,100 yen higher than the average value in Table 2. As mentioned in
Section 1, however, nonworking elderly single-person households and nonworking elderly couple
households respectively su¤er a de…cit in income of approximately 432,000 yen and 660,000
yen per year. The predicted value of …nancial assistance in the above average case is far below
these values. Despite the fact that the number of children who can provide 432,000 or 660,000
yen per year to their parents is small, above the 89.8 or 96.4 percentile of the distribution,
children are likely to do so when the predicted value of the inheritance propensity is 65.4 or 73.6
percent. Suzuki (2007) predicted that the elderly could extract 810,000 yen per year if theyused formal reverse mortgages. Aging parents can receive this same value using intrafamily

15

reverse mortgages when they grant their children a 78.0 percent housing inheritance probability.
This is despite the number of adult children who could provide 810,000 yen per year to theirparents being much smaller, above the 98.3 percentile of the distribution. In sum, intrafamily
reverse mortgages appear to serve as substitutes for formal reverse mortgages if parents give
their children a substantially high expectation of inheriting the parental home.
We also check whether …nancial assistance varies among subgroups according to child’s
income: household incomes below the 25th percentile (low-income child) and those at or above
the 25th percentile (high-income child). Table 5 demonstrates that adult children in the highincome group signi…cantly increase their transfers when they expect to receive the parental
home. Combined with the results from the …rst-stage probit model in Table 3, we can observea strong interdependence between parents and their wealthy children. However, the coe¢ cientof housing inheritance is insigni…cant for children from the low-income group. This may re‡ect
the fact that children with limited resources are more likely to give parents nonmonetaryassistance when they cannot a¤ord to o¤er monetary support (Taniguchi and Kaufman, 2017).
Alternatively, some elderly parents are purely altruistic, therefore, they bequest housing assets
without an expectation of receiving …nancial help while they are alive from their low-income
children.

3.4

Robustness checks

The remainder of this section reports the results of addtional speci…cations to assess the robustness of our main …ndings. In Table 6, we show the empirical results of the OLS and Tobit
models with a zero–one dummy for inheritance propensity, to see how the models in Table 4
modify possible bias. However, it is not easy to compare the magnitude of the coe¢ cients,
because the generated regressor of inheritance propensity in Table 4 is a continuous variableranging from zero to one, while inheritance propensity in Table 6 is a dummy variable taking
on the values of zero or one. The results show that the estimated coe¢ cients for this dummy
variable are positive and signi…cant in both models, which yield results that are qualitatively
similar to those in Table 4.

16

Table 7 presents the empirical results of the instrumental variable (IV) regression andthe IV Tobit model. We again …nd that the estimated coe¢ cients of the dummy variable
instrumented by the generated instruments indicating that adult children expect to receive theparental home are positive and signi…cant. The test statistics of endogeneity are su¢ ciently
large in both models, indicating rejection of the null hypothesis that inheritance propensity is
an exogenous variable at conventional signi…cance levels.
Instead of ti , we can consider an observed dummy variable measuring whether adult children
give …nancial transfers tdi . Then, the latent variable t#i is estimated by a probit model, which
estimates the upstream transfers on the extensive margins (Cox, 1987). The zero–one dummy
tdi is de…ned as follows:
tdi = 1; if t#
i >0= 0; otherwise.
Model [1] in Table 8 demonstrates the empirical results of the second-stage probit model.
The coe¢ cient of housing inheritance suggests that children are statistically more likely togive …nancial transfers when they expect to receive the parental home, which is consistent
with our expectation. The estimated marginal e¤ect is 0.87 and its bootstrap standard error
is 0.45. Models [2] and [3] in Table 8 show the empirical results of the probit and the secondstage IV probit models with a zero–one dummy for inheritance propensity. Both models also
correspond with our expectation, because the coe¢ cients of housing inheritance dummy havea signi…cantly positive sign. Overall, the results in Tables 6, 7, and 8 provide some con…dence
that our preferred …ndings are not unduly in‡uenced by alternative empirical models.

4

Conclusion

In Japan, elderly homeowners generally leave their housing assets to their children. It is alsoquite common that adult children demonstrate their appreciation to their aging parents byproviding …nancial support while they are alive. This reciprocal interdependence appears toindicate that adult children and aging parents enter into an implicit annuity contract in the17form of an informal intrafamily reverse mortgage, whereby children agree to support theirparents …nancially in exchange for inheriting the parental home. The purpose of this paper isto theoretically and empirically examine this possibility.
We applied a simple noncooperative game framework with a Stackelberg equilibrium to
examine the reciprocal interdependence between the propensity of housing inheritance and…nancial assistance when formal care a¤ects decision-making. Theoretical models have suggested that adult children increase the amount of …nancial support to their parents when theprobability of housing inheritance increases, which is consistent with a bequest motive arisingfrom an implicit annuity contract.
We used data from Japanese households to test this reciprocal interdependence. Considering both the censoring of …nancial transfers and the speci…cation of the inheritance propensity,
which are controlled using information on formal care, our empirical results indeed suggestthat the propensity to inherit the parental home encourages transfers from adult children to
their elderly parents. This may con…rm that the implicit annuity contract in the form of an
intrafamily reverse mortgage appears to exist in Japanese society. However, altruism may also
be a motive for bequeathing housing assets and engaging in …nancial provision. For example,
altruistic children may o¤er …nancial assistance when parents run out of funds for living expenses. Parents then tend to show their appreciation to their children by bequeathing housing
wealth. Instead, the bequest motive related to an implicit annuity contract may be an additional motivator in societies where assets, particularly illiquid housing assets in our context,
are quite di¢ cult to convert into cash.
The estimated results, however, suggest that on average, the amount of …nancial transfersfrom children tends to be too small to cover the welfare needs of their parents. Intrafamily
reverse mortgages are e¤ectively available to elderly homeowners if children have high expectations of inheriting the parental home. This could be resolved if adult children were to legallycontract with their elderly parents in relation to housing inheritance and …nancial assistance.
For example, in the USA, National Family Mortgage, LLC provides a family-funded reverse
mortgage called the Caregiver Mortgage, whereby adult children crowdfund a line of credit

18

against the equity in the parental home.
Subsample analysis indicated that the reciprocal interdependence found tends to operate
best for children whose income is relatively high. However, …nancial support from children
to parents is small when the income of the children is su¢ ciently low. These children cannota¤ord to assist their elderly parents …nancially even if they receive the parental home in the
future. Prolonged economic stagnation in Japan has resulted in a decreasing share of adultchildren in the higher income class. This suggests that intrafamily reverse mortgages may
be available to even fewer elderly homeowners in the not-too-distant future. Nevertheless,this could be resolved if the commercial …nancial sector promoted customer-friendly reverse
mortgage products to elderly homeowners.
There is, however, a consideration in that waiving inherited housing is becoming more common in Japan (Hirayama, 2010). Indeed, the number of vacant houses is soaring in unattractive
locations in Japan. Intrafamily reverse mortgages therefore would not be e¤ective in maintaining the welfare of the elderly in such areas. It is also di¢ cult for the commercial …nancial
sector to develop reverse mortgages in locations with little prospect for pro…t. This situation ismore likely to occur when adult children live a considerable distance away from their parents.
Because we restricted our sample to respondents whose parents reside in the same prefecture,
this issue remains a topic for future research.
Acknowledgments

The authors would like to thank Junya Hamaaki, Shih-Hsun Hsu, Takuya Ishino, Movshuk Oleksandr, Aslan
Zorlu, seminar participants at UiT the Arctic University of Norway, University of Toyama, Nihon University,and conference attendees at ARSC, AsRES, ENHR, JEA for their valuable comments and suggestions. This
research was part of a project by the Housing Research and Advancement Foundation of Japan, and supported
by JSPS KAKENHI Grant Numbers JP16K03616 and JP17H00988. The authors are grateful to the Panel Data
Research Center at Keio University for access to its microdata. The authors would also like to thank Michio
Naoi and Kazuto Sumita for useful advice on using these data.

19

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23

Figure 1: Kernel densities of predicted value of housing inheritance probabilities with and without

heritability

Figure 2: Predicted value of housing inheritance probabilities and financial assistanceTable 1: Descriptive statistics of the full sample
Variables
Financial assistance (10,000 yen)
Positive assistance (%)
Housing inheritance (dummy)
Eldest son (dummy)
Only child (dummy)
AgeChild’s income (10,000 yen)
Nonworker (dummy)
Household size (#)
LTC capacity (1,000 beds/100,000 elderly)Home helper (1,000 person/100,000 elderly)
Observations

Mean

8.17
13.57
0.48
0.25
0.06
46.00
734.38
0.07
3.73
2.98
1.41
14,204

Std. Dev.
58.37
34.25
0.50
0.43
0.23
10.97
485.26
0.25
1.39
0.65
0.51

Min.

Note: Descriptive statistics for region, city size, and survey year dummies not shown.

Table 2: Annual financial assistance from adult children to parents
Mean (10,000 yen)

Positive assistance (%)
Observations

Note: Standard deviation in parentheses.

With heritability
11.67(81.25)
16.64
6,760

0.00
0.00
0.00
0.00
0.00
20.00
0.00
0.00
1.00
1.54
0.61

Without heritability
4.98(22.04)
10.79
7,444

Table 3: Estimation results of the first-stage probit model
Variables
Coef.
Robust Std. Err.
Eldest son
0.478***
0.025
Only child
0.452***
0.050
Age–0.012***0.001
Child’s income
0.021***
0.003
Nonworker
0.027
0.046
Household size
0.088***
0.008
LTC capacity
0.023
0.033
Home helper–0.094***0.033
Constant–0.186
0.129
Pseudo R2
0.050

Note: Number of observations is 14,204.
Model controls for region, city size, and survey year (estimates not shown).
*** denotes significance at the 1% level.

Max.
5197.51
100.00
1.00
1.00
1.00
86.00
9771.31
1.00
10.00
5.99
2.74

Table 4: Estimation results of the second-stage OLS and Tobit models
OLS
Tobit
Variables
Coef.
Bootstrap Std. Err. Coef.
Bootstrap Std. Err.
Housing inheritance
70.650*40.309745.531*303.193
Eldest son–10.491
8.495–105.806**
63.082
Only child–10.2677.726–108.225**
56.222Age
0.258*
0.146
1.783
1.144
Child’s income
0.059
0.268
–0.715
1.889
Nonworker–1.2681.950–2.50716.604
Household size
–3.542***
1.364–34.205***
10.795Constant–21.037
16.124–541.079***141.986R2
0.006
2
Pseudo R
0.008
Note: Number of observations is 14,204.
Housing inheritance is the generated regressor obtained from the first-stage probit model.
Child’s income is divided by 100.
Models control for region and survey year (estimates not shown).
Bootstrap Std. Err. obtained by bootstrap approximation using 500 resamples.
***, **, * denote significance at the 1%, 5%, 10% level, respectively.

Table 5: Estimation results of the subsamples according to child's income
High-income child
Low-income child
Variables
Coef.
Bootstrap Std. Err. Coef.
Bootstrap Std. Err.
Housing inheritance
968.678**400.128–40.185
300.073
Eldest son–151.055*
82.09938.96672.133Only child–133.046*
72.133
1.646
82.099
Age
2.081
1.499
–0.144
1.086
Child’s income–2.4862.467–0.708
4.086
Nonworker
12.02225.922–10.457
15.131
Household size
–44.345
14.413–1.081
10.349Constant–630.499***184.615–128.288
119.606
Pseudo R2
0.009
0.008
Observations
10,655
3,549

Note: Housing inheritance is the generated regressor obtained from the first-stage probit model.
Child’s income is divided by 100.
Models control for region and survey year (estimates not shown).
High-income child is defined as a child whose household income is at or above the 25th percentile.
Low-income child is defined as a child whose household income is below the 25th percentile.
Bootstrap Std. Err. obtained by bootstrap approximation using 500 resamples.
***, **, * denote significance at the 1%, 5%, 10% level, respectively.

Table 6: Estimation results of the OLS and Tobit models
OLS
Variables
Coef.
Robust Std. Err.
Housing inheritance dummy
6.281***
1.113
Eldest son
1.273
1.004
Only child
0.180
2.044
Age
–0.032
0.028
Child’s income
0.545**
0.146
Nonworker–0.573
1.334
Household size
–1.352***
0.514
Constant
4.236
2.630
R2
0.008
Pseudo R2

Tobit
Coef.
47.282***22.196**3.986–1.375***4.572***
5.148–10.534***–263.258***

Robust Std. Err.
11.7886.518
10.5800.401
1.232
10.3703.540
65.025

Table 7: Estimation results of the second-stage IV regression and IV Tobit models
IV regression
IV Tobit
Variables
Coef.
Robust Std. Err. Coef.
Housing inheritance dummy
47.444**20.708502.358***
Eldest son–6.2684.061–61.072**
Only child–6.7204.873–71.399**
Age
0.226
0.234
0.688
Child’s income
0.154
0.102
1.074
Nonworker–1.0891.47–0.439Household size
–2.745***0.788–25.987***
Constant–11.8788.921–442.013***
4.566[0.033]15.964
Tests of endogeneity [p-value]

Robust Std. Err.
168.732
29.52230.9730.72
1.347
12.931
7.766
111.108[0.001]

Note: Number of observations is 14,204.
Child’s income is divided by 100.
Models control for region and survey year (estimates not shown).
***, ** denote significance at the 1%, 5% level, respectively.

0.010

Note: Number of observations is 14,204.
Housing inheritance dummy is the generated IV obtained from the first-stage probit model.
Child’s income is divided by 100.
Models control for region and survey year (estimates not shown).
The null hypothesis that all independent variables including housing inheritance dummy are exogenous in the IV
regression model is tested using a Wooldridge (1995) robust regression-based test.
The null hypothesis that housing inheritance dummy is exogenous in the IV Tobit model is tested using the Wald
test.
***, ** denote significance at the 1%, 5% level, respectively.

Table 8: Estimation results of the probit models[1]
Variables
Probit (2nd stage)
Housing inheritance
4.105**(2.008)
Housing inheritance dummy
Eldest son
Only child
AgeChild’s income
Nonworker

Household size
Constant

Pseudo R2
Tests of endogeneity–0.578(0.420)–0.601(0.374)0.008(0.008)–0.004(0.013)0.003(0.107)–0.184***(0.065)–2.784***(0.845)0.028[2]Probit0.223***[0.028]0.133***[0.031]0.024[0.057]–0.009***[0.001]0.025***[0.003]0.044[0.059]–0.052***[0.011]–1.251***[0.122]0.032[3]
IV probit (2nd stage)
1.747***[0.172]–0.210***[0.057]–0.250***[0.058]0.001[0.002]0.003[0.005]0.009[0.046]–0.087***[0.008]–1.420***[0.119]18.630{0.000}Note: Number of observations is 14,204.
Housing inheritance in Model [1] is the generated regressor obtained from the first-stage probit model.
Housing inheritance dummy in Model [3] is the generated IV obtained from the first-stage probit model.
Child’s income is divided by 100.
Models control for region and survey year (estimates not shown).
The null hypothesis that housing inheritance dummy is exogenous in the IV probit model is tested using the Wald
test.
Bootstrap Std. Err. in parentheses, Robust Std. Err. in brackets, p-value in braces.
Bootstrap Std. Err. obtained by bootstrap approximation using 500 resamples.
***, ** denote significance at the 1%, 5% level, respectively.