The Nexus between Long-term Care Insurance, Formal Care,
Informal Care, and Bequests: The Case of JapanCharles Yuji Horioka
Kobe University, Osaka University, Asian Growth Research Institute, andNational Bureau of Economic Research
Emin Gahramanov
American University of Sharjah
Xueli Tang
Deakin University

Working Paper Series Vol. 2024-16
July 2024

The view expressed in this publication are those of the author(s) and do
not necessarily reflect those of the Institute.

No part of this article may be used or reproduced in any mannerwhatsoever without written permission except in the case of brief
quotations embodied in articles and reviews. For information, pleasewrite to the Institute.

Asian Growth Research InstituteThe Nexus between Long-term Care Insurance, Formal Care, Informal Care, andBequests: The Case of JapanCharles Yuji Horioka*(Kobe University, Osaka University, Asian Growth Research Institute, and National Bureau of
Economic Research)
Emin Gahramanov(American University of Sharjah)
Xueli Tang
(Deakin University)

June 2024

Abstract
The purpose of this paper is to conduct a theoretical and empirical analysis of the nexus between
long-term care insurance (LTCI), formal care, informal (family) care, and bequests. In ourempirical analysis, we use micro data from the Japan Household Panel Survey on Consumer
Preferences and Satisfaction (JHPS-CPS), formerly known as the Preference Parameter Study,
conducted by Osaka University. Japan is an interesting case to analyze because a public LTCI
system was introduced there in 2000. Our analysis shows that, in the case of Japan, if parents are
eligible for public LTCI benefits, their children will be less likely to be their primary caregiverand that this, in turn, will reduce their children’s perceived likelihood of receiving a bequest fromthem. This result implies that bequests are selfishly or strategically motivated (i.e., that parents
leave bequests to their children in order to elicit care from them) and that the introduction of apublic LTCI system will reduce the likelihood of children providing care to their parents andthrough this channel reduce their perceived likelihood of receiving a bequest from them.
JEL classification codes: D11, D12, D15, D64, E21, I13, J14
Keywords: Altruistic bequests; bequests; caregiving; elderly care; family care; formal care;informal care; long-term care; long-term care insurance; parental care; selfish bequests; strategic
bequests*Corresponding author: Charles Yuji Horioka. Address: Research Institute for Economics andBusiness Administration, Kobe University, 2-1, Rokkodai-cho, Nada-ku, Kobe, Hyogo 657-8501,
JAPAN. E-mail: horioka@rieb.kobe-u.ac.jp

1. Introduction
Population ageing is occurring in many countries in the world due to increases in life expectancy
and declines in fertility although its timing and speed varies greatly from country to country. This
will greatly increase the burden of long-term care of the elderly, and in fact, this issue is such anurgent and important one that the National Bureau of Economic Research (NBER) recently
embarked on a large-scale research project on this topic and will soon publish a book on this topic(Gruber and McGarry, forthcoming). This book compares long-term care in 10 major developed
countries and finds that spending on formal long-term care is a large and growing share of GDP
in all 10 of the countries they studied, increasing, on average, from 1.4 percent of GDP in 2000 to
2.1 percent of GDP in 2019 (see Gruber, et al., 2023). The increase in spending on long-term carehas been even more pronounced in Japan, where the share of formal long-term care in GDP
increased from 0.7% in 2000 to 2.1% in 2019, a three-fold increase. This sharp increase is
primarily due to the fact that Japan introduced a public long-term care insurance (LTCI) system
in 2000. Moreover, these figures would be even higher if informal care by family members were
to be included (which Gruber and McGarry (forthcoming) attempt to do in their book). In fact,
Gruber, et al. (2023) and Fu, et al. (2023) estimate that the aforementioned figures for Japan wouldbe 75 percent higher if informal long-term care were to be included.
Given how onerous the burden of long-term care of the elderly has become, it has become difficult
for the necessary long-term care services to be financed solely by the private sector. Partly inresponse to this challenge, many countries including Germany, the Republic of Korea, Japan, andSingapore have introduced public LTCI systems. Moreover, many other countries provide publicfunding for long-term care through other means (for example, by using general tax revenue orincorporating it into their public health insurance systems) (see Li, et al., 2023, for more details).
However, despite the growing importance of long-term care spending and government funding
for such spending, relatively little research has been conducted on the nexus between LTCI, formalcare, informal (family) care, and bequests.
The purpose of this paper is to construct a theoretical model of this nexus and to test this modelusing micro data from Japan, where, as mentioned earlier, a public LTCI system was introduced
in 2000. In particular, we use data from the Japan Household Panel Survey on Consumer
Preferences and Satisfaction (JHPS-CPS), formerly known as the Preference Parameter Study,
conducted by Osaka University, to analyze the impact of LTCI on informal parental care andthrough this channel on bequests. Our reasoning is that the introduction of a public LTCI system
will lower the price of formal care relative to the price of informal care (at least in a country like
Japan where there are no cash benefits for informal care), induce the substitution of formal carefor informal care, and reduce the prevalence of bequests (to the extent that bequests are
strategically or selfishly motivated—i.e., to the extent that parents leave bequests to their children
in order to elicit care from them). Thus, our findings have important implications for thedesirability and optimal design of public LTCI programs, for the extent to which wealth disparities
are passed on from generation to generation, and for labor force participation, especially of women.
To summarize the main findings of this paper, we find that, if parents are eligible for public LTCI
benefits, their children will be less likely to be their primary caregiver and that this, in turn, will
reduce their children’s perceived likelihood of receiving a bequest from them. This result implies
that bequests are selfishly or strategically motivated (i.e., that parents leave bequests to theirchildren in order to elicit care from them) and that the introduction of a public LTCI system will
reduce the likelihood of children providing care to their parents and through this channel reduce1their perceived likelihood of receiving a bequest from them. Our findings imply that both parents
and children are selfish, at least in the case of Japan.
This paper makes important contributions to the literature both theoretically as well as empirically.
Theoretically, it analyzes all four possible cases (the case of an altruistic parent and an altruistic
child, that of a selfish parent and a selfish child, that of an altruistic parent and a selfish child, andthat of a selfish parent and an altruistic child) and shows how the impact of LTCI and informalparental care on bequests differs among the four cases.
Empirically, there is a large literature on whether LTCI and informal care are substitutes for one
another starting with Mellor (2001) and there is an equally large literature on whether providing
informal care to one’s parents enhances a child’s prospects of receiving a bequest starting with
Menchik (1988). However, to the best of our knowledge, there are no previous studies that haveexamined the two issues simultaneously, and the current paper is virtually the first to examine thenexus between LTCI systems, formal care, informal care, and bequests in a unified framework.
Moreover, it estimates the impact of LTCI eligibility on informal parental care and bequests using
an innovative instrumental variables approach to control for endogeneity (it uses parental
eligibility for LTCI benefits as an instrument for informal parental care). Finally, the estimation
strategy in our paper enables us to determine which of the four theoretical cases applies in the realworld.
The paper is organized as follows: Section 2 conducts a survey of the relevant literature, section
3 discusses Japan’s public LTCI system, section 4 presents the theoretical model, section 5
discusses the data source used in this paper and the sample selection criteria, section 6 discusses
the estimation model, section 7 presents descriptive statistics, section 8 presents the estimation
results, and section 9 summarizes the findings of this paper and discusses the policy implications
thereof.

2. Literature Survey
Since this paper examines the nexus between LTCI, formal care, informal care, and bequests, it isrelated to at least five strands of literature.
First and most obviously, our paper is related to the extensive literature on the interrelationshipbetween bequests and other intergenerational transfers from parents to children and the informalcare children provide to their elderly parents. The most well-known hypothesis that explains thisconnection is the strategic bequest motive of Bernheim et al. (1985). According to this hypothesis,
parents leave bequests to their children in order to induce them to provide care and attention during
old age, and conversely, children provide care and attention to their parents during old age in orderto obtain a larger share of their parents’ inheritance (see also Horioka et al. 2018).
Thus, the empirical relevance of the strategic bequest motive can be tested in one of two ways—
first, by examining whether or not parents who expect to receive informal care from their children
are more likely to leave bequests or to leave larger bequests, and second, by examining whether
or not children who expect to receive bequests or who expect to receive larger bequests from theirparents are more likely to provide informal care to their parents during old age. There are manystudies that attempt to shed light on the validity of the strategic bequest motive, with some of them
adopting the first strategy and others adopting the second strategy. For example, Menchik (1988),
Sloan et al. (1997), Norton and Taylor (2005), Brown (2006), Norton and van Houtven (2006),2and Groneck (2017) adopt the first strategy. Turning to studies that adopt the second strategy,
Bernheim et al. (1985) and Perozek (1998) use data for the United States, while Noguchi et al.
(1989), Komamura (1994), Ohtake and Horioka (1994), Horioka et al. (2000), Yamada (2006),
Wakabayashi and Horioka (2009), Kohara and Ohtake (2011), and Horioka et al. (2018) use data
for Japan, Almas, et al. (2020) use data for China, and Ho (2022) uses data for Singapore (seeLaferrère and Wolff 2006, Arrondel and Mason 2006, Horioka et al. 2018, and Horioka 2021a,
2021b for more extensive surveys of this literature). Since direct data on bequest receipts or
bequest expectations are usually not available, most of these studies use various proxies thereforsuch as the bequeathable wealth or educational attainment of parents. As for care-related variables,
previous studies use a variety of measures including frequency of visits and phone calls, coresidence, living nearby, help with housework, help with nursing care, help with ADL (Activities
of Daily Living) and/or IADL (Instrumental Activities of Daily Living), and financial assistance.
Finally, there are some studies such as Cox (1987), Cox and Rank (1992), Henretta et al. (1997),
McGarry and Schoeni (1995, 1997), and Norton et al. (2013) that look at the related issue of
whether there is a correlation between inter vivos transfers from parents to children and informalcare of parents by children but it is possible that inter vivos transfers and bequests are governedby different considerations.
Another strand of literature to which our paper is related is the literature on the determinants of
who provides care to parents requiring care. For example, Stern (1995) and Chechovich and Stern(2002) conduct an econometric analysis of what parent and child characteristics influence thecaregiving decision (see Grabowski, et al., 2012, for a useful survey of this literature).
A third strand of literature to which our paper is related is the literature on the substitutability
between informal (family) care and formal care and on what impact the availability of public andprivate LTCI, which reduces the relative price of formal care, has on this substitutability. There
will be less need for children to provide informal care to their parents during old age if theirparents have access to formal care and/or are covered by LTCI, and conversely, that there will beless need for formal elder care and/or for LTCI if there are children who can provide informalcare to their parents during old age. Mellor (2001) examines whether children and other family
members are substitutes for LTCI and finds that the availability of informal caregivers does nothave a statistically significant impact on the actual or intended purchase of LTCI. Lockwood(2012, 2018) shows that bequest motives (which, in turn, presumably precipitate greater informalcare) significantly reduce the demand for LTCI. Mommaerts (2018) examines the extent to which
nursing home care and co-residence with adult children are substitutes for one another and findsthat changes in eligibility for public LTCI (Medicaid) benefits could have large impacts on theprobability of co-residence with adult children. Finally, Sloan and Norton (1997) and Norton(2000) and Bonsang (2009) look at the related issue of the substitutability between public LTCI
(Medicaid in the United States) and private LTCI in the United States and Europe, respectively.
A fourth strand of literature to which our paper is related is the literature on the impact of LTCI
on children’s incentive to provide care to their parents during old age (see, for example, Stern,
1995, and Grabowski et al., 2012). For example, Sloan and Norton (1997) and Courbage andZweifel (2011) point out that, if the parents have LTCI, their children will be less likely to provide
informal care to them during old age because LTCI will protect the parents’ bequest from the costof nursing home care. Conversely, if the parents have no LTCI, their children will be more likely
to provide informal care to them during old age because failure to do so may necessitate putting
their parents in a nursing home, which means that children will not be able to receive as large abequest. Thus, parents who want their children to provide informal care to them during old age

3may decide not to purchase LTCI because they want to give their children as much of an incentive
to provide informal care as they can (see, for example, Pauly, 1990).
A fifth and final strand of literature to which our paper is related is the literature on thedeterminants of the demand for private LTCI. For example, Braun, et al. (2019) analyze thedeterminants of the demand for private LTCI in the United States in order to shed light on why
the demand for private LTCI is so low in the United States despite the absence of a public LTCI
system.
3. An Overview of Japan’s Public LTCI System
Before turning to our analysis, we provide a brief overview of Japan’s public LTCI system, which
was introduced in 2000 (see Fu, et al., 2017; Iwagami and Tamiya, 2019; and Kikuchi, et al.
(2024) for more details). In Japan as well as in any other country, care of the elderly can beprovided either by family members, in which case it is called “informal care” or by professionalcare workers, in which case it is called “formal care.” Moreover, formal care can be financed
either by the individual’s own savings or by public or private LTCI.
Almost no Japanese people have purchased private LTCI either before or after the introduction of
public LTCI in 2000 even though it is available, but one very important thing to note is that there
were means-tested subsidies for nursing home care and at-home care even before 2000 (in fact,
since 1963). Thus, low-income people could obtain subsidies for nursing home care and at-homecare even before 2000, and in fact, the subsidies they could receive declined after 2000 in somecases. By contrast, middle- to high-income people had to pay almost the full cost of nursing homecare before 2000, but they sometimes relied on long-term hospitalization (in which case medical
insurance could be used to cover all or part of the cost) although this is no longer possible. The
introduction of the LTCI system in 2000 was not as abrupt a change as one might think because
similar systems were already in place even before then, but it is true that LTCI benefits became
more generous and were expanded to a larger segment of the population (in particular, to middleto high-income people) after 2000.
The public LTCI system that was introduced in Japan in 2000 covers everyone aged 65 or older
as well as younger people with an aging-related disability. If a person meets these eligibility
requirements and is certified as needing care, the public LTCI system will cover 90% of the costof the formal care that he or she is deemed to require, and the person himself/herself needs to pay
only 10% of the cost.1 The system covers formal care that is provided by professional care workers(home helpers) who visit you at home, formal care that is provided by “day service” facilities
where the elderly person is dropped off in the morning and picked up in the evening in the same
way that a young child is taken care of at a daycare center, and formal care provided by nursing
homes but does not cover informal care provided by family members.
The amount of care that is subsidized by the government depends on the person’s need level. The
person’s need level, in turn, depends on the mental and physical condition of the person and isdetermined by the Long-term Care Approval Board based on the opinion of a regular medical
doctor. There are seven need levels (support level 1 is the lowest need level, followed by support
level 2, care level 1, care level 2, care level 3, care level 4, and care level 5), and the amount of
Pursuant to the 2015 revision of Japan’s LTCI system, the copayment rate was raised from 10% to 20% for those
whose income is above a certain level, but since the data we use in this paper pertain to 2011, we did not need to takeaccount of this revision.
14

required care that the government will subsidize increases with the person’s need level (i.e., withthe severity of the person’s disability).
To enable the reader to better understand Japan’s public LTCI system, Table 1 presents
information on the requirements, standardized care times, and maximum benefits for each needlevel. As can be seen from this table, a recipient with the lowest need level (support level 1) isestimated to require 25 to 32 minutes of care per day whereas a recipient with the highest needlevel (care level 5) is estimated to require 110 or more minutes of care per day, which is about 4times as much as the amount of care that a recipient with the lowest need level is estimated torequire.
Table 1 here
Similarly, Table 1 also shows that the maximum benefit is 50,320 yen per month for a recipientwith the lowest need level (support level 1) whereas the maximum benefit is 362,170 yen for arecipient with the highest need level (care level 5), which is more than 7 times as much as the
maximum benefit of a recipient with the lowest need level.
Thus, Japan’s LTCI system is needs-based, with benefits increasing sharply with the recipient’s
need level (degree of disability) and is not means-tested (i.e., it does not depend on the person’s
income or wealth).
As noted earlier, Japan’s public LTCI system does not pay cash benefits for informal care provided
by family members, unlike in the case of, for example, the German system. Thus, the systemcreates a bias toward formal care, or to put it another way, it lowers the price of formal care relative
to the price of informal care. Thus, the person is eligible for benefits equal to 90 percent of thecost of formal care that he/she is deemed to require based on his/her need level but receives nobenefits for formal care in excess of the required amount or for informal (family) care.
The introduction of Japan’s public LTCI system in 2000 had an enormous impact, with spending
on formal long-term care increasing from about 0.7% of GDP in 2000 when the LTCI system was
first introduced to 2.1% of GDP in 2019 (see Gruber, et al., 2023, and Fu, et al., 2023), a threefold increase in less than 20 years, as already noted.
However, it should be noted that, although Japan’s public LTCI covers all “required” care,eligibility requirements are very strict, meaning that the system seldom covers all of the recipient’s
care needs. For example, the public LTCI system may cover the cost of a home helper coming to
the recipient’s home twice a week even though he/she actually needs the home helper to comeevery day.

4. The Theoretical ModelIn our theoretical model of the nexus between the LTCI system, formal care, informal care, andbequests, we consider the following four cases, which differ with respect to whether parents andchildren are selfish or altruistic: the case of a selfish parent and a selfish child in Case 1, the caseof an altruistic parent and a selfish child in Case 2, the case of an altruistic parent and an altruistic
child in Case 3, and the case of a selfish parent and an altruistic child in Case 4.

5

Assume that, at any point in time, one parent interacts with one child of her own, and we arbitrarilyrefer to both economic agents as being of feminine gender. A young adult agent (parent) entersthe model in the first period of economic life and lives for two periods. In the first period, theyoung parent decides how much to save for the future and how much care to provide to her own
elderly parent. In the second stage of life, the agent becomes elderly and begins an “economic”
interaction with her own grown-up child. The elderly parent decides how much care to purchasefrom outside the family and how much bequest to leave behind to her child (while possibly
expecting some care in return).
Let the current period be 𝑡 = 0. In the previous period (𝑡 = −1), a young parent has alreadyformed expectations about uncertainties regarding her future (time 𝑡 = 0) health status, care needs,
the characteristics of her offspring, and so on. As a result, when young in period 𝑡 = −1, the𝑝parent has already decided how much to save for old age, and let that saving be 𝑠−1, wherehereafter the superscript 𝑝 denotes the current “parent.” We also assume that, in period 𝑡 = −1,
the young parent took care of her own parents and possibly received a bequest from them. In any𝑝event, the parent has decided with how much saving (𝑠−1) she would arrive at the old-age stageof life in period 𝑡 = 0. In what follows, we consider four separate cases.
Case 1: Selfish parent and selfish child𝑝
Given the saving carried over from the first period of life, 𝑠−1, the elderly parent begins tostrategically interact with her child in period 𝑡 = 0. The parent is selfish in the sense that she cares
only about her own well-being, and so is the child. One might assume, following Zweifel andStrüwe (1996), that some minimum bequest level (𝐵𝑚𝑖𝑛 > 0) is guaranteed to the child. One might
think that the parent has some assets that are of no use outside the family. Alternatively, there
might be a social norm that requires leaving something behind to one’s offspring, and the parent
may not desire to be ostracized for not following this tradition. In a simpler setting, one can set
𝐵𝑚𝑖𝑛 = 0.

The parent will strategically leave part of her saving to her child as a bequest (possibly more thanthe minimum level 𝐵𝑚𝑖𝑛 ) to incentivize her child to provide care to the parent. The parent also
needs to decide how much extra health and emotional care to acquire from private providers(optional care expenditures). After leaving a bequest and taking care of her health and emotional
well-being, the parent would simply consume what is left over until she exits the model at thevery end of period 𝑡 = 0.
Hereafter, let superscript 𝑐ℎ denote the parent’s child. Assume that our elderly parent wants toadhere to some bequest rule by choosing the bequest rule parameter 𝛼 in the following function:
𝐵 𝑝 = 𝑓(𝐵𝑚𝑖𝑛 ; 𝛼; 𝐶 𝑐ℎ ),(1)where 𝐵 𝑝 is the amount the parent will leave as a bequest, 𝐶 𝑐ℎ is the “care level/amount”
𝜕𝑓

𝜕2 𝑓

ultimately received from the child (at time 𝑡 = 0), 𝜕𝐶 𝑐ℎ ≥ 0, 𝜕𝐶 𝑐ℎ 𝜕𝛼 ≥ 0. We make the assumptionthat the amount of care the child provides to her parent will increase the bequest the parent leaves
to her child only for Case 1, where all agents are assumed to be selfish. To ensure that totallyselfish children would provide care to their parents, the child must recognize that there will be a
reward for her efforts. We do not preclude the theoretical possibility that the amount of care thechild provides might have no impact whatsoever on the amount of bequest she receives from her
6parent. Furthermore, as will be made clear below, the choice of bequest level (𝐵 𝑝 ) is endogenous
since the parameter 𝛼 is a choice variable, and 𝐵 𝑝 could in principle be zero. Thus, we assume
that the bequest is a non-decreasing function of care provided by the child as it would becounterintuitive to presume that selfish children will be systematically fooled into providing care
for a “negative” reward from their parents. We also note that, if parameter 𝛼 > 0, it reflects the“price” parents are willing to pay to their children (in the form of a bequest) for care received
during old age, or to put it another way, this parameter reflects how much parents value receiving
care from their children (as opposed to receiving it from outside sources). In this section, we
assume that 0 ≤ 𝐶 𝑐ℎ < 1 is simply the time spent by the child caring for her parent. The total timeendowment of an economic agent is normalized to unity.
𝑝
Let 𝐻𝐸−1
be the parent’s health and emotional well-being level at the very end of period 𝑡 = −1.
Assume that the parent’s health and emotional well-being can be enhanced by increasing the levelof 𝑇𝐶 𝑝 , representing the total amount of care and attention available to the elderly (which might
include, among others, nursing care, care from her child, medical attention, and psychologicalsupport, to name a few). Following Ariizumi (2008), let there be a production function for theparent’s health and emotional well-being that depends on 𝑇𝐶 𝑝 . Thus, we assume that, in thecurrent period (𝑡 = 0), the parent’s realized health and emotional well-being level is given by𝑝
𝐻𝐸0𝑝 = (1 − 𝑑)𝐻𝐸−1+ 𝜆(𝛽; 𝑇𝐶 𝑝 ),(2)
𝜕𝜆where 0 < 𝑑 < 1 is the depreciation rate, 𝛽 > 0 is the productivity parameter, 𝜕𝑇𝐶 𝑝 > 0 ,𝜕2 𝜆𝜕𝑇𝐶 𝑝 𝜕𝛽> 0. In other words, we assume that an increase in the total amount of care and attention

increases the parent’s health and emotional well-being and that the impact of the total amount ofcare and attention is higher, the higher is the productivity parameter.
Let the parent’s total care input from outside sources be summarized by 𝐶 𝑝,𝑜𝑢𝑡 , which can besubstituted for care provided by the child, 𝐶 𝑐ℎ . Thus,
𝑇𝐶 𝑝 = 𝜃1 𝐶 𝑐ℎ + 𝜃2 𝐶 𝑝,𝑜𝑢𝑡 ,(3)

where 𝜃1 , 𝜃2 ≥ 0. Both 𝐶 𝑝,𝑜𝑢𝑡 and 𝐶 𝑐ℎ are endogenous, as explained shortly.
In the Japanese LTCI system, the government pays for up to 90 percent of the cost of requiredcare, with the amount of required care being determined by the person’s need level. There isusually a cap on the monthly co-payment amount, but to keep things simple, we assume that theco-payment rate (0 < 𝜑 ≤ 1) is constant. This will not be an impediment to the focus of our study.
Let 𝑅𝐶 be the amount of “required” care (which depends on one’s health status), a proportion𝑝(1 − 𝜑) of the cost of which is paid for by the government. Thus, 𝑅𝐶 = 𝑅𝐶(𝐻𝐸−1),𝑝𝑑𝑅𝐶(𝐻𝐸−1 )
𝑝

𝑑𝐻𝐸−1

<

0. In other words, the amount of required care is higher, the lower is the parent’s health andemotional well-being in the previous period. The amount of required care is the minimum carelevel deemed necessary by the government’s Long-term Care Approval Board. We assume thatthe parent would incur this necessary level of expenditures even in the absence of LTCI (i.e., evenif 𝜑 = 1) but that this care level would be considered insufficient by most people, in which casethey would opt for additional (optional) care.
7

Denoting 𝑂𝐶 𝑝 as the amount of optional care chosen by the parent, the total amount of outsidecare can be expressed as𝑝
𝐶 𝑝,𝑜𝑢𝑡 = 𝑅𝐶(𝐻𝐸−1) + 𝑂𝐶 𝑝 .

(4)

We normalize the price of optional care services to unity. Let us assume that the elderly parent
has no earnings, and let the elderly parent’s utility function at time 𝑡 = 0 take the general form𝑝𝑝
𝑈 𝑝 = 𝑈(𝑠−1− 𝜑𝑅𝐶(𝐻𝐸−1) − 𝑂𝐶 𝑝 − 𝐵 𝑝 , 𝐻𝐸0𝑝 ),

(5)

𝑝
𝑝
where the first argument in the utility function, 𝑠−1− 𝜑𝑅𝐶(𝐻𝐸−1) − 𝑂𝐶 𝑝 − 𝐵 𝑝 , denotes theconsumption of the elderly parent. 2 We assume that the utility function is increasing in both𝑝arguments, and note also that 𝐻𝐸0 is a function of 𝐶 𝑝,𝑜𝑢𝑡 (and thus 𝑂𝐶 𝑝 ) due to (2), (3) and (4).
The elderly parent will maximize her utility by choosing 𝑂𝐶 𝑝 and 𝛼.

In the first period of her economic life (𝑡 = 0), the young adult child of our elderly parent only
decides how much to save for old age and how much care time to offer to her parent. However, it
is obvious that the child’s optimal saving amount and time sacrifice for her parent at time 𝑡 = 0
might depend on how uncertain her own future is. First, the child is not sure about her own healthand emotional well-being level at the very end of her young life (at the beginning of her elderly
life at time 𝑡 = 1); i.e., 𝐻𝐸0𝑐ℎ is random. Second, she does not know about the attitude andeconomic conditions of her own offspring, and therefore is not sure how much care, if any, shewill receive from her own child at time 𝑡 = 1. Denoting that care amount by 𝐶̅ 𝑐ℎ , we reason that𝐶̅ 𝑐ℎ is also a random variable at time 𝑡 = 0. Third, the young adult child at time 𝑡 = 0 is not surewhat will be the amount of outside care that she will ultimately purchase herself at 𝑡 = 1 (i.e.,
𝐶 𝑐ℎ,𝑜𝑢𝑡 is also random but only because future optional care purchased (𝑂𝐶 𝑐ℎ ) as well as 𝐻𝐸0𝑐ℎ
are random). Finally, partly due to the aforementioned reasons and partly due to other unforeseen
circumstances, the young adult child is not sure about the amount of the bequest that she mightend up leaving to her own offspring (i.e., 𝐵 𝑐ℎ is random). Thus, we have four random variablesof immediate interest: 𝐻𝐸0𝑐ℎ , 𝐶̅ 𝑐ℎ , 𝑂𝐶 𝑐ℎ , and 𝐵 𝑐ℎ , and let us assume that these variables arecontinuous random variables (that are not necessarily independent) with the following respective̅̅̅], [𝑐1 , 𝑐̅1 ], [𝑐2 , 𝑐̅2 ], and [𝑏, 𝑏̅].
realization ranges: [ℎ𝑒, ℎ𝑒Assume simply that, based on historic evidence and her own intuition, the young person at time
𝑡 = 0 guesses a probability function that in her view describes the “simultaneous behavior” of thefour random variables. That is, the adult child guesses the joint probability density function (pdf).
Hereafter, we will use lower-case characters to denote the realizations of these respective four
random variables. Thus, let the joint pdf be𝜉 ≡ 𝜉𝐻𝐸0𝑐ℎ ,𝐶̅ 𝑐ℎ ,𝑂𝐶 𝑐ℎ ,𝐵𝑐ℎ (ℎ𝑒0𝑐ℎ , 𝑐̅ 𝑐ℎ , 𝑜𝑐 𝑐ℎ , 𝑏 𝑐ℎ ).

(6)Note that we assume that wealth (net of one’s healthcare needs) that is not left as a bequest is used for the elderly
agent’s own consumption. In actual practice, bequests are a function of assets that are left over at death, net of, forexample, charitable contributions. One could endogenize charitable contributions and other possible outside options,but doing so would complicate the closed-form derivations. It would be worthwhile to pursue such an extension in
future work. We thank an anonymous referee for bringing this issue to our attention.
28

Next, let us assume that the young adult child at time 𝑡 = 0 inelastically supplies 0 < 𝜀 < 1 unitsof time to the labor market, and let her total after-tax income be 𝑦0𝑐ℎ . Hence, the lifetime utility of
the child at time 𝑡 = 0 (𝐸𝑈 𝑐ℎ ) depends on current consumption and leisure (1 − 𝜀 − 𝐶 𝑐ℎ ), and an
expectation term relating to future consumption and health and emotional well-being. (Note that
leisure at old age is unity as 𝜀 = 0 when old and as we assume that family care is provided only
when one is young, meaning that we do not need to include the old-age leisure term in the utility
function). Assuming no discounting and a zero interest rate, expected utility is given by
𝐸𝑈 𝑐ℎ = 𝑍(𝑦0𝑐ℎ + 𝐵 𝑝 − 𝑠0𝑐ℎ , 1 − 𝜀 − 𝐶 𝑐ℎ )𝑏̅ 𝑐̅2 𝑐̅1 ̅̅̅̅ℎ𝑒+∫ ∫ ∫(7)∫ Ω𝑑ℎ𝑒0𝑐ℎ 𝑑𝑐̅𝑐ℎ 𝑑𝑜𝑐 𝑐ℎ 𝑑𝑏 𝑐ℎ ,𝑏 𝑐2 𝑐1 ℎ𝑒where the argument 𝑦0𝑐ℎ + 𝐵 𝑝 − 𝑠0𝑐ℎ of function 𝑍 denotes the young adult’s consumption, while
the argument 1 − 𝜀 − 𝐶 𝑐ℎ denotes the young adult’s leisure. Function 𝑍 is increasing in botharguments. Further, letΩ ≡ 𝜉𝑉(𝑠0𝑐ℎ − 𝜑𝑅𝐶(ℎ𝑒0𝑐ℎ ) − 𝑜𝑐 𝑐ℎ − 𝑏 𝑐ℎ , ℎ𝑒1𝑐ℎ ).

(8)

As before, function 𝑉 on the right-hand-side of (8) denotes utility at old age (which is a randomvariable at time 𝑡 = 0), where we conventionally use lower-case characters as this term appears
in the integrand of (7). Clearly, utility is increasing in both arguments, consumption and healthstatus. Note from (8) that we have multiplied the bracketed term by the joint pdf, 𝜉.
Note that 𝑇𝐶 𝑐ℎ is a random variable that denotes the total amount of care that is available to thechild in the next period. Clearly, 𝑇𝐶 𝑐ℎ = 𝜃1 𝐶̅ 𝑐ℎ + 𝜃2 𝐶 𝑐ℎ,𝑜𝑢𝑡 , where 𝐶 𝑐ℎ,𝑜𝑢𝑡 = 𝑅𝐶(𝐻𝐸0𝑐ℎ ) +𝑂𝐶 𝑐ℎ . Using lower-case characters to denote the realizations of the random variables, andrecalling (2)-(4), we can now set ℎ𝑒1𝑐ℎ (the realization of the agent’s health and emotional wellbeing status at the very start of period 𝑡 = 1) in (8) toℎ𝑒1𝑐ℎ = (1 − 𝑑)ℎ𝑒0𝑐ℎ + 𝜆(𝛽; 𝑡𝑐 𝑐ℎ )= (1 − 𝑑)ℎ𝑒0𝑐ℎ + 𝜆(𝛽; 𝜃1 𝑐̅𝑐ℎ + 𝜃2 𝑐 𝑐ℎ,𝑜𝑢𝑡 )(9)= (1 − 𝑑)ℎ𝑒0𝑐ℎ+ 𝜆(𝛽; 𝜃1 𝑐̅𝑐ℎ + 𝜃2 (𝑅𝐶(ℎ𝑒0𝑐ℎ ) + 𝑜𝑐 𝑐ℎ )).
The child needs to maximize (7) by choosing 𝑠0𝑐ℎ and 𝐶 𝑐ℎ . The sequence of events at time 𝑡 = 0
is as follows. First, nature reveals the form of the bequest rule function (1) that then becomes
common knowledge. Second, the parent chooses the amount of optional outside care and thebequest rule parameter (𝛼). Finally, after observing the parent’s behavior, the child chooses the
optimal saving level and the amount of care to provide to the parent. We solve the model
backwards, starting from the third and second stages. Thus, for a given value of 𝛼, the child uses9the bequest rule in (7) to obtain the optimal care function, 𝐶 𝑐ℎ (along with 𝑠0𝑐ℎ ). Next, the parent
observes 𝐶 𝑐ℎ , and maximizes (5) with respect to 𝑂𝐶 𝑝 and 𝛼.
Clearly, once the optimal 𝛼 is determined, the actual realized value of 𝐶 𝑐ℎ (and also the child’s
optimal saving amount, 𝑠0𝑐ℎ ) will be determined. Thus, we can determine the optimal amount of
total care that the parent will receive, 𝑇𝐶 𝑝 ,3 and the actual amount of the bequest that the parent
will end up leaving (𝐵 𝑝 ).
Remark 1. We next proceed to solving the model, and for that purpose, we need to specify
functional forms. Unfortunately, due to the presence of random variables and integrals, realistic
functional forms do not lead to closed-form solutions, and even somewhat simpler ones lead to
extremely cumbersome solutions.
Hence, we proceed by assuming simple functional forms. First, analogous to well-known twovariable joint uniform pdf’s commonly used in probability theory and mathematical statistics, we
use the following joint pdf for general 4-space:𝜉=1.
̅̅̅ − ℎ𝑒)(𝑐̅1 − 𝑐1 )(𝑐̅2 − 𝑐2 )(𝑏̅ − 𝑏)
(ℎ𝑒

(10)

Furthermore, we can safely set 𝑐1 = 𝑐2 = 𝑏 = 0. Next, note that it is not uncommon in theeconomics literature to consider a utility function that is linear in one argument and concave inanother (e.g., Acemoglu and Robinson 2000; Carlstrom and Fuerst 2001; Cremer et al. 2004;
Chang 2009), and we do likewise. Specifically, we assume that utility functions are quadratic in
consumption, yet linear in leisure and health status. Certainly, we will need to ensure that the
optimal consumption level does not exceed a bliss point because otherwise marginal utility will
be negative. Thus, let𝑝𝑝
𝑈 𝑝 = 𝜇1 (𝑠−1− 𝜑𝑅𝐶(𝐻𝐸−1) − 𝑂𝐶 𝑝 − 𝐵 𝑝 )

−

𝜇1 𝑝
2
𝑝
(𝑠−1 − 𝜑𝑅𝐶(𝐻𝐸−1) − 𝑂𝐶 𝑝 − 𝐵 𝑝 ) + 𝜌1 𝐻𝐸0𝑝 ,2

𝑍 = 𝜇2 (𝑦0𝑐ℎ + 𝐵 𝑝 − 𝑠0𝑐ℎ ) −

(11)

𝜇2 𝑐ℎ
2
(𝑦0 + 𝐵 𝑝 − 𝑠0𝑐ℎ ) + 𝛾(1 − 𝜀 − 𝐶 𝑐ℎ ), (12)2

3

We are explicitly assuming that agents uphold verbal commitments and honor intergenerational contracts due tosocial norms, their desire to maintain their reputation, or other enforcement mechanisms. This is a common
assumption in this line of literature (see, e.g., Bernheim et al. 1985; Raut and Tran 2005; and Barczyk and Kredler
2018). Yet strictly speaking, it is optimal for parents to break their promise with their children and to just choose theirmaximum possible consumption without leaving any bequest to their children. Foreseeing this outcome, it is rational
for the child not to provide any care to the parent. The purpose of using perfect Bayesian equilibrium or subgame
perfect Nash equilibrium in game theory is exactly to resolve the issue of sequential irrationality that happens at Nashequilibria. We thank Ching-Jen Sun for this comment.

10V = 𝜇3 (𝑠0𝑐ℎ − 𝜑𝑅𝐶(ℎ𝑒0𝑐ℎ ) − 𝑜𝑐 𝑐ℎ − 𝑏 𝑐ℎ )−𝜇3 𝑐ℎ(𝑠 − 𝜑𝑅𝐶(ℎ𝑒0𝑐ℎ ) − 𝑜𝑐 𝑐ℎ − 𝑏 𝑐ℎ )2 + 𝜌2 ℎ𝑒1𝑐ℎ .
2 0

(13)

For simplicity, we set 𝐵𝑚𝑖𝑛 = 0 and assume that𝐵 𝑝 = 𝛼𝐶 𝑐ℎ ,(14)

𝜆 = 𝛽𝑇𝐶 𝑝 ,

(15)

𝑝
𝑝
𝑅𝐶(𝐻𝐸−1) = 1 − 𝑞1 𝐻𝐸−1,

(16)

𝑅𝐶(ℎ𝑒0𝑐ℎ ) = 1 − 𝑞2 ℎ𝑒0𝑐ℎ .

(17)

To reduce notational clutter, we set 𝜌1 = 𝜌2 = 𝜌, 𝑞1 = 𝑞2 = 𝑞, and 𝜇1 = 𝜇2 = 𝜇3 = 𝜇, while
𝛾 > 0. By using asterisks to denote optimal solutions, we find that the bequest left by the selfish
elderly parent is
𝐵 𝑝∗ =−4𝜃2 𝛾 + 𝜃1 𝜇(4 + 𝑏̅ + 𝑐̅2 − 2𝑦0𝑐ℎ + 2𝜑 − ℎ𝑒𝑞𝜑 − ̅̅̅
ℎ𝑒𝑞𝜑)
,
4𝜃1 𝜇

(18)

while the amount of optional care chosen by the selfish parent is
𝑂𝐶 𝑝∗
𝑝
𝑝
̅̅̅ 𝑞𝜑 − 4𝑞𝜑𝐻𝐸−1
4𝜃2 𝛾 + 𝜃1 (4𝛽𝜃2 𝜌 − 𝜇(8 + 𝑏̅ + 𝑐̅2 − 4𝑠−1
− 2𝑦0𝑐ℎ + 6𝜑 − ℎ𝑒𝑞𝜑 − ℎ𝑒
))
=
.
4𝜃1 𝜇

The optimal care provided to the parent by her selfish child is given by
𝐶 𝑐ℎ∗ =

16𝜃22 𝛾 2 − 𝜃12 𝜇 2 (4 + 𝑏̅ + 𝑐̅2 − 2𝑦0𝑐ℎ + 2𝜑 − ℎ𝑒𝑞𝜑 − ̅̅̅ℎ𝑒𝑞𝜑)2, (20)−32𝜃21 𝛾𝜇while the optimal saving amount of the adult selfish child is
𝑠0𝑐ℎ∗
̅̅̅𝑞𝜑)−4𝜃2 𝛾 + 𝜃1 𝜇(4 + 3𝑏̅ + 3𝑐̅2 + 2𝑦0𝑐ℎ + 6𝜑 − 3ℎ𝑒𝑞𝜑 − 3ℎ𝑒
=
.
8𝜃1 𝜇

11

(21)

(19)

Note that to obtain 𝐵 𝑝∗ in (18), we first need to solve for the optimal value of 𝛼 (see expression
14). We obtain
𝛼∗ =

8𝛾𝜃1
.
̅
4𝜃2 𝛾 + 𝜃1 𝜇(4 + 𝑏 + 𝑐̅2 − 2𝑦0𝑐ℎ + 2𝜑 − ℎ𝑒𝑞𝜑 − ̅̅̅ℎ𝑒 𝑞𝜑)(22)

It is straightforward to show that both 𝛼 ∗ and the optimal amount of care from the child, 𝐶 𝑐ℎ∗, arestrictly increasing in 𝜃1 , and when 𝜃1 = 0, 𝛼 ∗ is zero, too. That is, when parents do not consider
their children’s care as being valuable for their health and well-being (𝜃1 = 0 means that aparent’s health and emotional well-being is unaffected by her child’s input), there will be noparental bequest, and as a result, no child will take care of her parent. In that case, an LTCI
program will have no impact on the amount of bequests or on the amount of informal care.
We next consider the effect of the introduction of a LTCI program, i.e., we contrast the case of
0 < 𝜑 < 1 (i.e., an LTCI system exists) and the case of 𝜑 = 1 (i.e., an LTCI system does notexist).4
Remark 2. If the amount of required care is non-negative in value and positive (however small)for at least half of the possible realizations of the health and emotional well-being outcomes, theintroduction of a LTCI system will increase the amount of care provided by the child and theamount of the bequest left by the parent in families with selfish children and selfish parents. By
contrast, the abolition of a LTCI system will reduce the optional amount of outside care purchasedby the parent. Interestingly, the magnitudes of these effects will be larger for cohorts that are
relatively less healthy.
To see this, first note that
𝐵

𝐶

̅̅̅𝑞)
−4𝜃2 𝛾 + 𝜃1 𝜇(6 + 𝑏̅ + 𝑐̅2 − 2𝑦0𝑐ℎ − ℎ𝑒𝑞 − ℎ𝑒
,
𝜑=1 =
4𝜃1 𝜇

(23)

16𝜃22 𝛾 2 − 𝜃12 𝜇 2 (6 + 𝑏̅ + 𝑐̅2 − 2𝑦0𝑐ℎ − ℎ𝑒𝑞 − ̅̅̅ℎ𝑒 𝑞)2,𝜑=1 =−32𝜃21 𝛾𝜇

(24)

𝑝∗ |

𝑐ℎ∗ |

𝑂𝐶 𝑝∗ |𝜑=1(25)𝑝𝑝4𝜃2 𝛾 + 𝜃1 (4𝛽𝜃2 𝜌 − 𝜇(14 + 𝑏̅ + 𝑐̅2 − 4𝑠−1
− 2𝑦0𝑐ℎ − ℎ𝑒𝑞 − ̅̅̅ℎ𝑒 𝑞 − 4𝑞𝐻𝐸−1
))
=
.
4𝜃1 𝜇
The bequest level given by (23) will be strictly greater than that given by (18) as long as 2 −̅̅̅̅𝑝̅̅̅ ) > 0 (or, equivalently, 1 − 𝑞 (ℎ𝑒+ℎ𝑒) > 0), while if 𝑅𝐶(𝐻𝐸−1𝑞(ℎ𝑒 + ℎ𝑒) ≥ 0, under the same2

condition, the optional care level given by (25) will be strictly less than that given by (19). The

4

Even though hereafter we consider the two extreme cases (an LTCI system exists or does not exist), our results
hold for any increase in the co-payment rate 𝜑, which would indicate a less generous LTCI system.

12̅̅̅̅)(ℎ𝑒+ℎ𝑒condition 1 − 𝑞 2> 0 means that the amount of required care is positive (however small)at least for those people who have experienced health and emotional well-being levels that areless than or equal to the midpoint value of possible health and well-being outcomes (recall thatfrom the perspective of any young adult, future health status is a random variable). In other words,
selfish decision-making agents need to be convinced that requiring some care in the future is a“sufficiently viable” possibility. Similarly, based on (24), it can be shown that the amount of careprovided to the parent by her selfish child in the absence of a LTCI will be strictly greater thanthe care level given by (20) so long as the optimal bequest 𝐵 𝑝∗ > 0 and optimal care time provided
̅̅̅̅ )(ℎ𝑒+ℎ𝑒by the child is positive (or, more precisely, 0 < 𝐶 𝑐ℎ∗ < 1), while 1 − 𝑞 2> 0 still holds.
Intuitively, abolishing the LTCI system will increase the potential care expenses of young people
when they become old because they will have to bear the full cost of the required care (unless they
are reasonably confident that they will not require any care, in which case the LTCI program isirrelevant to them). Provided that parents (however selfish) recognize that their children’s carecan positively impact their own well-being—i.e., children’s care is worthy of a reward—young
people will be incentivized to provide more care to their parents in order to “earn” a larger bequest.
Consequently, the amount of optional outside care purchased by their elderly parents will decrease.
Thus, eliminating LTCI benefits will induce parents to seek more family care from their children,which has become less expensive relative to outside care. This happens because forward-looking
children are more willing to provide such care to their parents as the LTCI program becomes lessgenerous, i.e., as the price of children’s care relative to the price of outside care (the optimal valueof the 𝛼 parameter in (14)) decreases. Indeed, recall the optimal price of children’s care from (22),and note that𝛼 ∗ |𝜑=1 =8𝛾𝜃1.
4𝜃2 𝛾 + 𝜃1 𝜇(6 + 𝑏̅ + 𝑐̅2 − 2𝑦0𝑐ℎ − ℎ𝑒𝑞 − ̅̅̅
ℎ𝑒𝑞)

(26)

̅̅̅̅)
(ℎ𝑒+ℎ𝑒Again, the right-hand side of (26) is strictly less than that of (22) as long as 1 − 𝑞 2 > 0.
That is, because children are more willing to “earn” a bequest when public LTCI is abolished, theprice of their care decreases, encouraging their parents to substitute care from their children foroutside optional care. The fact that a greater amount of care from children reduces their leisuretime and therefore their utility is of no concern to selfish parents. Their interaction with theirchildren is merely a business transaction and nothing more.
If, in addition, we conduct comparative statics to find out how the magnitude of the above choicevariables change with the co-payment rate (see earlier remark in footnote 4), it would follow thatthe magnitude of our comparative statics are larger for a less healthy society. For such a society,the lower (ℎ𝑒 + ̅̅̅ℎ𝑒)/2 value (the midpoint of the possible health outcome values) will make the̅̅̅term 𝑞(ℎ𝑒 + ℎ𝑒) smaller, ceteris paribus. Intuitively, for a given distribution of health outcomes,a lower midpoint value of the support of the random variable means that society is relatively lesshealthy. Thus, young decision-making agents would expect to require more care in the future (thusexpecting to pay an even larger amount when the co-payment rate increases), and this possibility
magnifies the comparative statics effects.
Case 2: Altruistic parent and selfish child13

We assume that an altruistic parent cares about her child through two channels. First, even though
the care from her child enhances the parent’s health and emotional well-being on the one hand,the parent does derive disutility from the fact that the child cannot consume as much leisure if she
provides more care time to the parent. Thus, the parent derives utility from the child’s leisureconsumption. Second, the parent cares about the child’s consumption and recognizes that abequest left to her child might increase the child’s lifetime consumption by some magnitude.
Regarding the second channel, it is possible that the parent assumes that a dollar of bequest given
to the child will increase the child’s lifetime consumption by exactly one dollar. Yet since theparent and the child essentially live separate lives and will overlap only during the old age stageof the parent’s life, it is plausible that the parent will worry about possible uncertainty and assume
that one unit of bequest left would increase the child’s lifetime consumption by 𝑋 units, where𝑥 ≤ 𝑋 ≤ 𝑥̅ is a random variable with a known pdf 𝑓𝑋 (𝑥), and 𝑥 ≥ 0. Let us define𝑥̅Λ ≡ ∫ 𝑥𝑓𝑋 (𝑥) 𝑑𝑥.

(27)

𝑥

Drawing an analogy to expression (11), we can state the expected utility of the parent at time 𝑡 =0 as𝑝𝑝
𝐸𝑈 𝑝 = 𝜇1 (𝑠−1− 𝜑𝑅𝐶(𝐻𝐸−1) − 𝑂𝐶 𝑝 − 𝐵 𝑝 )

−

𝜇1 𝑝
2
𝑝
(𝑠−1 − 𝜑𝑅𝐶(𝐻𝐸−1) − 𝑂𝐶 𝑝 − 𝐵 𝑝 ) + 𝜌1 𝐻𝐸0𝑝
2

(28)

𝜎
+ 𝛾 𝑝 (1 − 𝜀 − 𝐶 𝑐ℎ ) + 𝜎𝐵𝑝 Λ − (𝐵 𝑝 Λ)2 ,2where 𝛾 𝑝 > 0 is the weight the parent places on the child’s leisure consumption and 𝜎 > 0 is theweight the parent places on the child’s expected consumption (𝐵 𝑝 Λ). To be consistent with theagent’s preferences over her own consumption, we assume that the parent’s preferences over thechild’s consumption possibilities are quadratic (hence, we have two quadratic terms on the righthand-side of (28)). As for the random variable 𝑋, note that the integral on the right-hand side of(27) sums up to some constant value (possibly a positive fraction or unity). Thus, from the parent’s
viewpoint, one unit of bequest will, on average, increase the lifetime consumption of the child bythat constant amount.
The child is as selfish as in Case 1, so her lifetime utility function has the same form as expression(7). The stages of the game are similar to Case 1, and we solve the model starting from the laststage. The optimal solutions for the parent’s problem are given as follows:𝐵 𝑝∗ =𝑝
𝑂𝐶 𝑝∗ = 𝑠−1−1+−𝛽𝜃2 𝜌 + 𝜎Λ
,
𝜎Λ2

(29)

𝛽𝜃2 𝜌
𝛽𝜃2 𝜌 1𝑝
− 𝜑 + 𝐻𝐸−1
𝑞𝜑 +
− .
𝜇
𝜎Λ2 Λ

14

(30)

The optimal solutions for the child’s problem are given as follows:𝐶 𝑐ℎ∗ = 0,(31)

−2𝛽𝜃2 𝜌 + 2𝜎Λ + 𝜎(𝑏̅ + 𝑐̅2 + 2𝑦0𝑐ℎ + 2𝜑 − ℎ𝑒𝑞𝜑 − ̅̅̅ℎ𝑒𝑞𝜑)Λ2
=
.
4𝜎Λ2

(32)

𝑠0𝑐ℎ∗

These results can be summarized by the following remark:Remark 3. In the case of an altruistic parent and a selfish child, the parent, being altruistic, will
generally leave a positive bequest to her child, which is independent of the presence of the public
LTCI system, regardless of whether or not her child provides any care, but her child, being selfish,
will not provide any care because she knows that she will be able to receive the same bequest
regardless of whether or not she provides care.
In addition, note that𝑝
𝑂𝐶 𝑝∗ |𝜑=1 = 𝑠−1
−2+

𝛽𝜃2 𝜌
𝛽𝜃2 𝜌 1𝑝
+ 𝐻𝐸−1
𝑞+
− .
𝜇
𝜎Λ2 Λ

(33)

Unless the parent does not require any care, the optional care level given by (33) is strictly lessthan the one given by (30). Intuitively, abolishing the public LTCI system will reduce the wealthof the altruistic parent, who is committed to a fixed bequest amount, and the parent will have to
reduce her expenditure on outside optional care. We thus state the following remark:Remark 4. If the amount of care required is positive in value (however small), abolishing the
public LTCI system for families with selfish children and altruistic parents will reduce the optionalamount of outside care purchased by the parent.
Case 3: Altruistic parent and altruistic childThis case is similar to Case 2 except that now we assume that the child is altruistic towards herparent. Namely, the child derives utility from the health and emotional well-being of her parent.
The parent’s utility is the same as in expression (28). The child’s utility is given by15

𝐸𝑈 𝑐ℎ = 𝑍(𝑦0𝑐ℎ + 𝐵 𝑝 − 𝑠0𝑐ℎ , 1 − 𝜀 − 𝐶 𝑐ℎ )𝑏̅ 𝑐̅2 𝑐̅1 ̅̅̅̅ℎ𝑒+ ∫ ∫ ∫ ∫ Ω𝑑ℎ𝑒0𝑐ℎ 𝑑𝑐̅𝑐ℎ 𝑑𝑜𝑐 𝑐ℎ 𝑑𝑏 𝑐ℎ + 𝜋𝐻𝐸0𝑝(34)

𝑏 𝑐2 𝑐1 ℎ𝑒−𝜋(𝐻𝐸0𝑝 )2 ,2where we assume that preferences over the parent’s health and emotional well-being are quadratic(as they are over consumption) and that 𝜋 > 0. The sequence of interactions and the solution
structure resemble those in Case 2. Recalling expressions (2), (3) and (4), we need to bear in mind
that the 𝐻𝐸0𝑝 term in (34) depends on the amount of outside optional care purchased by the parent,i.e., 𝑂𝐶 𝑝 . We thus state the following remark:Remark 5. The optimal amounts of the bequest and of outside optional care are identical to thosegiven in expressions (29) and (30), respectively. The optimal amount of saving for old age chosen
by the child is identical to the one given in expression (32). The optimal amount of care provided
by the child is given by
𝐶 𝑐ℎ∗
𝑝
𝑝
𝜋𝛽𝜃1 (1 − 𝐻𝐸−1
(1 − 𝑑)) − 𝛾 − 𝜋𝛽 2 𝜃1 𝜃2 (𝑂𝐶 𝑝∗ + 𝑅𝐶(𝐻𝐸−1))=,
𝜋𝛽 2 𝜃12(35)

where 𝑂𝐶 𝑝∗ in (35) is identical to expression (30). Note that the LTCI co-payment parameter, 𝜑,enters (35) via 𝑂𝐶 𝑝∗ . Using (30), we evaluate 𝑂𝐶 𝑝∗ at 𝜑 = 1, substitute it into (35) and obtain𝑝
𝐶 𝑐ℎ∗ |𝜑=1 . After some algebra, we deduce that so long as 𝑅𝐶(𝐻𝐸−1) > 0, the following inequality
holds:
𝐶 𝑐ℎ∗ |𝜑=1 > 𝐶 𝑐ℎ∗ .

(36)

Based on (36), and the results that are identical to those in Case 2, we summarize our findings in
the following remark:Remark 6. If the amount of care required is positive in value (however small), abolishing the
LTCI system for families with altruistic children and altruistic parents will reduce the amount of
optional outside care purchased by the parent (recall (33)), and will increase the amount of careprovided by the child (recall (36)). Parents will leave some bequest, which is independent of the
public LTCI system, as can be seen from (29).
Thus, the key difference between Cases 2 and 3 is that, in Case 3, the child, being altruistic, will
provide care to her parents even if the parent is altruistic, instead of no care as in Case 2. In
addition, in both Cases 1 and 3, parents do leave a positive bequest, and a less generous public
LTCI system tends to reduce the amount of optional outside care purchased by the parent. Thus,
there is an obvious similarity between Cases 1 and 3. And in fact, many studies admit that even if
their results show that the children are proving care to their parents and that their parents are16

leaving bequests to their children, this result is consistent with both the selfish strategic bequest
motive and the reciprocal altruism model and that the two cases cannot be distinguished from one
another. Yet our results show one important difference, which can help distinguish the two
scenarios. We thus state the following remark:Remark 7. Even though parents leave a bequest to their children in both Case 3 (reciprocal
altruism) and in Case 1 (the selfish parent-selfish child case), the abolition of the public LTCI
system will not affect the amount of the bequest in Case 3 but will increase the amount of bequest
in Case 1. In Case 1, the parent, being selfish, will leave a larger bequest to her child when LTCI
benefits are reduced or disappear as this would increase the relative price of formal care and induce
parents to substitute care from her child for outside care and because the parent will not care even
if the greater care provided by her child reduces her child’s leisure enjoyment. By contrast, inCase 3, when LTCI benefits are reduced or disappear, this will not cause any change in the amountof the bequest the parent leaves to her child while her child, being altruistic, will provide morecare to the parent to compensate her for the drop in the amount of outside care that is caused by
the reduction of LTCI benefits. Conversely, the introduction of a public LTCI system will
generally decrease the amount of care that children provide to their parents in both Cases 1 and 3,
whereas it will generally decrease the amount of the bequest that parents leave to their children inCase 1 but keep the amount of the bequest unchanged in Case 3.
Case 4: Selfish parent and altruistic childIn this case, we assume that the parent is selfish and that the child is altruistic. The child, being
altruistic, does not consider the possibility of obtaining an extra reward from the parent by raising
the amount of care she provides to her parent. The parent’s utility is the same as in (11), and thechild’s utility is the same as in (34) for a given 𝐵 𝑝 . We derive the optimal solution to this problem,and summarize the main results in the following remark:Remark 8. The selfish parent in Case 4 will not leave any bequest. The optimal amount of careprovided by the child is the same as in (35). Moreover, the relationship between the care level andthe existence of LTCI system follows condition (36).
Thus, the parent will not leave a bequest under any circumstances. She will not leave a bequestout of altruism because she is selfish, and moreover, she will not leave a bequest to induce her
child to provide care because she knows that her child, being altruistic, will provide care whether
or not the parent leaves a bequest. By contrast, the child, being altruistic, will provide care to herparent regardless of whether or not the parent leaves a bequest. Moreover, the introduction of a
LTCI system will not affect parent's bequest behavior because the parent will not leave a bequest
whether or not there is an LTCI system, but it will influence the child's care behavior because thechange in relative prices brought about by the introduction of the LTCI system will induce thesubstitution of formal care for informal care.
Summary of the four cases
The predictions of the four cases of the theoretical model are summarized in Table 2, and as canbe seen from this table, all four cases make different predictions about whether parents will leave
bequests to their children, about whether children provide care to their parents, and about whether
the provisions of the LTCI system will affect the bequest behavior of parents and the caregiving
behavior of children. Thus, we can infer which case applies in the real world by looking at the17actual behavior of parents and children, and it is to this exercise that we turn in the remainder ofthis paper.
Table 2 here

5. Data Source and Sample Selection Criteria
The data source we use for our empirical analysis is the 2011 wave of the Japan Household Panel
Survey of Consumer Preferences and Satisfaction (JHPS-CPS), formerly called the Preference
Parameters Study (Kurashi no Konomi to Manzokudo ni tsuite no Chousa), a panel survey that isbeing conducted by Osaka University in Japan and three other countries (China, India, and theUnited States). Funding for the survey was provided by the 21st Century Center of Excellence(COE) Program “Behavioral Macrodynamics Based on Surveys and Experiments,” the Global
COE Project “Human Behavior and Socioeconomic Dynamics” of Osaka University, and theJapan Society for the Promotion of Science (JSPS) KAKENHI Projects “Behavioral-Economic
Analysis of Long-Run Stagnation” (15H05728) and “Economic Stagnation and Widening WealthInequality: Crises of the World Economy and a Construction of a Unified Macroeconomic Theory.”
The survey has been conducted since 2003, but we chose to use data from the 2011 wave of theJapanese survey because the questions about bequest motives and parental care are not asked inevery year and 2011 was the most recent year in which all of necessary questions were asked. The
survey collects data on a nationwide random sample of both sexes aged 20 to 69, and the 2011
wave had 4934 respondents.
The micro data from this survey are perfectly suited for our purposes because they contain detailed
information on bequest expectations, informal care children provide to their parents and parentsin-law, eligibility for public LTCI benefits, and other socioeconomic variables relating to the
respondent, his or her spouse, his or her parents, and his or her parents-in-law. The complete
survey instrument (questionnaire form) for the survey that we used for our analysis can be foundat the following website: https://www.iser.osaka-u.ac.jp/survey_data/doc/japan/questionnaire/
english/2011QuestionnaireJAPAN.pdf
Since the data source we used is a panel survey, it would have been preferable to do a panel
analysis with fixed effects to control for individual heterogeneity, but unfortunately, we were notable to do so because, as already explained, some of the questions such as the ones pertaining tobequest expectations, informal care, and eligibility for public LTCI benefits were not asked inevery wave. Fortunately, however, the survey we used collects information on a multitude ofindividual and household attributes, so we were able to control for such heterogeneity by including
a large number of individual- and household-related control variables.
The sample selection criteria we used are as follows:
We kept only observations for which exactly one of the respondent’s parents is still alive (in otherwords, we dropped all observations for which both of the respondents’ parents are still alive orfor which both of the respondents’ parents are deceased because there is the possibility of one
parent taking care of the other parent in the case of respondents with two living parents andbecause there is no need for parental care if both parents are deceased. This reduced the sample
size to 1667.

18

We also dropped all observations for which there were missing values for at least one of thevariables used in the estimations, which further reduced the sample size to 571, and this is the
sample that we used for our estimation.
We also considered dropping those with siblings from the estimation sample because ourtheoretical model assumes that the child has no siblings and because the presence of siblings
complicates the analysis, as pointed out by Stern (1995) and Chechovich and Stern (2006), but wewere not able to do so because there were only 29 respondents who had no siblings.

6. Estimation Model
The first two objectives of our empirical analysis are (1) to test our theoretical model of the nexus
between LTCI, formal care, informal care, and bequests for the case of Japan and (2) to determine
which of the four cases applies in the case of Japan. Two additional objectives of our empiricalanalysis are (1) to examine what impact Japan’s LTCI system has had on the amount of informalcare provided by children to their parents and (2) to examine what impact Japan’s LTCI system
has had on bequests from parents to children via its impact on the amount of informal careprovided by children to their parents.
Thus, we estimate two equations—one that analyzes the determinants of whether children provide
informal care to their parents (more specifically, of whether or not they are their parent’s primary
caregiver) and another that analyzes the determinants of whether children expect to receive
bequests from their parents.
Our analysis is important and interesting because it can shed light on whether or not parents are
selfish or altruistic. If parents are selfish, we would expect respondents who are their parent’s
primary caregiver to have a higher probability of receiving a bequest from his/her parent, whereas
if parents are altruistic, we would expect respondents who are their parent’s primary caregiver tobe no more or less likely to receive a bequest from their parent, as our theoretical analysis showed.
The problem is that we cannot estimate the two equations independently because children’s
decisions concerning whether or not to provide informal care to their parents are likely to beendogenous. For example, children may provide care to their parents in the belief that theirprobability of receiving a bequest from their parents will be enhanced by providing care to them.
In other words, the direction of causality might be reversed. In order to control for this endogeneity,
we will estimate a bivariate probit model in which we use the respondent’s parent’s eligibility for
public LTCI benefits as an instrument for whether or not the respondent provides informal care to
his or her parent.
In order for this variable to be a good instrument for providing informal care, it must meet the two
conditions for a good instrument. First, it must be correlated with whether or not the respondent
provides care to his or her parent. We will shortly test econometrically if this condition is met, butintuitively, if the respondent’s own parent is eligible for public LTCI benefits, the parent is likely
to rely more on formal care and less on his or her child (the respondent) because eligibility for
public LTCI reduces the price of formal care relative to the price of informal care.
The second condition for a good instrument is that it must not have a direct impact on bequest
expectations and that its only impact on bequest expectations is through whether or not the
respondent provides care to his or her parent. It is quite possible that the parent’s eligibility for19

public LTCI benefits will affect the amount of the bequest that the parent can afford to leave tohis or her child because a person who becomes disabled will incur considerable medical and longterm care expenses and that the parent’s financial burden may well increase even if he or she iseligible for public LTCI benefits. However, the bequest expectations variable that we use in our
analysis is not the amount of the bequest that the respondent expects to receive from his or her
parent but whether or not he or she expects to receive a bequest of any amount from his or her
parent. It is plausible that this variable will not be affected by the parent’s eligibility for public
LTCI benefits and that it will depend more on the parent’s degree of altruism towards his or her
child and on the parent’s preference for being taken care of by his or her own child.
Accordingly, we will estimate a bivariate probit model, in which one dependent variable is adummy variable for whether or not the respondent or the respondent’s spouse is the parent’s
primary caregiver and the other dependent variable is a dummy variable for whether or not the
respondent expects to receive a bequest from his or her parent. In the caregiving equation, we will
use the parent’s eligibility for public LTCI benefits as an instrument for whether or not the
respondent is the parent’s primary caregiver.
Thus, the estimation model is as follows:(First stage)
Prob(Primary caregiver) = a0 + a1*(Eligibility for public LTCI benefits) + a2*X + u, where X =a vector of control variables(Second stage)
Prob(Bequest) =b0 + b1*Prob(Primary caregiver) + b2*X + v
Note that the dependent variable in the second stage is whether or not the respondent expects toreceive a bequest (or inter vivos transfer) from his or her parent, not whether or not the respondent
will actually receive a bequest, and furthermore, bequest expectations will not necessarily be
accurate. However, we unfortunately do not have information on whether or not the respondent
will actually receive a bequest. Moreover, we believe that it is actually preferable to use bequest
expectations because it is bequest expectations (whether or not they are accurate), not actual
bequests received, that influence the caregiving and other behavior of children.
As discussed in section 3, there are 7 need levels in Japan’s public LTCI system, but the surveythat we used for our empirical analysis groups the 7 need levels into three groups (support levels
1-2, care levels 1-2, care levels 3-5), where support levels 1-2 are the lowest need levels and carelevels 3-5 are the highest need levels. We therefore initially planned to use two instruments--adummy variable that equals one if the respondent’s parent’s need level for public LTCI purposes
is one of the four lowest levels (support level 1 or 2 or care level 1-2) and a dummy variable that
equals one if the respondent’s parent’s need level for public LTCI purposes is one of the threehighest levels (care levels 3-5). However, the first of these was totally insignificant as adeterminant of the probability of the respondent being his or her parent’s primary caregiver,indicating its weakness as an instrument. Thus, in the end, we used only the second dummy
variable (eligibility for the three highest need levels) as an instrument for whether or not the
respondent is the parent’s primary caregiver.

20

One other candidate we considered as a possible instrument for whether or not the respondent is
the parent’s primary caregiver was the parent-in-law’s eligibility for public LTCI benefits. If the
respondent’s parents-in-law are eligible for public LTCI benefits, they would be expected to rely
more on formal care and less on the respondent (or the respondent’s spouse), leaving the
respondent (or the respondent’s spouse) with more time to provide informal care to his or her own
parent. Moreover, there is no reason to expect that the respondent’s parents-in-law’s eligibility for
public LTCI benefits would influence the bequest behavior of the respondent’s own parent. Thus,
this variable appears to meet the two conditions for a good instrument, but we found that it was
totally insignificant as a determinant of the probability of the respondent being the primary
caregiver of the his or her parent. Because of its weakness as an instrument, we ultimately decided
not to use this variable as an instrument for whether or not the respondent is his or her parent’s
primary caregiver.
We also included the following control variables in both our caregiving and bequest expectation
equations, learning from previous studies such as Menchik (1988), Sloan et al. (1997), Norton andTaylor (2005), Brown (2006), Norton and van Houtven (2006), and Groneck (2017): therespondent’s age, a dummy variable for whether or not the respondent is a college graduate,
dummy variables for whether or not the respondent and the respondent’s parent are female, adummy variable for whether or not the respondent is the eldest son, a dummy variable for thenumber of living siblings the respondent has, a dummy variable for whether or not the respondentis an only child, a dummy variable for whether or not the respondent is married, and a dummy
variable for whether or not the respondent has any cohabiting children. Our rationale for including
a dummy variable for the respondent being the eldest son is that the social norm in Japan has been
for the eldest son to live with, and provide care to, his parents and to receive the parent’s entire
bequest.

7. Descriptive Statistics
Table 3 shows descriptive statistics for all variables included in the regression analysis, and as canbe seen from this table, more than half (59.6%) of respondents expect to receive a bequest fromtheir parents,5 while 38.7% of respondents or their spouses are their parent’s primary caregiver.
Thus, it appears that, in Japan, it is quite common for parents to leave bequests to their children
and that it is also quite common for respondents (or their spouses) to provide care to their parents.
Table 3 here
Turning to correlations among the explanatory variables, the correlation matrix of the explanatory
variables is not shown due to space limitations, but an examination of this matrix shows that all
correlations are relatively low (in absolute value). Thus, there does not appear to be any need toworry about multicollinearity among the explanatory variables.

The 59.6% figure may seem low since there are presumably very few people who die penniless and since Japan’s
postwar civil code states that the parents' bequest will be divided equally among their children unless they leave awill specifying otherwise. However, Japan’s prewar civil code stated that the eldest son would receive the parents’
entire bequest, and the social norm of the eldest son receiving all or most of the parents’ bequest prevails even today
to some extent. This social norm can be implemented by the parents leaving a will that specifies that the eldest son
will receive more and/or by the other children “voluntarily” relinquishing their right to receive a bequest but note thatJapan’s civil code also specifies that no child can be totally written out of the will. Another possibility is that bequest
expectations are pessimistic and that there are at least some people who do not expect to receive a bequest but end up
receiving one unexpectedly.
521

Table 3 also shows descriptive statistics for those who are primary caregivers and those who are
not primary caregivers, and as this table shows, the proportion of respondents who expect toreceive a bequest from their parents is much higher for those who are their parent’s primary
caregiver than it is for those who are not their parent’s primary caregiver (61.5% vs. 43.7%). This
result is consistent with the case of selfish parents and selfish children or the case of altruistic
parents and altruistic children in the theoretical model we developed in section 4. However, weneed to do a more formal econometric analysis to ascertain whether these results hold up evenafter we control for other factors and for the endogeneity of the primary caregiver variable.
As for other differences between caregivers and non-caregivers, college graduates, eldest sons,and only children are more likely to be caregivers, while those whose parents are eligible forpublic LTCI benefits, who have a larger number of siblings, and are married are less likely to becaregivers. However, we will not know if these differences hold up even after controlling for otherfactors until we examine the results of our econometric analysis in the next section.
Table 4 shows the impact of LTCI eligibility on caregiving, and as can be seen from this table,
the proportion of respondents who are their parent’s primary caregiver is much higher in the caseof those whose parent is not eligible for LTCI benefits than it is for those whose parent is eligiblefor LTCI benefits (43.4% vs. 30.6%). Moreover, the proportion of respondents who are theprimary caregiver of their surviving parent decreases with their parent's need level, which
determines how much subsidized formal care the parent is eligible for. This proportion is 42.5%
in the case of those whose parent is eligible for support levels 1-2 (the lowest level), but 25.4%
and 23.3%, respectively, in the case of those whose parent is eligible for care levels 1-2 and carelevels 3-5. All of these results strongly suggest that there is an inverse relationship between LTCI
eligibility and caregiving, with those whose parent is not eligible for LTCI being much more likely
to be their parent's primary caregiver and with their likelihood of being their parent's primary
caregiver decreasing as their parent's need level increases. These results are consistent with thetheoretical model we developed in section 4.
Table 4 here

8. Estimation Results
The estimation results (average marginal effects) are shown in Table 5, and looking first at thedeterminants of whether or not the respondent is the parent’s primary caregiver, eligibility for thethree highest levels of public LTCI benefits has a negative and significant impact, as expected. In
other words, respondents are less likely to be their parent’s primary caregiver if their parents are
eligible for the three highest levels of public LTCI benefits. The average marginal effect of the
LTCI eligibility variable is -0.203, which implies that being eligible for the three highest levels of
public LTCI benefits reduces the respondent’s probability of becoming the parent’s primary
caregiver by a full 20.3 percentage points. The magnitude of this effect is considerable because it
implies that the proportion of children serving as their parent’s primary caregiver would increase
from the current 38.7% to 59.0% if Japan’s public LTCI system were to be abolished entirely.
This finding establishes that the parent’s need level meets one of the two conditions for being agood instrument for whether or not the respondent is the primary caregiver.6
It is possible that the probability that the respondent becomes his or her parent’s primary caregiver decreases withneed level not because the relative price of formal care declines with need level but because parental preferences forformal care increases with need level, but unfortunately, we did not have the data to test this proposition (see Lehnert
et al., 2019).
6

22

Table 5 here
In addition, being the eldest son also makes it more likely for the respondent to be the parent’s
primary caregiver, which is also not surprising since the social norm in Japan has been for theeldest son to live with, and take care of, his parents. By contrast, being females also makes it more
likely for the respondent to be the parent’s primary caregiver, which is consistent with theconventional wisdom that females typically bear a disproportionate share of caregiving
responsibilities. A related finding that being married makes it less likely for the respondent to be
the parent’s primary caregiver is as one might expect since a married respondent may be too busy
taking care of his or her own family to take care of his or her parent. These two findings are
consistent with the finding of previous studies (e.g., Hanaoka and Norton, 2008, and Niimi, 2016)
that, in Japan, the traditional role of daughters-in-law in providing informal care to parents isincreasingly being taken over by unmarried children, especially unmarried daughters, in response
to significant changes in family structure and social norms. Finally, being an only child makes it
more likely for the respondent to be the parent’s primary caregiver, which is not surprising because
there are fewer potential caregivers in the case of only children. However, this result isinconsistent with Bernheim, et al.’s (1985) strategic bequest motive, which predicts that only
children will be less likely provide care to their parents because their parents’ threat to disinherit
them is not as credible in the case of only children. In any case, most, but not all, of the results,
are consistent with the earlier findings from Table 2.
Turning next to the results for the determinants of whether or not the respondent expects to receive
a bequest from his or her parent, being the parent’s primary caregiver has a positive and significant
impact on the probability of receiving a bequest from his or her parent, which implies that parental
bequests are motivated by selfish or strategic considerations (i.e., that they are a quid pro quo for
informal care during old age). The average marginal effect of the primary caregiver variable is0.444, which implies that being one’s parent’s primary caregiver increases one’s probability ofreceiving a bequest from one’s parent by 44.4 percentage points, which is an enormous amount.
If we consider the estimation results of the two equations collectively, they imply that abolishing
Japan’s public LTCI program would cause the proportion of people who are their parents’ primary
caregiver to increase by 20.3 percentage points from 38.7% to 59.0%, which in turn will cause theproportion of people who expect to receive a bequest from their parents to increase by
0.203*44.4=9.0 percentage points from 59.6% to 68.6%.
In addition, being female reduces one’s probability of receiving a bequest from one’s parent,
which is not surprising since the social norm in Japan has been for sons (especially eldest sons) toreceive a disproportionate share of parental bequests. Moreover, having more siblings also reduces
one’s probability of receiving a bequest from one’s parent, which is also not surprising since moresiblings means more competitors for the parent’s bequest. Finally, being a college graduate
increases one’s probability of receiving a bequest, which is a somewhat puzzling result. It seems
to suggest that parents are not altruistic toward their children because we would expect an altruistic
parent to be less likely to leave a bequest to a highly educated and presumably affluent child.
It is interesting to note that being the eldest son significantly increases one’s probability of being
one’s parent’s primary caregiver but that it does not significantly increase one’s probability ofreceiving a bequest from one’s parent. Similarly, being female significantly increases one’s
probability of being one’s parent’s primary caregiver but it does not significantly increase one’s
probability of receiving a bequest from one’s parent. This suggests that both eldest sons and23daughters receive an unfair deal, being more likely to be their parent’s primary caregiver but not
being more likely to receive a bequest from their parents.
These results also suggest that social norms influence people’s behavior to some extent even inthis day and age. It appears that social norms vary substantially across countries and even withincountries and that they change only slowly over time (see, for example, Alesina and Giuliano,2014).
Looking finally at the estimated value of rho, which indicates the correlation between the residualsof the two equations, it is negative but not significant, which suggests that whether or not the
respondent is the primary caregiver may not necessarily be endogenous after all and that abivariate probit estimation may not have been necessary. We therefore also estimated a singleequation probit model and found that the results are very similar and that being the parent’s
primary caregiver is still positively and significantly associated with bequest expectations.
Note that our empirical findings are broadly consistent with previous empirical analyses of related
topics. For example, our finding that parental eligibility for public LTCI reduces the likelihood of
their children becoming the parent’s primary caregiver is consistent with the many previous
studies of the substitutability between formal care and informal care. Moreover, our finding thatbeing the parent’s primary caregiver enhances the child’s probability of receiving a bequest is
consistent with the many previous studies that find evidence in favor of the strategic bequest
motive. It is reassuring that both findings still hold even after controlling for the simultaneity of
the caregiving and bequest decisions.

9. Conclusion
The purpose of this paper was to construct a theoretical model of the nexus between LTCI, formalcare, informal care, and bequests and to test that model using micro data from Japan, where apublic LTCI system was introduced in 2000. In particular, we used data from the Japan Household
Panel Survey of Consumer Preferences and Satisfaction (JHPS-CPS) (formerly called thePreference Parameter Study), conducted by Osaka University, to analyze whether or not the
introduction of a public LTCI system affected the likelihood of children to provide informal careto their parents and, through this channel, affected the likelihood of children to receive a bequestfrom their parents.
To summarize the main findings of this paper, we found that, if parents are eligible for public
LTCI benefits, their children will be less likely to be their primary caregiver and that this, in turn,will reduce their children’s perceived likelihood of receiving a bequest from them. This result
implies that bequests are selfishly or strategically motivated (i.e., that parents leave bequests totheir children in order to elicit care from them) and that the introduction of a public LTCI system
will reduce the likelihood of children providing care to their parents and through this channel
reduce their perceived likelihood of receiving a bequest from them.
Turning to the issue of what our findings imply about which model of household behavior applies
in Japan, we can rule out Case 2 (the case of an altruistic parent and a selfish child) because it
predicts that children will never provide care to their parents whereas we found that a substantial
share of Japanese children provide care to their parents, with more than a third serving as theirparents’ primary caregiver. Similarly, we can rule out Case 4 (the case of a selfish parent and an24altruistic child) because it predicts that parents will never leave a bequest to their children whereas
we found that more than half of Japanese children expect to receive a bequest from their parents.
That leaves Case 1 (the case of a selfish parent and a selfish child) and Case 3 (the case of an
altruistic parent and an altruistic child). Both cases predict that parents will leave a bequest to theirchildren and that children will provide care to their parents. Since we found that a substantial
proportion of Japanese parents leave a bequest to their children and that a substantial proportionof Japanese children provide care to their parents, both cases seem to apply in the case of Japan,
suggesting that it is not possible to determine which of the two cases applies in Japan.
However, Cases 1 and 3 yield different predictions regarding the impact of the LTCI system onparents’ bequest behavior. Case 1 implies that increasing the generosity of the LTCI system will
reduce the amount of the bequest that parents leave to their children, whereas Case 3 implies that
increasing the generosity of the LTCI system will have no impact on the amount of the bequestthat parents leave to their children. Thus, our finding that a more generous LTCI system will
reduce the probability of being one’s parent’s primary caregiver and thereby reduce the probabilityof receiving a bequest from one’s parent suggests that it is Case 1 (the case of a selfish parent anda selfish child), not Case 3 (the case of an altruistic parent and an altruistic child), that applies inJapan.
Thus, we can conclude from our theoretical analysis and our empirical findings that both Japaneseparents and Japanese children are selfish in their interactions with one another. This, in turn,implies that theoreticians should use case 1 (the case of a selfish parent and a selfish child) when
they conduct theoretical analyses of Japanese household behavior. This conclusion is consistent
with the findings of Noguchi et al. (1989), Komamura (1994), Ohtake and Horioka (1994),
Horioka et al. (2000), Horioka (2002, 2014, 2021a, 2021b), Yamada (2006), Wakabayashi andHorioka (2009), Kohara and Ohtake (2011), and Horioka, et al. (2018).
Turning finally to the policy implications of the findings of this paper, which apply not only to
Japan but to all countries, our findings imply that public LTCI systems will have important
impacts on individuals’ formal care, informal care, and bequest behavior and that these impacts
should be taken into account when introducing and designing public LTCI systems. In particular,
it must be borne in mind that the introduction of a public LTCI system that does not provide cash
benefits for informal care will lead to a substitution of formal care for informal care, which in turn
may lead to a larger than expected increase in the demand for (and cost of) formal care.
However, one silver lining of introducing a public LTCI system without cash benefits for familycare is that it may lead to a decline in the prevalence of bequests, thereby alleviating the extent towhich wealth disparities are passed on from generation to generation.
Moreover, another benefit of introducing a public LTCI system without cash benefits for familycare is that it will reduce the amount of informal care that is needed and will make it easier forchildren (especially females) to engage in market work and to realize their full potential in market
work. This is a substantial benefit not only for the children themselves but also for the economy
as a whole given that population ageing is projected to lead to severe labor shortages.

25

Acknowledgements
The empirical work undertaken in this paper utilizes micro data from the Japan Household Panel
Survey on Consumer Preferences and Satisfaction (JHPS-CPS) (formerly called the Preference
Parameters Survey), which has been conducted by the Institute of Social and Economic Researchof Osaka University with funding from the 21st Century Center of Excellent Program “Behavioral
Macrodynamics based on Surveys and Experiments” (2003-2008), the Global Center of
Excellence Program “Human Behavior and Socioeconomic Dynamics” (2008-2013) of Osaka
University, and two Grants-in-Aid for Scientific Research (KAKENHI) from the Japan Society
for the Promotion of Science: “Behavioral-Economic Analysis of Long-Run Stagnation(15H05728) and “Economic Stagnation and Widening Wealth Inequality: Crises of the World
Economy and a Construction of a Unified Macroeconomic Theory” (20H05631). We
acknowledge the survey’s co-investigators─Yoshiro Tsutsui, Fumio Ohtake, and Shinsuke Ikeda.
We are also grateful to the participants of the Family Economics Workshop held at the Faculty of
Economics, Keio University; the Annual Meeting of the Society of Economics of the Household;the Applied Economics Seminar of the Graduate School of Economics, Kyoto University; theVirtual Workshop on the Economic Impacts of Demographic Transition: Cases of Asia andEurope, jointly organized by the Asian Development Bank Institute (ADBI), Tokyo, Japan, andthe Fulbright School of Public Policy and Management (FSPPM), Hanoi, Vietnam; theInternational Conference on Changing Family Life in East Asia held at Academia Sinica; theHousehold Economics Workshop of the Research Institute for Economics and Business
Administration, Kobe University; the Singapore Economic Review Conference; Korean
Economic Association/Korea University International Conference; Asian Meeting of the
Econometric Society in East and Southeast Asia; East Asian Economic Association International
Conference; Meeting on the Implications of Elderly Care Provision for Caregivers in Japan(Institut National d'Etudes Demographiques (INED)); seminars held at the University of Hawaii,
De La Salle University; New Zealand Treasury, the University of Auckland, and the Universityof Canterbury; Takanori Adachi, Yuya Aikawa, Mika Akesaka, Christopher Cabuay, Chia Ngee
Choon, Jeremy Clark, Dieter Eissel, Zheng Fang, Jesus Felipe, Shoshana Grossbard, Junya
Hamaaki, Makoto Hasegawa, John Hillas,Cheng Hsiao, Yoko Ibuka, Ancilla Inocencio, Yumi
Ishikawa, Shinya Kajitani, Kamhon Kan, Kyeongbae Kim, Hisaki Kono, Wataru Kureishi,
Sumner LaCroix, Sang-Hyop Lee, Steffen Lippert, Andrea Menclova, Joel Kayembe Mpoy,
Patrick Nolan, Jan Ondrich, Euston Quah, Ekaterina Sherstyuk, Ching-Jen Sun, Luigi Ventura,
Philip Vermeulen, Midori Wakabayashi, Xiangyun Yin, Jongsay Yong, Michio Yuda, andespecially R. Anton Braun, Colin McKenzie, Yoko Niimi, Edward Norton, and Ken Yamada for
their valuable comments, discussions, and assistance. This work was supported by JSPS (Japan
Society for the Promotion of Science) KAKENHI Grant Numbers 18H00870, 20H01513,
20H05633, and 23H00831.
Conflicts of Interest
The first author received funding from JSPS (Japan Society for the Promotion of Science)
KAKENHI Grant Numbers 18H00870, 20H01513, 20H05633, and 23H00831 for the researchleading to these results. The authors have no competing interests to declare that are relevant to thecontent of this article.

26

References
Acemoglu, D., and J. A. Robinson (2000), “Why Did the West Extend the Franchise? Democracy,
Inequality, and Growth in Historical Perspective,” Quarterly Journal of Economics, 115(4):1167-1199.
Alesina, A., & P. Giuliano, P. (2014), “Family Ties” in P. Aghion and S. N. Durlauf, eds.,
Handbook of Economic Growth, vol. 2 (New York: Elsevier B.V.), pp. 117-215.
Almas, I., E. Freddi, and O. Thogersen (2020), “Saving and Bequest in China: An Analysis ofIntergenerational Exchange, Economia, 87: 249-281.
Ariizumi, H. (2008), “Effect of public long-term care insurance on consumption, medical caredemand, and welfare,” Journal of Health Economics, 27(6): 1423-35.
Arrondel, L., and A. Masson (2006), “Altruism, Exchange or Indirect Reciprocity: What Do the
Data on Family Transfers Show?” in S.-C. Kolm and J. M. Ythier, eds., Handbook of the
Economics of Giving, Altruism and Reciprocity, vol. 2 (New York: Elsevier Science B.V.), pp.
971-1053.
Barczyk, D., and M. Kredler (2018), “Evaluating long-term-care policy options, taking the family
seriously,” Review of Economic Studies, 85(2): 766-809.
Bernheim, B. D., A. Shleifer, and L. H. Summers (1985), “The Strategic Bequest Motive,”
Journal of Political Economy, 93(6): 1045–1076.
Bonsang, E. (2009), “Does informal care from children to their elderly parents substitute forformal care in Europe?” Journal of Health Economics, 28(1): 143–154.
Braun, R. A., K. A Kopecky, and T. Koreshkova (2019), “Old, frail, and uninsured: accounting
for features of the US Long‐Term care insurance market,” Econometrica, 87(3): 981-1019.
Brown, M. (2006), “Informal Care and the Division of End-of-Life Transfers,” Journal of Human
Resources, 41(1): 191–219.
Carlstrom C. T., and T. S. Fuerst (2001), “Timing and real indeterminacy in monetary models,”
Journal of Monetary Economics, 47: 285-298.
Chang, Y.-M. (2009), “Strategic Altruistic Transfers and Rent Seeking within the Family,”
Journal of Population Economics, 22: 1081-98.
Chechovich, T. J., and S. Stern (2002), “Shared caregiving responsibilities of adult siblings withelderly parents,” Journal of Human Resources, 37(3): 441-478.
Courbage, C., and P. Zweifel (2011), “Two-Sided Intergenerational Moral Hazard, Long-TermCare Insurance, and Nursing Home Use,” Journal of Risk and Uncertainty, 43(1): 65-80.
Cox, D. (1987), “Motives for Private Income Transfers.” Journal of Political Economy, 95(3):508–546.

27

Cox, D., and M. R. Rank (1992), “Inter-vivos Transfers and Intergenerational Exchange,” Review
of Economics and Statistics, 74(2): 305–314.
Cremer H., J. Lozachmeur, and P Pestieau (2004), “Social security, retirement age and optimal
income taxation,” Journal of Public Economics, 88: 2259-2281.
Fu, R., H. Noguchi, A. Kawamura, and H. Takahashi (2017), “Spillover Effect of Japanese LongTerm Care Insurance as an Employment Promotion Policy for Family Caregivers,” Journal of
Health Economics, 56: 103-112.
Fu, R., T. Iizuka, and H. Noguchi (2023), “Long-term Care in Japan,” NBER Working Paper No.
31829, National Bureau of Economic Research, Cambridge, Massachusetts, USA.
Grabowski, D., E. C. Norton, and C. H. Can Houtven (2012), “Informal Care,” in A. M. Jones,ed., The Elgar Companion to Health Economics, 2nd ed. (Northampton, MA: Edward Elgar),
pp. 318-328.
Groneck, M. (2017), “Bequests and Informal Long-Term Care: Evidence from HRS Exit
Interviews,” Journal of Human Resources, 52(2): 531-572.
Gruber, J., and K. M. McGarry, eds. (forthcoming), Long-term Care around the World (Chicago,
Illinois, USA: University of Chicago Press.
Gruber, J., K. M. McGarry, and C. Hanzel (2023), “Long-term Care around the World,” NBER
Working Paper No. 31882, National Bureau of Economic Research, Cambridge, Massachusetts,
USA.
Hanaoka, C. and E. C. Norton (2008), “Informal and formal care for elderly persons: How adultchildren’s characteristics affect the use of formal care in Japan,” Social Science and Medicine,67(6): 1002-1008.
Henretta, J. C., M. S. Hill, W. Li, B. J. Soldo, and D. A. Wolf (1997), “Selection of Children to
Provide Care: The Effect of Earlier Parental Transfers,” Journals of Gerontology Series B:
Psychological Sciences and Social Sciences, 52 (Special Issue): 110-119.
Ho, C. (2022), “Strategic Parent Meets Detached Child? Parental Intended Bequest Division andSupport from Children,” Demography, 59(4): 1353-1376.
Horioka, C. Y. (2002), “Are the Japanese Selfish, Altruistic, or Dynastic?” Japanese Economic
Review, 53(1): 26-54.
Horioka, C. Y. (2014), “Are Americans and Indians More Altruistic than the Japanese andChinese? Evidence from a New International Survey of Bequest Plans,” Review of Economicsof the Household, 12(3): 411-437.
Horioka, C. Y. (2021a), “Does the Selfish Life-Cycle Model Apply in the Case of Japan and, If
So, Why? A Literature Survey,” Review of Economics of the Household, 19(1): 157-187.
Horioka, C. Y. (2021b), “Nihon de Raifu Saikuru Kasetsu ha Naritatteiruka? (Is the Life Cycle
Hypothesis Applicable in Japan?)” in T. Ui, T. Kanou, J. Doi, and Y. Nishiyama, eds., Gendai
28

Keizaigaku no Choryuu (Trends in Contemporary Economics) (Tokyo, Japan: Toyo Keizai
Shinposha), pp. 35-59 (in Japanese).
Horioka, C. Y., H. Fujisaki, W. Watanabe, and T. Kouno (2000), “Are Americans More Altruistic
than the Japanese? A U.S.-Japan Comparison of Saving and Bequest Motives,” International
Economic Journal, 14(1): 1-31.
Horioka, C. Y., E. Gahramanov, A. Hayat, and X. Tang (2018), “Why Do Children Take Care of
Their Elderly Parents? Are the Japanese Any Different?” International Economic Review,
59(1): 113-136.
Iwagami, M., and N. Tamiya (2019), “The Long-Term Care Insurance System in Japan: Past,
Present, and Future,” JMA (Japan Medical Association) Journal, 2(1): 67-69.
Kohara, M., and F. Ohtake (2011), “Altruism and the Care of Elderly Parents,” Japanese Economy,
38(2): 3-18.
Komamura, K. (1994), “Koureisha Kakei ni okeru Isan Koudou no Keizai Bunseki (An Economic
Analysis of Bequest Behavior in Elderly Households),” Kikan Shakai Hoshou Kenkyuu, 30(1): 6274 (in Japanese).
Konishi, T., H. Inokuchi, and H. Yasunaga (2024), “Services in public long-term care insurance inJapan,” Annals of Clinical Epidemiology, 6(1): 1-4.
Laferrère, A., and F.-C. Wolff (2006), “Microeconomic Models of Family Transfers,” in S.-C.
Kolm and J. M. Ythier, eds., Handbook of the Economics of Giving, Altruism and Reciprocity,
vol. 2 (New York: Elsevier Science B.V.), pp. 889–969.
Lehnert, T., M. Heuchert, K. Hussain, and H. König (2019), “Stated preferences for long-term
care: A literature review,” Ageing and Society, 39(9): 1873-1913.
Li, S.-H., Y.Chon, and Y.-Y. Kim (2023), “Comparative Analysis of Long-Term Care in OECDCountries: Focusing on Long-Term Care Financing Type,” Health Care, 11(206): 1-13.
Lockwood, L. M. (2012), “Bequest Motives and the Annuity Puzzle,” Review of Economic
Dynamics, 15(2): 226-243.
Lockwood, L. M. (2018), “Incidental Bequests and the Choice to Self-Insure Late-Life Risks,”
American Economic Review, 108(9): 2513-2550.
McGarry, K. (1999), “Inter Vivos Transfers and Intended Bequests,” Journal of Public Economics,
73(3): 321–351.
McGarry, K., and R. F. Schoeni (1995), “Transfer Behavior in the Health and Retirement Study:
Measurement and the Redistribution of Resources Within the Family,” Journal of Human
Resources, 30 (Special Issue): S184–S226.
McGarry, K., and R. F. Schoeni (1997), “Transfer Behavior Within the Family: Results from theAsset and Health Dynamics Study,” Journals of Gerontology Series B: Psychological Sciences
and Social Sciences, 52 (Special Issue): 82–92.
29

Mellor, J. M. (2001), “Long-Term Care and Nursing Home Coverage: Are Adult Children
Substitutes for Insurance Policies?” Journal of Health Economics, 20(4): 527-547.
Menchik, P. L. (1988), “Unequal Estate Division: Is it Altruism, Reverse Altruism, or Simply
Noise?” in D. Kessler and A. Masson, eds., Modeling the Accumulation and Distribution of
Wealth, Oxford: Clarendon Press, pp. 105–116.
Mommaerts, C. (2018), “Are Coresidence and Nursing Homes Substitutes? Evidence from
Medicaid Spend-Down Provisions,” Journal of Health Economics, 59: 125-138.
Niimi, Y. (2016), “The “Costs” of Informal Care: An Analysis of the Impact of Elderly Care on
Caregivers’ Subjective Well-being in Japan,” Review of Economics of the Households, 14(4):779-810.
Noguchi, Y., K. Uemura, and Y. Kitou (1989), “Souzoku ni yoru Sedai-kan Iten no Kouzou:
Shutoken ni okeru Jittai Chousa Kekka (The Structure of Intergenerational Transfers via
Bequests: Results of a Survey in the Tokyo Metropolitan Area),” Kikan Shakai Hoshou
Kenkyuu (Quarterly of Social Security Research), 25(2): 136-144 (in Japanese).
Norton, E. C. (2000), “Long-Term Care,” in A. J. Culyer and J. P. Newhouse, eds., Handbook of
Health Economics, vol. 1 (New York: Elsevier B.V.), pp. 955–994.
Norton, E. C., L. H. Nicholas, and S. S.-H. Huang (2013), “Informal Care and Inter-vivos
Transfers: Results from the National Longitudinal Survey of Mature Women,” BE Journal of
Economic Analysis and Policy, 14(2): 1–24.
Norton, E. C., and D. H. Taylor (2005), “Equal Division of Estates and the Exchange Motive,”
Journal of Aging and Social Policy, 17(1): 63–82.
Norton, E. C., and C. H. Van Houtven (2006), “Inter-Vivos Transfers and Exchange,” Southern
Economic Journal, 73(1): 157–172.
Ohtake, F. and C. Y. Horioka (1994), “Chochiku Douki (Saving Motives),” in T. Ishikawa, ed.,Nihon no Shotoku to Tomi no Bunpai (The Distribution of Income and Wealth in Japan) (Tokyo
Daigaku Shuppankai, Tokyo, Japan), pp. 211-244 (in Japanese).
Pauly, M. V. (1990), “The Rational Nonpurchase of Long-term-Care Insurance,” Journal of
Political Economy, 98(1): 153-168.
Perozek, M. G. (1998), “A Reexamination of the Strategic Bequest Motive,” Journal of Political
Economy, 106(2): 423–445.
Raut, L.,and L. H. Tran (2005), “Parental human capital investment and old-age transfers fromchildren: Is it a loan contract or reciprocity for Indonesian families?” Journal of Development
Economics, 77: 389-414.
Sloan, F. A., and E. C. Norton (1997), “Adverse Selection, Bequests, Crowding Out, and Private
Demand for Insurance: Evidence from the Long-Term Care Insurance Market,” Journal of Risk
and Uncertainty, 15(3): 201-219.
30

Sloan, F. A., G. Picone, and T. J. Hoerger (1997), “The Supply of Children’s Time to Disabled
Elderly Parents.” Economic Inquiry, 35(2): 295–308.
Stern, S. (1995) “Estimating Family Long-term Care Decisions in the Presence of Endogenous
Child Characteristics,” Journal of Human Resources, 30(3): 551-580.
Wakabayashi, M., and C. Y. Horioka (2009), “Is the Eldest Son Different? The Residential Choiceof Siblings in Japan,” Japan and the World Economy, 21(4): 337-348.
Yamada, K. (2006), “Intra-family Transfers in Japan: Intergenerational Co-residence, Distance,
and Contact,” Applied Economics, 38(16): 1839-1861.
Zweifel, P., and W. Struwe (1996), “Long-Term Care Insurance and Bequests as Instruments for
Shaping Intergenerational Relationships,” Journal of Risk and Uncertainty, 12(1): 65-76.

31

Table 1: The Structure of Long-Term Care Insurance Benefits in Japan
Support or carelevel

Requirement for certification

Standardizedcare times(minutes perday)

Maximum
benefits(Japanese yen
per month)

The recipient lives independently but
25.0-31.9
50,320requires assistance with IADL
The recipient requires more assistance with
Support level 2 IADL than a recipient at support-required
32.0-49.9
105,310level 1 and might deteriorate to care level 1
The recipient requires more assisance wih
Care level 1 IADL than a recipient at support-required
32.0-49.9
167,650level 1 or 2
The recipient requires more assistance with
Care level 2
50.0-69.9
197,050
IADL than a recipient at care level 1
The recipient requires more assistance thanCare level 3 a recipient at care level 2 and thus needs
70.0-89.9
270,480
total care
The recipient cannot live without care andCare level 490.0-109.9
309,380functions poorly in terms of ADL
It is impossible for the recipient to live
without care and he/she has more
Care level 5110.0362,170
substantial ADL needs than a recipient at
care level 4
Note: "ADL" denotes "activities of daily living" while "IADL" denotes "instrumental activities
of daily living."
Support level 1

Sources: Fu, et al. (2023) and Konishi, et al. (2024).

32

Table 2: Summary of the Four Theoretical Models
Informal
Impact of LTCI on Impact of LTCI on
Bequests
care
informal carebequests
Case 1: Selfish parent,
Generally
Yes
Yes
Generally negative
selfish childnegative
Case 2: Altruistic parent,
No
Yes
None
None
selfish child
Case 3: Altruistic parent,
Yes
Yes
Negative
None
altruistic child
Case 4: Selfish parent,
Yes
No
Negative
None
altruistic childSource: See section 4 of the main text.

33

Table 3: Descriptive Statistics
Full sample

Primary caregivers

Non-primary
caregivers

Variable
Bequest expectations

Mean
0.596

Std. dev.
0.500

Mean
0.615

Std. dev.
0.488

Mean
0.437

Std. dev.
0.497

Primary caregiver
Parent's eligibility for LTCI

0.387
0.128

0.488
0.334

100.000
0.077

0.000
0.267

0.000
0.160

0.000
0.367

Age of respondent
College graduate

52.492
0.350

9.040
0.477

51.208
0.389

8.772
0.489

53.303
0.326

9.125
0.500

Female respondent
Female parent

0.545
0.839

0.498
0.368

0.543
0.842

0.499
0.366

0.546
0.837

0.499
0.370

Eldest son

0.333

0.472

0.385

0.488

0.300

0.459

Number of siblings
Only child

1.734
0.051

1.084
0.220

1.525
0.086

1.021
0.281

1.866
0.029

1.103
0.167

MarriedPresence of cohabiting children

0.853
0.599

0.355
0.491

0.801
0.606

0.400
0.490

0.886
0.594

0.319
0.492

Table 4: The Impact of LTCI Eligibility on Caregiving
Proportion of respondents
Parent's eligibility for
who are their parent's
No. of obs.
LTCI
primary caregiver (%)
Not eligible for LTCI
43.4
362
Eligible for LTCI
30.6
209
Support levels 1-2
42.5
73Care levels 1-2
25.4
63Care levels 3-5
23.3
73
Full sample
38.7
571

34

Explanatory variable

Primary caregiver
Parent's eligibility for LTCIAge of respondent
College graduate
Female respondent
Female parent
Eldest son
Number of siblings
Only child

Table 5: Bivariate Probit Results
Primary caregiver
Average
Std. error
marginal effect-0.203 ***-0.0020.036
0.143 **
0.030
0.181 ***
-0.0280.253 **

0.051
0.002
0.046
0.062
0.053
0.069
0.022
0.105

Bequest expectations
Average
Std. error
marginal
0.444 ***
0.147
-0.0010.085 *
-0.149 ***0.000-0.044-0.051 **-0.105

0.002
0.048
0.056
0.047
0.000
0.025
0.079

Married
-0.168 ***
0.065
0.013
0.060
Presence of cohabiting children
0.031
0.046
-0.0500.040
RHO-0.576
0.316
Wald test of RHO=0, chi2(1)1.924
Prob>CHI2
0.165
Log-likelihood-719.350
No. of obs.
571
Wald CHI2(20)169.800
Notes: * denotes significant at the 10% level, ** denotes significant at the 5% level, and *** denotes
significant at the 1% level.

35