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Three essays on aging, wealth, and housing tenure transitions

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Three essays on aging, wealth, and housing tenure transitions

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Three Essays on Aging, Wealth, and Housing Tenure Transitions

by

Linna Zhu

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PUBLIC POLICY AND MANAGEMENT)

December 2021

Copyright 2021 Linna Zhu
ii
Dedication

To my dear parents and grandparents.

iii
Table of Contents
Dedication ...................................................................................................................................... ii
List of Tables ................................................................................................................................. iv
List of Figures ................................................................................................................................ v
Abstract ......................................................................................................................................... vi
Chapter 1: General Introduction ................................................................................................. 1
Introduction .................................................................................................................................. 1

Chapter 2: Housing Tennure Transitions among Older Households: The Role of Financial
Precarity and Health ..................................................................................................................... 4
2.1 Introduction ............................................................................................................................ 5
2.2 Theory and Background ......................................................................................................... 6
2.3 Data and Methodology ........................................................................................................... 9
2.4 Results .................................................................................................................................. 17
2.5 Conclusions .......................................................................................................................... 23
2.6 Tables and Figures ............................................................................................................... 26

Chapter 3: Has the Effect of Housing Wealth on Household Consumption Benn
Overestimated? New Evidence on Magnitude and Allocation ................................................ 34
3.1 Introduction .......................................................................................................................... 35
3.2 Data and Methodology ......................................................................................................... 40
3.3 Results .................................................................................................................................. 44
3.4. Conclusion .......................................................................................................................... 56
3.5 Tables and Figures ............................................................................................................... 58
Appendix .................................................................................................................................... 68

Chapter 4: The Feasibility of Reserve Mortgages in Japan .................................................... 71
4.1 Introduction .......................................................................................................................... 72
4.2 Background .......................................................................................................................... 74
4.3 Modeling Strategy ................................................................................................................ 76
4.4 Cross-over Risks Estimation ................................................................................................ 82
4.5 Conclusion and Policy Implications .................................................................................... 85
4.6 Tables and Figures ............................................................................................................... 89

References .................................................................................................................................... 96
iv
List of Tables
Table 2.1a Variables and Definitions: Buffers, Financial Precarity, and Health Conditions ........ 27
Table 2.1b Variables and Definitions: Demographics and Intergenerational Factors .................. 28
Table 2.2 Housing Tenure Transitions .......................................................................................... 29
Table 2.3a Summary Statistics: Buffers by Transition Types ....................................................... 29
Table 2.3b Summary Statistics: Financial Precarity by Transition Types .................................... 30
Table 2.3c Summary Statistics: Health Conditions and Health Shocks by Transition Types ....... 30
Table 2.4 Cox Proportional Hazards Results: Owning to Renting ................................................ 31
Table 2.5 Cox Proportional Hazards Results: Owning to Downsizing ......................................... 32
Table 2.6 Cox Proportional Hazards Results: Other Transitions .................................................. 33
Table 3.1 Descriptive Statistics ..................................................................................................... 61
Table 3.2 Cross-Check of PSID with SCF: Age Distribution of Homeowners (weighted) .......... 62
Table 3.3 Housing Wealth and Personal Consumption: Elasticity Results ................................... 62
Table 3.4 Housing Wealth and Personal Consumption: MPC Results ......................................... 63
Table 3.5 Housing Wealth and Home Equity Extraction: Logit Model ........................................ 64
Table 3.6 Housing Wealth and Personal Consumption: Robustness Check ................................. 65
Table 3.7 Housing Wealth and Personal Consumption: IV Approach .......................................... 66
Table 3.8 Housing Wealth and Personal Consumption: Subcategories ........................................ 67
Table A1. Housing Wealth and Consumption: Inverse Mills Ratio .............................................. 68
Table A2. Housing Wealth and Personal Consumption: Weighted Fixed Effects ........................ 69
Table 4.1 Estimated Regression Results with 10-year and 30-year horizons ............................... 89
Table 4.2 Summary Statistics of the Hedonic Land Pricing Regression Model. .......................... 91
Table 4.3. Hedonic Land Prices: Annual Growth Rates and Weighted Average Growth Rate .... 93
Table 4.4 Brownian Motion: Variance-Covariance Matrix .......................................................... 93
Table 4.5 Default Risk Estimation Model ..................................................................................... 94
Table 4.6 Four Simulation Scenarios ............................................................................................ 95

v
List of Figures
Figure 2.1 Homeownership Rates (1998-2016) ............................................................................ 26
Figure 2.2 Homeownership Rates by Demographic Cohorts ........................................................ 26
Figure 3.1 Annual Percentage Change in House Price Index and Personal Consumption ........... 58
Figure 3.2 Annual Consumption Over Time for Homeowners (2015 inflation-adjusted dollars) 58
Figure 3.3 Homeowners’ per Capita Consumption Over Time by Spending Type ...................... 59
Figure 3.4 Total Wealth and Housing Wealth for Homeowners Over Time ................................ 60
Figure A1. Comparisons of FHFA HPI and Quality-Adjusted HPI: Selected MSAs ................... 70
Figure 4.1 JGB Yields with Various Maturities: December 1986 – March 2017 ......................... 89
Figure 4.2 Jurisdictional and Geographical Characteristics of the 7 Merged Regions. ................ 90
Figure 4.3 Constructed Land Price Index (LPI) ............................................................................ 92
Figure 4.4 LPA: Estimated Land Price Appreciation (LPA) Rates. .............................................. 92
Figure 4.5 One Pair of Simulation Result: Brownian Motion vs. Bootstrapping. ......................... 94
Figure 4.6 Distributional and Descriptive Statistics of the Simulation Results ............................ 95

vi
Abstract
The world’s population is rapidly aging, as are people in the United States. For most
senior home-owning households, housing wealth accounts for the greatest share of their assets,
along with wealth from Social Security and employer-provided retirement plans. How
households react to changes in their housing wealth, and how they consume it are critical
questions as they are not only relating to individual’s own well-being but also having a
significant impact on the macroeconomic situations. The big issue animating my dissertation
research is to understand the intersection of aging, wealth, and housing tenure transitions.
Throughout my dissertation research, I have found that: 1) Aging in place is the dominant
housing tenure choice among the Silent Generation and the Greatest Generation; 2) Financial
precarity and uninsurable health risks associated with cognitive declines and major motor
functions are the key factors driving low-income homeowners out of homeownership in their late
lives; 3) Households do not adjust their consumption behaviors when they experience shocks in
their house prices, indicating the impact of low interests rates on boosting households’
consumption via the housing wealth channel has been overestimated; 4) The non-recourse
mortgage structure, the increasing longevity risk, the dominant lump-sum withdrawal plan, and
the stagnancy of local housing market are the key factors affecting the performance of the
reverse mortgages.

1
Chapter 1
Introduction
The world’s population is rapidly aging, as are people in the United States. Interestingly,
among the older homeowners in the U.S., nearly 65% are choosing to age in place. The big issue
animating my dissertation research is to understand the merits of aging in place. The three
chapters of my dissertation aim at exploring the intersection of housing and aging at the
household, market and policy levels.
The first chapter examines the impact of uninsurable health risks and financial precarity
on housing tenure transitions among older homeowners, including exiting owning to renting,
relocating and downsizing, and moving to assisted living facilities. Exploiting the restricted
version of the Health and Retirement Study, this research shows that financial precarity and
uninsurable health shocks are the key factors in determining tenure transitional patterns. Families
with greater liquidity-constraints, and higher share of out-of-pocket medical expenditure out of
income, are more likely to exit the status of aging in place. Interestingly, among all four
dimensions of health conditions, cognitive decline is the most important factor to make
households leave their primary residence. Having difficulties with IADLs forces people to move
to rental housing instead of downsizing, and experiencing depressive symptoms can lead
households either to downsize or to rental housing.
Those findings call attention to growing inequality among older households across
different demographic cohorts. Additionally, the model implies that ongoing demographic shifts
will bring more Baby Boomers to age in place, and therefore will reshape the housing supply
market for Millennials and Gen Xers in the long run. This aging in place trend accounts for about
1.6 million houses held back from the market through 2018, representing about one year’s
2
typical supply of new construction, or more than half of the current shortfall of 2.5 million
housing units.
The problem with aging in place is that being retired, the elderly might not have
sufficient income and non- housing wealth to buffer shocks associated with aging, such as the
need for long-term care. One potential policy instrument to help the elderly is the reverse
mortgage, which allows retired people to draw on their home equity without requiring the
household to make periodic payments on the mortgage. The second chapter examines the
feasibility of reverse mortgages in Japan, with a context of extremely low interest rates,
adequately high land values, and tremendous longevity risk. Among countries, Japan has been a
leader in rapid aging over the past several decades. Using data from the Ministry of Land,
Infrastructure, Transport, and Tourism of Japan, this paper employs hedonic modeling to develop
a house price index for Japan and uses time series simulation methods to characterize the
stochastic movements of interest rates, land prices and mortality rates. To minimize the exposure
of the tail risk of reverse mortgages loans in Japan, this chapter sheds light on the possibility of
designing reverse mortgages as annuities rather than lines of credit from which people might take
a lump-sum withdrawal.
Moving the discussion on the role of housing wealth back to the United States, the third
chapter investigates whether and how households react to their housing wealth changes
associated with house price fluctuations. The relationship between housing wealth and
consumption has gained substantial attention from academics and policymakers as it not only
relates to the household’s own well-being but has a broader impact on the macroeconomy.
Employing the restricted version of the Panel Study of Income Dynamics and constructing an
innovative IV for housing wealth, this paper shows that a one percent increase in perceived
3
housing wealth is associated with only a 0.01-0.02 percent increase in real, non-housing
consumption, after directly controlling for the collateral channel. More specifically, consumption
items that are necessary for daily lives, such as food and transportation, do not respond to
changes in perceived housing wealth, whereas auxiliary consumption, such as clothes and
recreation, slightly increase as perceived housing wealth increases. Those results indicate that the
housing wealth effect on non-housing consumption has long been overestimated, due to
limitations in data and methodology.

4
Chapter 2
Housing Tenure Transitions among Older Households: The Role of
Financial Precarity and Health

Linna Zhu, and Gary Painter
Price School of Public Policy
University of Southern California

Abstract
Understanding why older households make housing tenure decisions is of growing importance as
the U.S. population ages. By using the restricted version of the Health and Retirement Study, this
analysis is able to estimate how changes in health conditions and financial precarity impact a
variety of household housing decisions in a much more precise manner than previous literature.
The results suggest that financial precarity and uninsurable health risks are two key factors in
determining housing tenure transitional patterns. Families with greater liquidity-constraints, and
higher share of out-of-pocket medical expenditure out of income, are more likely to exit the
status of aging in place. Among all four dimensions of health conditions, cognitive decline is the
most important factor to make households leave their primary residence. Having difficulties with
IADLs forces people to move to rental housing instead of downsizing, and experiencing
depressive symptoms can lead households either to downsize or to rental housing. The results
imply that more Baby Boomers will choose to age in place when they enter their 70s, which will
reshape the housing supply market for Millennials and Gen Xers in the long run.

5
2.1 Introduction
The number of households over 75 in the United States is currently close to 14 million.
In the next twenty years, the number is expected to increase to close to 30 million. Past research
has investigated a number of factors that impact the housing tenure transitions for the elderly in
their late lives. These studies often rely on variants of the life cycle hypothesis (Jones, 1997;
Yaari, 1965) or based on transition events in the life of an older household (Venti and Wise,
1990; Feinstein and McFadden, 1989).
There remain many questions about how uninsurable health risks and financial precarity
would affect tenure decisions that the previous literature do not answer. Older households are
subject to several sources of risks, including mortality risk, health contingencies, medical
expenditure shocks, and income shocks. Previous literature suggests that physical limitation,
such as disability, affects housing tenure transitions (Hayward, 2004; Painter and Lee, 2009).
However, these past studies are quite limited in the focus on broad categories of physical
disability. Neglected in past studies are controls of other dimensions of health, such as
depressive symptoms, health conditions associated with cancers, and cognitive declines, which
might be related to housing tenure transitions. Further, a focus on the level of income and wealth
can mask the impact of unexpected expenses.
This paper contributes to the literature on the housing tenure transitions of older
households in several ways. First, this paper includes a more comprehensive set of variables than
previous studies. Using the Health and Retirement Survey and its restricted geographical data
(1996-2014), we are able to control for similar factors examined in previous literature, such as
sociodemographic characteristics, inter-vivo transfers and bequest motives, child proximity and
co-residence (Painter and Lee 2004). In addition to these controls, we include new measures of
6
financial buffers and precarity. Next, we decompose the health risks into four dimensions:
physical dysfunctions, depressive symptoms, diseases, and cognitive declines. In this way, this
paper uncovers the heterogeneous impacts of various dimensions of health risks on tenure
decisions. Finally, we construct an absorbing housing tenure transition set, including exiting
owning to renting, relocating and downsizing, moving to assisted living facilities, and exiting
aging in place. This enables us to uncover the heterogeneous impacts of those key factors across
different transitional types.

2.2 Theory and Background
2.2.1 Our Model
We develop a model that incorporates both life-cycle and non life-cycle factors that
would affect housing tenure transitions for elderly households. In our model, it is assumed that at
each age, each household maximizes its utility function:
𝐸𝑡#$𝑈(𝑋
!
)×*(1−𝑑
!
)
"
!#$
+𝛽𝑑
!
𝑈(𝑋
!
)0
"
!#$
/(1+𝛿)
"%$

Where, 𝑋
!
=𝐶
!
+𝐻
!
+𝑀
!

Subject to the wealth constraint:
𝐹𝑊
!
+𝐸
!
𝑃
!
ℎ
;
+𝑌
!
=𝐹𝑊
!%&
(1+𝜔
!%&
)+𝐸
!%&
𝑃
!%&
ℎ
;
(1+𝜃
!%&
)+𝑌
!
−(1−𝐸
!%&
)𝑃
!%&
ℎ
@
𝑟−𝑋
!
𝑃
!

𝑋
!
is the total consumption, which includes medical expenses 𝑀
!
, housing consumption 𝐻
!
, and
the remaining consumption 𝐶
!
. 𝑑
!
is the mortality rate at each stage, and 𝛽 is the bequest
parameter. At each stage, the expected utility of each household consists of the utility from
consuming all kinds of goods, as well as the utility from bequeathing wealth to descendants.
7
Households hold certain levels of wealth and income. 𝐹𝑊
!
is the non-housing wealth,
𝐸
!
𝑃
!
ℎ
;
is the housing wealth, and 𝑌
!
represents household income. We assume that each
household owns fixed units of housing ℎ
;
, with house prices 𝑃
!
varying across time. We allow the
access to debt for each household, where 𝐸
!
represents their equity share, and (1-𝐸
!
) is the
corresponding loan-to value ratio at each period. 𝜔 is the return on non-housing wealth, 𝜃 is the
house price appreciate rate, and r is the mortgage interest rate.
At certain point t*, the household in late life will experience uninsurable contingencies
associated with aging which lead the family to reach the stage where
𝑋
!∗
𝑃
!∗
>𝜔
!%&
𝐹𝑊
!∗%&
+𝜃
!∗%&
𝐸
!∗%&
𝑃
!∗%&
ℎ
;
+𝑌
!∗
−(1−𝐸
!∗%&
)𝑃
!∗%&
ℎ
@
𝑟
After this point, the family will have to finance their desired level of consumption by
spending their stock level of wealth, which is 𝐹𝑊
!∗
+𝐸
!∗
𝑃
!∗
ℎ
;
.
The question here is, for each household, in what manner do they consume 𝑊
!∗
+
𝐸
!∗
𝑃
!∗
ℎ
;
? Do they treat financial wealth and housing wealth differently? Do they consume
housing wealth by reducing 𝐸
!∗
via reverse mortgages or HELOC to age in place, or by reducing
ℎ
;
to downsize or relocate? What factors affect their housing tenure decisions?
2.2.2. Insights from Previous Literature
Theories have mixed predictions on those questions. Traditional life-cycle hypothesis
(Yaari, 1965; Artle and Varaiya, 1978; Jones, 1997) predict that people will consume their
housing wealth in late life just as they do with financial wealth. The consumption pattern for
housing wealth should be hump-shaped, with households accumulating housing wealth before
retirement and then running down the wealth, either by downsizing or moving to rental housing,
in their late lives. Contrary to the life-cycle hypothesis, the fully consumption insurance
hypothesis (Cochrane, 1991) and the buffer-stock hypothesis (Carroll and Hubbard, Skinner and
8
Zeldes, 1994; Kimball, 1996; Carroll, 1997; Yang, 2009; Iacoviello and Pavan, 2013) treat
housing wealth as precautionary savings to insure against wealth-impairing contingencies.
Housing wealth will be spent after financial wealth and will only be consumed when such
contingencies realized.
A number of studies have established a set of factors that affect an older household’s
housing tenure choices via altering their tastes for owner-occupied housing. The first category of
factors relates to households’ sociodemographic characteristics. Older age, a recent transition to
retirement status, the dissolution of a family, such as divorce or a recent loss of a spouse, would
lead households to exit homeownership or downsize (Feinstein and MacFadden, 1989;
VanderHart, 1994; Megbolugbe, Sa-Aadu, and Shilling, 1997; Myers and Ryu, 2008; Painter and
Lee, 2009; Lee and Painter, 2014). The second category focuses on intergenerational factors.
Households with inter-vivo transfers or bequest motives tend not to consume their housing
wealth and thus age as owners. Parents’ bequest motives are negatively correlated with their
children’s financial well-beings (Hurd, 1990; Bernheim, 1991; Megbolugbe et al., 1997;
McGarry, 1999; Kopczuk and Lupton, 2007). Therefore, housing wealth is treated as
bequeathable wealth and will not be consumed even in late life as predicted by the life-cycle
hypothesis. Moreover, child proximity and co-residence with children will make households
more likely to age in place instead of exiting ownership (Lee and Painter, 2014). The underlying
mechanisms could be either the parental need for physical care or psychic need for living closer
to kids (Crimmins and Ingegneri, 1990; Choi, 2003). The third category involve economic
factors, such as liquidity-constraints, wealth, and house price volatility (Feinstein and
MacFadden, 1989; Hayward, 2004; Bian, 2016; Sinai and Souleles, 2005; Banks, Blundell,
Oldfield, and Smith, 2012; Nakajima and Telyukova, 2013; Nakajima and Telyukova, 2017).
9
Households with greater liquidity constraints, lower possessions of wealth are more likely to exit
ownership. Households experiencing greater volatility in their house values have a greater
likelihood of relocating and downsizing in late lives.
As noted previously, these past studies include imprecise measures of health and often do
not focus on financial precarity. Below we outline how this study includes these measures.

2.3 Data and Methodology
2.3.1 Data
In this study, we exploit the Health and Retirement Survey (HRS), including its restricted
geographic data, collected by the Institute for Social Research at the University of Michigan. The
Health and Retirement Survey is a national longitudinal dataset funded by the National Institute
of Aging and the Social Security Administration that samples households with initial respondents
over the age of 50, starting in 1992. HRS surveys a representative sample of approximately
20,000 people in America, with questions at both the individual and household levels. Our study
uses the household as the unit of analysis. We assign a unique ID for each family and observe
extensive information of each family and its members from 1996 to 2014. We use the Rand
version of the data as our primary data source and combine it with information from the core
interviews, the tracker file, and the restricted geographical data.
In our analysis, household-level information includes household income and wealth,
housing status, mobility, family structure, and intergenerational wealth transfers. Individual-level
information includes demographics, retirement plans, health insurance, medical expenditure, and
detailed health status. Because of the longitudinal nature of the data, we can capture transitions
on housing tenure status and household formation, as well as shocks on wealth and health status
10
at physical, mental, and cognitive dimensions. Table 1a and 1b contains a complete list of
variables in the survival analysis.
[Insert Table 2.1a and Table 2.1b Here]
- Sociodemographic Characteristics
The sociodemographic variables of each household are age, education, race, marital
status, retirement status, recent widowhood and divorce, and recent transition to retirement.
Because we have information on both the respondent and the spouse, we generate all
demographic variables at the household level: We take the age of the older member in each
household (spouse of an age-eligible respondent but with her age below 50 is also surveyed in
the data), the highest degree achieved within each household, and the race of the respondent
answering wealth related questions, as the proxies for household age, education status and race.
As for the retirement status, each household member can be either completely retired or not
retired. For couple or partnered household, if both members are completely retired, we treat this
household as completely retired. If at least one of the couples is not retired, we treat the family as
not retired. For divorced, widowed, or never married household, we take the retirement status of
the single respondent in the family. Additionally, we add recent shocks due to divorce or loss of
a spouse within the last two years as our controls.
-- Intergenerational Factors
In this paper, intergenerational factors consist of inter-vivo transfers, intended bequests,
child proximity, co-residence, and help from kids on parental care.
To measure inter-vivo transfers, we generate a dummy variable with 1 indicating the
household has at least one of their kids on the deed of their house (if they are homeowners), and
0 if none of the kids is on the home deed. However, it is likely that a household has a bequest
11
motive but hasn't put their kids' names on the deed. Therefore, we further capture this expected
bequest motive based on the self-reported probability of leaving a bequest greater than $100,000
and $500,000.
- Financial Buffers
We utilize a set of variables to capture the buffers that each household possesses in face
of uncertainties in late life. In the regression analysis, this set includes household income,
financial wealth, housing wealth, house price appreciations, and health insurance coverage.
We measure household income as the sum of individual earnings, pensions, income from
social security disability and social security retirement, unemployment compensation, and other
government transfers. Financial wealth consists of stocks, investments, checking and savings
accounts, government bonds, and all types of additional savings. Housing wealth is equal to the
net value of housing value excluding all mortgages on the primary residence. We generate the
loan to value ratio (LTV) measured by the amount of all mortgages on primary residence divided
by the self-reported value of a primary residence. Moreover, we control for the home type of
each household, including a single-family house, duplex, townhouse or apartment, or mobile
home. We measure other wealth as the sum of vehicles, business, IRA and Keogh accounts, as
well as the net value of a secondary residence. Total wealth is the summation of financial wealth,
housing wealth, and other wealth. In the survival analysis described below, we take the log forms
of income, financial wealth, and housing wealth. Because some families have zero financial
wealth, taking the log form will shrink our sample size. We thus increase the values of income,
financial wealth, and housing wealth by five dollars, respectively. With this parellel-shifitng, we
save our sample size and avoid selection bias.
12
To measure how well households are self-insured for health risks, we generate four
dummy variables: Medicare, Medicaid, long-term care insurance, and private insurance. We
assign 1 to those dummy variables if at least one of the family members have the insurance
coverage, and 0 if none of the couples has them.
- Financial Precarity
To capture the liquidity constraint, we generate the loan to value ratio (LTV) measured
by the amount of all mortgages on primary residence divided by the self-reported value of a
primary residence. Besides out-of-pocket payments (OOPs), we generate a precarity ratio
measured by the OOPs divided by household income, and categorize the ratio into four brackets:
below 10%, 10%-30%, 30-80%, and above 80%. Given that richer households are financially
more capable of spending more on OOPs, having only OOPs will not adequately capture the
precarity from medical expenditure. Therefore, we use the share of OOPs out of household
income as a proxy for precarity. Additionally, we attempt to capture a sudden shock in OOPs due
to some health contingencies. We define such shock as experiencing more than 50% increase in
OOPs within the past two years.
- Health Conditions and Health Shocks
We decompose health risks into four dimensions: physical dysfunctions, depressive
symptoms, diseases, and cognitive declines. One of the advantages of using HRS to research on
aging and housing is that it contains tremendously more extensive measurements on health status
than any other dataset does. We pick constructed indices from RAND HRS data to measure
health for each household at each dimension.
Physical Dysfunctions
13
ADL Index: The five tasks in this ADL index include bathing, eating, dressing, walking
across a room, and get in or out of bed. Index value ranges from 0 to 5.
IADL Index: The five tasks in this IADL index include using a telephone, taking
medication, handling money, shopping, preparing meals. Index value ranges from 0 to 5.
Those two indices are difficulty indices. The higher the number of the index, the more
difficulties the individual has with the associated tasks. For example, the ADL index has a
minimum value of zero, meaning no trouble with any of the five tasks, and a maximum value of
five, indicating having difficulty with all five tasks. We generate a dummy variable based on
each index which equals 1 when the index value is greater than 1, and 0 when the index value is
no greater than 1. We then take the value of the sicker individual within each household as the
proxy measurement for household functional disabilities. We define a physical dysfunction
shock in ADLs or IADLs as the values switching from 0 to 1.
Depressive Symptoms
Depression Index: The seven negative sentiments in the depression index include
everything is an effort, sleep is restless, felt alone, felt sad, could not get going, felt unhappy, and
could not enjoy life most of the time. Values range from 0 to 7. The higher the number, the more
depressed the respondent is.
We generate a dummy variable based on this index which equals 1 when the index value
is greater than 3, and 0 when the index value is no greater than 3. We use this dummy to proxy
for depression. We take the value of the sicker individual within each household as the proxy
measurement for household depression level. We define a depression shock as the value
switching from 0 to 1.
Diseases
14
Disease Index: The eight conditions in this index include high blood pressure, diabetes,
cancer, lung disease, heart disease, stroke, psychiatric problems, and arthritis. Values range from
0 to 8. The higher the number, the more types of diseases the respondent has.
We generate a dummy variable based on this index which equals 1 when the index value is
greater than 2, and 0 when the index value is no greater than 2. We use this dummy to proxy for
disease status. We take the value of the sicker individual within each household as the proxy
measurement for household disease conditions. We define disease shock as the value switching
from 0 to 1.
Cognitive Decline
McArdle and Fisher (2007) conducted a common factor analysis and suggests that
episodic memory and mental status are two key factors determining cognitive status.
Episodic Memory Index: This index is constructed based on the immediate word recall
test. Starting from year 1994, the respondent is randomly assigned with a wordlist containing 40
words (for the year 1992 and 1993, the wordlist contained 20 words). Values in this index
represent the number of words correctly recalled by the respondent. We generate a dummy
variable based on this index which equals 1 when the index value is no greater than 8, and 0
when the index value is greater than 8. We use this dummy to proxy for episodic memory
decline. We then take the value of the sicker individual within each household as the proxy
measurement for household episodic memory decline.
Mental Status Index: This index is constructed by summing the results from the Serial 7’s
test, backwards counting test, naming tests, and vocabulary questions. Serial 7’s test asks the
individual to subtract seven from the prior number, beginning with 100 for five trials. Correct
subtractions are based on the preceding number given so that even if one subtraction is incorrect,
15
subsequent trials are evaluated on the given (perhaps wrong) answer. Valid scores are from 0 to
5. Backwards counting tests examine whether the respondent was able to successfully count
backwards for ten continuous numbers from 20 and 86, respectively. Two points are given if
successful on the first try, one if successful on the second, and zero if not successful on either
try. Therefore, valid scores range from 0 to 2. Date naming tests examine whether the respondent
was able to report today’s date correctly, including the day of the month, month, year, and day of
the week, respectively. Valid scores range from 0 to 4. Object naming tests whether the
respondent was able to correctly name these objects, cactus, and scissors, based on a verbal
description. Valid scores range from 0 to 2. President naming tests examine whether the
respondent was able to correctly name the current president and vice-president of the United
States, with scores ranging from 0 to 2. Vocabulary questions test whether the respondent can
provide definitions of five given words. The possible scores for each word are perfectly correct
(=2), partially correct (=1), and incorrect (0). Thus, total scores for this vocabulary test range
from 0 to 10. To sum the scores of all the tests, values of the mental status index range from 0 to
20.
We generate a dummy variable based on this index which equals 1 when the index value
is no greater than 12, and 0 when the index value is greater than 12. We use this dummy to proxy
for a mental status decline. We then take the value of the sicker individual within each household
as the proxy measurement for mental status decline at household level. We then flag a household
with cognitive decline if at least one of the household members suffer either episodic memory
deteriorations or a mental status decline. We define a cognitive decline shock as the value
switching from 0 to 1.
16
2.3.2 Methodology
We conduct the survival analysis to model the time it takes for different types of tenure
transitions from homeownership to occur. We utilize the Cox proportional hazard model as the
primary empirical framework to examine the determinants for housing tenure choices. We
restrict our sample to households in which the elder (the head) of the couple is 51 or more years
old. Each household is followed throughout the analysis period, 1996 to 2014, until they exit
homeownership, die (not considered as a housing tenure transition), or are completely dropped
from the sample. After the head of households dies, the wife would become the new head, and
the observation remains classified as the same family unit. However, if the wife is below age 51,
this household will be dropped from our analysis. There is a total of 141 households dropped due
to this reason, accounting for less than 0.5% of the total sample (the total number of families is
28525). We think dropping those families will not bias our estimates.
Table 2 provides an absorbing set of elderly housing tenure transitions. If the household
enters the sample as homeowners, it can have three types of tenure status throughout the analysis
period: always-owning, exit owning with one single transition, and exit owning with multiple
transitions. We further decompose the always-owning type into three sub-categories: aging in
place, downsizing and moving. We define a tenure as aging in place if the household enters the
sample as a homeowner and never moves out of their primary residence. We define a transition
as downsizing if the new house value is at least 10% lower than the previous house value. If we
treat downsizing as an option to cash out home equity, then using depreciation in home values is
a better measurement for downsizing than the number of rooms. A family may move from
Wisconsin to San Diego with less number of rooms but higher home values. The remaining ones
in the always-owning category are the other movers who enter the sample as a homeowner but
moves to another property as a homeowner in later years. If the household decides to exit owning
17
status, it can either exit to renting, or move to nursing homes. If the household enters the sample
as non-homeowner, it can also have three types of tenure status throughout the period: stay non-
owning, transition to owning with a single change, and transition to owning with multiple
changes.
In this paper, we only explore the transitions from homeownership. We restrict our
sample to households entering the sample analysis period as homeowners. As indicated in Table
2, among older homeowners, around 62% are choosing to age in place. Among those who
transition out of ownership (single transition), 76% exit to rental housing, and 20% of the elderly
move to assisted living facilities in their late lives.
[Insert Table 2.2 Here]
In the survival analysis, we define five hazard events as 1) owning to renting; 2) owning
to downsizing; 3) owning to relocating, 4) owning to assisted living facilities (nursing homes),
and 5) exiting the status of aging in place. For each hazard event, we estimate the time it takes to
occur, with the starting status as homeowners.

2.4 Results
2.4.1 Summary Statistics
As highlighted in Figure 1, the homeownership rates of households with head age groups
in 51-55 and 56-60 have been decreasing significantly since 2010, probably due to the relatively
lower homeownership rates among the Baby Boomers before age 70. The homeownership rates
of households with head age groups in 71-75, 76-80, and 81 above have been steadily increasing
over the past ten years. This may reflect a change in preferences towards exiting ownership in
late life. Figure 2 illustrates heterogeneity across demographic cohorts in transitioning rates. The
18
Greatest Generation, born before 1927, is the eldest cohort among all senior households. Born
after the Greatest Generation, the Silent Generation has been showing different transition rates.
Compared to the Greatest Generation, the Silent Generation starts to exit homeownership around
the same age, which is their early 70s, but with a significantly slower pace, indicating that a
greater share of the Silent Generation has been choosing to age in place in their late life. The
homeownership rates are still above 70% in their mid-80s. Table 1 substantiates this preference
for staying owning, especially aging in place. Among the households who are homeowners,
around 62% choose to age in place, 7% decide to downsize, 9% relocate but still as homeowners,
and 12% move to rental units, and 3% to assisted living facilities.
Tables 3a-3c provide basic summary statistics for buffers, financial precarity, and health
risks. On average, people who exit to rental housing have the smallest buffers. Those exiting
ownership own substantially lower housing wealth, financial wealth, and household income.
Fewer people in this transition type have private insurance coverage compared to other types.
Table 3b further suggests that exiting ownership is correlated with higher LTVs, higher share of
out-of-pocket medical expenditure out of income, and more shocks in medical expenditure.
Moreover, compared to those always staying as homeowners, households transitioning to rental
housing are in face of more health risks. They have more difficulties with ADLs and IADLs,
experience more depressive symptoms and diseases, and suffer from faster cognitive decline.
Additionally, they also experience more health shocks at all four health dimensions.
Tables 3a-3c reveal several interesting characteristics about those who move but still as
homeowners. Compared to people aging in place without moving, households who choose to
downsize and relocate are on average having significantly greater amount of financial wealth.
More households own a secondary residence and long-term care insurance in this downsizing
19
transition type. Those who relocate but not downsizing have the greatest buffers, the least
financial precarity, and the slowest deteriorations in health.
Because people above age 65 are automatically enrolled in Medicare, the share of people
having Medicare is indeed an indicator for age. Among all transition types, households moving
to nursing homes are the eldest group who have the severest physical dysfunction and cognition
decline. They own more housing wealth and financial wealth than those exiting to rental housing,
but very few of them have a secondary residence.
[Insert Table 2.3a Table 2.3b Table 2.3c Here]
2.4.2 Survival Analysis Results
a. Exit Ownership to Rental Housing
Table 4 displays the survival analysis results for owning to renting transition. Numbers in
all regression tables are hazard ratios, with numbers greater than 1 indicating a greater likelihood
of exiting ownership. The first model includes sociodemographic characteristics and the buffers.
Greater income, financial wealth, and housing wealth are associated with a greater likelihood of
aging in place. However, once variables that control for financial precarity (Table 4: Column 2)
are added, both household income and housing wealth are not significant. All our financial
precarity measurements are having significant impact on exiting ownership. With LTVs greater
than 50%, a huge increase in OOPs, and OOPs more than 10% of income, households are more
likely to be forced to move out to rental housing. Model 2 indicates that financial precarity is an
important factor driving older people out of homeownership. Moreover, households with long-
term care insurance and private insurance are more likely to age in place due to the fact that they
have more buffers to cope with uncertainties in life. The significance of financial precarity stays
consistent once we add controls for health conditions and health shocks. As shown in Column 3
of Table 4, health deteriorations and uninsurable health shocks drive people out of
20
homeownership. Having difficulties with IADLs, experiencing depressive symptoms and
cognitive declines increase the likelihood of exiting homeownership to renting by more than
20% compared to healthy households. Moreover, suffering a recent health shock in ADLs,
IADLs, diseases also lead people to exit ownership. Interestingly, suffering from a recent shock
in depressive symptoms make people to stay in place rather than moving out.
Model 4 (Table 4: Column 4) further controls for intergenerational factors, including
child proximity, co-residence, kids helping with IADLs, inter-vivo transfers, and intended
bequest motives. Once those variables are added, long-term care insurance and private insurance
are no longer significant. This suggest that, even though long-term care insurance covers in-
home care or nursing home expenses, living closer to children and getting help from kids (via co-
living with kids) on IADLs would ease the burden of aging in place and thus make long-term
care or private insurances no longer important in making tenure transitions. Moreover,
intergenerational factors decrease the significance and magnitude of hazard ratios on health
conditions. Physical dysfunctions are not significant at 5% significance level. Additionally, if
households experience a positive shock in their house prices (with more than 5% increase), they
tend to age in place. If a household is in the process of debating whether or not exiting
ownership, then having this positive shock in housing value will incentivize them to wait longer
so that they can cash out more home equity when they move out in the future.
In sum, households with less buffers in financial wealth, more financial precarities with
liquidity-constraints and medical expenditure, health issues with depression and cognition
decline, more health shocks associated with physical dysfunctions and diseases, are more likely
to exit ownership to rental housing. Income, housing wealth, and insurance coverage do not
affect exiting ownership decisions.
21
[Insert Table 2.4 Here]
b. Downsizing
Table 5 displays the survival analysis results for owning to downsizing transition. Same
as exiting to rental housing, once we control for financial precarity and intergenerational factors,
household income and long-term care insurance are no longer significant. Financial wealth is
also not significant at 5% significance level. In terms of making the transition of downsizing,
having greater housing wealth and owning a secondary residence lead household to exit the
status of aging in place and downsize to a new property. Within the financial precarity
measurements, liquidity-constraints here have greater impact than medical expenditure precarity.
Households with LTV greater than 80% are 350% more likely to downsize compared to those
debt-free households.
Contrary to the impact on exiting ownership, physical dysfunctions are associated with a
greater likelihood of aging in place (though only significant at 10% level). At 1% significance
level, health conditions do not matter. Only shocks in IADLs increase the likelihood of
downsizing.
Therefore, less buffers in housing wealth, more financial precarity with liquidity-
constraint and medical expenditure, shocks in IADLs, are the key factors driving people to
exiting aging in place and downsizing. Health risks is a relatively minor concern compared to the
transition to rental housing.
[Insert Table 2.5 Here]
c. All Transition Types
We conduct survival analysis for five transition types: 1) owning to renting; 2) owning to
downsizing; 3) owning to relocating, 4) owning to assisted living facilities (nursing homes), and
22
5) exiting the status of aging in place. Table 6 combines the results from those five hazard
regressions, with full set of controls. Column 5 captures the net effect on exiting aging in place
for buffers, financial precarity, and health risks. The transition of exiting aging in place contains
exiting to rental housing, to relocating (downsizing is one form of relocating), and to nursing
homes. Because some factors have opposite effect on various types of transitions, the hazard
ratios shown in Column 5 are the net effect taking account of the offsetting effect. For example,
having greater financial wealth enables households to age in place without moving out to rental
house, but also increases the likelihood of downsizing or relocating. Due to this offsetting effect,
the net effect of financial wealth on exiting aging in place is zero.
Buffers: Owning greater housing wealth and having a secondary residence are associated
with a greater likelihood to exit the status of aging in place, mostly in the form of downsizing.
This is consistent with the life-cycle hypothesis. After controlling for bequest motives, people do
consume some portion of their housing wealth in late lives, not by cashing out all home equity
but rather by downsizing. However, if they experience a recent positive housing wealth shock,
then households tend to age in place without moving. Additionally, both long-term care
insurance and private insurance are not significant in the decision of exiting aging in place.
Financial Precarity: Precarities associated with liquidity-constraints and medical
expenditure make people exit the status of aging in place. More specifically, having LTV greater
than 50%, experiencing a huge increase in out-of-pocket payments (OOPs), or spending more
than 30% of household income on OOPs, will lead households exit aging place. Liquidity-
constraints affect mostly the decision on downsizing. Medical expenditure precarity affect more
on the decision on exiting ownership.
23
Health Risks: Among all four dimensions of health conditions, cognitive decline is the
most important factor which make households leave their primary residence. Among all four
types of health shocks, shocks in IALDs and diseases are the two key factors that drive
households to move out.
[Insert Table 2.6 Here]

2.5 Conclusions
Understanding the housing tenure decisions of older households is of great importance as
the U.S. population is rapidly aging. Among the older homeowners in the U.S., around 62%
choose to age in place, 7% decide to downsize, 9% relocate but still as homeowners, and 12%
move to rental units, and 3% to assisted living facilities. Housing, the most important asset in
households' portfolios, has large implications for post-retirement financial security for older
families. How households manage their home equity and alter tenure forms in the face of
uncertainties and shocks exerts an influential impact on their post-retirement living standards and
well-being. While research has investigated a number of factors that impact the well-being of
adults as they age, there remain many questions about interactions among buffers, financial
precarity, health risks, and housing tenure transitions among the elderly.
This paper exploits a rich longitudinal data set, the Health and Retirement Survey and its
restricted geographical data, to examine the determinants for various types of housing tenure
transitions among the elderly, encompassing a focus on the interplay among buffers, financial
precarity, and health risks. We conduct survival analysis for 5 types of transitions based on a
constructed absorbing tenure transition choice set: exiting owning to renting, downsizing and
relocating, moving to assisted living facilities, and exiting the status of aging in place. To get
24
credible estimates on buffers, financial precarity and health risks, we include a more
comprehensive set of controls to characterize each household than has previous literature. More
specifically, we control for sociodemographic characteristics including dissolutions in family,
bequest motives (both inter-vivo transfers and intended bequests), child proximity, and help from
kids on physical dysfunctions.
This is the first paper to experiment with new measurements on financial precarity and
health risks associated with physical dysfunctions, depressive symptoms, diseases and cognitive
declines. By conducting survival analysis on all types of transitions out of aging in place, this
paper sheds light on the heterogeneous impacts of variables of interest across various types of
tenure transitions.
Financial Buffers: Household income does not have any predicting power in any of the
transition types. Having greater financial wealth enables households to age in place without
moving out to rental house, but also increases the likelihood of downsizing or relocating. This
offsetting effect makes the net effect of financial wealth on exiting aging in place zero. Owning
greater housing wealth and having a secondary residence are associated with a greater likelihood
to exit the status of aging in place, mostly in the form of downsizing. This is consistent with the
life-cycle hypothesis. After controlling for bequest motives, people do consume some portion of
their housing wealth in late lives, not by cashing out all home equity but rather by downsizing.
However, if they experience a recent positive housing wealth shock, then households tend to age
in place without moving. Additionally, both long-term care insurance and private insurance are
not significant in any type of transitions.
Financial Precarity: Precarities associated with liquidity-constraints and medical
expenditure make people exit the status of aging in place. More specifically, having LTV greater
25
than 50%, experiencing a huge increase in out-of-pocket payments (OOPs), or spending more
than 30% of household income on OOPs, will lead households exit aging place. Liquidity-
constraints mostly affect the decision on downsizing. Medical expenditure precarity affect more
on the decision on exiting ownership. Experiencing a shock in medical expenditure with an
increase of more than 50% is a persistent predictor of triggering the hazard event across all
transition types. Households who spend more than 10% of their income on out-of-pocket medical
expenditure face a significantly greater likelihood of exit ownership. Our measurements of
precarity provide consistent results across models and transition types.
Health Risks: Among all four dimensions of health conditions, cognitive decline is the
most important factor to make households leave their primary residence. Having difficulties with
IADLs force people to move to rental housing instead of downsizing. Experiencing depressive
symptoms can lead households either to downsize or to rental housing. Among all four types of
health shocks, shocks in IALDs and diseases are the two key factors that drive households to
move out.

26
2.6 Tables and Figures
Figure 2.1 Homeownership Rates (1998-2016)

Figure 2.2 Homeownership Rates by Demographic Cohorts

27
Table 2.1a Variables and Definitions: Buffers, Financial Precarity, and Health Conditions
Variables Definitions
Buffers
Household Income
Sum of individual earnings, pension, social security retirement income, social security
disability income, unemployment compensation and other government transfers. Natural
log form.
Financial Wealth
Sum of stocks, investments, checking and saving accounts, government bonds, and all
types of other savings. Natural log form.
Housing Wealth
Net value of housing value excluding all mortgages on the primary residence. Natural log
form.
Secondary Residence 1 = Own a second home; 0=otherwise
HP increases by 5% or more
1 = House price appreciates for at least 5% from the last survey year, after adjusting for
inflation; 0 = otherwise
Total Wealth Sum of financial wealth, housing wealth, and other wealth. Natural log form.
Medicare 1 = At least one of the couples has Medicare; 0 = otherwise
Medicaid 1 = At least one of the couples has Medicaid; 0 = otherwise
Long-term Care Insurance 1 = At least one of the couples has long-term care insurance; 0 = otherwise
Private Insurance 1 = At least one of the couples has at least one private insurance; 0 = otherwise
Financial Precarity
Loan-to-Value ratio (LTV)
The value of all mortgages on the primary residence divided by the self-reported value of
the primary residence. There are five brackets: debt-free, 0-25%, 25-50%. 50-80%, and
80% or more
Out-of-Pocket Payments (OOPs) Out-of-pocket medical expenditure. Natural log form.
OOPs shock 1 = OOPs increased by more than 50% from last survey year; 0 = otherwise
OOPs/HH Income
Share of out-of-pocket medical expenditure out of household income. There are four
brackets: 0-10%, 10%-30%, 30-80%, and 80% or more
Health Conditions
Difficulty with ADLs
1 = At least one of the couples have two or more difficulties with: Bathing, eating,
dressing, walking across a room, getting in or out of bed; 0 = otherwise
Difficulty with IADLs
1 = At least one of the couples have two or more difficulties with: Using a telephone,
taking medication, handling money, shopping and preparing meals; 0 = otherwise
Depressive Symptoms
1 = At least one of the couples have three or more negative segments: everything is an
effort, sleep is restless, felt alone, felt sad, could not get going, felt unhappy, and could not
enjoy life most of the time; 0 = otherwise
Diseases
1 = At least one of the couples have two or more of the eight diseases: high blood pressure,
diabetes, cancer, lung disease, heart disease, stroke, psychiatric problems, and arthritis;
0=otherwise
Cognition Decline
Episodic Memory Decline: Achieved less than 8 scores (out of 40) in a word recall test.
Mental Status Decline: Achieved less than 12 scores (out of 20) in Serial 7’s test,
backwards counting test, naming tests, and vocabulary questions. 1 = At least one of the
28
household members suffer either episodic memory decline or a mental status decline; 0 =
otherwise
Health Shocks
ADLs, IADLs, Depressive
Symptoms, Diseases, and
Cognition Decline
1 = The value for variables in health conditions switch from 0 to 1 since last survey year.

Table 2.1b Variables and Definitions: Demographics and Intergenerational Factors
Variables Definitions
Demographic Characteristics
age51-55 1 = Maximum age among the household head/wife 51-55; 0 = otherwise
age56-60 1 = Maximum age among the household head/wife 56-60; 0 = otherwise
age61-65 1 = Maximum age among the household head/wife 61-65; 0 = otherwise
age66-70 1 = Maximum age among the household head/wife 66-70; 0 = otherwise
age71-75 1 = Maximum age among the household head/wife 71-75; 0 = otherwise
age76-80 1 = Maximum age among the household head/wife 76-80; 0 = otherwise
age81+ 1 = Maximum age among the household head/wife >=81; 0 = otherwise
Less than high school
1 = The most educated one within the household is not a high school
graduate; 0 = otherwise
High school graduate and
some college
1 = The most educated one within the household has some college but not
a college graduate; 0 = otherwise
College and above
1 = The most educated one within the household is a college graduate or
more; 0 = otherwise
Married 1 = Household head is married; it is a couple household; 0 = otherwise
Partnered 1 = Household head is partnered with someone; 0 = otherwise
Divorced/Separated 1 = Household head divorced at the time of the interview; 0 = otherwise
Widowed 1 = Household head widowed at the time of the interview; 0 = otherwise
Never Married 1 = Household head never gets married; 0 = otherwise
Divorced in past 2 years 1 = Household head divorced within the past 2 years; 0 = otherwise
Widowed in past 2 years
1 = Household head became widowed within the past 2 years; 0 =
otherwise
Retired 1 = Both of the couples are completely retired; 0 = otherwise
Retired in past 2 years 1 = The household was retired within the past 2 years; 0 = otherwise
Intergenerational Factors
Inter-vivo transfers 1 = The household has their kids' names on their home deed; 0 = otherwise
Intended Bequest_10K
1 = Self-reported probability of leaving a bequest with more than $10,000
is greater than 50%; 0 = otherwise
Intended Bequest_100K
1 = Self-reported probability of leaving a bequest with more than $100,000
is greater than 50%; 0 = otherwise
29
With kids 1 = The household has at least one in-contact alive kid; 0 = otherwise
Child Proximity
1 = The household has at least one of their kids living within 10 miles
from their primary residence; 0 = otherwise
Co-residence
1 = The household has at least one of their kids co-living with them; 0 =
otherwise
Kids help with
ADLs/IADLs
1 = The household has at least one of their kids helping with their ADLs or
IADLs; 0 = otherwise

Table 2.2 Housing Tenure Transitions
Tenure Transitions Number of Families Percentage of the Total
Percentage of the Analysis
Sample
Always Owning 15052
53.39% 78.00%
Age in Place 11996 42.55% 62.17%
Downsize 1316 4.67% 6.82%
Move 1740 6.17% 9.02%
Exit Owning, Single Change 3063 10.87% 15.87%
Own to Rent 2329 8.26% 12.07%
Own to Nursing Homes 618 2.19% 3.20%
Own to Other 116 0.41% 0.60%
Exit Owning, Multiple Changes 1182 4.19% 6.13%
Always Non-Owning 7052 25.02%

Enter Owning, Single Change 1170 4.15%

Enter Owning, Multiple Changes 672 2.38%

Total 28191 100.00%

Table 2.3a Summary Statistics: Buffers by Transition Types
Transition Types
Househol
d Income
(Median)
Housing
Wealth
(Median)
Financial
Wealth
(Median)
Secondary
Residence
Total
Wealth
(Median)
Medi
care
Medi
caid
LTC
Private
Insurance
Always Owning

Age in Place 59384 128750 25000 0.14 276201 0.48 0.04 0.13 0.78
Downsize 58933 146300 40250 0.22 368173 0.57 0.03 0.17 0.78
Move 71882 149500 50400 0.2 403200 0.53 0.03 0.18 0.81
Exit Owning
(Once)

Own to Rent 31105 24000 9730 0.08 103075 0.73 0.10 0.12 0.63
Own to Nursing
Homes
26256 85260 22800 0.04 175560 0.92 0.13 0.13 0.66
Exit Owning
(Multiple)
37584 58800 11500 0.12 135660 0.63 0.08 0.13 0.66

30
Table 2.3b Summary Statistics: Financial Precarity by Transition Types
Transition Types LTV
OOPs
(Mean)
OOPs
(Median)
OOPs/Income
(Mean)
OOPs/Income
(Median)
OOPs Inrease by
50% or more
Always Owning

Age in Place 0.24 5329 2643 6.65 0.04 0.29
Downsize 0.21 5954 3090 2.90 0.05 0.32
Move 0.23 5705 3047 2.57 0.04 0.31
Exit Owning (Once)

Own to Rent 0.45 6359 2300 12.92 0.06 0.33
Own to Nursing
Homes
0.05 14650 2966 20.24 0.09 0.38
Exit Owning
(Multiple)
0.18 5775 2346 13.58 0.05 0.32

Table 2.3c Summary Statistics: Health Conditions and Health Shocks by Transition
Types

Health Conditions
Health Shocks
Transition
Types
ADLs IADLs
Depressive
Symptoms
Diseases
Cognition
Decline
ADLs IADLs
Depressive
Symptoms
Diseases
Cognition
Decline
Always
Owning

Age in Place 0.08 0.06 0.17 0.60 0.23 0.07 0.08 0.12 0.17 0.08
Downsize 0.07 0.06 0.17 0.65 0.21 0.07 0.08 0.14 0.19 0.09
Move 0.06 0.04 0.12 0.62 0.19 0.06 0.06 0.12 0.18 0.08
Exit Owning
(Once)

Own to Rent 0.15 0.15 0.25 0.70 0.38 0.13 0.15 0.17 0.21 0.12
Own to
Nursing
Homes
0.30 0.31 0.48 0.71 0.56 0.22 0.24 0.23 0.23 0.13

31
Table 2.4 Cox Proportional Hazards Results: Owning to Renting

(1) (2) (3) (4)

Demos &
Buffers
+Financial
Precarity
+Health Shocks
+Intergenerational
Factors
VARIABLES HR. HR. HR. HR.
Buffers

Household Income 0.939*** 1.004 0.994 1.007
Financial Wealth 0.916*** 0.924*** 0.931*** 0.974***
Housing Wealth 0.972*** 0.994 0.997 1.012
Secondary Residence 1.146* 1.138 1.139* 1.257***
HP increases by 5% or more 0.856*** 0.856*** 0.852*** 0.850***
Medicare 0.989 1.011 0.998 0.989
Medicaid 1.154 1.112 0.985 0.891
Long-term Care 0.804*** 0.810*** 0.828** 0.912
Private Insurances 0.862** 0.886** 0.904* 0.944
Financial Precarity

LTV: 0-0.25

0.832* 0.829* 0.819**
LTV: 0.25-0.5

0.998 0.990 0.980
LTV: 0.5-0.8

1.253** 1.243** 1.148
LTV: >0.8

1.894*** 1.888*** 1.779***
OOPs

0.910*** 0.908*** 0.919***
OOPs increase by 50% or more

1.232*** 1.223*** 1.185***
OOPs/Income: 10%-30%

1.272*** 1.213*** 1.160**
OOPs/Income: 30%-80%

1.587*** 1.465*** 1.324***
OOPs/Income: >80%

1.792*** 1.532*** 1.435**
Health Conditions

Difficulty with ADLs

0.954 0.908
Difficulty with IADLs

1.238** 1.203*
Depressive Symptoms

1.201*** 1.136**
Diseases

1.019 0.990
Cognition Decline

1.224*** 1.186***
Health Shocks

ADLs

1.218** 1.217**
IADLs

1.464*** 1.398***
Depressive Symptoms

0.852** 0.864**
Diseases

1.161*** 1.187***
Cognition Decline

0.951 0.930
Demographic Controls Y Y Y Y
Intergenerational Factors N N N Y
State Dummies Y Y Y Y
Year Dummies Y Y Y Y
Observations 78,532 78,532 78,532 78,532
Note: *** p<0.01, ** p<0.05, * p<0.1
32
Table 2.5 Cox Proportional Hazards Results: Owning to Downsizing
(1) (2) (3) (4)

Demos &
Buffers
+Financial
Precarity
+Health Shocks
+Intergenerational
Factors
VARIABLES HR. HR. HR. HR.
Buffers
Household Income 0.985 0.950 0.947 0.952
Financial Wealth 1.022 1.029* 1.030** 1.026*
Housing Wealth 1.269*** 1.526*** 1.532*** 1.542***
Secondary Residence 1.822*** 1.790*** 1.791*** 1.783***
HP increases by 5% or more
0.826*** 0.806*** 0.805*** 0.805***
Medicare 0.728*** 0.745** 0.734*** 0.730***
Medicaid 0.749 0.765 0.760 0.775
Long-term Care 0.973 0.959 0.962 0.950
Private Insurances 1.016 1.008 1.013 1.022
Financial Precarity

LTV: 0-0.25

1.058 1.060 1.058
LTV: 0.25-0.5

1.490*** 1.491*** 1.476***
LTV: 0.5-0.8

1.965*** 1.969*** 1.939***
LTV: >0.8

4.564*** 4.612*** 4.533***
OOPs

0.959* 0.959* 0.957*
OOPs increase by 50% or more

1.207** 1.203** 1.203**
OOPs/Income: 10%-30%

1.029 1.018 1.019
OOPs/Income: 30%-80%

1.312* 1.291* 1.298*
OOPs/Income: >80%

0.847 0.811 0.811
Health Conditions

Difficulty with ADLs

1.242 1.247
Difficulty with IADLs

0.735* 0.732*
Depressive Symptoms

1.155* 1.156*
Diseases

0.952 0.951
Cognition Decline

0.974 0.983
Health Shocks

ADLs

0.938 0.939
IADLs

1.281** 1.274**
Depressive Symptoms

0.856 0.855
Diseases

1.085 1.086
Cognition Decline

0.958 0.944
Demographic Controls Y Y Y Y
Intergenerational Factors N N N Y
State Dummies Y Y Y Y
Year Dummies Y Y Y Y
Observations 78,532 78,532 78,532 78,532
Note: *** p<0.01, ** p<0.05, * p<0.1
33
Table 2.6 Cox Proportional Hazards Results: Other Transitions
(1) (2) (3) (4) (5)

Own to Rent
Own to
Downsize
Own to
Relocate
Own to
Nursing
Homes
Exit Aging in
Place
VARIABLES HR. HR. HR. HR. HR.
Buffers

Household Income 1.007 0.952 1.023 1.227 1.025
Financial Wealth 0.974*** 1.026* 1.018** 0.974 0.997
Housing Wealth 1.012 1.542*** 1.147*** 1.026 1.072***
Secondary Residence 1.257*** 1.783*** 1.688*** 1.693 1.575***
HP increases by 5% or more 0.850***
0.805*** 0.836*** 0.830 0.855***
Medicare 0.989 0.730*** 0.728*** 0.477 0.779***
Medicaid 0.891 0.775 0.683*** 2.297 0.913
Long-term Care 0.912 0.950 1.045 0.967 0.984
Private Insurances 0.944 1.022 1.007 0.599 0.961
Financial Precarity

LTV: 0-0.25 0.819** 1.058 1.038 2.658* 0.953
LTV: 0.25-0.5 0.980 1.476*** 1.227*** 0 1.097*
LTV: 0.5-0.8 1.148 1.939*** 1.451*** 0.433 1.290***
LTV: >0.8 1.779*** 4.533*** 2.167*** 4.975* 1.944***
OOPs 0.919*** 0.957* 0.981 0.715*** 0.951***
OOPs increase by 50% or more 1.185*** 1.203** 1.288*** 3.060*** 1.253***
OOPs/Income: 10%-30% 1.160** 1.019 1.021 1.878 1.070
OOPs/Income: 30%-80% 1.324*** 1.298* 1.124 8.041*** 1.200***
OOPs/Income: >80% 1.435** 0.811 1.048 21.83*** 1.285***
Health Conditions

Difficulty with ADLs 0.908 1.247 1.049 2.758** 0.994
Difficulty with IADLs 1.203* 0.732* 0.925 2.692* 1.106
Depressive Symptoms 1.136** 1.156* 1.012 1.109 1.047
Diseases 0.990 0.951 0.912* 1.135 0.939*
Cognition Decline 1.186*** 0.983 0.963 5.330*** 1.110**
Health Shocks Y Y Y Y Y
ADLs 1.217** 0.939 0.942 2.311** 1.049
IADLs 1.398*** 1.274** 1.107 2.327* 1.201***
Depressive Symptoms 0.864** 0.855 0.976 1.090 0.930
Diseases 1.187*** 1.086 1.167*** 0.897 1.180***
Cognition Decline 0.930 0.944 1.106 0.524 0.987
Demographic Controls Y Y Y Y Y
Intergenerational Factors Y Y Y Y Y
State Dummies Y Y Y Y Y
Year Dummies Y Y Y Y Y
Observations 78,532 78,532 78,532 78,532 78,532

Note: *** p<0.01, ** p<0.05, * p<0.1
34
Chapter 3
Has the Effect of Housing Wealth on Household Consumption Been
Overestimated? New Evidence on Magnitude and Allocation

Linna Zhu
University of Southern California
Jung Hyun Choi
Urban Institute

Abstract
The effect of housing wealth on household consumption is puzzling as the measured housing
wealth effect is substantially larger than what the theory predicts. Using the restricted version
of the Panel Study of Income Dynamics, this study finds that pure housing wealth effect on
consumption decreases substantially once addressing the endogeneity bias from unobservables.
After directly controlling for the collateral channel, we find that a one percent increase in
perceived housing wealth is associated with only 0.01-0.02 percent increase in real, non-housing
consumption. Using an innovative IV – quality-adjusted house price index – to disentangle
permanent housing wealth shocks from transitory housing wealth shocks, we conclude that the
housing wealth effect on non-housing consumption has long been overestimated, due to
limitations in data and methodology. Additionally, we find heterogeneity in MPCs across
consumption categories – consumption items that are necessary for daily lives, such as food and
transportation, do not respond to changes in perceived housing wealth, whereas auxiliary
consumption, such as clothes and recreation, slightly increases as perceived housing wealth
increases.

Keywords: Housing Wealth, Consumption, Elasticity, MPC

JEL: D12, D11, D15

35
3.1 Introduction
The relationship between housing wealth and consumption has gained substantial
attention from academics and policymakers because it shapes both household well-being and the
macroeconomy. For most homeowners, housing wealth is their largest asset, while household
personal consumption accounts for about two-thirds of the gross domestic product in the United
States. Uncovering how housing wealth affects household consumption is important for
understanding how house price fluctuations impact economic cycles and designing appropriate
macroeconomic policy instruments.
Consumption spending and house prices have shown a strong co-movement since the
1980s (Figure 1). However, the joint movement between the two variables does not confirm
causality. Estimating the effect of changes in housing wealth on household consumption is
empirically challenging because of the unobservables—such as household preferences and
expectations of future income growth—associated with changes in both house prices and
consumption levels. Identifying the mechanisms underlying household adjustments to
consumption in response to changes in housing wealth is also difficult.
Two channels provide possible explanations: pure housing wealth and collateral. The housing
wealth channel states that households increase their consumption as their housing wealth rises
because they expect future wealth increases. The collateral channel suggests that households
increase their consumption as the rise in housing wealth increases their borrowing capacity.
Previous studies (Bostic, Gabriel, and Painter, 2009; Cooper, 2013; Aladangady, 2017) have
tried to disentangle the two channels by comparing households with high borrowing constraints
to those with low constraints, assuming the collateral effect will be stronger for the former group.
However, their methods only indirectly estimate the collateral effect based on their assumption
36
that households with higher loan-to-value (LTV) ratios are more likely to use home equity for
additional consumption needs. This hypothesis is unsubstantiated because it is unclear who took
out home equity and how the behavior relates to their borrowing constraints.
[Insert Figure 3.1 Here]
When estimating the housing wealth effect, existing studies have measured either the
marginal propensity to consume (MPC) out of housing wealth or the elasticity of household
consumption on household wealth. Most studies have found a sizable and significant housing
wealth coefficient, ranging between 0.04 and 0.09. However, because of data limitations, most
studies have not adequately separated the pure wealth channel from the collateral channel while
properly controlling for the unobserved variables.
The lack of datasets with both consumption and housing wealth information has long
been a major barrier to estimating the housing wealth effect. Previous studies have used either
macro/aggregate-level data or various statistical imputation methods to overcome data
limitations, both of which potentially bias the findings. For example, Mian, Rao, and Sufi (2013)
employed zip-code and county-level datasets to examine the relationship between housing
wealth and consumption. When using aggregated geographic data, researchers cannot control for
heterogeneities in demographic and economic characteristics (e.g., age, income, marital status)
across households, causing endogeneity (Bostic, Gabriel, and Painter, 2009).
Bostic, Gabriel, and Painter (2009) exploited household-level data, by matching the
Survey of Consumer Finances (SCF) with the Consumer Expenditure Survey (CEX) using age,
marital status, race, and education variables. One of the first studies to use micro-level data on
this issue, its major drawback was that the consumption and housing wealth variables were from
different households.
37
More recent studies have imputed either consumption or housing wealth within the same
dataset. Using the Panel Study of Income Dynamics (PSID) between 1968 and 2007, Cooper
(2013) imputes non-housing consumption by subtracting estimated tax and estimated savings
from household income. Before 2005, the PSID did not collect full consumption information and
only provided subcategories, such as food, housing, and health care. Aladangady (2017) uses the
CEX data, which has household-level consumption data but not housing wealth data. Housing
wealth is estimated using the mean value of house prices and changes in the house price index at
the zip code level. In both cases, the statistical imputation could lead to measurement errors and
alter the housing wealth coefficient.
Using the PSID between 2005 and 2015, our study makes several improvements to the
previous studies. Since 2005, the PSID has comprehensively covered household consumption.
Several researchers have compared the dataset with the CEX and have concluded that the major
expenditure components are consistent (Li et al., 2010; Andreski et al., 2014). Additionally, as
the PSID contains rich wealth information by household, we are able to test the relationship
between housing wealth and consumption at the micro level without using any statistical
imputation to measure either households’ housing wealth or their consumption.
Using the panel structure of the data, we also directly control for the household-specific
unobserved factors by including household fixed effects. Once household fixed effects are
included, the housing wealth effect on household consumption becomes significantly smaller
than previously estimated: the elasticity of household consumption on household wealth
decreases from 0.058 to 0.012, and the marginal propensity to consume out of housing wealth
decreases from 0.026 to 0.008. These findings are in line with theoretical models (Flavin and
Nakagawa, 2008; Buiter, 2008) that predict pure housing wealth effects should be small.
38
We are also able to disentangle the pure wealth effect from the collateral effect by
directly controlling for households that extract home equity. The PSID-surveyed participants
provide information on their mortgage type. Thus, we can identify whether their first or second
mortgage is a home equity loan and track changes in the mortgage type. We also follow Zhu et
al. (2019) and use changes in mortgage debt as another proxy for home equity extraction. After
directly controlling for the collateral channel, the pure housing wealth effect on consumption
(elasticity) remains largely unchanged at 0.012.
As expected, we find that households that extracted home equity increase their
consumption, and that households are more likely to extract home equity when their housing
wealth increases. However, we also find that households with higher LTV ratios are less likely to
extract home equity when their house price increases, which is inconsistent with the collateral
channel hypothesis held in previous literature. One interpretation of this finding is that, while
borrowing-constrained households may be able to increase consumption by extracting home
equity, they may be more reluctant to take on additional debt as it will increase their default
propensity. Additionally, households with higher LTV ratios may find it more difficult to extract
their equity, especially when the credit market tightens, and banks become reluctant to lend to
borrowers with higher leverages (Choi, Noh, and Zhu, 2019). Our findings suggest that using
household-level borrowing constraint to disentangle the pure wealth channel and the collateral
channel can lead to inaccurate estimates.
The life-cycle hypothesis and permanent income hypothesis imply that long-term MPC
out of all kinds of wealth equals the annuity value of permanent wealth changes (Modigliani and
Brumberg, 1954; Ando and Modigliani, 1963; Case, Quigley, and Shiller, 2005). Only
permanent changes in housing wealth can shape households’ lifelong consumption patterns.
39
Moreover, the user-cost model suggests that the positive endowment effect of higher housing
wealth is offset by higher costs of living (Sinai and Souleles, 2005; Flavin and Nakagawa, 2008;
Buiter, 2008; Cooper, 2013), indicating no long-term effect on consumption if the shock in
housing wealth is transitory.
According to the extant theory, transitory housing wealth shocks should have no impact
on household consumption after controlling for the collateral channel. In other words,
households should not respond to perceived changes in housing wealth by adjusting their
consumption, and the MPC out of housing wealth should approximate zero. While we find little
impact of housing wealth on consumption, it is important to further distinguish between
households reacting to permanent versus transitory changes in housing wealth. This helps us
understand whether households are changing their consumption based on fundamental changes
or short-term perceptions shaped by house price fluctuations.
To test this theory, we use a unique instrumental variable that measures local housing
price changes based on market fundamentals. This quality-adjusted house value is a good proxy
to capture the fundamental value changes in both land values and housing unit quality over the
analysis period; it captures permanent factors affecting the housing market over 12 years while
maintaining exogenous to transitory local economic shocks. We find evidence that household
consumption changes are largely driven by households’ perception of their housing wealth rather
than local house values that are driven by the shifts in market fundamentals.
Finally, we investigate which consumption categories are most sensitive to changes in
housing wealth. We find that the more auxiliary and one-time consumption categories, such as
recreation and clothing, are more sensitive to changes in income and wealth. Consumption
categories more directly related to basic needs, such as food and transportation, are less sensitive
40
to changes in housing wealth. Consistent with the independent variable (IV) results, this suggests
that a household’s response to housing wealth changes is likely one-time and transitory.
The remainder of the paper proceeds as follows: Section 2 explains the data and
methodology. Section 3 provides baseline results followed by robustness checks, and Section 4
concludes.

3.2 Data and Methodology
3.2.1 Data
We use the Panel Study of Income Dynamics, which has followed a sample of U.S.
households since 1968. Surveys were conducted annually between 1968 and 1997 and biennially
after 1997. The number of surveyed households increased from 4,802 in 1968 to 9,063 in 2013,
as children in the original households became adults and formed households of their own. The
major advantage of the PSID is that it contains extensive information on individual and family
characteristics, including housing, mortgage status, consumption, employment, education level,
health, income, and wealth. The PSID has both family- and individual-level data, enabling us to
use the family as our unit of analysis for income, wealth, and consumption while controlling for
extensive household-level demographic and socioeconomic characteristics based on the unique
ID for each household head. The PSID has also included detailed mortgage information since
2009. In addition, we have access to restricted geo-coded PSID data and thus can use different
proxies of house values with geographic information.
To cover the most recent housing boom and bust cycle and take advantage of the new
consumption data in the PSID, this study examines the relationship between wealth shocks and
consumption behaviors using consumption data from 2005 to 2015 along with income and
41
wealth data from 2003 to 2015. Before 1999, the PSID only included food and housing
expenditures in its consumption component, making the dataset less representative to research
consumption before the recent housing cycle. Since 1999, the PSID has included additional
variables on consumption, including data on transportation, education, childcare, health care, and
entertainment expenditures. Starting in 2005, the consumption data expanded to clothing, home
repair and maintenance, household furnishing, and travel expenses. The updated consumption
data in the PSID makes it a comparable and representative dataset in household consumption
study as the CEX (Li et al., 2010; Attanasio and Pistarferri, 2014).
Our research interest lies not only in examining the impact on total consumption level but
also in detecting where consumption changes occur. We sort consumption into seven categories:
food, housing, transportation, clothing, education, health, and recreation. Figure 2 and Figure 3
illustrate total consumption changes and per capita consumption changes by types of spending
from 2005 to 2015. On average, homeowners’ total consumption increased slightly between
2005 and 2007 and then decreased from 2007 until the housing market started to recover around
2013. Consumption in food and health remained largely stable over time while other
consumption categories showed greater fluctuation.
[Insert Figure 3.2 and Figure 3.3 Here]
Table 1 displays the descriptive statistics. All values are inflation-adjusted to 2015
dollars. The average household consumption for homeowners between 2005 and 2015 was
$56,024. Housing cost accounted for the largest share of consumption ($23,053) followed by
transportation ($11,063), which includes automobile consumption as well as other transportation
expenses. Average financial wealth was about $50,000 higher than average housing wealth. The
standard deviation for financial wealth was more than three times that of housing wealth,
42
showing that financial wealth varied widely across households. The average family income for
homeowners was slightly lower than $100,000.
[Insert Table 3.1 Here]
The average head of household in our sample was 55 years old. Female heads accounted
for less than a quarter of a sample. About 20 percent of the household heads were people of
color, and over 60 percent were married. Close to 60 percent of household heads had received at
least some college education. The average share of unemployed heads of household was lower
than the state unemployment rate, reflecting the fact that homeowners have a lower
unemployment rate than renters. The average family size was 2.43, and about 8 percent of
households had at least one member with a bad health condition. About 13 percent had moved
since the previous period of survey (two years ago). Thirty-two percent of households had
refinanced their mortgage, and about 10 percent held home equity loans. Households with LTV
ratios higher than 80 percent accounted for about 18 percent of the sample.
To check the representativeness of the PSID, we cross-check its wealth variables and age
distribution with the corresponding variables in the SCF. The PSID and the SCF have different
survey years: the PSID provides biennial data while the SCF data are triennial. For the PSID we
use data for 2005, 2007, 2009, 2011, 2013, and 2015; for the SCF we use data for 2004, 2007,
2010, 2013, and 2016. Table 2 and Figure 4 display the results of the cross-check. These two
datasets share a similar age distribution among homeowners, as well as comparable magnitudes
and volatilities in both housing wealth and total wealth.
[Insert Table 3.2 and Figure 3.4 Here]
3.2.2 Model Specification
In this paper, we employ a step-by-step analysis to show how the housing wealth effect
decreases as biases from unobserved variables are properly addressed. We start with the OLS
43
regression as our baseline model to compare our estimates with previous literature. Following
Lehnert (2004), Campbell and Cocco (2007) and Bostic, Gabriel, and Painter (2009), the basic
regression model to estimate the elasticity of consumption with respect to wealth and income is
the following:
𝑙𝑛𝐶
(!
=𝛼+𝛽𝑙𝑛𝐻𝑊
(!
+𝛾𝑙𝑛𝐹𝑊
(!
+𝜂∆𝑌
(!
+𝛿𝑋
(!
+𝜇
)
+𝜋
!
+𝜀
(!

We take a logarithmic transformation to linearize consumption, housing wealth, financial
wealth, and income variables. 𝐶
(!
is non-housing total consumption for household i at time t.
𝐻𝑊
(!
,𝐹𝑊
(!
, and 𝑌
(!
are housing wealth, financial wealth, and household income for household i
at time t. 𝑋
(!
is a vector of demographic controls including age, race, marital status, the presence
of children, household size, household members’ health status, whether the household moved
between survey years, and unemployment status. Given that we are focusing on homeowners,
our OLS regression may have selection bias; we include inverse mills ratio derived from a tenure
choice probit model in OLS regression as part of our robustness checks. 𝛽 and 𝛾 are the two
coefficients of interest that estimate the consumption elasticity for housing wealth and financial
wealth. We also control for the state (𝜇
)
) and year fixed effects (𝜋
!
). To address the potential
impact of outliers in wealth variables, we conduct a median regression following the OLS
regression.
In addition to the consumption elasticity, we estimate the MPC of housing wealth, to
show how a dollar increase in housing wealth affects household consumption. These dollar-to-
dollar comparisons enable us to compare our results with some of the prior studies, such as Mian
and Sufi (2009) and Aladangady (2017), that measured MPC to estimate the housing wealth
effect.
44
Using the longitudinal data structure of the PSID, we then move on to fixed-effect
models to control for those unobserved time-invariant preferences and other household-level
factors that significantly alter consumption behaviors. We add direct measurements (two proxies)
on the collateral channel in the fixed-effect model, and we examine the relationship between the
borrowing constraint and the likelihood of extracting home equity. Following the fixed-effect
model, we employ an IV approach to address the endogeneity in housing wealth shocks and
disentangle transitory and permanent housing wealth shocks.

3.3 Results
3.3.1 Elasticity Results
Table 3 presents the results estimating the non-housing consumption elasticity relative to
housing wealth. The OLS result in column 1 shows that a 1 percent increase in housing wealth is
associated with a 0.058 percent increase in consumption. This number is similar to Bostic,
Gabriel, and Painter (2009), whose housing wealth elasticity is around 0.06. The coefficients of
financial and family wealth are 0.043 and 0.362, respectively. All coefficients are statistically
significant. Column f2 presents the result using the median regression to see if the OLS results
are driven by outliers. The coefficients of housing wealth and financial wealth decrease by about
0.015 percentage points, but the coefficient for the family income increases.
1
Given that we are
focusing on homeowners, our OLS regression may have selection bias, so we also include
inverse mills ratio derived from a tenure choice probit model in OLS regression as part of our

1 As for other control variables, we find that consumption increases with age and family size. In addition, increases in state
unemployment rates negatively affect household consumption. Other variables are statistically insignificant.
45
robustness checks, shown in Appendix Table A1. We find that our results remain largely
unchanged.
[Insert Table 3.3 Here]
Both the OLS and the median regressions do not address unobserved household factors,
such as spending disposition, that may bias the result. Column 3 shows the results of a fixed-
effect regression that includes household dummies. The coefficient shows how changes in
housing wealth affect consumption within the same household. Once household dummies are
included, the housing wealth elasticity coefficient drops significantly to 0.012. However, the
coefficient for financial wealth does not show much difference from the median regression in
column 2. The remaining two columns show the housing wealth effect after directly controlling
for the collateral channel. Prior studies (e.g., Bostic, Gabriel, and Painter, 2009; Cooper, 2013;
Aladangady, 2017) tried to disentangle pure wealth effect from collateral by comparing housing
wealth coefficients across households with different borrowing constraint levels – measured by
such indicators as LTV ratio or debt service ratios. However, this method does not clearly
separate the two effects. The method does not directly control for households that extracted
home equity, and the interpretation of the results depends on how the level of borrowing
constraint relates to the likelihood of extracting a home equity loan. Rather than looking at the
size of the housing wealth coefficient across different groups of households, we directly control
for the borrowing collateral channel using the two proxies of home equity extraction. Once the
borrowing collateral channel is controlled, the housing wealth coefficient measures the pure
housing wealth effect on consumption.
46
We directly control for the borrowing collateral channel using the two proxies of home
equity extraction. Once the borrowing collateral channel is controlled, the housing wealth
coefficient measures the pure housing wealth effect on consumption.
The first home equity extraction proxy is measured using the type of mortgage reported by the
household. Since 1996, the PSID has asked whether the first or the second mortgage is a home
mortgage, a land contract, or a home equity loan. If households responded that any of their
mortgages are home equity loans, we assign a dummy variable 1 and define these households as
having extracted a home equity loan. Our second proxy follows Zhu et al. (2019) and defines
households as having extracted home equity if their mortgage debt increased from the previous
period. In contrast to Zhu et al. (2019), we exclude households whose mortgage debt increased
because of moving, as they are not tapping into their home equity to obtain additional cash.
Columns 4 and 5 show that both coefficients of the home equity extraction proxies are positive
and significant, suggesting that households that extract home equity consume more, agreeing
with the collateral channel. However, including the two dummies does not change the
relationship between housing wealth and consumption shown in column 3. The pure housing
wealth elasticity is estimated at 0.012–0.013. This number is statistically significant, but the size
is smaller than most of the previous empirical results, corresponding to the theoretical
predictions.
3.3.2 MPC Results
Table 4 shows the results that estimate the MPC on housing wealth. The OLS result in
column 1 shows that a one-dollar increase in housing wealth is associated with a 2.6-cent
increase in non-housing consumption. This number is similar to the OLS results in Aladangady
(2017), which finds MPC out of housing wealth is 2.5 cents, and smaller than the results of Mian
47
and Sufi (2003), which finds an MPC of 5–7 cents. However, the unit of analysis in Mian and
Sufi’s paper is the zip code, which does not allow them to control for household-level
characteristics correlated with both housing wealth and consumption.
[Insert Table 3.3.4 Here]
The housing wealth coefficient from the median regression in column 2 decreases,
similar to the elasticity results in Table 3. This coefficient further decreases to 0.008 once
household-level fixed effects are included (columns 3–5). This again is in line with the results in
Table 3 showing the pure housing wealth effect is small.
The MPC on family income is larger than on housing wealth (similar to the results in
Table 3) but the MPC on financial wealth is smaller than on housing wealth. This is related to
our findings in the descriptive statistics in Table 1, which showed that financial wealth has a
significantly higher standard deviation than housing wealth. Almost 50 percent of our sample
households have financial wealth below $10,000 while 25 percent of households have financial
wealth greater than $100,000. This means that a percentage increase in financial wealth is greater
than a percentage increase in housing wealth, resulting in a larger elasticity of consumption on
financial wealth (Table 3). However, as the majority of households have smaller financial
wealth, relative to income or housing wealth, small changes in financial wealth are unlikely to
noticeably affect consumption. Since the relationship between housing wealth and non-housing
consumption shows a similar pattern between Table 3 and Table 4, we focus on the elasticity
measure in the remaining analyses.
48
Columns 4 and 5 of Table 4 show that households extracting home equity increase their
consumption. The size of the coefficient and the statistical significance are larger for the first
measure of home equity extraction.
Our results differ from Aladangady (2017) who shows that MPC increases from 0.026 in the
OLS results to 0.047 in the IV results. The study uses the interaction between long-term interest
rates and both MSA-level land unavailability and zoning/land use regulation from Saiz (2010) as
IVs. The result is puzzling because the OLS coefficients are likely biased upward. If the two IVs
properly address the unobserved shifts in preferences and expected economic prospects that are
likely to be positively correlated with both house price and consumption changes, the housing
wealth coefficients in the IV regression would decrease.
Aladangady’s study states that the instruments are valid as long as consumption
responses to interest rate shocks do not vary systematically with housing supply variables.
However, we argue that these instruments are invalid since households are likely to
systematically adjust their responses to interest rates depending on the housing supply elasticity
where they live. For example, if an interest rate decline increases housing demand, households
living in areas where the housing supply is inelastic will expect their house price to go up more
than those living in places where housing supply is elastic. Homeowners who expect their house
value to go up more in the future and realize greater gain when they sell their house are more
likely to increase their consumption. This explains why the housing wealth coefficient in
Aladangady’s paper was only significant for homeowners in the IV results and insignificant for
renters. The MPC in the IV results of Aladangady’s paper is likely inflated since it amplifies the
effect of the future house price expectation.
49
3.3.3 Housing Wealth and Home Equity Extraction
Before proceeding to the robustness check, we look into the collateral channel by
examining how borrowing constraints affect the likelihood of extracting home equity. While
those with higher debt and few financial resources can be more inclined to extract home equity
when additional cash is needed, they may also be reluctant to do so as taking additional debt
increases their default probability. Additionally, when economic conditions worsen, lenders tend
to tighten credit, which makes it difficult for those with higher leverage to extract home equity.
(Choi, Noh, and Zhu, 2019). Therefore, the relationship between borrowing constraint and home
equity extraction is less clear than what prior studies have assumed.
Table 5 presents the result of the logit regression where the dependent variables are the
two proxies of home equity extraction: (1) household reported its mortgage type changed to
home equity loan or (2) mortgage debt increased from the previous period for households that
did not move. As taking out a home equity loan affects current housing wealth, we use the lag
value of housing wealth growth to examine the relationship between housing wealth growth and
the likelihood of extracting home equity. We use the LTV to estimate the level of borrowing
constraint. If the LTV ratio is greater than 80 percent, then the household is defined as borrowing
constrained. This dummy variable is interacted with the lag housing wealth growth to identify
whether the constrained households are more likely to extract their home equity when their
housing wealth increase. The logit regression controls for additional factors that may affect home
equity extraction such as age, race and ethnicity, marital status, education level, employment
status, and changes in family size. Financial wealth and family income, as well as changes in
family income and financial wealth, are also included.
[Insert Table 3.5 Here]
50
We find that homeowners are more likely to extract their home equity when their housing
wealth increased for both proxies of home equity extraction (columns 1 and 3). This supports the
existence of the collateral channel. However, columns 2and 4 show that those with higher LTV
ratios are less likely to extract home equity. Further, the interaction term shows that those with
lower LTV ratios are much more likely to extract home equity when housing wealth increases.
2

The results suggest that households that already have high mortgage debt are more cautious of
taking additional mortgage debt or face greater barriers to extracting their home equity. This is
opposite to the assumptions previous studies have made to separate the pure wealth and the
collateral channels (Bostic, Gabriel, and Painter, 2009; Cooper, 2013; Aladangady, 2017). Our
results show that using the level of borrowing constraint as a proxy for extracting home equity
can lead to inaccurate findings.
3.3.4 Robustness Check
Table 6 provides additional tests to check the robustness of the estimates in Table 3 that
looked at the elasticity of non-housing consumption on housing wealth. First, housing wealth and
consumption can both be correlated with expected future income. For example, households that
expect their future income growth to be higher could have a larger consumption response to their
housing wealth than those with lower expectations of future income growth. This can inflate our
housing wealth coefficient. We follow Cooper (2013) and include a two-year ahead income
growth to capture the expectation of households. Agreeing with Cooper (2013), we find that the
expected future income does not change the relationship between housing wealth and

2 As for other variables we find that likelihood of extracting home equity increases with age, but the
effect becomes smaller as people become older. Those who have never married are less likely to extract
home equity. Those with greater wealth are less likely to extract home equity, but those with higher
income are more likely to do so. Other variables are statically insignificant.
51
consumption (column 2). The expected income coefficient is positive and significant, showing
that households that expect their income to increase spend more.
[Insert Table 3.6 Here]
Columns 3 and 4 examine whether the housing wealth effect differs between working-age
households and households that have retired. Once the collateral channel is controlled for, the
retired should have smaller housing wealth elasticity since they are significantly less likely to
move and obtain housing wealth increases. While downsizing may provide financial benefits for
older households, the proportion of older households that move decreases over time (Zhu and
Painter, 2020). More than 95 percent of households over age 65 live in the same house since the
last survey period; this share is even higher for homeowners (Choi, Noh, and Zhu, 2019). The
results in the two columns show that the pure housing wealth effect is larger for the working-age
population: the elasticity for those between ages 25 and 65 is 0.016, while that of those over age
65 is 0.011 and statistically insignificant.
The tight credit condition following the housing market crisis could affect the
consumption response to changes in housing wealth. However, once the collateral channel is
controlled for, it is unclear why the pure wealth effect would differ across time. As the PSID
provides full consumption data starting in 2005, we cannot use these data to compare the housing
wealth coefficient before and after the crisis. To address this issue, we use a subset of the
consumption data obtainable from 1999. This subset excludes clothing and recreation
consumption. In column 5, we use this variable to estimate the housing wealth effect for 2005–
15 to compare the coefficient with our base result. The housing wealth elasticity drops slightly to
0.011, and the statistical significance decreases, but the results remain largely similar. Using this
consumption variable, we compare the housing wealth effect between 1999–2007 and 2009–15.
52
The elasticity measure is 0.013 before the housing market crisis and 0.010 after. Both
coefficients are insignificant, which is likely a result of the inaccurate consumption measure and
smaller sample sizes. We cannot reject the hypothesis that the two coefficients are statistically
different, suggesting that the size of the pure wealth effect does not differ across time. On the
other hand, we find that households that extracted home equity increased their consumption after
the crisis.
Finally, we use a different proxy to measure housing wealth. In addition to the self-
reported house value, we use the HPI-adjusted house value to measure housing wealth. Using the
geocoded PSID data, we appreciate the initial sales price by the zip code HPI provided by the
Federal Housing Finance Agency (FHFA). Households are likely to report their house price as
higher than the estimated house price (Kain and Quigley, 1972; Goodman and Ittner, 1992;
Benítez-Silva et al.,2015, Choi and Painter, 2018). While it is questionable which measure is
more accurate, once the collateral channel is controlled for, the difference between the results
using two different home prices shows whether households adjust their consumption to the
housing wealth value they perceive or to the market-based house estimate. Columns 8 and 9
show that the coefficient for the housing wealth variable is greater for the measure using the self-
reported house value than measure using the HPI-adjusted house value. The smaller sample size
leads to less statistical precision, but the housing wealth elasticity using the self-reported house
value remains at 0.012. In contrast, the elasticity for the estimated housing wealth value is 0.006
and statistically insignificant. The results suggest that households that perceive an increase of
housing wealth are likely to adjust their consumption upward, although the adjustment is small.
3.5 Disentangling Permanent and Transitory Housing Wealth Shock: IV Approach
53
While our estimates show that households’ consumption increases slightly as housing
wealth increases, it is uncertain whether this change is the result of permanent or transitory
wealth shock. We employ a quality-adjusted local hedonic house price constructed in Green and
Zhu (2018) to instrument for the permanent changes in house values. The model specification for
constructing this house value follows the general hedonic regression modeling procedure in
Malpezzi, Chun, and Green (1998) as follows:
Log𝑅 =𝛽
*
+𝛽
&
𝑆+𝛽
+
𝑁+𝛽
,
𝑆+𝛽
-
𝐿+𝛽
.
𝐶+𝜀
where
R = housing values;
S = structural characteristics;
N = neighborhood characteristics;
L =geographical characteristics within the market; and
C = contract characteristics, such as utilities included in rent
The structural, neighborhood, geographical, and contract-related characteristics variables
are obtained from the American Community Survey, between 2005 and 2016. β
/
(i > 0) is the
hedonic regression coefficient, capturing the implicit marginal prices of these hedonic attributes.
This specification process is conducted for each MSA over time. The estimated coefficients are
then used to construct a place-to-place price index for a constant quality dwelling by the
following steps. First, we bundle a set of hedonic variables
3
significantly explaining the
variations in house prices. Second, for each selected hedonic variable, we take the population-
weighted grand mean of 348 MSAs over 12 years from 2005 to 2016. The goal of this step is to

3 Those hedonic variables include property type, number of bedrooms, complete kitchen, complete
plumbing, built year, move-in date, number of person per room, and we control for location at PUMA
level.
54
construct a national representative quality-adjusted housing unit. Changes in house prices of
quality-adjusted units capture more of the permanent and fundamental changes in the housing
market. Third, we multiply the grand means with the estimated coefficients for each MSA each
year. Fourth, we take the exponential value of the summation number to get back to dollar values
given the semi-log form of rents or housing values.
This quality-adjusted house value is a good proxy to capture fundamental value changes
in both land values and housing unit quality over time because it captures permanent factors
affecting the housing market over 12 years while maintaining exogenous to transitory local
economic shocks. Comparisons between our quality-adjusted house price index and FHFA house
price index for three selected MSAs—Houston, Atlanta, and San Francisco—are shown in
Appendix Figure A1. The graph shows that the discrepancy between our quality-adjusted HPI
and the FHFA HPI became greater during the recovery period after the Great Recession than in
the housing bust period. We use the log value of the quality-adjusted house value as the
instrument of housing wealth changes to disentangle transitory shocks from permanent housing
wealth shocks.
The results are shown in Table 7. The first stage regression results in column 1 show that
our quality-adjusted HPI is a strong predictor of the housing wealth changes. Using this IV we
find that the housing wealth elasticity becomes insignificant. This finding sheds light on the
possibility that the consumption response in face of perceived housing wealth shocks, if there is
any, might be based not on fundamental changes in housing wealth but on household’s
expectations of their future housing wealth fluctuations. For an average household,
distinguishing between changes in housing wealth driven by the market fundamentals and
transitory fluctuations is difficult. In the short run, if households observe an increase in home
55
equity, they may adjust their consumption accordingly. In the long run, however, households
would have to readjust their consumption once they realize their perceived house values have
deviated from the fundamental equilibrium values. Our IV result suggests that the deviation
between perceived house price appreciation rate and the real house price appreciation rate in
fundamental values generates a small magnitude of housing wealth elasticity in the short run, but
the wealth effect will move toward zero in the long run as perceived values converge with true
values.
[Insert Table 7 Here]
3.3.6 Heterogeneity in the Subcategories of Consumption
Finally, we examine whether there is heterogeneity in housing wealth elasticities across
six consumption categories: food, clothing, education, health, transportation, and recreation.
Because housing wealth is less liquid than financial wealth and income (especially when the
collateral channel is controlled for), households may adjust different consumption categories
when housing wealth increases versus when financial wealth and income increase. Table 8 shows
that only clothing and recreation spending increase in response to housing wealth increases. A 1
percent increase in housing wealth leads to a 0.026 percent increase in clothing consumption and
a 0.023 increase in recreation consumption. Other consumption categories including food, health,
and transportation do not show any statistically significant response to changes in housing
wealth.
[Insert Table 8 Here]
On the other hand, households increase their spending on all consumption categories as
their income rises, and they increase all consumption except education as their financial wealth
increases. Overall, our findings suggest when perceived housing wealth increases, households
adjust their consumption slightly upward as their expected future wealth increases, and this
56
consumption adjustment occurs in clothing and recreation, which are more likely to be one-time
and auxiliary expenses compared to consumption such as food and transportation. In addition,
we find that people who extract home equity increase their spending on health and recreation.
Our results suggest that households use their housing wealth to serve specific consumption needs
rather than to increase consumption broadly.

3.4. Conclusion
Using the PSID, we find that households increase their consumption, albeit only slightly,
as their perceived housing wealth increases. In response to the housing wealth increase, they buy
more clothing and spend more on recreation, but spending in other areas remain largely
unchanged. We also find that households extract their home equity to serve medical needs, which
are more likely to be one-time large expenditures. Consumption out of housing wealth differs
from financial wealth and income, which are more liquid. When financial wealth or income
increases, consumption increases in all categories. This suggests that households’ perception and
use of housing wealth differs from use of financial wealth and income.
Our findings agree with theoretical predictions that indicate housing wealth is not wealth, and
therefore the pure wealth effect should be small or insignificant. While the elasticity of
consumption relative to housing wealth is around 0.012, we find that this is not based on changes
in the fundamental changes in housing wealth but on households’ views toward their housing
wealth. When we use the estimated HPI or the IV approach, we find that the pure housing wealth
effect is zero. This suggests that housing market conditions alter households’ perceptions of their
house value and affect consumption. Our results also show that households’ perception of their
housing wealth is not based on the fundamental market value of their house. In the long run,
57
households may have to readjust their consumption as they realize that their expectation of their
future housing wealth did not match the real value.
58
3.5 Tables and Figures
Figure 3.1 Annual Percentage Change in House Price Index and Personal
Consumption

Source: FRED Economic Data.

Figure 3.2 Annual Consumption Over Time for Homeowners (2015 inflation-
adjusted dollars)

Source: Panel Study of Income Dynamics.

-10
-5
0
5
10
15
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
2014
2016
2018
∆ Personal Consumption Expenditure (%) ∆ House Price Index -All Transaction (%)
59
Figure 3.3 Homeowners’ per Capita Consumption Over Time by Spending Type

Source: Panel Study of Income Dynamics.

60
Figure 3.4 Total Wealth and Housing Wealth for Homeowners Over Time

Sources: Panel Study of Income Dynamics and Survey of Consumer Finances.

225,480
239,560
194,700
173,145 174,420
188,500
230,200
266,634
187,408
197,549
226,792
0
50,000
100,000
150,000
200,000
250,000
300,000
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
TOTAL WEALTH
PSID SCF
108,000
114,130
96,250
89,250
86,700
99,000
107,186
119,160
81,242 80,838
98,000
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
HOUSING WEALTH
PSID SCF
61
Table 3.1 Descriptive Statistics
Variable Mean Std. Dev. Median Std. Dev.
Consumption ($)
Total Consumption 56024 54687 58206 55726
Food 8552 5473 8749 5469
Housing 23053 25686 23820 26788
Clothing 1773 5919 1881 6471
Health 4511 6182 4748 5823
Education 2879 32893 3051 32611
Transportation 11063 12170 11400 12531
Recreation 3683 8353 4024 8833
Wealth & Income ($)
Total Wealth 568089 2079368 629853 1935721
Housing Wealth 167612 255633 188040 270718
Financial Wealth 220662 825534 255906 888082
Family Income 98086 141309 106134 152942
Demographic & Socioeconomic
Age (years) 55.5 16.0 55.8 15.8
Female 0.23 0.42 0.22 0.41
Race and Ethnicity

Black 0.09 0.29 0.06 0.23

Hispanic 0.08 0.27 0.05 0.22

Asian/Others 0.03 0.17 0.03 0.18
Marital Status

Never Married 0.09 0.28 0.08 0.28

Widowed 0.12 0.32 0.11 0.31

Divorced or Separated 0.16 0.37 0.16 0.36
Education

High School 0.31 0.46 0.29 0.45

Some College 0.23 0.42 0.24 0.43

College or More 0.36 0.48 0.40 0.49
Unemployed 0.03 0.17 0.03 0.16
Family Size (persons) 2.43 1.34 2.39 1.28
Family Member with Bad Health 0.08 0.27 0.07 0.26
Moved since Previous Survey 0.13 0.33 0.12 0.33
Mortgage
Refinanced 0.32 0.47 0.34 0.47
Home Equity Loan 0.10 0.31 0.11 0.31
Loan-to-Value > 80 0.18 0.39 0.14 0.35
State
State Unemployment Rate 0.07 0.02 0.07 0.02
62
Observations 28,839 21,399

Table 3.2 Cross-Check of PSID with SCF: Age Distribution of Homeowners (weighted)
40 or Younger 41–62 62 or Older
PSID 20% 44.66% 35.34%
SCF 21.7% 44.7% 33.7%

Table 3.3 Housing Wealth and Personal Consumption: Elasticity Results
(1) (2) (3) (4) (5)
VARIABLES OLS Median
Fixed
Effects
Fixed
Effects
Fixed
Effects

Log(housing wealth) 0.058*** 0.044*** 0.012** 0.012** 0.013**
(0.006) (0.004) (0.005) (0.005) (0.005)
Log(financial wealth) 0.043*** 0.028*** 0.030*** 0.030*** 0.030***
(0.004) (0.002) (0.003) (0.003) (0.003)
Log(family income) 0.362*** 0.434*** 0.138*** 0.138*** 0.138***
(0.018) (0.007) (0.014) (0.014) (0.014)
Extract home equity I

0.031***

(0.012)

Extract home equity II

0.020**

(0.010)
Control variable Y Y Y Y Y
State unemployment
rate Y Y Y Y Y
Year fixed effects Y Y Y Y Y
State fixed effects Y Y Y Y Y
Observations 21,282 21,282 21,282 21,282 21,282
R-squared 0.515

0.100 0.101 0.101
Notes: Dependent variable is the log value of non-housing consumption. The first proxy of home equity extraction is measured
using the household’s reported mortgage type; the second is measured using changes in the remaining mortgage principal for
non-movers. Household-level control variables include head’s age, head’s age

squared, family size, a dummy variable that equals
1 if any family member has bad health status, a dummy variable for moving, and head’s unemployment status. The state
unemployment rate is also included in all regressions. Standard errors are clustered by the household head’s identification
number. (*** p<0.01, ** p<0.05, * p<0.1).

63
Table 3.4 Housing Wealth and Personal Consumption: MPC Results
(1) (2) (3) (4) (5)
VARIABLES OLS Median
Fixed
Effects
Fixed
Effects
Fixed
Effects

Housing wealth 0.026*** 0.012*** 0.008** 0.008** 0.008**
(0.005) (0.001) (0.004) (0.004) (0.004)
Financial wealth 0.001 0.001 0.003** 0.003** 0.003**
(0.002) (0.001) (0.001) (0.001) (0.001)
Family income 0.070*** 0.132*** 0.029*** 0.029*** 0.029***
(0.012) (0.003) (0.011) (0.011) (0.011)
Extract home equity I

1,978**

(840.4)

Extract home equity II

992.0

(885.7)
Control variable Y Y Y Y Y
State unemployment
rate
Y Y Y Y Y
Year fixed effects Y Y Y Y Y
State fixed effects Y Y Y Y Y
Observations 26,744 26,744 26,744 26,744 26,744
R-squared 0.131 0.019 0.020 0.020
Notes: Dependent variable is the dollar value of non-housing consumption. The first proxy of home equity extraction is measured
using the household’s reported mortgage type; the second is measured using changes in the remaining mortgage principal for
non-movers. Household-level control variables include head’s age, head’s age

squared, family size, a dummy variable that equals
1 if any family member has bad health status, a dummy variable for moving, and head’s unemployment status. The state
unemployment rate is also included in all regressions. Standard errors are clustered by the household head’s identification
number. (*** p<0.01, ** p<0.05, * p<0.1).

64

Table 3.5 Housing Wealth and Home Equity Extraction: Logit Model
(1) (2) (3) (4)
VARIABLES
Obtained Home
Equity Loan Mortgage Debt Increased
L1_∆ Log (housing wealth) 0.144** 0.194*** 0.297*** 0.306***
(0.061) (0.066) (0.040) (0.047)
L1_LTV>80 -0.265* -0.732***
(0.153) (0.118)
L1_LTV>80# L1_∆ Log (housing
wealth) -0.241* -0.268***
(0.139) (0.094)
Demographic and socioeconomic
characteristics Y Y Y Y
Wealth and income Y Y Y Y
Year fixed effects Y Y Y Y
State fixed effects Y Y Y Y
Observations 13,108 13,108 13,154 13,154
Notes: Dependent variable is 1 if household extracted home equity. For columns 1 and 2, we consider households to have
extracted home equity if the mortgage type for either a first or second loan switched to a home equity loan, or if mortgage debt
increased from the prior survey year. Respondents’ whose mortgage debt increased because of moving are excluded. Control
variables include head’s age, head’s age

squared, race and ethnicity, marital status, education level, employment status, and
change in family size. Total household wealth and income, as well as changes in financial wealth and family income, are also
included. Standard errors are clustered by the household head’s identification number. (*** p<0.01, ** p<0.05, * p<0.1).

65
Table 3.6 Housing Wealth and Personal Consumption: Robustness Check
(1) (2) (3) (4) (5) (6) (7) (8) (9)

Base
Expected
Income
Age Group Pre-Post Crisis House Wealth Estimate
25–65 >65
2005–
2015
1999–
2007
2009–
2015 Reported Estimated

Log(housing wealth)
0.012** 0.013** 0.016** 0.011 0.011* 0.013 0.010 0.012*

(0.005) (0.006) (0.007) (0.023) (0.006) (0.008) (0.006) (0.007)

Log(zip code HPI
adjusted housing
wealth)

0.006

(0.007)
Log(financial wealth) 0.030*** 0.028*** 0.035*** 0.026*** 0.024*** 0.022*** 0.019*** 0.028*** 0.028***

(0.003) (0.003) (0.004) (0.010) (0.003) (0.004) (0.003) (0.004) (0.004)
Log(family income) 0.138*** 0.186*** 0.124*** 0.081*** 0.122*** 0.082*** 0.104*** 0.142*** 0.142***

(0.014) (0.021) (0.031) (0.024) (0.014) (0.020) (0.012) (0.020) (0.020)
Extracted home equity 0.031*** 0.027** 0.026* 0.047 0.033*** -0.005 0.045** 0.031** 0.031**

(0.012) (0.013) (0.014) (0.043) (0.012) (0.014) (0.018) (0.014) (0.014)
Expected income
growth 0.065***

(0.011)

Control variable Y Y Y Y Y Y Y Y Y
State unemployment
rate
Y Y Y Y Y Y Y Y Y
Year fixed effects Y Y Y Y Y Y Y Y Y
State fixed effects Y Y Y Y Y Y Y Y Y
Observations
21,282 16,568 17,326 3,703 21,281 17,918 13,753 12,681 12,681
R-squared 0.101 0.084 0.096 0.127 0.083 0.063 0.061 0.099 0.099
Notes: Dependent variable is the log value of non-housing consumption. The proxy of home equity extraction is measured using the household’s reported mortgage type.
Household-level control variables include head’s age, head’s age

squared, family size, a dummy variable that equals 1 if any family member has bad health status, a dummy
variable for moving, and head’s unemployment status. The state unemployment rate is also included in all regressions. Standard errors are clustered by the household head’s
identification number. (*** p<0.01, ** p<0.05, * p<0.1).
66

Table 3.7 Housing Wealth and Personal Consumption: IV Approach
(1) (2) (3)
First Stage Fixed Effect
Fixed Effect
with IV

Log(Quality Adjusted House
Price)
0.833***
(0.070)
Log(housing wealth) 0.011* -0.053

(0.006) (0.044)
Log(financial wealth) 0.031*** 0.032***

(0.003) (0.004)
Log(family income) 0.146*** 0.147***

(0.016) (0.017)
Extracted home equity 0.034*** 0.029***

(0.013) (0.013)
Control variable Y Y Y
State unemployment rate Y Y Y
Year fixed effects Y Y Y
State fixed effects Y Y Y
Observations 16,978 16,978 16,978
F-statistic 103.46
R-squared 0.305
Notes: Dependent variable is the log value of housing wealth for column (1) and the log value of non-housing consumption for
columns (2) and (3). The proxy of home equity extraction is measured using the household’s reported mortgage type. Household-
level control variables include head’s age, head’s age

squared, family size, a dummy variable that equals 1 if any family member
has bad health status, a dummy variable for moving, and head’s unemployment status. The state unemployment rate is also
included in all regressions. Standard errors are clustered by the household head’s identification number. (*** p<0.01, ** p<0.05,
* p<0.1).

67

Table 3.8 Housing Wealth and Personal Consumption: Subcategories
(1) (2) (3) (4) (5) (6)
VARIABLES Food Clothing Health Education Transportation Recreation

Log(housing wealth) 0.009 0.026** 0.000 0.022 0.002 0.023*
(0.006) (0.011) (0.013) (0.043) (0.009) (0.013)
Log(financial wealth) 0.023*** 0.045*** 0.037*** 0.010 0.022*** 0.068***
(0.003) (0.006) (0.006) (0.021) (0.005) (0.007)
Log(family income) 0.099*** 0.188*** 0.047** 0.198*** 0.164*** 0.261***
(0.011) (0.023) (0.023) (0.073) (0.020) (0.025)
Extracted home
equity 0.006 0.009 0.087*** 0.106 0.010 0.055**
(0.011) (0.023) (0.028) (0.088) (0.020) (0.027)
Control variable Y Y Y Y Y Y
Year fixed effects Y Y Y Y Y Y
State fixed effects Y Y Y Y Y Y
Observations 21,228 20,617 20,639 6,742 20,963 19,665
R-squared 0.075 0.081 0.069 0.073 0.045 0.049
Number of IDs 6,674 6,587 6,541 3,351 6,626 6,337
Notes: Dependent variable is the log value of each consumption category. The proxy of home equity extraction is measured using the household’s reported mortgage type.
Household-level control variables include head’s age, head’s age squared, family size, a dummy variable that equals 1 if any family member has bad health status, a dummy
variable for moving, and head’s unemployment status. The state unemployment rate is also included in all regressions. Standard errors are clustered by the household head’s
identification (ID) number. (*** p<0.01, ** p<0.05, * p<0.1).

68

Appendix
Table A1. Housing Wealth and Consumption: Inverse Mills Ratio
(1) (2)
VARIABLES OLS Median

Log(housing wealth) 0.060*** 0.044***
(0.006) (0.004)
Log(financial wealth) 0.042*** 0.026***
(0.004) (0.002)
Log(family income) 0.316*** 0.387***
(0.016) (0.009)
Inverse Mills Ratio
-
0.228***
-
0.233***
(0.074) (0.032)
Control variable Y Y
State unemployment rate Y Y
Year fixed effects Y Y
State fixed effects Y Y
Observations 20,716 20,716
R-squared 0.518
Notes: Dependent variable is the log value of non-housing consumption. Household-level control variables include head’s age,
head’s age

squared, family size, a dummy variable that equals 1 if any family member has bad health status, a dummy variable
for moving, and head’s unemployment status. The state unemployment rate is also included in all regressions. Standard errors are
clustered by the household head’s identification number. (*** p<0.01, ** p<0.05, * p<0.1).

69
Table A2. Housing Wealth and Personal Consumption: Weighted Fixed Effects
(1) (2)

Log(housing wealth) 0.015** 0.016**
(0.007) (0.007)
Log(financial wealth) 0.032*** 0.032***
(0.004) (0.004)
Log(family income) 0.117*** 0.116***
(0.022) (0.022)
Extracted home equity

0.028**
(0.013)
Year fixed effects Y Y
State fixed effects Y Y
Observations 21,282 21,282
R-squared 0.102 0.102
Notes: Dependent variable is the log value of non-housing consumption. The proxy of home equity extraction is measured using
the household’s reported mortgage type. Household-level control variables include head’s age, head’s age

squared, family size, a
dummy variable that equals 1 if any family member has bad health status, a dummy variable for moving, and head’s
unemployment status. The state unemployment rate is also included in all regressions. Standard errors are clustered by the
household head’s identification number. (*** p<0.01, ** p<0.05, * p<0.1).

70
Figure A1. Comparisons of FHFA HPI and Quality-Adjusted HPI: Selected MSAs

Sources: FHFA and authors’ calculations using the ACS.

0
50
100
150
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Houston-The Woodlands-Sugarland
FHFA HPI Quality-adjusted HPI
0
50
100
150
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
San Francisco-Oakland-Hayward
FHFA HPI Quality-adjusted HPI
0
20
40
60
80
100
120
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Atlanta-Sandy Springs-Roswell
FHFA HPI Quality-adjusted HPI
71

Chapter 4
The Feasibility of Reverse Mortgages in Japan

Richard K. Green, and Linna Zhu
Price School of Public Policy
University of Southern California

Abstract
This paper examines the feasibility of reverse mortgages in Japan by utilizing stochastic modeling
to characterize the movements of three stochastic variables—interest rates, property values and
mortality—the fundamentals of reverse mortgages. We use the yield curve to forecast future
interest rates, taking into account the interest arbitrage condition and the term premium. We
employ hedonic modeling to develop a house price index for Japan, and then use two time series
methods—Brownian Motion and Bootstrapping—to forecast house prices. We take the Japanese
Ministry of Health, Labor and Welfare life expectancy tables to model mortality. We then integrate
these three variables into our default risk estimation model in which we predict the magnitude of
potential losses associated with default risk. Our simulation results show that home equity
withdrawal rates matter significantly in determining the magnitude of tail risk. Lines of credit plans
increase the feasibility of reverse mortgages relative to lump-sum plans in Japan. We also examine
the impact of raising the mortgage insurance premiums paid by borrowers on feasibility. Higher
premiums add cash to the default insurance pool, but also slightly raise the risk of default.

Keywords: Reverse Mortgages, Aging in Place, Housing Wealth

72
4.1 Introduction
Japan faces a problem many other countries face, only more so. The elderly share of
Japan’s population is rising rapidly, in part because of low birth rates, in part because of very low
levels of immigration, and in part because people in Japan live longer than any other country that
isn’t very small. The last of these is, of course, good news—long, healthy lives are things that
species strive for. But a rapidly aging population puts financial pressure on societies, as the share
of people working falls relative to the share of people receiving old-age benefits. The extraordinary
demographic characteristics of Japan have been well documented in many other papers (Kitao,
2015; Hansen and Selahattin, 2016), and so we won’t spend time documenting it here.
Because of its aging population, Japan’s gross savings rate has also dropped from very high levels
to slightly above average levels for the OECD, as its elderly spends its wealth. But as is the case
with the US, the Japanese elderly do have wealth—in the form of home equity.
4
Unlike their
counterparts in the US, however, the elderly have most of their home equity wealth tied up in land,
rather than improvements. The reasons for this are simple: Japan, as a highly urbanized and
residentially dense country, has valuable land, but it also has houses that last, on average, for less
than 35 years (Yoshida, 2016).
As the Japanese people live into their 70s and 80s, they will therefore not be only facing
the health issues that people do around the world, but also issues with their housing—it will need
to be either replaced or, at minimum, recapitalized. While many of the elderly in Japan have cash
available to them, they often lack sufficient cash to both maintain a decent living standard and the
ability to recapitalize their houses.

4 https://data.worldbank.org/indicator/NY.GDS.TOTL.ZS?locations=JP
73
A natural mechanism that would allow the Japanese to rebuild their improvements would
be a mortgage secured by the land lying underneath houses. Because land values are high, they
would be sufficient to secure debt, and therefore allow the elderly in Japan to take advantage of
that country’s very low interest rates. The problem, of course, is that being retired, the elderly
might not have sufficient income to sustain payments on a forward mortgage. But a reverse
mortgage might be a feasible mechanism to allow retired people in Japan to draw on their home
equity to maintain their improvements (or to insure against long-term care risk, although the
Japanese government does make reasonably priced long-term care insurance available to the
Japanese people). A reverse mortgage, known in the U.S. Federal Housing Administration (FHA)
context as a Home Equity Conversion Mortgage (HECM), is a mortgage that does not require
borrowers to make periodic payments, but rather allows them to accrue interest until they decide
to move or refinance, or until the time of death. In the United States, FHA is a subsidiary of the
US Department of Housing and Urban Development that provides mortgage insurance, most often
on loans that are not attractive to the private sector.
The organization of this paper is as follows. We begin by describing briefly the mechanics
of a reverse mortgage, and the implications of those mechanics for mortgage pricing. We then
discuss how we model the risks endemic to investors in or guarantors of reverse mortgages. We
follow by describing how we forecast the variables of interest—interest rates, property values, and
mortality—that underpin the value and risks of reverse mortgages. We next discuss the simulations
we run using our forecasts to characterize the tail risks associated with mortgages. We then show
the implications of our simulations, including findings on the feasibility of reverse mortgages in
Japan, and conclude with policy recommendations. This conclusion contains some implications
about the US experience with HECMs for Japan.
74
4.2 Background
The mechanism for HECMS is straightforward—a lender provides a mortgage secured by
a house to a household. The household makes no periodic payments on the mortgage, but interest
does accrue on it. Suppose the house has a value of Vo at time the mortgage is originated. The
house grows in value in each period of g
0
, and the mortgage carries a variable rate of r
0
.
At some time, T, the mortgage is repaid, either because the household moves, refinances
its loan, or has its final head of household die. At that point, the payoff to the lender is
𝑚𝑉
*
∏ (1+𝑟
!
)
"
!#&
, if 𝑚𝑉
*
∏ (1+𝑟
!
)
"
!#&
< 𝑉
*
∏ (1+𝑔
!
)
"
!#&
, where m is the draw as a share of
house value at time zero, and is 𝑉
*
∏ (1+𝑔
!
)
"
!#&
otherwise. In other words, if the value of the
mortgage balance is less than the value of the house, at time T, the lender gets the full balance;
otherwise the lender gets the value of the house (which should be net of selling costs). But because
the lender is insured by FHA, so long as the lender has originated and serviced the loan properly,
the government compensates it for its losses. The cost of the loan to FHA at time zero is therefore
the discounted value of the expected payoff from the government to the lender, assuming an
appropriate discount rate and an expected time T. One could then set a premium based on an
expected time to payoff and appropriate discount rate, in a manner similar to how the US
Government Sponsored Enterprises are supposed to set their guarantee fees.
The issue with pricing HECMs appropriately is not so much finding a premium necessary
to repay expected losses, but it is rather determining a premium and contract such that the
maximum feasible loan loss exposure is minimized. In particular, attempts to value HECMs
require forecasts of interest rates, house prices, and mortality—the first two of these three random
variables are, at times, volatile, and as we shall see, skewed.
75
Because reverse mortgages carry tail risk, they have not been embraced in the private market in
the United States. Nearly all the roughly $100 billion of reverse mortgages currently outstanding
in the US are HECMs. This means that the establishment of a reverse mortgage in Japan will
almost surely require government backing, and therefore put Japanese taxpayers at risk.
It is also important to note that an inherent characteristic of reverse mortgages is that they
are non-recourse—a feature that might make them attractive is that the elderly may extract home
equity to finance needs (one of the most important of these in the Japanese context is home
maintenance) without burdening their children. This can only happen if, at the time of death, the
homeowner’s estate can extinguish its loan obligations by either repaying the loan in full through
home sales proceeds, or by conveying the house securing the property to the lender.
Our modeling strategy is straightforward. Three stochastic variables—interest rates,
property values, and mortality—underpin the value of reverse mortgages. We use well-known
techniques to model all of these variables. We use the yield curve to forecast future interest rates,
taking into account the interest arbitrage condition and the term premium. We use hedonic
modeling (Sheppard, 1999) to develop a land price index for Japan, and then use two time series
method—Brownian Motion (Hida, 1980) and Bootstrapping (Mooney et al., 1993)—to forecast
house prices. We take the Japanese Ministry of Health, Labor and Welfare life expectancy tables
to model mortality.
Both our house price and interest rate forecasts contain structural component and random
components. We use these to perform 5000 Monte Carlo simulations to determine the relationship
between house prices and mortgages balances over the distribution of mortality (Robert, 2013).
We then plot these simulations to determine how often we observe losses, and the size of these
losses when they do occur.
76
4.3 Modeling Strategy
4.3.1 Interest Rates Estimation
It is hard to forecast interest rates in Japan right now, because it has recently been
influenced by unprecedented interventions by the central monetary authority.
The housing crash associated with the 2008 global financial crisis, stagnant economic
growth, and deflation have incentivized the Bank of Japan to exert a series of unprecedented
expansionary monetary policies. The Quantitative and Qualitative Monetary Easing (QQE) in
2013, followed up by the Quantitative and Qualitative Monetary Easing with a Negative Interest
Rate (QQE-NIR) in 2016, have pushed interest rates down to historically low levels in the most
recent years. Exhibit 1 shows Japanese Government Bonds (JGB) yields with various constant
maturities for the years 1986 to 2017. Continuously aggressive Japanese monetary policy has
dragged the 5-year JGB rate (cmt05) from 0.4% in 2013 down to around -0.1% in 2017. The spread
between the 20-year and the 10-year JGB yields has been positive since 1990. However, the
negative spread of 5-year over 1-year JGB yields in 2016 indicates a short-term inverted yield
curve in Japan. We think the most recent QQR_NIR monetary policy contributes to the inverted
yield curve.
[Insert Figure 4.1 Here]
To forecast the distribution of interest rates, we employ a two-step model based on the term
structure of interest rates and Monte-Carlo simulation, which allow us to simulate the stochastic
movement of 1-Year interest rates (R1) for the next 30 years in Japan. To better capture the
volatility in interest rates associated with several business cycles and various monetary policies
over the past 30 years, we first utilize JGB daily yields data with constant maturity of various years
from 2007 to 2017 to compute the 1-year forward rates based on the term structure of interest rates.
77
We then predict the stochastic movement of interest rates by modeling the constant driving drift
and random component using a Monte-Carlo simulation. The specific estimation process is as
follows.
Term Structure Theory (Cox, Ingersoll and Ross, 2005) shows:
𝒇
𝒕𝟏,𝟏
=]
(𝟏5𝒓
𝒕𝟐
)
𝒕
𝟐
(𝟏5𝒓
𝒕𝟏)
𝒕
𝟏
^
𝟏
𝒕
𝟐
%𝒕
𝟏
−𝟏 (1)
𝒇
𝒕𝟏,𝟏
represents the forward rates starting at year 𝑡
&
and lasting for 1 year, given spot rates r
0&
and
r
0+
. For each business day starting from November 6, 2007 to March 24, 2017, we obtain a
sequence of spot interest rates 𝒓
𝒕
, where t (t=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30 and 40) is
the maturity of JGB starting at the current time 𝑡
*
. Therefore, we can then apply equation (1) to
obtain a set of fourteen forward rates 𝒇
𝒕,𝟏
for each business day in our sampling period, where t=1,
2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25 and 30. Given that we have 2297 business days from November
2007 to March 2017, we will eventually have 32,158 computed 1-year forward rates.
To characterize the stochastic movement of the interest rates in the next 30 years, we need
to model both the overall constant driving force (the drift) of the interest rates, and the random
component of interest rates associated with the error term.
First, we model the 1-year forward rates 𝒇
𝒕,𝟏
computed in equation (1) as a linear function
of T and T
+
, where T=t+1:
𝒇
𝒕,𝟏
=𝜶
𝟎
+𝜷
𝟏
𝑻+𝜷
𝟐
𝑻
𝟐
+𝜺 (2)
The estimated regression results are presented in Exhibit 2. Both T and T
+
are statistically
significant. The calculated forward rates are positively associated with T and slightly negatively
associated with T
2
, indicating a flattening of the yield curve as maturities increase. We treat T and
T
+
as the key components in the drift. We also replicate this process by utilizing interest rates data
78
from 1986 to 2017, with an attempt to include more volatilities over a longer horizon. However,
as shown in Exhibit 2, the explanatory power of our model based on the longer horizon is quite
limited. We have decided to use the more recent 2007-2017 interest rate regime as the basis of our
simulation.
[Insert Table 4.1 Here]
Second, we run Monte-Carlo simulation on the residuals in the linear regression of (2) to
obtain the standard deviation of the mean of the residuals. With 1000 replications, the estimated
standard deviation of the mean is 0.0036.
Third, combining the estimates from the linear regression and the Monte-Carlo simulation,
we model the stochastic 1-Year interest rates as:
𝑹
𝒕,𝟏
= 𝜶
𝟎
h +𝜷
𝟏
i
𝑻+𝜷
𝟐
i
𝑻
𝟐
+𝟎.𝟎𝟎𝟑𝟔 ∗𝑵𝑶𝑹𝑴𝑺𝑰𝑵𝑽(𝑹𝑨𝑵𝑫( )) (3)
where ( 𝜶
𝟎
h +𝜷
𝟏
i
𝑻+𝜷
𝟐
i
𝑻
𝟐
) is the overall constant driving force, or the drift, of the 1-year interest
rates derived from the linear regression, and 𝟎.𝟎𝟎𝟑𝟔 ∗𝑵𝑶𝑹𝑴𝑺𝑰𝑵𝑽(𝑹𝑨𝑵𝑫( ))is the random
stochastic component of the 1-year interest rates. 𝑵𝑶𝑹𝑴𝑺𝑰𝑵𝑽(𝑹𝑨𝑵𝑫( )) provides the random
Z scores. The estimated standard deviation of the mean of the residuals captures the dispersion
magnitude of the error term. The product of the dispersion magnitude and the random Z scores
formulates the random component of the stochastic movement.
4.3.2 Housing Price Appreciation Rates Estimation
This paper uses transaction-based land price data from “Real Estate Transaction-Price
Information System” published by the Ministry of Land, Infrastructure, Transport and Tourism
(MLIT) of Japan. Transaction prices on land allow us to detect the price changes of the
fundamental structures in the most recent housing boom and bust cycle associated with the 2008
global financial crisis. To capture the geographic dispersion of land prices, we build a region-level
79
hedonic land pricing model with land price data from 2006 to 2016, and then construct the national
land price index (LPI) weighted by the market value of residential lots of those regions in 2014.
As shown on the map in Exhibit 3, Japan has eight jurisdictional regions: Hokkaido, Tohoku,
Kanto, Chubu, Kansai, Chugoku, Shikoku, and Kyushu (with Okinawa). Land transactions during
2006 and 2016 in the Chugoku and Shikoku regions were small in number and this undermined
our capability to estimate tight coefficients in those markets. Consequently, we merged Chugoku
and Shikoku into one “region”. Our national land price index and land price appreciation rates are
thus built for 7 regions. Exhibit 3 illustrates the jurisdictional and geographical information of the
7 merged regions in our analysis.
[Insert Figure 4.2 Here]
To estimate housing price risk, we first use a hedonic land pricing model to estimate the
land price appreciation rates and construct a land price index in Japan from 2006 to 2016, covering
the most recent housing boom and bust cycle. Based on this constructed land price index, we then
utilize both Brownian motion and Bootstrapping simulation methods to characterize a distribution
of forecasts of housing prices for the next 30 years in Japan.
a. Hedonic Land Pricing Model and Land Price Index (LPI)
We specify the regional land price to depend on its fundamental characteristics, location
features, land-use regulation factors, and time effects. We focus on land, instead of land and
structures, because its value is exogenous with respect to household characteristics. Table 4.2
provides the summary statistics of dependent and explanatory variables in this analysis.
[Insert Table 4.2 Here]
The hedonic land pricing model takes the following form:
𝑳𝒐𝒈_𝑼𝒏𝒊𝒕𝑳𝒂𝒏𝒅𝑷𝒓𝒊𝒄𝒆
𝒊𝒋𝒕
=𝜷𝑿
𝒊
+𝜹𝑳
𝒊
+𝝉𝑨
𝒊
+𝝉𝝀
𝒕
+𝝅
𝒋
𝑫
𝒊𝒋𝒕
+𝝁
𝒊𝒋𝒕
(4)
80
--Xi (Landshape, Surregion, Frontrbreath and Frontrtype) represents fundamental characteristics
of each property, including general shape of the land, surrounding area purposes, frontage road
width and frontage road types.
--Li (Cityplanning, Maxbcr and Maxfar) represents land-use regulatory factors, including use
districts, maximum building coverage ratio and maximum floor-area ratio.
--𝑨
𝒊
(Nearestdit, Location) controls for the location features. We control at the town or ward
jurisdiction level and also control for the time commuting to the nearest train station.
--Dijt includes 7 dummies for the merged regions (j=1,2…7).
--λt controls for the time effect.
Because we are regressing the land-only transactions, our hedonic variables cover both
fundamental characteristics and locational factors, as well as land-use regulatory features. Based
on the quarterly transaction periods, we set Q2 of 2006 as our base period. After controlling for all
the other relevant factors, the estimated coefficients for 𝝀
𝒕
captures the quarterly time effect of
land price appreciation compared to the base level. Therefore, we can construct the hedonic LPI
and the corresponding land price appreciation (LPA) rates for each region from 2006 to 2016 by
extracting the differences between the coefficients. The estimation results for LPI and LPA are
presented by Exhibit 5 and Exhibit 6. Our constructed LPA reveals the great heterogeneity in
Japanese local land markets. The severe Great East Japan Earthquake and the tremendous
reconstruction afterward help explain the amplitude of the housing cycle in Tohoku. Moreover,
the large increase of foreign investors in recent years contributes to the land price increase in
Hokkaido.
[Insert Figure 4.3 and Figure 4.4 Here]
81
b. HPA Prediction Model: Brownian Motion and Bootstrapping
Based on the constructed LPI and LPA, we move on to predict the future housing price
risk. We first assume that house prices move with a Brownian Motion, as shown in equation (5)
and (6). We derive the annual excess returns based on the estimated LPA from the hedonic pricing
model and then calculate the variance-covariance matrix of the 7 merged regions. Then using the
weights derived from the residential property values in 2014, we compute the mean, variance and
standard deviation of our portfolio of Japanese housing regions to calculate the asset drift, as shown
in equation (7). Exhibit 7, Exhibit 8 provide detailed information about this process.
Brownian Motion: HPAT = HPAT-1 × e
r
(5)
r = Asset Drift + Std×NORMSINV(Rand()) (6)
Asset Drift = Portfolio Mean – 1/2×Portfolio Variance (7)
[Insert Table 4.3 and Table 4.4 Here]
However, when we check for skewness, we find the distribution of the sampling house
price appreciation (HPA) rates is right-skewed, indicating that a Brownian Motion simulation
model underestimates housing price appreciation rates and thus overestimates the ultimate
potential losses. Therefore, we also employ the Bootstrapping method which requires no
impositions on the sampling distribution. With replacement, the bootstrapping method allows us
to simulate on the empirical distribution of housing price returns and, to some extent, corrects the
underestimation of future HPA. Exhibit 9 displays one pair of simulation results based on both the
Brownian Motion model and the Bootstrapping model. Bootstrapping methods on average provide
higher housing price appreciation (or, to characterize it more accurately, lower house price
depreciation) forecasts for Japan for the next 30 years. Because bootstrapping characterizes tail
82
risk based on empirics, instead of distributional assumptions, we consider it more relevant for
modelling potential reverse mortgage cost exposure.
[Insert Figure 4.5 Here]
4.3.3 Mortality Risks
We make the simplifying assumption that the mortality of the borrower is the only reason
for the termination of reverse mortgage loans. We exclude the possibility of refinancing,
mobility, and co-borrowing (couples) in our model so that the simulation results can provide the
upper bound of the potential default losses (anything that shortens the life of a reverse mortgage
reduces its accrued interest, and therefore makes it less likely to incur a loss). The life table data
of 2015 from the Ministry of Health, Labor and Welfare in Japan provides the conditional
probability of death M(T), which is the probability that a borrower will die at time T given the
borrower’s survival at time (T−1), for both men and women. We then calculate the
corresponding unconditional probability of death m(T) using:
𝒎(𝑻)=𝑴(𝑻)×𝟏−∑ 𝑴(𝑻−𝟏)
𝑻
𝟎
(𝟖)

4.4 Cross-over Risks Estimation
So far we have modeled the stochastic processes of interest rates and housing prices in the
next 30 years in Japan. We have also calculated the unconditional mortality rates at every age for
men and women. In this session, we integrate these three variables into our default risk estimation
model in which we aim at predicting the magnitude of potential losses associated with default risk.
We assume that an elder individual becomes a borrower in reverse mortgage loan at age 62 and
the maximum length of stay in the program is 30 years. As shown in Exhibit 10, at each time
period, the unpaid mortgage balance for a borrower is a function of initial housing value (𝐻𝑃
*
),
83
reverse mortgage interest rates 𝑅
",&
and home equity withdrawal rates 𝛾
"
. We assume zero
transaction cost in selling the house at loan termination and thus the housing values at each period
is determined by the housing price in the previous period and the current housing price appreciation
rates 𝑔
"
. If the unpaid mortgage balance is greater than the housing price at time T, then the
undiscounted potential losses associated with default risk will be (𝑀𝐵
"
−𝐻𝑃
"
)×m(T), where
m(T) is the unconditional mortality rates. The potential loss will be zero and independent of the
unconditional mortality rate if the housing price is greater than the unpaid mortgage balance. Then
we discount all the potential losses at each stage back to T=0 to get the net present values of the
potential losses. For each pair of simulations on interest rates and housing price appreciation rates,
we obtain one net present value. Therefore, we can characterize both the significance and
magnitude of the default risk in this reverse mortgage program by replicating the overall simulation
process on those stochastic variables 5000 times to get a distribution of the expected losses.
[Insert Table 4.5 Here]
From Exhibit 10, we can see that several parameters might exert significant influence on
the estimated loss magnitude:
1. Home equity withdrawal rates 𝛾
"
: Borrowers can choose different kinds of withdrawal
plans, including term plan (fixed monthly cash payment over a specified number of years,
30 years at maximum in our model), a line of credit plan (withdrawal different amounts of
allowances at different times), lump-sum plan and combinations. For the term plan, 𝛾
"
is
a constant term. For lump-sum plan, 𝛾
"
=0 for T=1, 2, …, 30. For the line of credit plan,
𝛾
"
varies with T increases.
84
2. Housing price appreciation rates 𝑔
"
: The returns on housing assets determine the sign of
(𝑀𝐵
"
−𝐻𝑃
"
) and thus exert a direct impact on default risk. Brownian motion and
bootstrapping provide different forecasts on housing price appreciation rates.
3. Mortgage interests spread: We did not add any spread into the predicted 1-Year interest
rates 𝑅
!,&
in section II. However, the mortgage interest rates for reverse mortgage program
should include a risk premium to capture the default risk associated with unstable housing
prices and the program’s non-recourse characteristics. Given the monotonically increasing
unpaid mortgage balances over time, higher spreads will be associated with greater default
risk.
To better detect the influence of those parameters, we apply four alternative scenarios to
conduct the overall simulations and measure the magnitude of the potential losses. Those four
scenarios compare the impact of various spread levels, home equity withdrawal rates, and housing
price estimation methods, as shown in Exhibit 11. Exhibit 12 displays the simulated distributional
results of the potential losses with 5000 replications for those 4 alternative scenarios.
[Insert Table 4.6 and Figure 4.6 Here]
Our simulation results substantiate the fact that the Brownian Motion method does not take
into account skewness, and tends to overstate the simulated frequencies of sever house price
declines. The average risk and the standard deviation of the risk with the Brownian Motion
simulation are higher than those with the Bootstrapping method. And yet, even using the
Bootstrapping, which we think better reflects observed outcomes, we see substantial tail risk
associated with the lump-sum withdrawal plan.
Comparing scenario 3 with scenario 1, we find that increasing (50bps) risk premiums only
slightly increases the default risk (and of course allows for the build-up of a larger insurance fund).
85
On the one hand, the risk premiums (or spreads) are set to capture the default risk and non-recourse
risk. On the other hand, this hedging mechanism will in turn increase the default risk itself by
ballooning the unpaid mortgage balance over time. Finding an optimal spread is a topic for future
research.
Finally, Scenario 4 dominates the other 3 alternative scenarios, indicating the significant
impact of home equity withdrawal rates. By tapping on only 5% of home equity each year for the
first 10 years, borrowers lower their interest rates risk while achieving the overall 50% extraction
at the end of the 10
th
year. Scenario 4 shows that line of credit plans with limits to annual
withdrawals are far more feasible than lump sum plans.

4.5 Conclusion and Policy Implications
Reverse mortgages seem like a good solution to a very real policy problem—many elderly
people are house rich and cash poor, and yet also don’t want to move. The desire to avoid moving
is understandable, in that the act of moving is itself complicated, and that many people want to
retain their ties to nearby friends and family. At the same time, the elderly can find themselves in
need of cash, both for health emergencies (although this is perhaps more of an issue in the United
States, which lacks a government-sponsored long term care program for its middle-class) and
housing emergencies (say the need to replace a furnace or repair a foundation, problems that may
be more endemic to Japan, which has a more fragile housing stock than many other countries).
But in the US, where reverse mortgages have been around for more than 30 years, the take-
up rate has been low. In 2017, only about 55,000 elderly Americans will have taken out reverse
86
mortgages, while the population of adults over the age of 65 increased by nearly 2 million
5
.
Currently, reverse mortgages make up barely one percent of mortgage debt outstanding in the US.
This is perhaps because the experience with reverse mortgages in the US, both for borrowers and
for guarantors has not been good (Moulton, Haurin and Shi, 2015; Moulton, Loibl and Haurin,
2017).
As Jack Guttentag has pointed out
6
, one problem with reverse mortgages in the US is that
their costs have not been transparent, and, perhaps, as a result, been high. If substantial amounts
of home equity are going to lenders in the form of origination fees, both the purpose of reverse
mortgages for borrowers and the attractiveness of these mortgages to guarantors are compromised.
That it costs so much in the U.S. to originate a reverse mortgage is puzzling, given that the default
risk attached to them is born by the government, rather than lenders (Lucas, 2015; Davidoff, 2015).
Therefore, if Japan wants to consider backing reverse mortgages, in the manner of FHA, it will
need to come to grips with appropriate policies for originators. The specifics of those policies are
beyond the scope of this paper.
But on the guarantee side, there are some things that Japan can learn from the US
experience. We should note that the HECM program has bedeviled FHA, in that the valuation of
its HECM book swings wildly from one year to the next. The reason for this was not changing
credit conditions, but duration risk. Between 2010 and 2013, more than two-thirds of FHA
guaranteed HECMs had fixed interest rates (HUD, 2016). This meant that HECMS, which may be
thought of as zero-coupon bonds, had long duration. Given that life expectancies at the time of

5 See https://census.gov/data/tables/2014/demo/popproj/2014-summary-tables.html and
https://www.nrmlaonline.org/2017/12/04/annual-hecm-endorsement-chart.
6 http://realestate.wharton.upenn.edu/wp-content/uploads/2017/03/780.pdf
87
HECM eligibility in the US (age 62) is more than 20 years, a one percentage point change in an
interest rate forecast would produce a 20 percent change in HECM values—assuming no credit
risk. This is why we recommend that were Japan to implement a reverse mortgage program, it
should have variable rates attached to it, so that the government may avoid duration risk. This is
also why we model one year interest rates going forward.
The second issue with the HECM program is that many borrowers take out a lump sum
amount that accrues interest until the loan matures-whether it be because of refinancing, moving
or death. Among other things, this creates an adverse selection problem (Davidoff, 2004) that we
don’t even model in our paper. In the event of a house price collapse, HECM borrowers with a line
of credit that allows for large lump sums would have every incentive to use their full line, knowing
that the value of the house would likely be less than the value of the mortgage at maturity.
Remarkably, we see little evidence that people do in fact take advantage of this feature.
More problematic is the possibility that people will take out a lump sum, spend it, and then
not have sufficient funds for making property tax payments. In the US, municipalities have senior
lien positions relative to mortgages, and so property tax defaults compromise the value of reverse
mortgages to their guarantors (Bishop, Bowen and Shan, 2008; Moulton et al., 2015).
Most problematic still in the Japanese context is that lump-sum reverse mortgages would
almost certainly, as our simulations show, have large costs. The average losses associated with a
reverse mortgage under our preferred scenarios would be about 5-6 percent. The reasons for this
are: (1) Japanese land prices have generally been falling, meaning that the collateral underpinning
a reverse mortgage could well deteriorate and (2) the Japanese people have extraordinarily long
life expectancies, meaning that interest will accrue on a reverse mortgage for many years. The one
88
benign characteristic with respect to reverse mortgages in the Japanese environment is that interest
rates in Japan have long been, by world standards, low.
The combination of falling house prices and low interest rates is almost surely not
coincidental—they reflect a society that is losing population. Hence in our simulations, we see
little need to contradict what data are telling us about the likely future of property values and
interest rates. Perhaps most important, by modeling property values as declining, we are capturing
some of the tail risk that the Japanese taxpayer might face if asked to guarantee reverse mortgages.
But there could be a role for reverse mortgages in Japan, if they are designed as annuities,
rather than lump-sum. If homeowners were permitted to extract five percent of their home equity
each year for ten years, rather than 50 percent all at once, the average amount of time that interest
would accrue would be considerably shortened. Interest owed would be much lower at time of
death, so much so that under most scenarios, even tail losses would be quite low. This is a program
that could be priced and, while not eliminating possible risk exposure to the Japanese taxpayer,
would considerably mitigate it.

89
4.6 Tables and Figures
Figure 4.1 JGB Yields with Various Maturities: December 1986 – March 2017

Source: Authors’ calculations based on data of JGB daily yields from 1986 to 2017.

Table 4.1 Estimated Regression Results with 10-year and 30-year horizons

JGB Daily Yields Data:
November 6, 2007 -- March 24, 2017
JGB Daily Yields Data:
December 1, 1986 -- March 24, 2017

Coef. Std Dev t-value Prob>|t| Coef. Std Dev t-value Prob>|t|
T
0.273 0.002 157.71 0 0.254 0.003 78.67 0
T
2
-0.006 0.000 -120.16 0 -0.008 0.000 -75.06 0
Constant
-0.430 0.010 -42.3 0 1.371 0.018 -42.3 0
Adj. R
2
0.581 0.065
Source: Authors’ regression results on the drift of 1-Year forward rates.

90
Figure 4.2 Jurisdictional and Geographical Characteristics of the 7 Merged Regions.

Map Source: www.japan-guide.com

91
Table 4.2 Summary Statistics of the Hedonic Land Pricing Regression Model.
Variables Description Category Mean
Standard
Deviation
Log_unitprice Log of unit land price per square
meter,price unit in 10,000 yen.
Dependent
Variable
10.54 1.40

Landshape The general shape of the land, such as
square, rectangle, trapezoid, irregular,
etc.
Fundamental
Characteristics 4.08 1.84

Surregion The characteristics of surrounding area
include residential area, commercial
area, industrial area or potential
residential area.
Fundamental
Characteristics
3.64 0.84

Frontrbreath The width (in meter) of the front raod
in contact with the land.
Fundamental
Characteristics
6.95 4.78

Frontrtype Frontage road types, such as
prefecrure road, city road, agriculture
road, private road, etc.
Fundamental
Characteristics
5.48 3.54

Cityplanning The use districts designated by the
City Planning Act
Land Use
Regulation
7.31 5.67

Maxbcr The designated maximum building
coverage ratio(%)
Land Use
Regulation
59.90 8.98

Maxfar The designated maximum floor-area
ratio (%)
Land Use
Regulation
189.57 77.12

Nearestdist The time distance (minute) from the
land location to the nearest train
station or ground station.
Location 3.55 2.30

Location Addresses are shown up to town or
ward.
Location

92
MergedRegion 7 Regions: Hokkaido, Tohoku, Kanto,
Chubu, Kansai, Chugoku_Shikoku,
Kyushu_Okinawa.
Location

Transperiod The transactin period means the date
of contract, displayed on a quarterly
basis.
Time

Figure 4.3 Constructed Land Price Index (LPI)

Source: Authors’ calculations on land price index based on the hedonic land pricing model and land-only transaction data from
MLIT.

Figure 4.4 LPA: Estimated Land Price Appreciation (LPA) Rates.

Source: Authors’ calculations on land price appreciation rates based on the constructed LPI.

93
Table 4.3. Hedonic Land Prices: Annual Growth Rates and Weighted Average Growth
Rate

Source: Authors’ calculations based on the estimated LPA.

Table 4.4 Brownian Motion: Variance-Covariance Matrix

Source: Authors’ calculations based on the estimated LPA.

Year Hokkaido Tohoku Kanto Chubu Kansai Chugoku_Shikoku Kyushu&Okinawa National
2006 0.03% 4.33% 1.31% -2.15% 1.24% 3.99% 0.64% 0.97%
2007 -0.63% 1.13% 2.24% 1.97% 1.05% 2.32% 0.54% 1.79%
2008 -0.84% -1.13% -1.70% -0.95% -1.10% -1.40% -0.71% -1.36%
2009 -3.66% -2.04% -2.08% -1.77% -2.46% -1.19% -2.39% -2.09%
2010 0.11% -0.56% -0.43% -0.70% -0.37% -0.28% -0.47% -0.45%
2011 -0.10% -1.13% -0.41% -0.92% -1.35% -0.89% -0.68% -0.72%
2012 -1.39% 0.01% -1.70% -1.15% -0.50% -0.65% -1.40% -1.25%
2013 -0.04% 0.77% -1.33% -0.96% -0.86% -2.22% 0.19% -1.04%
2014 -0.53% -0.05% 0.41% -0.42% -1.80% -0.82% -0.09% -0.24%
2015 -0.29% -0.94% 0.45% -0.30% 0.52% 1.49% -0.15% 0.30%
2016 1.66% 2.44% -1.09% -1.90% -0.74% -2.28% 0.60% -0.93%
Skewness -118.38% 116.10% 65.98% 164.91% 20.48% 114.02% -105.17% 76.51%
Kurtosis 383.72% 123.80% -41.59% 413.38% -52.96% 59.57% 102.51% 35.38%
Weights 1.86% 3.70% 48.66% 15.33% 17.13% 6.20% 7.11% 100.00%
Geometric Mean of
Growth Rates
-0.52% 0.24% -0.40% -0.85% -0.58% -0.19% -0.36% -0.46%
Standard Deviation 1.23% 1.75% 1.31% 1.06% 1.10% 1.87% 0.88% 1.06%
Variance 0.02% 0.03% 0.02% 0.01% 0.01% 0.04% 0.01% 0.01%
Weighted Average
Growth Rate
-0.46%
Hokkaido Tohoku Kanto Chubu Kansai Chugoku_Shikoku Kyushu&Okinawa Weights
Hokkaido 0.017% 0.014% 0.006% 0.000% 0.006% 0.000% 0.010% 1.861%
Tohoku 0.014% 0.034% 0.012% -0.004% 0.013% 0.017% 0.013% 3.705%
Kanto 0.006% 0.012% 0.019% 0.009% 0.011% 0.022% 0.009% 48.657%
Chubu 0.000% -0.004% 0.009% 0.012% 0.004% 0.006% 0.003% 15.330%
Kansai 0.006% 0.013% 0.011% 0.004% 0.013% 0.018% 0.007% 17.127%
Chugoku_Shikoku 0.000% 0.017% 0.022% 0.006% 0.018% 0.039% 0.007% 6.205%
Kyushu&Okinawa 0.010% 0.013% 0.009% 0.003% 0.007% 0.007% 0.009% 7.115%
Portfolio Variance 0.01246%
Portfolio Mean -0.464%
Portfolio Variance 0.01246%
Standard Deviation 1.116%
Asset Drift -0.4699%
Variance-Covariance Matrix
Housing Market Portfolio
94

Figure 4.5 One Pair of Simulation Result: Brownian Motion vs. Bootstrapping.

Source: Authors’ simulation results on housing price appreciation rates based on the estimated LPA.

Table 4.5 Default Risk Estimation Model

Time

Mortgage Balances

Housing Values
Undiscounted
Potential Losses
with Default Risk
0
𝑴𝑩
𝟎
=𝜸
𝟎
×𝑯𝑷
𝟎
𝑯𝑷
𝟎
=𝟏

At each stage,
if 𝑴𝑩
𝑻
>𝑯𝑷
𝑻
,
then the expected losses
equal to
(𝑴𝑩
𝑻
−𝑯𝑷
𝑻
)×𝐦(𝐓)
1 𝑴𝑩
𝟏
=𝑴𝑩
𝟎
0𝟏+𝑹
𝟏,𝟏
3+(𝜸
𝟏
×𝑯
𝟎
) 𝑯𝑷
𝟏
=𝑯𝑷
𝟎
×(𝟏+𝒈
𝟏
)
2 𝑴𝑩
𝟐
=𝑴𝑩
𝟏
0𝟏+𝑹
𝟐,𝟏
3+(𝜸
𝟐
×𝑯
𝟎
) 𝑯𝑷
𝟐
=𝑯𝑷
𝟏
×(𝟏+𝒈
𝟐
)
3 𝑴𝑩
𝟑
=𝑴𝑩
𝟐
0𝟏+𝑹
𝟑,𝟏
3+(𝜸
𝟑
×𝑯
𝟎
) 𝑯𝑷
𝟑
=𝑯𝑷
𝟐
×(𝟏+𝒈
𝟑
)
… … …
T 𝑴𝑩
𝑻
=𝑴𝑩
(𝑻, 𝟏)
0𝟏+𝑹
𝑻,𝟏
3+(𝜸
𝑻
×𝑯
𝟎
) 𝑯𝑷
𝑻
=𝑯𝑷
𝑻, 𝟏
×(𝟏+𝒈
𝑻
)

95
Table 4.6 Four Simulation Scenarios
Alternative
Scenarios
Spreads Home Equity
Withdrawal Rates
HP Estimation
Methods
1 50bps 50%at T=0 Bootstrapping
2 50bps 50%at T=0 Brownian Motion
3 100bps 50%at T=0 Bootstrapping
4 50bps 5% per year for the
first 10 years
Bootstrapping

Figure 4.6 Distributional and Descriptive Statistics of the Simulation Results

96
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Abstract (if available)

Abstract The world’s population is rapidly aging, as are people in the United States. For most senior home-owning households, housing wealth accounts for the greatest share of their assets, along with wealth from Social Security and employer-provided retirement plans. How households react to changes in their housing wealth, and how they consume it are critical questions as they are not only relating to individual’s own well-being but also having a significant impact on the macroeconomic situations. The big issue animating my dissertation research is to understand the intersection of aging, wealth, and housing tenure transitions. Throughout my dissertation research, I have found that: 1) Aging in place is the dominant housing tenure choice among the Silent Generation and the Greatest Generation; 2) Financial precarity and uninsurable health risks associated with cognitive declines and major motor functions are the key factors driving low-income homeowners out of homeownership in their late lives; 3) Households do not adjust their consumption behaviors when they experience shocks in their house prices, indicating the impact of low interests rates on boosting households’ consumption via the housing wealth channel has been overestimated; 4) The non-recourse mortgage structure, the increasing longevity risk, the dominant lump-sum withdrawal plan, and the stagnancy of local housing market are the key factors affecting the performance of the reverse mortgages.

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Asset Metadata

Creator Zhu, Linna (author)

Core Title Three essays on aging, wealth, and housing tenure transitions

School School of Policy, Planning and Development

Degree Doctor of Philosophy

Degree Program Public Policy and Management

Degree Conferral Date 2021-12

Publication Date 12/20/2021

Defense Date 04/27/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag aging in place,housing tenure,housing wealth,OAI-PMH Harvest,reverse mortgages

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Green, Richard (committee chair), De la Roca, Jorge (committee member), Painter, Gary (committee member), Ramcharan, Rodney (committee member), Zissimopoulos, Julie (committee member)

Creator Email linnazhu@usc.edu,lzhu@urban.org

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