Reverse Mortgages, Housing and Consumption: An
Equilibrium Approach
∗
Shize Li
†
Jialu Shen
‡
Ariel Sun
§
PRELIMINARY VERSION
Please do not circulate without permission.
Jan 2024
Abstract
Reverse mortgages (RMs) oer eligible senior homeowners liquidity of their home equity without
them moving out and repayments before loan termination. By incorporating RMs into a quanti-
tative equilibrium life-cycle model, we assess their impacts on household decisions, the mortgage
and housing market. We show that retired RM borrowers experience enhanced signicant con-
sumption smoothing. Additionally, the presence of RMs in the mortgage market enhances the
perceived value of houses to households, making homeownership a more nancially attractive op-
tion and stimulating demand for housing. This also leads to increased overall household welfare
in our model, highlighting the positive impact of RMs.
JEL Classication: G21, E21, J14
Key Words: Reverse Mortgage, Mortgage, Housing, Retirement, Welfare
∗
We thank Wei Jiang and Adam Guren for their helpful comments. The paper is presented at Sapienza University
of Rome, Italy, and is accepted for American Real Estate Annual Conference 2024, Royal Economic Society Annual
Meeting 2024 and 2nd Contemporary Issues in Financial Markets and Banking, Nottingham Trent University, UK.
Authors thank participants and discussants for suggestions and advice.
†
Hong Kong University of Science and Technology, [email protected]
‡
Trulaske College of Business, University of Missouri, [email protected].
§
Imperial College Business School, Imperial College London, js308@imperial.ac.uk
1
1 Introduction
The global challenge of managing later-life nancial security exists widely: The problem arises from
accelerating life expectancy and socioeconomic inequality in later lives, coupled with insucient
public resources to fund social security. The long-term trend of the growing ageing population has
posed a two-fold problem: On the one hand, considerable families’ wealth has accumulated in the
form of housing estates (or home equity), an illiquid asset, which has experienced signicant price
growth over the past decades (1960-2006) during the housing market boom in the US.
1
On the other
hand, retirees need to make intelligent decisions on their pension plans, and their under-saving
for retirement results in insucient retirement cash ow. These factors make ordinary families
“equity-rich and cash poor”(see Caplin (2002)). Reverse mortgage loans (RMs) present a potential
solution for older homeowners to access their home equity and fund their retirement consumption.
2
Granular loan-level data such as CoreLogic and Black Knights, on open liens including mortgages
(rst liens,) and RMs (second liens), show that RMs have become an increasingly important
retirement solution, with a growing presence in the nancial and housing markets. As a result,
their impacts on the nancial and housing markets are non-negligible, especially in the long-term.
While the RMs market’s rapid growth improves the nancial well-being of older homeowners,
3
,
the complexities of RMs hinder our understanding of their interaction with the broader mortgage
and housing markets, as well as their impact on inter-generational wealth transfers and overall
societal welfare improvements. Thus, key questions remain unanswered: How do RMs aect the
mortgage and housing market, and what are the implications for societal welfare gains?
Our paper addresses these questions with a quantitative equilibrium model featuring heteroge-
neous households and competitive lenders, with endogenous house prices and rates of conventional
1
Housing estates are in the order of magnitude of 10 times liquid assets such as cash and equivalents (nancial
securities (equities, and bonds), according to Chen et al. (2020). Similarly, Nakajima and Telyukova (2020) states
that excluding housing wealth, retirees’ net worth would be 28% - 44% lower, depending on age groups. Iacoviello
(2011) also estimates that about one-half of the total household net worth with the U.S. data.
2
In the US, RMs are commonly FHA-insured Home Equity Conversion Mortgages (HECMs), available to in-
dividuals aged 62 and older, primarily used to nance retirement consumption. Home equity nancing solutions
encompass various instruments, including non-age-restricted home equity loans (HELs), Home Equity Lines of
Credit (HELOCs), and second mortgages that utilize housing equity as collateral. Similar retirement products, al-
beit under dierent names, are oered in other developed countries and regions, such as the UK, Canada, Australia,
and the EU, as well as emerging economies such as Brazil, South Africa, China, Thailand and India.
3
See Nakajima and Telyukova (2017), Nakajima and Telyukova (2020), and Chen et al. (2020).
2
mortgages and RMs. Besides, we introduce cyclical interest rates and allow the economy to transit
between booms, recessions, and crises. Lenders set spreads for mortgages and reverse mortgages to
break even in equilibrium. In this economy, households’ decisions inuence the equilibrium house
prices and spreads of mortgage and reverse mortgage, which feed back to household decisions.
Our model considers multiple sources of household risk, including un-insurable labour income
risk, health risk, longevity risk, interest rate risk, and uncertainty in house prices and the macroe-
conomic environment. Based on households’ expectation of equilibrium house prices, mortgage
and reverse mortgage rates, households make decisions on consumption, saving, homeowner-ship
(purchasing v.s. renting), and (re)nancing through conventional mortgages and RMs, facing
property maintenance costs, ownership preferences and bequest motives.
At a high level, our general equilibrium model has three unique features. First, to the best of
our knowledge, our model is one of the rst few to clear the housing and the credit market simul-
taneously with both conventional mortgages and RMs. In comparison, Nakajima and Telyukova
(2020) and Nakajima and Telyukova (2017) model home equity in retirement with RM and deter-
ministic house prices, and Cocco and Lopes (2020) model the demand of RMs and incorporate a
random walk process of house prices. Moreover, most papers on RMs focus on the demand side
of the equation and analyze the reasons for the low demand despite obvious benets for eligible
senior households.
4
These papers follow a partial equilibrium life-cycle model, which focuses on
the household balance sheet, without consideration of the interactions with the nancial market
(mortgage market) and the real economy (housing market).
5
Second, we allow households to load RMs after retirement to repay conventional mortgages
subject to specic loan-to-value ratio (LTV) constraints, which is also feasible in the real market.
This feature depicts the possibility of an alternative ‘renancing’ for mortgage borrowers. Unlike
renancing conventional mortgages, RMs exempt borrowers from monthly repayments and thus
substantially mitigate the liquidity issues faced by senior households. Moreover, we calibrate our
model with proprietary datasets from CoreLogic and Black Knights, which oer detailed and
4
The reasons for the low RM take-up rates include bequest motives, precautionary savings, uncertainty in
longevity and medical expenses, etc.
5
See Cocco and Lopes (2020)’s model on the impact of maintenance costs on RM demand, and Nakajima and
Telyukova (2017)’s model on the impact of bequest motives and initial set-up costs on RM demand.
3
comprehensive information on anonymous households, ensuring granularity and completeness.
6
The third main feature is that our calibrated model generates homeownership rate, households’
net wealth, and Loan-To-Value (LTV) ratio close to the Survey of Consumer Finances (SCF). In
addition, our model result matches Payment-to-Income (PTI) ratio with the empirical evidence
very well, with the introduction of RM. However, Guren et al. (2021)’s model generates a PTI ratio
growing exponentially during retirement, which deviates signicantly from the empirical evidence.
Moreover, the renancing rate of conventional mortgages in our model remains relatively stable
and moderate upon retirement. These ndings dier from the study by Guren et al. (2021),
which indicates a low renancing rate during the working period followed by a sudden spike
after retirement. The dierence may results from the introduction of RMs into our model, such
that households can use RMs as a substitution for renancing with the additional benet of no
monthly repayments and an embedded put option of housing price; thus the renancing rate
becomes moderate after retirement.
Our main ndings suggest that RMs play a signicant role in eectively smoothing household
consumption over the household life cycle. The consumption growth volatility of households with
RMs is reduced by 17.04% (working) and 8.36% (retiring) because RMs allow senior households
to extract home equity and address the reduction in income that typically occurs after retirement.
In addition, RMs provide liquidation for senior households, which, in their earlier years, enables
them to save slightly less or extend their mortgage borrowing period. This enhanced exibility
contributes to the smoothing of their consumption not only during retirement but also throughout
their working period.
One possible limitation of our model is that our model generates a relatively high level of RM
take-up rate of 10% among eligible homeowners aged 62 to 65, with a decreasing trend as they
age. This take-up rate is higher compared to the rates reported in the existing literature on RMs.
It is important to note that our model assumes perfect nancial and housing market conditions
while overlooking the initial RM set-up costs and product costs. When taking into account such
costs, the take-up rate shall drop signicantly and be closer to the rates in the existing literature,
6
For example, CoreLogic and Black Knights both provide households’ demographic, socioeconomic characteris-
tics, household consumption and investment behaviours, alongside their housing condition, house prices, conven-
tional (rst lien) and reverse (second or junior lien) mortgage (if any) information.
4
such as Cocco and Lopes (2020) and Nakajima and Telyukova (2017). Another reason for the high
take-up rate in our model is that under our equilibrium setting, households in our panel assume
perfect access to housing and credit markets without friction and information asymmetry, such
that they can make rational decisions on savings, consumption, mortgages, and RMs, as well as
housing. This is in line with the statements that the current RM market is far from saturated;
hence the take-up rate in the housing and credit market equilibrium in our model shall be higher
than the rates reported in the data and other papers that specically target the take-up rates.
To evaluate the eect of RMs on both the housing market and households’ welfare, we evaluate
an alternative economy without RMs in the credit market, with all other parameters held constant
as in our economy with RMs. We nd that given the same housing supply, house prices increase
signicantly (from
0
.
66%
to
1
.
90%
) in the economy with RMs. Meanwhile, homeowners attain
substantial welfare gains measured by the equivalent consumption variation as 1.29% (age <62),
4.77% (age 62 - 75) and 7.47% (age >75). Renters, on the other hand, enjoy marginal welfare
improvement. Moreover, households in the economy with RMs experience enhanced consumption
smoothing. Therefore, these ndings suggest that the introduction of RMs as a nancial product
for trading liquidations enhances the eciency of the housing market and benets the households.
Our paper builds on a large body of literature that studies senior households’ consumption
and investment behaviours and household balance sheet dynamics such as Cocco et al. (2005) and
Gourinchas and Parker (2002). These papers emphasize the importance of household balance sheet
dynamics through the life cycle, and the transition from the young, working and saving phase into
the retirement and consumption phase. Most of these papers overlook the role of home equity and
its interaction with other factors, such as the bequest motive and medical expense risk, in shaping
homeownership decisions of households. In contrast, our paper takes into account households’
decisions regarding homeownership and the utilization of home equity, including the consideration
of reverse mortgages. Therefore, our paper provides a more comprehensive understanding of
the dynamics and implications of homeownership decisions, as well as the potential benets and
challenges associated with RMs.
Further, our paper contributes to another strand of papers on household decisions on mortgage
default, which emphasizes the role of house prices and home equity extraction, such as the earlier
5
empirical papers, Campbell (1983), and later Deng et al. (2000) states borrowers do not default
when home equity becomes negative immediately, but wait until the default is irreversible and
their option to default is deep in the money. Chen et al. (2020) follows Campbell and Cocco
(2003)’s partial equilibrium approach and integrates mortgage renancing and home-equity-based
borrowing (HELOC). During the recession, when facing negative income shock, liquidity-driven
households renance, even with higher borrowing costs particularly more pronounced. This is in
contrast with traditional models that predict renancing activities are mainly driven by lowered
interest rates. Our paper contributes to this strand of literature that in our household panel,
households make decisions to buy or rent houses, borrow mortgages and RMs, under standard
life-cycle utility maximizing conditions, and housing and credit market equilibria.
Our paper is also related to the literature on reverse mortgages. For example, Cocco and
Lopes (2020) derives the household utility from remaining in their residential home, dampened
by large product costs and maintenance costs as a standard requirement of RM, leading to a
low borrowing rate.
7
In addition, they nd RMs with insurance against forced home sales (due
to large medical expenses) induced improving demand for RMs. The estimates of the group of
households who may potentially benet from RM varies signicantly due to dierent assumptions.
8
Nakajima and Telyukova (2017) nd that senior households face complex trade-os considering
various factors such as bequest motives, the desire to age in place termed by Cocco and Lopes
(2020) (strong to stay in current residence for retirement long-term), retirement cash shortfall,
longevity and health uncertainty, as well as interest rate and ination rate uncertainty. Nakajima
and Telyukova (2017)’s key model results include ex ante and ex post welfare benet of RM
borrowers.
9
Our model results are in comparison to Nakajima and Telyukova (2017)’s on welfare
7
Campbell and Cocco (2003) estimate only of 2-3% senior homeowners among eligible elderly homeowners
borrow RM, as reported by the US Census Bureau. On the other hand, Nakajima and Telyukova (2017) estimate
this ratio to be 1.9% in 2013, down from 2.1% in 2011.
8
Using dierent assumptions, Rasmussen et al. (1995) uses public microdata and estimate potential uses of
RMs, assuming retired households with home equity exceeding $30,000 and without mortgage loans potentially
benet from RMs, while Merrill et al. (1994) assumes potential RM borrowers with (1) home equity ranges from
$100,000 - $200,000 and (2) with annual income less than $30,000, (3) with strong intention of aging in place (4)
and owns home outright, Merrill et al. (1994) estimate of 9% of eligible homeowners could benet from RMs, while
Rasmussen et al. (1995) argue this ratio is about 80%.
9
Their key model results include ex ante welfare benet of RM for retirees aged 65, which is equivalent to a
lump-sum transfer of $252 per retired homeowner (0.84% of median annual after-tax income); the ex post welfare
gains for actual RM borrowers, equivalent to a lump-sum of $1,770 per borrower (5.1% of median annual income)
Also, the lowest income group (with a take up rate of 2.2%) with low wealth, poor health use RM to support
6
gains such that RMs aect households in our panel with a welfare gain for RM borrowers. Finally,
both Cocco and Lopes (2020) and Nakajima and Telyukova (2017)’s model generate low demand
for RM that matches well with empirical data
10
. However, they assume exogenous house prices,
mortgage rates, and reverse mortgage (RM) rates, while our model takes a dierent approach by
endogenizing both the housing and credit markets. This allows us to capture the feedback eects
and feedback loops that exist between these markets, leading to a more accurate assessment of
the impacts and outcomes of RMs on household decisions and welfare.
Lastly, our paper is also part of the literature on the interaction between mortgage and hous-
ing market. Several papers on conventional mortgages provide an earlier general equilibrium
framework with dynamic factors such as household characteristics and nancial variables such as
interest rate, ination, and house price. For example, Campbell and Cocco (2015) solve for house-
holds’ optimal decision on mortgage choice (FRM and ARM) and default decisions, incorporating
households’ labour income, house price, interest rate and ination rate risk. Under the zero-prot
lender function framework, they solves for equilibrium mortgage premia through a micro-founded
model. In addition, Kung (2014) develop an equilibrium model of housing and mortgagemarkets
where houseprices, mortgage interestrates, and leverage ratios are all determined endogenously.
Our paper introduces another mortgage product into the market. By considering the interaction
between multiple mortgage products, such as conventional mortgages and reverse mortgages, our
model captures the dynamics and complexities of the mortgage market more comprehensively.
The rest of the paper is organized as follows. Section 2 highlights the importance of RM from
the data. Section 3 introduces the model’s setup. Section 4 shows the calibration, and Section 5
presents the quantitative analysis. Section 6 concludes.
2 Empirical Motivation
RMs have emerged as a popular nancial instrument for senior households to nance their costs
and consumption during retirement. Since the rst RM was issued in the 1960s in US and UK,
consumption and medical expenses, although the general eligible population has a take-up rate of less than 1%
10
Nakajima and Telyukova (2017)’s model generates low demand of RM (0.89%), which matches with empirical
evidence (0.84%) from 1997-2013, and they nd the key factors that dampen demand of RM are bequest motives
and up-front costs, and analyzed the quantitative impacts of these factors on RM demand
7
these products have gained popularity in developed economies globally, including the US, UK,
Australia, Canada, Hong Kong, South Africa over the past two decades due to their unique
feature of allowing homeowners to extract the value of their homes without moving out. Many
emerging markets, such as Brazil, Chile, South Africa, and Thailand, have also adopted RMs. In
this paper, we focus on the US markets. Using proprietary dataset through Corelogic and Black
knights, we have access to a complete and granular dataset on household mortgage open liens
(up to four liens) information, including rst lien which is the conventional mortgage, and reverse
mortgage are identied as “Mortgage Subordinate Type” loans.
The advantage of our dataset is that ours covers the actual mortgage and RM borrowers’
property information such as their historical and market value, housing type and condition, as
well as all mortgage and reverse mortgages (initial balance, interest rate, terms, etc.) secured
on the properties in the entire country during our research period, which covers almost all of
the properties secured on such mortgages. Other datasets used in previous literature such as
Panel Study Income Dynamics (PSID) and Health Retirement Study (HRS) are surveys only
covering a subset of the population. These types of surveys use estimation and various weighting
methodologies which can sometimes make the model results biased because RM is a relatively
small market compared to conventional mortgages and other more developed nancial products.
This makes our contribution distinct and essential.
As depicted in Figure 1, calculated using the number of RMs in any given year throughout
the research period, divdided by eligible senior households in the US (statistics estimated from
Census), we rst notice that the RM take-up rate in the US has increased almost ten-fold, from
approximately 0 .3% in 1997 to 2.8% in 2021. Over the course of its development, RM has expe-
rienced several major milestones. The rst FHA-insured HECM was issued in 1989, followed by
the rst major news of HECM become permanent product by Housing and Urban Department
(HUD) Appropriations Act in 1994. During the 2000s’ housing market boom, demand for RM
surged such that homeowners take advantage of the insurance of housing value embedded in the
RM contract. At the same time, more lenders join the RM game as HUD increase origination
fees and engage American Association of Retired Persons (AARP) to improve counselling services
to boost the RM market. More rules were relaxed such as renancing existing HECM became
8
possible. RMs became ever more important for the elderly to boost their retirement incomes, and
proprietary RMs specically designed for those who are not eligible for HECM schemes emerged
in the market.
A second observation on Figure 1 is the obvious drop (from 1.4% to 1%) from 2008 to 2011.
Since the GFC in 2008, some lenders left the market, and proprietary RM disappeared for a while.
This results in RM plan issuance in the US reduced following the GFC (see Cocco and Lopes
(2020)). There is a similar eect in the UK market, which is evidenced in Figure 2 panel (a) from
2007 - 2011, during which the market contract by almost 2/3. This is due to the correction of the
US and international housing market following the previous articial housing boom from 1990s
to 2006. RMs were hit harder because the lending criteria is mainly based on LTV which heavily
relied on housing market performance. The US RM market gradually recovered in 2011 and has
increased signicantly over the past decade. Moreover,the newly approved legislation in 2015 of
RM being used as down payment for a property of the eligible senior homeowners’ ospring gives
another boost of this market.
A third observation on Figure 1 is the un-interrupted growth in the US RM market following
the Coronavirus crisis (COVID-19). This is in contrast to the market contraction following GFC.
The UK RM market initially suered a minor contraction (2019-2020) but quickly recovered from
2020 onwards. These can be seen in the panels of Figure 2 panel (a). Post-COVID-19 crisis
is a regime of the high interest rate as the central banks increase base rate multiple times in
short period of time, in order to cool o the ination build up due to the pro-longed extra-low
interest rate regime following the GFC. The empirical experience of international RM market
growth following the COVID-19 crisis is in contraction to some prediction that usually hightened
interest rates cool down the housing market and mortgage market, due to higher (re)nancing
costs. However, the surge of RM in the post-COVID-19 crisis regime supports the conclusion by
Hurst and Staord (2004) such that enabling households to converting home equity into liquid
assets re-adjusts households’ decision to re-nance, even at the costs of higher borrowing costs.
This is one of the reasons that RM becomes increasingly important in household nance and credit
literature such that RMs provide a direct way to borrow against home value, as an alternative to
mortgage renancing. For example, Chen et al. (2020) overshoot the average renancing rate (11%
9
by the model versus 7% in the empirical data) and the size of cash-outs conditional on renancing
(by nearly a factor of three). Such overestimation can be explained by the existence of RMs in
the credit market which boost the household’s renancing activities. Another direct factor that
boost UK RM market surge in the post-COVID-19 regime is the combination of negative labour
income shock, inated living costs, and energy crisis in Europe exacerbated by the war between
Russia and Ukraine.
In summary, the two crises periods (GFC in 2008 and COVID-19) have caused opposite RM
market movements due to varying dominant factors of central bank base rates, housing market
performances and labour income instability. These dynamics on the household balance sheet and
decision choices make the integration of consideration of LTV and LTI constraints and economic
states essential and highlight our contribution to this end.
1997 2002 2007 2012 2017 2022
Date
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Rate (%)
Figure 1: Take-up Rate of RM in the US
At the same time, the recent boom (in the past decade) in the international RM markets is
captured in Figure 2 (all panels). The consistent growth pattern has already been observed in
several developed countries such as the UK, Australia and Singapore (See details in Appendix),
with similar socio-economic, demographic shifting trend, pension system, as well as nancial
market advancement and consumer nancial literacy level. As a high-level snapshot, Figure 2
panel (a) and (c) shows the number of new RM plans (including all types such as lump sums,
draw downs, withdrawals and home reversion plans) in the UK and Hong Kong, respectively,
10
during the 2005 - recent period. In comparison, panel (b) shows the active number of RM plans
in any given year in Australia for the same period, allowing expired plans to drop out from the
database. In addition, according to Securities et al. (2018), from 2013 to 2017, there are more
than 17,000 RM plans issued by lenders, hence the market has the potential to reach up to 58,000
active plans in 2017, presented by the dash line from 2013-2017. All panels show signicant growth
in our studies during the past two decades. This signals strong and growing demand and supply
of the RM products in these countries, although with some uctuations (caused by crises), which
shows potential for this product to be popular in other countries with growing ageing population,
housing market and homeownership rate, as well as the (lack of) social security system. This
motivates our interest in quantitatively assess the impacts of RM on household decisions, the
housing market, and conventional mortgage rates. Moreover, while the take-up rate is small in
the US, the size of the RM market that it implies is nontrivial.
Finally, Figure 3 shows the growing trends of the conventional mortgage rates, reverse mort-
gage rates, and the housing price index (HPI) in the US since 2005 to recently. It reveals that, as
anticipated, reverse mortgage rates generally exceed conventional mortgage rates to compensate
the riskiness of such instruments. Although uctuating, there has been notable declines during
the past two decades, mainly due to increase of lenders’ appetite and improved regulation and
consumer knowledge on the product. In some periods, reverse mortgage rates fall below conven-
tional mortgage rates during housing and credit market frictions, e.g. the period following the
GFC in 2008, during which HPI drops signicantly, coupled with extra low interest rates. The
inherent reason of the lowered RM rate is driven by both the low central bank base rate and lack
of appetite of both consumers and lenders. RM rates recovered as the HPI gradualy picked up in
2010, and stayed above the conventional mortgage rates. Another period of RM rates sharp drop-
ping below the conventional mortgage rates is the period immediately following the Coronavirus
crisis (COVID-19) period in late 2019, but it quickly picked up and followed the pattern of ARM
since then. This is a short-term negative shock on the RM rates possibly due to the unstable
market activities due to COVID-19 crisis.
In recent years, there has been a remarkable increase in the HPI accompanied by signicant
decreases in both mortgage and reverse mortgage rates. This observation emphasizes the dynamic
11
1990 1995 2000 2005 2010 2015 2020 2025
Year
0
10000
20000
30000
40000
50000
60000
Number of RMs
(a) UK
2005 2010 2015 2020
Year
0
10000
20000
30000
40000
50000
60000
Number of RMs
(b) Australia
2010 2015 2020 2025
Year
0
1000
2000
3000
4000
5000
6000
7000
Number of RMs
(c) Hong Kong
Figure 2: Number of RMs in Dierent Markets
12
2005 2010 2015 2020 2025
Date
0
2
4
6
8
10
Rate (%)
RM rate
ARM
HPI
0
64
128
192
256
320
HPI
Figure 3: Mortgage Rates, Reverse Mortgage Rates, and Housing Price Index in the
US
nature of these variables and calls for integrated framework when considering reverse mortgages.
Such a framework should consider the interplay between the mortgage market and the housing
market, recognizing their simultaneous inuence on reverse mortgage dynamics.
3 Model
This section presents an annual equilibrium model considering the decisions of households and
nancial intermediaries. Households have a nite living span divided into two phases: the working
period and the retirement period. Over the lifecycle, households earn labor income (pension in
retirement) and allocate wealth to consumption, nancial investment, and housing. The nancial
market only provides a riskless bond. In addition, households can nance for housing by loaning a
mortgage in the working period and accessing home equity using a reverse mortgage with monthly
payments after retiring. Financial intermediaries decide mortgage and reverse mortgage spreads,
while the riskless interest rate is exogenous and depends on the economic state.
13
3.1 Economy
We use a discrete Markov process {Θ
t
} to describe the macroeconomic situation including ve
states: (1) Crisis With Tight Credit; (2) Recession With Tight Credit; (3) Expansion with loose
credit; (4) recession with tight credit; (5) Expansion with tight credit. We further assume that
Θ
t
determines the real interest rates (including riskless rate R
f
t
, mortgage rate R
m
t
and reverse
mortgage rate R
rm
t
) and real aggregate labor income Y
(agg)
t
.
The house price P
t
is determined by the equilibrium of the housing market each period. The
equilibrium also depends on the households’ distribution Π
t
. In summary, we denote the aggregate
state as a vector Σ
t
= (Θ
t
, P
t
, Ω
t
)
′
and the house price function as P (Ω
t
).
3.2 Households
Following the convention in life-cycle models, we assume households start working at 20 (t
0
= 0),
retire at 65 (K = 45), and can live up to 100 (T = 80).
3.2.1 Labor Income
Before retirement, households’ labor income is exposed to both aggregate shocks from the economic
state and idiosyncratic shocks. Specically, the labor income Y
it
is determined by the following
equation:
ln Y
it
= ln Y
p
it
+ ϵ
it
, t ≤ R, (1)
where the transient shock ϵ
it
follows N(0, σ
2
ϵ
) and the permanent labor income Y
p
it
is given by:
ln Y
p
it
= ln Y
(agg)
t
(
θ
t
) + u
it
,
(2)
where Y
(agg)
t
is a function of macroeconomic situation θ
t
and u
it
is normally distributed as
N(0, σ
2
u
(θ)).
After retirement, households still face aggregate and keep the same idiosyncratic income they
14
had at age R, reduced by ρ log points:
Y
it
= λY
p
iR
, t > R, (3)
There is a progressive tax system for households given by:
τ(Y
it
) = τ
y
Y
it
. (4)
3.2.2 Housing and Rental Market
Households can decide the housing size H
it
and to be a homeowner (denoted as o = 1) or a
renter(denoted as o = 0), of which the cost and utility are dierent. Each period, homeowners
must pay a maintenance cost C
ma
(H
it
|P
t
), while renters face a renting cost C
r
:
C
ma
(H
it
|P
t
) = c
ma
H
it
P
t
, (5)
C
r
= q. (6)
The homeowners get a utility benet as u
o
. We also assume that households may be shocked and
forced to move with a probability p
m
with moving cost C
ms
(H
it
|P
t
):
C
ms
(H
it
|P
t
) = k
ms
Y
p
it
+ c
ms
H
it
P
t
. (7)
In our paper, we do not dierentiate the owner-occupied house price and the rental property
price and only consider the equilibrium of owner-occupied housing stock.
3.2.3 Mortgage
In our modeling framework, working households have access to conventional residential mortgages
when purchasing houses, and can decide the fraction of down payments constrained by Loan-to-
value ratio (LTV) ϕ
m
determined by the macroeconomic state Θ. Specically, denote M
it
to be
the mortgage balance for household i at the start of period t, and for newly issued mortgages, the
15
initial balance M
it
satises:
M
it
≤ ϕ
m
(θ
t
)P
t
H
it
. (8)
Required mortgage payments depend on the type of mortgage. For simplicity, we only model
one type of the main residential mortgage, which is the long-term xed-rate mortgage (FRM).
Households with an FRM bear the same mortgage rate determined by the aggregate shock Θ
t
at
origination. Here we assume that mortgage rates do not change among individuals in the same
economy.
According to Guren et al. (2021), with the timing assumption that households pay their interest
between periods t and t + 1 in advance at time t, the minimum payment on a mortgage for an
agent who does not move or renance with age a
it
is given by:
M
it−1
− M
it
(1 − R
m
t
) ≥ M
it−1
R
m
it
(1 +
R
m
it
1 − R
m
it
T −a
it
+1
R
m
it
1 − R
m
it
T −a
it
+1
− 1
, (9)
where T is the term of the mortgage.
3.2.4 Reverse Mortgage
During their whole life, homeowners can liquidate the home value for consumption by selling. In
our model, we also allow the retiree to access the home value without selling it through RMs.
In the real market, lenders provide several types of payments for borrowers to choose from. For
simplicity, we only introduce a lump-sum RM, which is a single large payout at closing and
accumulates with variable interest rates until termination. Denote the RM balance as M
rm
it
, and
the initial balance is constrained by a function of age a
it
and the macroeconomic state Θ
t
:
M
rm
it
≤ ϕ
rm
(Θ
t
, a
it
)H
it
P
t
. (10)
The balance M
rm
it
includes the initial loan fee rate (arrangement and valuation fees) c
rm
0
and thus
the household will receive (1 − c
rm
0
)M
rm
it
at closing of the origination.
16
The reverse mortgage balance accumulates with the reverse mortgage rate R
rm
t
and the annual
loan fee rate c
rm
a
. Households are allowed to prepay at each period and the balance after the
settlement satises:
M
rm
it
≤ M
it−1
(1 + R
rm
t
+ c
rm
a
). (11)
The RM will terminate whenever the borrower moves or dies and will get paid at most of the
home value. The potential loss is insured by the insurance company. Thus, the mortgage rate
R
rm
t
includes both RM spread and insurance premium.
3.2.5 Health Risk and Medical Cost
Older households face medical expense conditional on health states. We assume that the health
state I
health
it
of household i in period t is a Markov process independent of the economic state and
idiosyncratic states. The health state I
health
it
can be either good (I
health
it
= 0) or bad (I
health
it
=
1). We further assume households start to have health risk after retiring and the probability of
transitioning from a good to a bad health state is 0.2 in each period. Households are assumed
to be in good health prior to retirement and keep the bad health state whenever they enter it.
Household i pays a medical expense c
med
(I
health
it
, a
it
)Y
it
with a rate c
med
determined by the health
state I
health
it
and the age a
it
.
3.3 Households Optimization Problem
At the start of each period t before making decisions, we can dene household i’s idiosyncratic
state S
it
including age a
it
, idiosyncratic labor income Y
p
it
, saving W
it
, ownership o
it
, mortgage
balance M
m
it
, mortgage accumulated rate R
m
it
, mortgage default ag d
it
, RM balance M
rm
it
, and
moving indicator m
it
as:
S
it
= (a
it
, W
it
, o
it
, M
it−1
, R
m
it−1
, M
rm
it−1
, m
it
)
′
. (12)
17
And household i makes decisions A
it
of saving, housing, loans’ states:
A
it
= (I
it
, s
it+1
, M
m
it+1
, M
rm
it+1
)
′
, (13)
where I
it
takes −1 if defaulting, 0 if renting, 1 if remaining the previous housing state, 2 if moving,
3 if buying a new house as a renter, 4 if renancing and 5 if initializing reverse mortgage. Given
S
it
and A
it
, household i faces total cost ϕ
c
(S
it
, A
it
) from housing, moving (shocked or voluntary
moving) and nancial service (renance):
ϕ
c
(S
it
, A
it
) =o
it+1
c
ma
H
it
P
t
+ (1 − o
it+1
)q + m
it
(k
ms
+ c
ms
P
t
)
+ (I
it
= 4)(k
re
+ c
re
M
m
it+1
). (14)
And the consumption C
it
determined by S
it
and A
it
is constrained to be positive:
C
it
(S
it
, A
it
|Σ
t
) = [Y
it
− τ (Y
it
)] −
W
it+1
1 + R
it
− W
it
− ϕ
c
(S
it
, A
it
) + (o
it+1
− o
it
)P
t
+ (I
it
≥ 0)
(1 − R
m
it
+1
)M
it+1
− M
it
+
M
rm
it+1
− (1 + R
rm
t
)M
rm
it
. (15)
One can understand equation (15) as dierent channels to nance consumption, cost, and inter-
est payments: (1) after-tax labor income; (2) saving; (3) house selling; (4) net cash ow from
mortgages. The total wealth Q
it
of household i can be computed by:
Q
it
(S
it
|Σ
t
) = W
it
− M
m
it
+ o
it
max(P
t
− M
rm
it
, 0). (16)
The households’ value function is dened as follows:
V (S
it
|Σ
it
) = max
I
it
V
I
it
(S
it
|Σ
it
)
. (17)
We rst denote p
s
is the survival probability to be alive at period s + 1, {C
it
} is the consumption
level, H
it
is the housing size, Q
it
is the amount of bequeathed wealth, β
i
is the discount factor,
γ
i
is the coecient of relative risk aversion, u
0
describes the utility from homeownership, ξ is the
bequest motive shifter.
18
Households lacking current housing and devoid of credit record defaults are faced with a
signicant choice: either to acquire a house through a new mortgage or to continue renting.
Renters with credit record defaults are precluded from pursuing homeownership. In the event that
homeowners experience a moving shock, they are confronted with the decision of either defaulting
on their existing mortgage and transitioning to renting or paying o the mortgage balance. By
opting for the latter, homeowners gain the exibility to freely choose between renting or obtaining
nancing for a new home purchase. Conversely, if homeowners do not encounter a moving shock,
they must evaluate the alternatives of defaulting, renancing, or fullling the minimum mortgage
balance.
Every period, households that remain to be renters have the value function
V
0
(S
it
|Σ
it
) = max
w
it+1
C
1−γ
i
it
1 − γ
i
+ α
ia
H
it
+ u
o
o
it+1
(18)
+ β
i
p
s
(a
it+1
)E
t
[V (S
it+1
|Σ
it+1
)] + (1 − p
s
(a
it+1
))ψ
bq
(Q
it
+ ξ)
1−γ
i
1 − γ
i
(19)
s.t. o
it+1
= M
m
it+1
= M
rm
it+1
= 0, (20)
d
it+1
= 0, (21)
C
it
(S
it
, A
it
|Σ
t
) > 0. (22)
Alternatively, households that decide to purchase houses and take on the mortgage have the
value function
V
4
(S
it
|Σ
it
) = max
w
it+1
C
1−γ
i
it
1 − γ
i
+ α
ia
H
it
+ u
o
o
it+1
(23)
+ β
i
p
s
(a
it+1
)E
t
[V (S
it+1
|Σ
it+1
)] + (1 − p
s
(a
it+1
))ψ
bq
(Q
it
+ ξ)
1−γ
i
1 − γ
i
(24)
s.t. o
it+1
= 1, (25)
M
m
it
≤ ϕ
m
(θ
t
)P
t
H
it
, (26)
R
m
it
= R
m
(θ
t
), (27)
M
rm
it
= 0, (28)
C
it
(S
it
, A
it
|Σ
t
) > 0. (29)
19
Subsequent to the initial purchase, households that select to retain their homes without en-
gaging in renancing and without encountering any moving shocks have the value function
V
1
(S
it
|Σ
it
) = max
w
it+1
C
1−γ
i
it
1 − γ
i
+ α
ia
H
it
+ u
o
o
it+1
(30)
+ β
i
p
s
(a
it+1
)E
t
[V (S
it+1
|Σ
it+1
)] + (1 − p
s
(a
it+1
))
(Q
it
+ ξ)
1−γ
i
1 − γ
i
(31)
s.t. o
it+1
= o
it
, (32)
M
m
it−1
− M
m
it
(1 − R
m
t
) ≥ M
m
it−1
R
m
it
(1 +
R
m
it
1 − R
m
it
T −a
it
+1
R
m
it
1 − R
m
it
T −a
it
+1
− 1
, (33)
M
rm
it
≤ M
rm
it−1
(1 + R
rm
t
), (34)
d
it+1
= 0, (35)
C
it
(S
it
, A
it
|Σ
t
) > 0. (36)
Households that experience default may lose their homes, but their savings remain intact.
These households, when faced with default, make decisions regarding consumption and savings
while considering their value function
V
−1
(S
it
|Σ
it
) = max
w
it+1
C
1−γ
i
it
1 − γ
i
+ α
ia
H
it
+ u
o
o
it+1
− u
d
(37)
+ β
i
p
s
(a
it+1
)E
t
[V (S
it+1
|Σ
it+1
)] + (1 − p
s
(a
it+1
))ψ
bq
(Q
it
+ ξ)
1−γ
i
1 − γ
i
(38)
s.t. o
it+1
= M
m
it+1
= M
rm
it+1
= 0, (39)
d
it+1
= 1, (40)
C
it
(S
it
, A
it
|Σ
t
) > 0. (41)
Households that renance make the same choices, but pay the xed and variable costs of
renancing (which can be rolled into their new mortgage) and face the LTV constraint rather
20
than the constraint. They have the value function
V
3
(S
it
|Σ
it
) = max
w
it+1
C
1−γ
i
it
1 − γ
i
+ α
ia
H
it
+ u
o
o
it+1
(42)
+ β
i
p
s
(a
it+1
)E
t
[V (S
it+1
|Σ
it+1
)] + (1 − p
s
(a
it+1
))ψ
bq
(Q
it
+ ξ)
1−γ
i
1 − γ
i
(43)
s.t. o
it+1
= 1, (44)
M
m
it
≤ ϕ
m
(θ
t
)P
t
H
it
, (45)
R
m
it
= R
m
(θ
t
), (46)
M
rm
it
= 0, (47)
C
it
(S
it
, A
it
|Σ
t
) > 0. (48)
Households that take up RMs solves
V
5
(S
it
|Σ
it
) = max
w
it+1
C
1−γ
i
it
1 − γ
i
+ α
ia
H
it
+ u
o
o
it+1
(49)
+ β
i
p
s
(a
it+1
)E
t
[V (S
it+1
|Σ
it+1
)] + (1 − p
s
(a
it+1
))ψ
bq
(Q
it
+ ξ)
1−γ
i
1 − γ
i
(50)
s.t. o
it+1
= 1, (51)
M
m
it
= 0, (52)
M
rm
it
≤ ϕ
rm
(θ
t
, a
it
)H
it
P
t
, (53)
C
it
(S
it
, A
it
|Σ
t
) > 0. (54)
In our model, households borrowing on a RM can exibly decrease their loan balance at any time.
However, it is worth noting that in reality, reverse mortgage lines of credit often prohibit partial
repayment until the loan is fully settled. Furthermore, in reality, households have the capacity to
accumulate nancial assets while simultaneously borrowing against an RM, which is not accounted
for in our model. Consequently, we interpret the exible adjustment of the RM loan balance in
our model as an approximation of this absent supplementary saving avenue.
Households that move choose their consumption, savings, mortgage balance if they purchased
21
the houses, and RM balance if they took up the RMs. They have the value function
V
2
(S
it
|Σ
it
) = max
w
it+1
C
1−γ
i
it
1 − γ
i
+ α
ia
H
it
+ u
o
o
it+1
(55)
+ β
i
p
s
(a
it+1
)E
t
[V (S
it+1
|Σ
it+1
)] + (1 − p
s
(a
it+1
))ψ
bq
(Q
it
+ ξ)
1−γ
i
1 − γ
i
(56)
s.t. M
m
it
≤ ϕ
m
(θ
t
)P
t
H
it
, (57)
M
rm
it
= 0, (58)
C
it
(S
it
, A
it
|Σ
t
) > 0. (59)
3.4 Mortgage Lenders
We assume that mortgages are supplied by competitive lenders who discount payos using an
SDF m
t,t+1
, which is a function of today’s aggregate state Θ
t
and tomorrow’s state Θ
t+1
. We will
calibrate the SDF from the data and use it as the pricing kernel in the equilibrium.
The net present value Π(S
jt
|Σ
t
) of the expected payments from the mortgage originated to
household j before termination is dened iteratively as:
Π
m
(S
jt
|Σ
t
) =
p
s
(a
jt
)
(I
it
= 1) (M
t−1
− M
t
(1 − R
m
t
) + E
t
[m
t,t+1
Π
m
(S
jt+1
|Σ
t+1
)])
+(I
it
= 0)λP
t
(I
it
= 2, 3)M
t−1
+ (1 − p
s
(a
jt
)) min(M
t−1
, w
jt
+ P
t
), a
jt
< T
m
p
s
(T
m
) ((I
it
= 0)λP
t
+ ( I
it
̸= 0)M
t−1
) + (1 − p
s
(T
m
)) min(M
t−1
, w
jt
+ P
t
), a
jt
= T
m
(60)
Π
rm
(S
jt
|Σ
t
) =p
s
(a
jt
)E
t
[m
t,t+1
Π
rm
(S
jt+1
|Σ
t+1
)] + (1 − p
s
(a
jt
)) min(M
rm
t−1
, P
t
) (61)
where λ is the foreclosure sale recovery rate.
3.5 Equilibrium
A competitive equilibrium for this economy consists of a law of motion for the aggregate state Σ
t
, a house
price function P (Σ
t
), mortgage rates R
m
(Θ
t
). R
rm
(Θ
t
), and an optimal decision rule A
it
for households,
which satises:
22
• Given the xed supply of homes, the housing market clears:
o
it
dΩ
t
=
o
it+1
dΩ
t+1
. (62)
• The mortgages’ lenders reach (exogenous) returns under the mortgages rates:
E
Θ
t
=Θ
i
E
Ω
orig
t
(S
jt
)
m
t,t+1
Π
x
(S
jt+1
|Σ
t+1
) − (1 − R
x
(Θ
i
))M
a
jt
= 0, x ∈ {m, rm}, ∀Θ
i
, (63)
where Ω
orig
t
is the distribution of newly originated mortgages at time t.
3.6 Solution Method
Solving the equilibrium requires households to forecast the law of motion for Σ
t
, which, however, includes
an innite-dimensional object Ω
t
. To address the problem, we follow the implementation of the Krusell
and Smith (1998) algorithm in Kaplan, Mitman and Viotante(2019). We focus directly on the law of
motion for home prices and assume that households use a simple AR(1) forecast rule that depends on
the economic states:
ln P
t+1
= f
(Θ
t
,Θ
t+1
)
(ln P
t
). (64)
We parameterize f as a linear spline:
f
(Θ
t
,Θ
t+1
)
(x) = b
hp
+
n−1
i=1
k
hp
i
(x − x
i
), (65)
where b
hp
, k
hp
i
depends on (Θ
t
, Θ
t+1
).
Denote the endogenous parameters of the equilibrium as Ξ = (b
hp
, k
hp
i
, R
m
, R
rm
)
T
. We further solve
the equilibrium numerically. First Initialize Ξ as Ξ
0
, and for n = 1, 2, · · ·
i) Solve the household’s optimization problem under Ξ
n−1
.
ii) Simulate 100,000 households for 19,000 periods with the home price decided by (62) each period.
iii) Estimate Ξ as Ξ
n
by (63) and (65) based on the simulation results.
23
iv) Terminate if:
||Ξ
n
− Ξ
n−1
||
∞
< ϵ. (66)
4 Calibration
We calibrate our baseline model with reverse mortgages using several data sources. To estimate the model,
we adopt a two-stage strategy, each with distinct purposes. Within our models, there are dierent sets of
variables related to macroeconomic states, human mortality and survival functions which are exogenous
variables, as well as initial mortgages and reverse mortgages interest rates. There are also variables
inherently estimated from our model setting such as mortgage and reverse mortgages interest rates at
equilibrium states, as well as household labour incomes, and their decisions on consumption, nancial
and housing conditions, etc.
In the rst stage estimation, we calibrate all the stand-alone parameters that can be clearly identied
without explicitly referring to our model setting. For example, the mortality and survival probabilities
are exogenous variables which do not depend on our model. Hence, we adopt such statistics published
by the National Center for Health Statistics to parameterize the conditional survival probabilities in
our transition matrix. In the second stage, we estimate the remaining parameters to align with spe-
cic moments of the empirical data, ensuring a overall goodness-of-t between the model and empirical
observations. Table 1 summarizes the calibrated parameter values.
4.1 First-stage Estimation
The rst-stage calibration process aims to simulate macroeconomics environments such as peaks, troughs,
recoveries and recessions for our model. In this process, we rst choose aggregate and idiosyncratic shocks
mimic the dynamics of modern business cycles in the US. subsequently, we exogenously calibrate a set of
parameters to widely accepted values found in the macroeconomic and housing literature.
Following Guren et al. (2021), we calibrate the Markov transition matrix between macroeconomic
states such as crisis, recession, and expansion based on the frequency and duration of such events dened
by NBER. Accordingly, crises happen every 75 years and that all other NBER recessions are regular,
cyclical recessions. Moreover, the economy switches to expansion following a crisis or recession. Another
assumption is that if the NBER peak of the previous expansion takes place in the rst half of a given
24
Table 1: Model Parameters in Baseline Parameterization
The table shows parameters for the baseline calibration. Average income is normalized to one. There are ve
aggregate states, θ
t
∈ {Crisis With Tight Credit, Recession With Tight Credit, Recession With Loose Credit,
Expansion With Tight Credit, Expansion With Loose Credit}, but we assume that income and monetary policy
are the same in a recession with loose or tight credit and in an expansion with loose or tight credit. The tuples of
interest rates reect the interest rate in a crisis, recession, and expansion, respectively.
Parameters Description Value
T Years in life 80
R Retirement age 62
ρ Log income decline in retirement 0.35
τ
0
Constant in tax function 0.8
τ
1
Curvature tax function 0.18
γ CRRA 3.0
ξ Bequest motive shifter 0.5
ψ
bq
Bequest motive multiplier 250
u
o
Utility from homeownership 10
β Discount factor 0.98
Υ Foreclosure sale recovery 0.654
ϕ
m
(Loose) Max LTV, loose credit 0.95
ϕ
m
(tight) Max LTV, tight credit 0.80
ϕ
rm
Max LTV, reverse mortgage 0.50
c
ms
Variable moving cost rate 3.0%
k
ms
Fixed moving cost 0.1
c
re
Variable renance cost rate 1.0%
k
re
Fixed renance cost 0.04
u
d
Default penalty 10
q Rent cost 0.20
c
ma
Maintenance cost rate 0.025
p
ms
(working) Prob. of moving, working 1/9
p
ms
(retiring) Prob. of moving, retiring 0.02
p
md
Prob. of default ag removed 0.1
c
rm
0
Initial fee of reverse mortgage 0.04
c
rm
a
Annual fee of reverse mortgage 0.025
H
r
Homeownership rate 0.65
r Short rate [0.26%, 1.32%, 3.26%]
Y
(agg)
Aggregate income [0.0976, 0.1426, 0.1776]
c
me
(Age [65, 85))
Medical cost rate
0.15(good), 0.2(bad)
c
me
(Age [85, 100)) 0.25(good), 0.35(bad)
25
year, that year is classied as the rst year of the new recession, whereas if the peak happens during
the second half of a year, the recession follows in the subsequent year. The ending date of a recession
is dened as the next year after the start year of the expansion announced by the NBER because the
unemployment rate is a lagging variable and does not immediately fall after NBER troughs. According
to this denition, recessions took place during the periods 1991-1992, 2001-2002, 2008-2010, and 2020.
Another condition in our model needs calibration is the the labor income process, in which the
replacement ratio during retirement is set to 0.68, and the deterministic component of the labor income
process is set to be the same as that in Cocco et al. (2005). We use 0.1
2
for the transitory variance, which
is similar to the value used in Gourinchas and Parker (2002). For permanent income shocks, we rely on
the estimates in Guvenen et al. (2014) and Shen (2022), who estimate a quantitative labor income model
using a large and condential US dataset. We allow skewness to depend not only on the business cycle but
also on expected growth rates. The moments of permanent income shocks can be easily calculated based
on these estimates, and therefore, the parameters with respect to the mixture of normal distributions
during expansions and recessions can be calibrated. We then estimate the remaining moments to match
the rst four moments during expansions and the rst four moments during recessions. We adjust the
income process to ensure that the average aggregate income equals 1, as the normalization convention.
The tax system is calibrated following the method proposed in Heathcote et al. (2017).
Subsequently, we calibrate the lender’s Stochastic Discount Factor (SDF) to match the interest rate
and mortgage spread. Following Backus et al. (2011), we set the risk price for the crisis state to be
6.1 times that of non-crisis states. By doing so, we make sure that lenders charge a fair premium for
insurance against crisis states.
E
t
[m(Θ
t
, Θ
t+1
] =
1
1 + R
f
t
+ κ
(67)
where R
f
t
is the riskless rate in state Θ
t
. Lenders impose a requirement that guarantees a certain return
on investment for a certain payo of one unit at date t + 1. This return is determined by adding the cost
of making mortgage loans, denoted as κ, to the risk-free rate R
f
t
. In this case, we have set κ to 125 basis
points (bps) to ensure that the average dierence between the FRM rate and a 10-year bond is 1.65%.
To determine the risk-free rate, we calibrate it based on the historical real interest rate observed
between 1985 and 2022. Specically, during recessions, the risk-free rate is set at 2.32%, reecting the
lower economic activity and market conditions. During expansions, when the economy is performing
26
well, the risk-free rate is set at 4.26%. In the case of a crisis, we assume a signicantly lower risk-free
rate of 1.26% to account for the heightened uncertainty and economic instability.
Furthermore, we calibrate all the reverse mortgage parameters and age-dependent collateral con-
straints based on the existing RM contracts. Table 2 shows the principal limit factor for reverse mort-
gages from HECM. For example, for the age group 60-65 and RM interest rate of 4.26%, homeowners
can only borrow 45.4% of their home equity. Our primary source of data on mortgage performance is
CoreLogic and Black Knights. The RM interest premiums are endogenized, depending on the aggregate
states and conventional mortgage rates. Unlike conventional mortgages, the amounts of loans given de-
pends on the ages of the borrowers which increase as they age. The intuition is that as the borrowers’
ages increase, the anticipated interest costs decrease and the expected future house price appreciation
diminishes, and hence lower overall risk for the lenders. In general, the collateral constraint related to
conventional mortgages becomes more stringent as the borrowers age. In contrast, RMs provide a more
relaxed collateral constraint that loosens with age, resulting in a more favorable borrowing environment
at all stages of life.
Table 2: Principal Limit Factor for Reverse Mortgages
Age
RM rate 60-65 65-70 70-75 75-80 80-85 85-90 90-95
4.26% 0.454 0.474 0.507 0.533 0.572 0.624 0.681
4.32% 0.454 0.474 0.507 0.533 0.572 0.624 0.681
5.26% 0.396 0.417 0.452 0.479 0.522 0.58 0.644
4.2 Second-stage Estimation
In the second-stage estimation, we estimate the rest of the parameters related to households’ consumption,
nancial and housing decision with the method of simulated moments (MSM). In particular, we nd the
set of parameters yielding the simulated life-cycle decision proles that match the proles from the
empirical data best. The mechanics of our MSM approach are fairly standard. We compute life-cycle
histories for a large number of articial households. Each of these households is endowed with a specic
value for the state vector, and a series of idiosyncratic shocks are assigned to them in a manner consistent
with the stochastic processes explicated in Section 3.
To facilitate the computational process, we discretize the state space and employ value function it-
27
eration to numerically solve the model. This iterative procedure enables us to derive a set of decision
rules that govern the choices made by the households. By combining these decision rules with the simu-
lated endowments and shocks, we are able to simulate various aspects of household behavior, including
wealth accumulation, labor income, housing decisions, renancing, and the decision to take up RMs.
Subsequently, we compute age proles based on the articial household histories, employing the same
methodology used in the analysis of the actual data. We adjust until the dierence between the data
and simulated proles is minimized as follows
( ˆm − m)
′
W ( ˆm − m), (68)
where ˆm refers to the simulated moments, m refers to the targets, and W is the inverse of the covariance
matrix of the empirical moments, which is estimated by bootstrapping the true data.
The empirical evidence we are trying to match our model parameters are from the American Housing
Survey (AHS) and the Survey of Consumer Finances (SCF). We assume that households start working at
age 20, retire at age 65, may live up to age 100, and have CRRA type of utility. The estimated discount
factor β is 0.98, which is within the accepted range of estimates in models of this kind. The coecient
of relative risk aversion is 3, which is in the middle of the spectrum in the literature.
11
We choose the
bequest motive parameters to match the ratio of total net worth at age 60 to net worth at age 45 in the
SCF.
The processes of household moving and renancing are associated with both the xed and variable
costs. Specically, we have established the xed cost of moving to be equivalent to 10% of the average
household annual income, approximately amounting to $5,000. Additionally, proportional costs, incurred
by both buyers and sellers, are set at 3% of the house value to account for expenses such as closing costs
and realtor fees. Renancing entails a xed cost equal to 4% of the average annual income, roughly
equating to $2,000, along with a variable cost equivalent to 1% of the remaining mortgage balance. This
variable cost aligns with the average renancing costs reported by the Federal Reserve.
For renters, a monthly rent payment is set at 20% of their income to maintain a rent-to-income ratio
of 20%. On the other hand, homeowners are required to contribute a maintenance cost of 2.5% of the
house value annually. To ensure a realistic moving frequency, we calibrate the moving shock parameter
11
Yogo (2016) uses Epstein-Zin preferences to study the portfolio choice in retirement with health risk and derives
risk aversion coecient to be 5. Nakajima and Telyukova (2020) only focus on retirees aged 65 and above, and
calibrate the risk aversion to be 2 to t the age proles in the Health and Retirement Study (HRS).
28
in a manner that results in homeowners moving on average every nine years, as observed in the AHS.
Finally, the homeownership rate is adjusted to match the long-term average homeownership rate of 65%
in the United States. To be consistent with the average homeownership in the AHS, we assign a utility
benet of 10 to owning a home.
Following a foreclosure event, we assume that the bank recovers 65% of the property’s market value.
Additionally, we consider two scenarios: loosening credit v.s. tightening credit regimes. Under loosening
credit regime, the maximum LTV at origination is set at 95%, meaning borrowers can obtain a loan up to
95% of the property’s value. In contrast, under tightening credit regime, the maximum LTV is reduced
to 80%, limiting borrowers to a loan amounting up to 80% of the property’s value. To replicate the
observed foreclosure rate of 8% in the housing stock between 2006 and 2013, we set the default penalty
to 10.
5 Quantitative Analysis
In this section, we rst investigate whether the model is able to quantitatively match the homeownership,
wealth accumulation (decumulation) and other life-cycle patterns, and compare the model with and
without RMs. Then we study the take-up rate as well as welfare.
5.1 Life-cycle Proles
We simulate the decisions of saving, consumption, housing, and RMs of 100,000 households over the life
cycle and present the average proles in Figure 4. For comparision, we also report the average proles
in the SCF from 2007 to 2019. The model matches the life-cycle patterns in the SCF data well.
In Panel A of Figure 4, we present the homeownership rate patterns over the life cycle. The model’s
simulations yield an average homeownership rate of 65%, which aligns with the data. However, we
observe that the model tends to underestimate the homeownership rate for very young households and
overestimate it for middle-aged households.
Panels B and C of Figure 4 show the LTV and PTI ratio by age. Our model eectively captures the
LTV ratios for young homeowners; however, it tends to overpredict the LTV ratios for older homeowners
and increases steadily during the retirement. This discrepancy can be primarily attributed to the inclusion
of RMs in our analysis. Reverse mortgages allow older homeowners to borrow against their home equity,
which increases their available funds without the need to sell the property. When older homeowners opt
29
20 40 60 80 100
Age
0.0
0.2
0.4
0.6
0.8
1.0
(a) Homeownership rate
ERM
SCF
20 40 60 80 100
Age
0.0
0.2
0.4
0.6
0.8
1.0
(b) LTV for owners
20 40 60 80 100
Age
0.0
0.2
0.4
0.6
0.8
1.0
(c) PTI for owners
20 40 60 80 100
Age
0
2
4
6
8
10
(d) Net wealth
20 40 60 80 100
Age
0.0
0.2
0.4
0.6
0.8
1.0
1.2
(e) Consumption
Consumption
Labor income
20 40 60 80
Age
0.000
0.025
0.050
0.075
0.100
0.125
0.150
0.175
0.200
(f) Fraction of owners refinancing
Figure 4: Life-cycle Proles
30
for reverse mortgages, they receive funds based on the accumulated value of their homes. This inux
of borrowed funds increases the overall value of available resources for these homeowners, resulting in
a higher loan amount in the LTV ratio calculation. At the same time, since reverse mortgages do not
require regular repayments like traditional mortgages, the property value remains relatively unchanged.
As a result, the LTV ratio for older homeowners increases, indicating a higher proportion of borrowing
relative to the value of their homes. Moreover, we observe a close alignment between the PTI ratios and
the data for the elderly population, in contrast to the results presented in the study by Guren et al. (2021).
This is because the fact that older homeowners have access to RMs, which serve as an additional source
of funds for mortgage repayment. Consequently, their PTI ratios decrease as this supplementary income
from RMs helps to alleviate the burden of mortgage repayments. This contrast in ndings highlights the
signicance of considering the impact of reverse mortgages on the PTI ratios of older homeowners.
Figure 4, Panel D, shows the net wealth accumulation over the life cycle. We nd that households
are liquidity constrained during the rst 15 years of their working lives. However, as time progresses,
households start accumulating wealth at an accelerated pace. This accumulation of wealth serves as a
crucial form of insurance, providing a cushion against adverse labor income shocks and uncertainties
in the macroeconomic environment. During retirement, we observe a rapid decumulation of wealth.
This decumulation reects the utilization of accumulated assets to support living expenses and maintain
the desired standard of living during the retirement phase. Overall, the dynamic patterns of wealth
accumulation and decumulation throughout the life cycle emphasizes the signicance of building a robust
nancial foundation and managing resources eectively to address income uctuations and retirement
needs.
Figure 4, Panel E, shows the proles of consumption and income. Consumption closely tracks income
over the life cycle. During the early working years, as households face liquidity constraints, their income
levels are relatively lower. Consequently, their consumption levels also remain restrained. However,
as households progress in their careers and accumulate wealth, their income increases, leading to a
corresponding rise in consumption. As households continue to age, the impact of liquidity constraints
on consumption diminishes. This is reected in the consumption prole reaching a point where further
increases cease, despite income still rising. This pattern suggests that as individuals advance in age,
they become less constrained by liquidity concerns. During retirement, we observe a downward slope
in the consumption path. This decline indicates a decrease in consumption as households rely on their
accumulated wealth and retirement income sources to sustain their desired lifestyle. The reduced income
31
ow during retirement necessitates a more prudent approach to consumption.
Figure 4, Panel F, shows the fraction of owners renancing. Renancing is relatively low across
all ages. Compared with Guren et al. (2021), our model does not generate jumps at the retirement, as
homeowners have additional options to smooth their consumption and manage their nancial obligations.
The availability of RMs serves as a supplementary avenue for homeowners to access their home equity
and alleviate liquidity constraints, reducing the need for traditional renancing. By considering the
impact of reverse mortgages on homeowners’ nancial strategies, our model provides insights into a
more nuanced understanding of renancing behavior, highlighting the role of alternative mechanisms in
managing liquidity.
5.2 Consumption Smoothing and Take-up Rate
Table 3, Panel A, reports the cross-sectional standard deviations of consumption growth for workers
and retirees. We nd that households utilizing reverse mortgages exhibit, on average, lower volatility
in consumption growth throughout their life cycle. Interestingly, for workers, which have often been
overlooked in previous literature on reverse mortgages, the availability of RMs as an additional option
for accessing home equity leads to a more substantial reduction in volatility of consumption growth.
Moreover, the presence of RMs serves to narrow the disparity in consumption growth volatility between
working households and retirees. These ndings underscore the signicance of RMs in enhancing the
consumption smoothing and bridging the gap between dierent household segments.
Table 3: Consumption Growth Volatility and Take-up Rates
Panel A: Consumption Growth Volatility
Age Groups Households without RMs Households with RMs Dierence
<
62
0.851
0.706
-17.04%
≥ 62 0.323 0.296 -8.36%
Panel B: Take-up Rate of RMs for Owners
Age groups [62,65] [66,70] [71,75] [76,80] [81,85] [86,90] [91,95] >95
Take-up Rate 10.71% 12.44% 10.24% 9.80% 9.64% 9.12% 8.62% 0.00%
Table 3, Panel B, shows the take-up rate of reverse mortgages across the age groups. We don’t
target the take-up rate of RMs by homeowners. Instead, we introduce a hypothetical assumption in
our analysis, considering a scenario where no upfront costs are imposed on homeowners when they opt
32
for RMs. Consequently, it is not surprising to observe a signicantly higher take-up rate under this
hypothetical condition. Consistent with previous studies such as Cocco et al. (2020) and Nakajima
(2017), which have identied the high costs associated with RMs as a contributing factor to the low take-
up rate. By considering the hypothetical elimination of upfront costs, our results provide further support
to the notion that reducing the nancial barriers linked to RMs could lead to an increased adoption rate
among homeowners.
Additionally, we observe a gradual decline in the proportion of homeowners opting for RMs as they
advance in age. Older homeowners are more hesitant to engage in RM agreements compared to their
younger counterparts. Several factors could potentially contribute to this trend. First, homeowners
approaching retirement age may have already made substantial progress in paying o their mortgage
or accumulating home equity, thereby reducing the immediate need for RM products. Second, older
homeowners may have concerns about the long-term nancial implications and potential risks associated
with RMs, leading them to opt for alternative strategies to access their home equity. The diminishing
take-up rate of RMs among older homeowners highlights the signicance of considering age-related factors
when examining the adoption and utilization patterns of these nancial instruments.
5.3 Mortgage, Reverse Mortgage, and House Prices
A signicant aspect of our analysis, which distinguishes it from previous literature, lies in the equilibrium
determination of conventional mortgage spreads, mortgage spreads, and housing prices. By considering
the equilibrium determination of these factors, we gain a more comprehensive understanding of the inter-
play between mortgage rates, reverse mortgage rates, credit constraints, and housing market conditions.
This approach allows us to capture the intricate relationships and feedback loops that exist within the
housing and mortgage markets.
Table 4 shows the conventional mortgage rate, reverse mortgage rate and corresponding spread under
dierent aggregate states. First, mortgage rates are inuenced by the prevailing economic conditions
and credit constraints. During the crisis, the mortgage rate reaches its lowest point, aligning with
our expectations. This is in line with the policy objective of stimulating the economy and promoting
borrowing by keeping interest rates low. In the recession phase with loose credit constraints, the mortgage
rate increases to 4.28%. The more relaxed lending standards during this period lead to higher mortgage
rates as lenders assume additional risk. Continuing into the expansion with loose credit constraints,
the mortgage rate further increases. This increase is attributable to heightened demand for loans and
33
increased economic activity, which exert upward pressure on interest rates. Conversely, when credit
constraints tighten, the mortgage rate experiences a decline. This decline is more pronounced during the
recession with tight credit constraints. Tight credit constraints signify lenders adopting a more cautious
and stringent approach to loan approvals, resulting in lower mortgage rates as borrowing becomes more
challenging.
Then we nd that reverse mortgage rates consistently remain higher than conventional mortgage rates
regardless of the aggregate states. Similar to the conventional mortgage, the reverse mortgage rate is
lowest during the crisis. This aligns with the broader interest rate environment during crises, which aims
to facilitate homeowners’ access to their home equity at more favorable rates. Moreover, we nd that
the reverse mortgage rates only depend on the macroeconomic environment and are irrelevant to credit
constraints. This distinction can be attributed to the unique characteristics of reverse mortgages. Unlike
conventional mortgages, reverse mortgages typically do not involve stringent credit checks or income
qualications. Instead, eligibility is primarily determined based on factors such as the homeowner’s age,
home value, and other specic criteria related to reverse mortgages. Furthermore, reverse mortgages
are structured as non-recourse loans. This means that the borrower’s liability is limited to the value of
the home. In situations where the loan balance exceeds the home’s value upon sale, the lender absorbs
the resulting loss instead of the borrower or their estate. This inherent feature of reverse mortgages
further mitigates the impact of credit constraints on reverse mortgage rates. Considering these factors,
it becomes evident that credit constraints play a minimal role in determining reverse mortgage rates.
Instead, reverse mortgage rates primarily hinge on the prevailing macroeconomic environment and the
specic attributes and regulations associated with reverse mortgage programs.
Moreover, the dierence between conventional mortgage rates and reverse mortgage rates tends to
be larger during periods of tight credit constraints. This is because conventional mortgages are more
sensitive to credit conditions. When credit becomes scarce or restricted, lenders adjust their strategies to
mitigate risk, often resulting in increased interest rates for conventional mortgages. In contrast, reverse
mortgage rates are not directly inuenced by credit constraints. As a result, the gap between conventional
mortgage rates and reverse mortgage rates widens.
In addition to examining the dynamics of reverse mortgage rates, conventional mortgage rates, and
interest rates, it is crucial to explore the implications of reverse mortgages on housing prices, as it sheds
light on the broader impact of reverse mortgage programs on the overall housing market. We nd that
the inclusion of RMs in the mortgage market contributes to an overalll increase in housing prices across
34
Table 4: Mortgage and Reverse Mortgage Rates
Mortgage Reverse mortgage
Rate Spread Rate Spread
Crisis 3.18% 1.92% 4.26% 3.00%
Recession and loose 4.28% 1.96% 4.32% 2.00%
Expansion and loose 5.12% 0.86% 5.26% 1.00%
Recession and tight 4.04% 1.72% 4.32% 2.00%
Expansion and tight 4.59% 0.33% 5.26% 1.00%
all aggregate states, which enhances the competitiveness of the housing market. This inclusion of RMs
in the mortgage market has both direct and indirect eects on housing prices.
One direct eect is that reverse mortgages can provide homeowners with additional nancial resources,
allowing them to invest in home improvements or other expenditures that can increase the value of their
property. This increased investment in housing puts upward pressure on housing prices.
Indirectly, RMs inuence the supply and demand dynamics of the housing market. By enabling older
homeowners to access their home equity without selling their homes, RMs reduce the supply of available
housing for sale. With a limited supply of housing but consistent or increasing demand, the scarcity of
available properties drives up prices.
Additionally, the presence of RMs in the mortgage market can inuence the overall dynamics of
housing transactions. As more homeowners opt for reverse mortgages, it can lead to a decrease in
traditional home sales, limiting the turnover of properties in the market. Reduced turnover can contribute
to a slower rate of housing entering the market, further exacerbating the scarcity of available homes and
potentially pushing prices higher.
However, it is worth noting that there is notable heterogeneity among the aggregate states. Specif-
ically, when credit conditions are tight, the housing price experiences a relatively smaller increase com-
pared to other states. This aligns with the expectation that when credit conditions are tight, potential
homebuyers may face greater diculties in obtaining mortgage nancing. This can lead to a decrease in
overall demand for homes, including those nanced through reverse mortgages. With lower demand, the
upward pressure on housing prices is alleviated, resulting in a smaller increase in prices.
Meanwhile, lenders tend to tighten their lending standards and criteria during tight credit conditions.
This means that borrowers, including those seeking reverse mortgages, may nd it more challenging to
qualify for loans. The reduced availability of credit can limit the number of potential buyers utilizing
35
reverse mortgages, thereby mitigating the impact on house prices.
Table 5: House Prices
Econ state Ignore RM Recognize RM Change No. of periods
Crisis 3.70 3.77 1.90% 60
Recession and loose 4.71 4.80 1.91% 203
Expansion and loose 4.54 4.57 0.66% 1015
Recession and tight 4.43 4.44 0.25% 113
Expansion and tight 4.25 4.27 0.48% 608
5.4 Welfare Gains
When examining the presence of reverse mortgages, the assessment of welfare gain becomes important
for comprehending the potential benets and implications of these nancial instruments. Table 6 reports
the welfare gains associated with the availability of reverse mortgages. In our analysis here, we refer
to the economy without reverse mortgages as Economy 0 and the economy with reverse mortgages as
Economy 1. To quantify the household welfare gains, we calculate the equivalent consumption variation.
This represents the amount by which households would need to increase their consumption in Economy
0 to achieve the same level of satisfaction as in Economy 1. Specically, we denote the value functions
under Economy 0 and Economy 1 as V
0
and V
1
, respectively. The equivalent consumption variation
∆ (S
it
|Σ
t
) is dened implicitly as
V
1
(S
it
|Σ
t
) =E
t
t+T −a
it
n=t
β
n−t
n
m=t+1
p
m
(a
im
)
(
C
0
n
(1+∆(S
n
|Σ
n
))
)
1−γ
i
1−γ
i
+ αH
0
n
+
I
0
in
> 0
u
o
−
I
0
in
= −1
u
d
+ β
n−t
1 −
n
m=t+1
p
m
(a
im
)
ψ
Q
0
in
+ ξ
1−γ
i
1 − γ
i
=V
0
(S
it
|Σ
t
) +
(1 + ∆ (S
n
|Σ
n
))
1−γ
i
− 1
E
t
t+T −a
it
n=t
β
n−t
n
m=t+1
p
m
(a
im
)
C
0
n
1−γ
i
1 − γ
i

,
(69)
36
where C
0
n
and I
0
in
are the corresponding policies, and Q
0
in
is the total wealth under Economy 0. Conse-
quently,
∆ (S
it
|Σ
t
) =
1 +
V
1
(S
it
|Σ
t
) − V
0
(S
it
|Σ
t
)
E
t
t+T −a
it
n=t
β
n−t
n
m=t+1
p
m
(a
im
)
(C
0
n
)
1−γ
i
1−γ
i
1
1−σ
− 1 (70)
We report the welfare gains for four groups of households: (1) Young, working homeowners, (2) young,
working renters, (3) Retired homeowners, (4) Retired renters. We nd that the retired homeowners
experience signicant welfare gains. As homeowners age, welfare gains increase. On the other side,
we also observe marginal improvement for the renters. While the rising housing prices may create
additional challenges for renters, especially young households who often aspire to become homeowners,
an economy equipped with reverse mortgages can provide some advantages for renters, albeit modestly.
This positive spillover eect on the rental market might come from the fact that renters still have the
potential to become homeowners in the future and utilize RMs as an additional option for accessing home
equity. Understanding the potential benets of RMs allows renters who have the intention to become
homeowners to incorporate this option into their long-term nancial planning and take advantage of the
nancial stability that RMs oer.
We can obtain additional insights into the dierences between the two economies from Table
6. Here
we show the cross-sectional standard deviations of consumption growth for workers and retirees under two
economies. In the economy where RMs are accessible, homeowners, regardless of whether they choose to
take up RMs or not, experience lower volatility in consumption growth compared to the economy where
RMs are not available. This suggests that the presence of RMs has a stabilizing eect on consumption
patterns for homeowners. On the other hand, it is indeed not surprising to nd that the consumption
smoothing eect is subtle for renters. The decrease in consumption volatility for both working and retired
renters, amounting to 0.004 and 0.003 respectively, suggests a relatively modest impact. While renters
may not have direct access to the consumption-smoothing benets oered by reverse mortgages, they
might become homeowners later. This contributes to a small but noticeable impact on consumption
smoothing. Overall, an economy with reverse mortgages oers potential benets and implications for
various segments of the population, including homeowners and renters.
37
Table 6: Comparison between Two Economies
Panel A: Welfare Gains
Homeowners Renters
Age groups <62 [62,75] >75 <62 [62,75] >75
Welfare Gains 1.29% 4.77% 7.47% 0.18% 0.31% 0 .76%
Panel B: Consumption Growth Volatility
Homeowners Renters
Age groups Ignore
RM
Recognize
RM
Change
Ignore
RM
Recognize
RM
Change
< 62 0.741 0.695 -6.21% 0.914 0.910 -0.44%
≥ 62 0.295 0.286 -3.05% 0.387 0.384 -0.78%
6 Conclusion
In this paper, we analyze the reverse mortgage using a quantitative model where households make deci-
sions of saving, consumption, homeownership and reverse mortgages over the life cycle. By doing so, our
model incorporates the mortgage market and housing market, enabling a comprehensive understanding
of how the presence of RM inuences both sectors.
Our analysis reveals that older households who opt for RMs experience enhanced consumption
smoothing compared to those who do not participate in RM programs. Additionally, our model demon-
strates that the inclusion of RMs has a signicant impact on housing prices, particularly during the
expansion with loose credit constraints. As a result, the housing market becomes more competitive,
making homeownership more appealing. While these dynamics pose challenges for young renters, as they
contend with rising house prices, it is important to consider their potential for future homeownership. In
an economy with reverse mortgages, young renters have the opportunity to aspire to become homeowners
and utilize RMs as an additional avenue for accessing home equity. Thus, even though they face some
hurdles, young renters still enjoy marginal benets in an economy that incorporates reverse mortgages.
However, as expected, older homeowners experience very notable welfare gains. Overall, an economy
that includes RMs exhibits superior total welfare benets.
From a policy perspective, policymakers play a crucial role in promoting the understanding of RMs
among households and minimizing the barriers that impede access to them, all while maintaining an
eective risk control framework. Encouraging older households to consider RMs carries multiple advan-
38
tages, beneting not only the households themselves but also the broader society. Additionally, such
encouragement helps alleviate the strain on public pension schemes, reducing the related pressures and
challenges.
39
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Appendix: Reverse Mortgage Markets in Global Context
Compared to the case of US and other developed countries of similar socio-economic, demographic con-
ditions and nancial market development, UK has the most sophisticated and penetrated RM market
in the world, dened by the product ranges and optional features such as repayment and withdrawal,
number of lenders and consumers, as well as consumer awareness and product reputation and regulation.
Since its inception in 1991, the RM market in the UK shows very healthy and signicant growth trend,
with several turning points. For example, the rst downturn of the UK RM market is caused by the
Great Financial Crisis (GFC) rooted by the subprime mortgage crisis in late 2007 in the US, causing
a global housing market slump. The RM market gradually recovered since 2008 low point, and has
remained healthy growth, with a threefold size in 2016, due to major new product introduction. Another
major turning point for the UK RM market is the Coronavirus (COVID-19) crisis, which induced the
prevailing extra-low interest rate regime during and after the crisis, boosting the housing market, causing
a temporary contraction of the new lump sum plans in 2019, and growth of further advance contracts.
Lump sum plans pick up the growth trend in 2020 during the living-cost crisis and stays as stable since
then.
2005 2010 2015 2020 2025
Year
0
10000
20000
30000
40000
50000
60000
Number of RMs
Total
Lumpsum
Returning drawdown
home reveresion/further advance
Figure 5: Number of RMs of Dierent Types in UK Market
Our estimates using the Equity Release Council (ERC) market report and Census data reveals that
around 12% of eligible senior households have taken up RM in the UK, which is a relatively high and
healthy number for this market and shows strong appetite by consumers and providers, thus a huge
42
potential for this product to succeed in other countries in similar economic and social conditions.
12
The case of Hong Kong is described in the Hong Kong Monetary Authority market reports. Although
still small, the RM market has gained signicant interest and growth since its inception in 2011. There
are multiple factors contributing to this slow but upward growth trend: Firstly, the lack of social security
(public pension plans) in Hong Kong forces senior households to consider alternative methods to increase
retirement income. Secondly, the housing market boom in Hong Kong makes housing asset a signicant
part of family’s wealth. However, the homeownership rate in Hong Kong is low compared to other
developed countries such as US and UK, due to the un-aordability of housing for local citizens, stated
by housing price to income ratio of 23.3.
13
Australian RM regulatory body SEQUAL uses a dierent estimation methods from the US and UK.
They calculate the RM participation rate using the population of suitable senior individuals instead of
number of eligible households. This makes the estimated RM take-up rate lower and not comparable to
those reported by the US and UK regulators or market participants. MortgageBusiness (2021) estimate
about half of collective wealth in Australia is tied up in housing, and it is skewed towards the senior
population, that is, around AUD$1 trillion. Out of this housing wealth, AUD$300 billion is being accessed
by RM, which amounts to only about 1%-1.5% in 2021, although the market has grown by more than 5
times since its inception. Product ranges, consumer knowledge and brand reputation are not as strong
as in the UK and US. The challenges of Australian RM market development is due to major lenders’
unwillingness to oer such products, and hence only proprietary, niche lenders are willing to take the
risk and oer such products. On the consumer side, consumer awareness, nancial literacy and product
education are not through.
12
The recent UK RM take-up rate is estimated by the cumulative number of RM plans issued since its inception
(1991-2022), e.g. according to ERC report, there are 592,000 RM plans issued during this period, divided by the
number of eligible senior households who own their main house outright. To make this ratio comparable to the
case of US and other countries, we use the number of households headed by someone 65+ by report Later Life
in UK (2019), 6,500,000, with the homeowner ratios of 78%, and the fraction of those still paying mortgages 6%,
this makes the RM eligible households to be 4,765,800. Hence the RM participation ratio is estimated to be 12%
in 2022. However, if instead the denominator is the population of 65+, the number becomes signicantly large,
estimated to be 15,500,000 (p4 ERC report 2022), then the RM take-up rate becomes 3.8%.
13
According to Secretariat (2021), in 2019, home ownership ratio in Hong Kong fell to the lowest point in
the past two decades, as 49.8%, following a nearly four-fold growth in at prices during that period. Although
homeownership rate modestly grows to 51.2% during 2020, it is still far below the prevailing 60% level in developed
countries. Ernst and Young (2022) states that the median house price to median income ratio of Hong Kong in a
2021 survey is 23.3, see (Cox (2023)), which compares house to income ratios over 92 major metropolitan areas.
Hong Kong was the highest for consecutive 12 years.
43