Reverse Mortgage Loans: A Quantitative Analysis

• Author: MAKOTO NAKAJIMA,IRINA A. TELYUKOVA
• DOI: http://doi.org/10.1111/jofi.12489
• Published date: 01 April 2017
• Date: 01 April 2017

THE JOURNAL OF FINANCE •VOL. LXXII, NO. 2 •APRIL 2017

Reverse Mortgage Loans: A Quantitative Analysis

MAKOTO NAKAJIMA and IRINA A. TELYUKOVA∗

ABSTRACT

Reverse mortgage loans (RMLs) allow older homeowners to borrow against housing

wealth without moving. Despite rapid growth in this market, only 1.9% of eligible

homeowners had RMLs in 2013. In this paper, we analyze reverse mortgages in a

calibrated life-cycle model of retirement. The average welfare gain from RMLs is $252

per homeowner, and $1,770 per RML borrower. Bequest motives, uncertainty about

health and expenses, and loan costs account for low demand. According to the model,

the Great Recession’s impact differs across age, income, and wealth distributions,

with a threefold increase in RML demand for lowest income and oldest households.

REVERSE MORTGAGE LOANS (RMLs) allow older homeowners to borrow against

their housing wealth without moving out of the house, while insuring them

against significant drops in house prices. Despite potentially large benefits

to older individuals, many of whom want to stay in their house as long as

possible, frequent coverage in the media, and attempts by the Federal Housing

Administration, which administers RMLs, to modify the terms to increase their

appeal to borrowers, research on reverse mortgages is not extensive. This paper

helps fill some of this void.

In Nakajima and Telyukova (2013), we find that older homeowners become

borrowing-constrained as they age and these constraints force many retirees to

sell their homes when faced with large medical expenses. In this environment,

it seems that an equity borrowing product targeted toward older homeowners

may be able to relax that constraint, and hence potentially benefit many owners

later in life. Empirical studies suggest a similar possibility, though estimates

range widely. For example, while Merrill, Finkel, and Kutty (1994) suggest

that about 9% of homeowner households over age 69 could benefit from RMLs,

Rasmussen, Megbolugbe, and Morgan (1995) argue, using 1990 U.S. Census

∗Makoto Nakajima is with the Federal Reserve Bank of Philadelphia. Irina A. Telyukova is

with Intensity Corporation. We thank the Editor, Ken Singleton, and two anonymous referees

for constructive comments and valuable feedback. We also thank the participants of seminars

at Maastricht University, San Diego State University, University of Colorado Boulder, Federal

Reserve Bank of San Francisco, Stony Brook University,UC Irvine, UBC Sauder School, University

at Albany,UCSD, as well as the 2014 National Reverse Mortgage Association Meetings, 2013 FRB

St. Louis/University of Wisconsin HULM Conference, 2011 SAET Meetings in Faro, and 2011 SED

Meetings in Ghent, for their feedback. The views expressed here are those of the authors and do

not necessarily represent the views of the Federal Reserve Bank of Philadelphia or the Federal

Reserve System. We have read the Journal of Finance’s disclosure policy and have no conflicts of

interest to disclose. All errors are our own.

DOI: 10.1111/jofi.12489

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data, that this number is nearly 80%.1Despite the apparent benefits, however,

just 1.9% of older homeowners held RMLs in 2013, down slightly from its all-

time high of 2.1% in 2011.

In this paper, we study determinants of demand for reverse mortgages, and

we consider its future post–Great Recession, in the face of complex trade-offs

that retirees face in deciding whether to borrow. Specifically, we address four

questions. First, we examine who benefits from reverse mortgages and by how

much, in welfare terms. Second, we investigate what prevents more retirees

from taking RMLs, given the current available RML contract. Here we focus

on retirees’ environment, such as the magnitude of risk that they face, and

preferences, such as their bequest motives. Third, we evaluate the impact of

the 2013 RML reform, and we study more generally whether and how the

existing reverse mortgage contract can be modified to make the RML more

attractive. Finally, we study how reverse mortgage demand may change as a

result of the Great Recession, which may have both a short-run and a long-run

impact on the financial security and incomes of future retirees.

To address these questions, we use a rich structural model of housing and

saving/borrowing decisions in retirement based on Nakajima and Telyukova

(2013). In the model, households are able to choose between homeownership

and renting, and homeowners can choose at any point to sell their house or

to borrow against their home equity. Retirees face uninsurable idiosyncratic

uncertainty in their life span, health, spouse’s mortality, medical expenses,

and house prices, and no aggregate uncertainty. Bad health states may force

older individuals into nursing homes, which we capture with an idiosyncratic

involuntary moving shock. The model is estimated to match life-cycle profiles

of net worth, housing and financial assets, homeownership rate, and home eq-

uity debt, which we construct from Health and Retirement Study (HRS) data,

controlling for time effects. Into this model, we introduce reverse mortgages,

study their use and value to different types of households, and conduct coun-

terfactual experiments to address the questions posed above. We find that the

model reproduces well key characteristics of the data, including many, though

not all, characteristics of the debt distribution, which are not targeted as part

of the estimation process.

The model predicts that the ex ante welfare benefit of reverse mortgages is

equivalent to providing a lump-sum transfer of $252 per retired homeowner

at age 65, which amounts to 0.84% of median annual after-tax income for this

group. The welfare gains are of course much larger for eventual borrowers,

amounting to $1,770 per borrower or 5.1% of median annual income. All home-

owners value, ex ante, the option of being able to tap their equity some time

during their retirement; however, ex post, only 0.89% of eligible retirees use

1Rasmussen, Megbolugbe, and Morgan (1995) assume that elderly households with home equity

exceeding $30,000 and without mortgage loans in 1990 benefit from having the option of obtaining

reverse mortgages. Merrill, Finkel, and Kutty (1994) assume that households with housing equity

between $100,000 and $200,000, income of less than $30,000 per year, a strong commitment to

stay in the current house (i.e., had not moved over the previous 10 years), and who own their house

free and clear benefit from reverse mortgages.

Reverse Mortgage Loans 913

RMLs in our model, which is close to the long-term data average of 0.84% be-

tween 1997 and 2013. Reverse mortgage demand is dampened by a combination

of substantial risks that households face late in life—such as health, medical

expense and long-term care risks, and house price uncertainty—as well as be-

quest motives, and significant costs of the contract. We find that the 2013 RML

reform is likely to further dampen demand going forward, stemming from its

tighter borrowing limit for most retirees, and in spite of lowered costs for some

borrowers.

More specifically, we find that retirees who use reverse mortgages tend to

have low income, low wealth, and poor health, and those who use them do

so primarily to support consumption expenditure in general, or in some cases

large medical expenses. While the aggregate take-up rate is less than 1%, it

is 2.2% for the lowest income quintile and 3.9% for low-income households

aged 90 and above. Bequest motives not only dampen RML demand, but also

change the way homeowners use RMLs; without a desire to bequeath, retirees

are over 17 times more likely to take RMLs, even without being pushed to do

so by a medical expense shock, and use them overwhelmingly for nonmedical

consumption. On the contract side, we find that eliminating up-front costs of the

loan more than triples demand for RMLs. In addition, reverse mortgages are

nonrecourse loans, which means that if the price of the collateral falls below

the loan value during the life of the RML, the lender cannot recover more

than the collateral value. Strikingly, we find that retirees do not value this

insurance component of RMLs due to low borrowed amounts and availability

of government-provided programs such as Medicaid. Thus, making the reverse

mortgage a recourse loan, which would remove substantial insurance premia

from the cost of the loan, would triple RML demand. In this sense, the oft-

heard claim that large contract costs suppress RML demand is supported by

our model. The FHA’s 2013 RML reform, in contrast, dampens demand in spite

of a lower up-front insurance cost for some retirees, because it also significantly

tightens the borrowing limit for most homeowners and raises insurance costs

for the most heavily indebted.

The Great Recession is likely to affect the RML market in different ways

in the short run and the long run. As a result of the recession, current re-

tirees have seen significant declines in housing and financial wealth. Thus,

in the short run, the aggregate RML take-up rate is likely to decline, from

0.89% to 0.71% in our model. However, the impact of the recession is heteroge-

neous across the income and wealth distributions: the most vulnerable retired

homeowners—those in the lowest income quintile in their 80s and 90s—may

have to rely increasingly on RMLs to finance their expenses. In this part of

the distribution, demand for RMLs may increase threefold. This raises impor-

tant policy trade-offs between the potentially increasing riskiness of the RML

portfolio held by the government and the need to provide access to one’s home

equity for those who most need it. In the long run, one impact of the Great

Recession will be lower incomes at retirement, stemming from protracted un-

deremployment spells earlier in the life-cycle. As a result of lower incomes,