Selection and Moral Hazard
in the Rever Mortgage Market
Thomas Davidoffand Gerd Welke∗
October27,2005
Abstract
Despite recent growth,the rever mortgage market remains smaller than might be expected given the large number of cash-poor,hou-rich elderly.This fact is in
part attributable to high fees,rationalized by fears of adver lection and moral
hazard.We prent a model of rever mortgage demand that shows lection on the
dimension of mobility can be advantageous rather than adver,becau the same
characteristics that make spending home equity through a rever mortgage attractive
also make disposing remaining home equity through moving attractive.Empirically,
high housing wealth and low non-housing wealth drive both rever mortgage demand
and mobility.Limited evidence supports a theoretical prediction that moral hazard
worns with weaker price appreciation.
∗Haas School of Business,UC Berkeley,Berkeley,CA,94720.davidoff@haas.berkeley.edu, welke@haas.berkeley.edu.We thank Wenlan Qian for rearch assistance and minar participants at UC Berkeley,the Federal Rerve Board,the AREUEA international conference,and the Universities of Wiscon-sin,Missouri,and Toronto for suggestions.We thank the Department of Housing and Urban Development for a grant through the Urban Scholars Postdoctoral Fellowship program.All opinions are our own,not HUD’s.
1Introduction
Rever mortgages offer liquidity to older homeowners and are widely viewed as a potentially enormous market.1While this market has grown considerably over the last few years,it remains quite small,with less than one percent of eligible homeowners taking part.2Adver lection on the dimension of mobility and moral hazard on the dimension of maintenance have been put forward as reasons for the market’s small size.
In this paper,we develop a model of demand for rever mortgages that allows for concave utility over wealth and a distaste for moving among borrowers.Our model demonstrates that adver lection is not guaranteed in this market,and suggests that the more important dimension of moral hazard is mobility rather than maintenance.Empirically,we show that in fact,advantageous,rather than adver,lection has contributed to the actuarial health of the largest US rever mortgage program.Rever mortgage borrowers have terminated their loans at a rate faster than predicted by population mobility and mortality rates,undoing for many loans the risk that mortgage debt will grow to exceed property value.We prent only weak evidence that moral hazard operates in this market.
Rever mortgages allow home-rich,cash-poor older homeowners,who may face high borrowing costs,to transfer money from the period after they have sold their home or died to the period while they remain alive in the home.The appeal of such a transfer if the home is exited while still alive is explored in Artle and Varaiya(1978).The appeal of transfers from the period after death to the period while still alive is discusd in Yaari(1965)and the literature on annuities that follows.
For rever mortgages to provide a a benefit,marginal utility of cash before moving must be larger than the benefit of savings held to death or the period of relative cash wealth that
1See Mayer(1994)and Kutty(1998)for discussions of the US market and Mitchell and Piggott(2005)for a discussion of the potential market in Japan.Back of the envelope estimates bad on Davis and Heathcote (2004)and the American Housing Survey suggest that older homeowners owned over$5trillion of home
equity in2003.
2Originations of the largest home equity product grew from157infiscal1990to43,131in2005.
follows exit from the home.We give little consideration to strong complementarities between remaining in place and other consumption or to strong bequest motives,acknowledging that they may help explain the smallness of the market.We also ignore the prence of Medicaid, which may undermine demand for rever mortgages(Caplin(2002)).
There are a large number of older homeowners who can be classified as home-rich,cash-poor,so the potential demand for rever mortgages is large.Bad on the2001Survey of Consumer Finances,Aizcorbe et al.(2003)show that76percent of houhold heads aged 75or over owned a home,with a median value of$92,500.Median net wealth among the houholds was$151,400.Just11%of the houholds owed any mortgage debt.Among the majority of older sin
gle women in the2000AHEAD survey who own homes,the median ratio of home value to total asts was79%.
Not only does home equity reprent the majority of wealth for older Americans,but it is wealth that frequently goes unspent.Sheiner and Weil(1992)report an annual mobility rate of approximately4%among older single women bad on the Panel Study of Income Dynamics.3Combined with mortality rates,this implies that approximately50%of recent retirees will die in their current home.This is consistent with the AARP surveyfinding, cited by Venti and Wi(2000),that89%of surveyed Americans over55reported that they wanted to remain in their current residence as long as possible.
Low interest rates and rising home values have contributed to a recent increa in the volume of conventional home equity borrowing among the elderly.4Home equity loans with growing balances can allow transfers of money from after sale or death to before.However, such loans provide little liquidity for older homeowners unable to pledge much non-annuitized income towards repayment becau of enforced minimum income to loan amount tests.5 Rever mortgages,unlike standard home equity loans,require borrowers to make only
3Similarly low mobility rates are found on inspection of the Survey of Income and Program Participation
and in the AHEAD survey of the elderly(e Venti and Wi(2000)).
4See,for example,Bayot(2004).
5Borrowers may simply not state income in loan contracts,but this involves steep increas in the interest rate,on the order of2%.
a single,“balloon”repayment at the time of move out or death(although full or partial pre-payment is also allowed).Also unlike conventional mortgages,the lender cannot force a borrower to move as long as they are alive.Rever mortgages loans are made without recour to borrowerfinancial asts.
The structure of rever mortgages implies that lenders earn profits through fees and an interest rate spread as long as the loan balance does not grow in value to exceed the value of the home.Home appreciation in excess of interest rates ems implausible in the long run:recent experience notwithstanding,this condition would imply that consuming more housing would make homeowners ri
cher,a violation of no arbitrage abnt borrowing constraints.Hence lenders are more likely to suffer loss if the borrower remains in the home for a long time and if the rate of appreciation is lower.
Rever mortgages thus bear considerable remblance to standard insurance products of economic theory.Lenders provide payments to borrowers in a state in which borrowers have high marginal utility(while they have not yet died or sold their home),in exchange for which borrowers sacrifice money in a state with plausibly lower marginal utility(after they have died or moved and taken out any remaining home equity).Just as insurers bear the risk that the high marginal utility state will occur with high probability,rever mortgage lenders bear the risk that the high marginal utility state will last for a long time.
Abnce of recour and borrowers’freedom to determine the date of exit from the home give ri to concerns of adver lection and moral hazard in the rever mortgage market and have been ud to rationalize high fees or limited market size.6Adver lection aris if consumers expecting an unusually long life,low mobility,or low rates of appreciation enter into rever mortgages at a rate disproportionate to their share of the population.The potential for adver lection in the rever mortgage industry is well illustrated by the ca of famed Frenchwoman Jeanne Calmet who lived to the age of121and her rever mortgagee Andre-Francois Raffray.As reported by the Associated Pres
s on August5,1997,Calmet sold her apartment forward to Raffray in her eighties,in what turned out to be a disastrous Chinloy and Megbolugbe(1994),Edward J.Szymanoski(1994),and Caplin(2002).
arrangement for Raffray and his heirs and a highly profitable arrangement for Calmet.
Rever mortgage design might invite two dimensions of moral hazard.Thefirst,modeled by Miceli and Sirmans(1994)and Shiller and Weiss(2000),is that a mortgagor facing default has no incentive to maintain property values.The cond moral hazard issue is that by giving funds to an older homeowner,life in the home is made relatively more attractive than life after moving or death,so the act of giving a borrower a rever mortgage may extend the borrower’s stay in the home.
This paper explains that neither adver lection nor moral hazard is guaranteed by the structure of the rever mortgage industry.Figure1demonstrates that,to date,rever mortgage borrowers in the US have moved out of their homes,whether due to death or vol-untary mobility,at a rate that far exceeds the rate of demographically similar non-borrowers.
de Meza and Webb(2001)argue that when actuarially unfair pricing renders full coverage undesirable,insurance markets may feature advantageous,rather than adver,lection.For exampl
e,they cite evidence that UK credit card holders who purcha insurance against lost cards are less likely to lo their credit cards.Finkelstein and McGarry(2003)find that older individuals who purcha long term medical care insurance are less likely to wind up in long term care than non-purchars.In both cas,the propod explanation is that more risk aver consumers are likely both to ek insurance and to behave in a way that avoids the insured event.Cohen and Einav(2004)find complicated lection effects relating both to underlying probability of accidents and to risk aversion in the Israeli auto insurance market.
The relatively rapid exit from homes on the part of rever mortgagors may be explained similarly.Rever mortgage borrowers are likely,by revealed preference,to have a greater gap between marginal utility before moving and marginal utility after moving(or in death) than tho whofind rever mortgages unattractive.Becau rever mortgages typically leave borrowers with considerable residual home equity,a substantial gap may remain even after the loan is funded.This gap has surely persisted for borrowers in the recent years of rapid home price appreciation.Just as the insured can act to reduce the probability of accidents through careful behavior,so rever mortgagors can act to reduce the length of the
high marginal utility state by moving relatively quickly.
Section2of this paper outlines the structure of the dominant rever mortgage product in the United States,the Home Equity Conversion Mortgage(HECM).Section3lays out a stylized model of the relationship between optimal move date and rever mortgage take-up.The model does not deliver clod form results,but inspection of the terms reflecting gains from taking on rever mortgage debt and gains from moving later in life suggest advantageous lection of the type described by de Meza and Webb(2001)is likely to operate in the rever mortgage market,at least when price appreciation is as strong as it has been over the life of most rever mortgages.Numerical examples broadly confirm the analysis. We also show that moral hazard on the dimension of maintenance need not ari.
Empirically,wefind in Section4that lection on the obrvable characteristics of income, wealth,and property value confirm theoretical considerations.Our analysis of lection on obrvables unud by the lender is akin to that in Finkelstein and Poterba(2005).However, advantageous lection on obrvables explains only a part of the large difference in mobility rates between rever mortgage borrowers and the rest of the population.
The theory is further confirmed in that the excess mobility of rever mortgage borrowers is smaller in states that have had historically low home price inflation.This fact is predictable becau in the
states,default is feasible and hence borrowers may ek to exploit the implicit free stay in homes offered by the rever mortgage.The difference across states suggests that a future slowdown in home inflation might undo the advantageous lection obrved to date.Large standard errors and patterns of mobility among non-borrowers weaken the moral hazard result.
We take the pricing and credit limits on rever mortgages as exogenously given,so that strategic behavior on the part of lenders is not considered.To date,pricing of the largest rever mortgage program has been driven by federal regulations and potential loss to the actual issuers of rever mortgages are small due to federal loan guarantees.The abnce of strategic supply behavior is illustrated by the fact that the Federal Housing Administration us an actuarial model in which loan termination rates are a function solely of borrower
