Selection and Moral Hazard. in the Reverse Mortgage Market

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1 Selection and Moral Hazard in the Reverse Mortgage Market Thomas Davidoff and Gerd Welke October 27, 2005 Abstract Despite recent growth, the reverse mortgage market remains smaller than might be expected given the large number of cash-poor, house-rich elderly. This fact is in part attributable to high fees, rationalized by fears of adverse selection and moral hazard. We present a model of reverse mortgage demand that shows selection on the dimension of mobility can be advantageous rather than adverse, because the same characteristics that make spending home equity through a reverse mortgage attractive also make disposing remaining home equity through moving attractive. Empirically, high housing wealth and low non-housing wealth drive both reverse mortgage demand and mobility. Limited evidence supports a theoretical prediction that moral hazard worsens with weaker price appreciation. Haas School of Business, UC Berkeley, Berkeley, CA, [email protected], [email protected]. We thank Wenlan Qian for research assistance and seminar participants at UC Berkeley, the Federal Reserve Board, the AREUEA international conference, and the Universities of Wisconsin, 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.

2 1 Introduction Reverse mortgages offer liquidity to older homeowners and are widely viewed as a potentially enormous market. 1 While this market has grown considerably over the last few years, it remains quite small, with less than one percent of eligible homeowners taking part. 2 Adverse selection 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 reverse mortgages that allows for concave utility over wealth and a distaste for moving among borrowers. Our model demonstrates that adverse selection 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 adverse, selection has contributed to the actuarial health of the largest US reverse mortgage program. Reverse 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 present only weak evidence that moral hazard operates in this market. Reverse 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 discussed in Yaari (1965) and the literature on annuities that follows. For reverse 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 1 See 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 based on Davis and Heathcote (2004) and the American Housing Survey suggest that older homeowners owned over $5 trillion of home equity in Originations of the largest home equity product grew from 157 in fiscal 1990 to 43,131 in

3 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 presence of Medicaid, which may undermine demand for reverse mortgages (see, e.g. Caplin (2002)). There are a large number of older homeowners who can be classified as home-rich, cashpoor, so the potential demand for reverse mortgages is large. Based on the 2001 Survey of Consumer Finances, Aizcorbe et al. (2003) show that 76 percent of household heads aged 75 or over owned a home, with a median value of $92,500. Median net wealth among these households was $151,400. Just 11% of these households owed any mortgage debt. Among the majority of older single women in the 2000 AHEAD survey who own homes, the median ratio of home value to total assets was 79%. Not only does home equity represent 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 approximately 4% among older single women based on the Panel Study of Income Dynamics. 3 Combined with mortality rates, this implies that approximately 50% of recent retirees will die in their current home. This is consistent with the AARP survey finding, cited by Venti and Wise (2000), that 89% of surveyed Americans over 55 reported 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 increase in the volume of conventional home equity borrowing among the elderly. 4 Home 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 because of enforced minimum income to loan amount tests. 5 Reverse mortgages, unlike standard home equity loans, require borrowers to make only 3 Similarly low mobility rates are found on inspection of the Survey of Income and Program Participation and in the AHEAD survey of the elderly (see Venti and Wise (2000)). 4 See, for example, Bayot (2004). 5 Borrowers may simply not state income in loan contracts, but this involves steep increases in the interest rate, on the order of 2%. 2

4 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. Reverse mortgages loans are made without recourse to borrower financial assets. The structure of reverse 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 seems implausible in the long run: recent experience notwithstanding, this condition would imply that consuming more housing would make homeowners richer, a violation of no arbitrage absent borrowing constraints. Hence lenders are more likely to suffer losses if the borrower remains in the home for a long time and if the rate of appreciation is lower. Reverse mortgages thus bear considerable resemblance 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, reverse mortgage lenders bear the risk that the high marginal utility state will last for a long time. Absence of recourse and borrowers freedom to determine the date of exit from the home give rise to concerns of adverse selection and moral hazard in the reverse mortgage market and have been used to rationalize high fees or limited market size. 6 Adverse selection arises if consumers expecting an unusually long life, low mobility, or low rates of appreciation enter into reverse mortgages at a rate disproportionate to their share of the population. The potential for adverse selection in the reverse mortgage industry is well illustrated by the case of famed Frenchwoman Jeanne Calmet who lived to the age of 121 and her reverse mortgagee Andre-Francois Raffray. As reported by the Associated Press on August 5, 1997, Calmet sold her apartment forward to Raffray in her eighties, in what turned out to be a disastrous 6 See, e.g. Chinloy and Megbolugbe (1994), Edward J. Szymanoski (1994), and Caplin (2002). 3

5 arrangement for Raffray and his heirs and a highly profitable arrangement for Calmet. Reverse mortgage design might invite two dimensions of moral hazard. The first, 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 second 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 reverse mortgage may extend the borrower s stay in the home. This paper explains that neither adverse selection nor moral hazard is guaranteed by the structure of the reverse mortgage industry. Figure 1 demonstrates that, to date, reverse mortgage borrowers in the US have moved out of their homes, whether due to death or voluntary 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 adverse, selection. For example, they cite evidence that UK credit card holders who purchase insurance against lost cards are less likely to lose their credit cards. Finkelstein and McGarry (2003) find that older individuals who purchase long term medical care insurance are less likely to wind up in long term care than non-purchasers. In both cases, the proposed explanation is that more risk averse consumers are likely both to seek insurance and to behave in a way that avoids the insured event. Cohen and Einav (2004) find complicated selection 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 reverse mortgagors may be explained similarly. Reverse 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 those who find reverse mortgages unattractive. Because reverse 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 reverse mortgagors can act to reduce the length of the 4

6 high marginal utility state by moving relatively quickly. Section 2 of this paper outlines the structure of the dominant reverse mortgage product in the United States, the Home Equity Conversion Mortgage (HECM). Section 3 lays out a stylized model of the relationship between optimal move date and reverse mortgage takeup. The model does not deliver closed form results, but inspection of the terms reflecting gains from taking on reverse mortgage debt and gains from moving later in life suggest advantageous selection of the type described by de Meza and Webb (2001) is likely to operate in the reverse mortgage market, at least when price appreciation is as strong as it has been over the life of most reverse mortgages. Numerical examples broadly confirm the analysis. We also show that moral hazard on the dimension of maintenance need not arise. Empirically, we find in Section 4 that selection on the observable characteristics of income, wealth, and property value confirm theoretical considerations. Our analysis of selection on observables unused by the lender is akin to that in Finkelstein and Poterba (2005). However, advantageous selection on observables explains only a part of the large difference in mobility rates between reverse mortgage borrowers and the rest of the population. The theory is further confirmed in that the excess mobility of reverse mortgage borrowers is smaller in states that have had historically low home price inflation. This fact is predictable because in these states, default is feasible and hence borrowers may seek to exploit the implicit free stay in homes offered by the reverse mortgage. The difference across states suggests that a future slowdown in home inflation might undo the advantageous selection observed 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 reverse mortgages as exogenously given, so that strategic behavior on the part of lenders is not considered. To date, pricing of the largest reverse mortgage program has been driven by federal regulations and potential losses to the actual issuers of reverse mortgages are small due to federal loan guarantees. The absence of strategic supply behavior is illustrated by the fact that the Federal Housing Administration uses an actuarial model in which loan termination rates are a function solely of borrower 5

7 age. 7 The paper also abstracts away from uncertainty in lifetime or macroeconomic variables such as interest and appreciation rates. The case of Mme. Calmet and the likely surprising nature of recent price growth suggests that these uncertainties may be important, but we leave their incorporation into our model for future work. 2 The Home Equity Conversion Mortgage In the late 1980s, the United States Department of Housing and Urban Development ( HUD ) devised the Home Equity Conversion Mortgage ( HECM ) program to stimulate development of what was then a trivially small US reverse mortgage market. The program works roughly as follows. 8 HECM loans are originated by financial institutions or by mortgage brokers. Almost all loans to date have been purchased and held by Fannie Mae, a large mortgage company. Borrowers must be over 62 years old and own their home. Borrowers cannot owe more pre-existing mortgage debt on the home the maximal allowed HECM loan amount. Before loan closing, the borrower must participate in educational seminars. Borrowers can receive payments in several forms: they may receive a lump sum payment, a line of credit, fixed monthly payments that last for a predetermined number of months, or fixed payments that last as long as the borrower is alive and has not yet moved. The most frequently chosen, and most flexible, option is the the line of credit. With a line of credit, the maximum outstanding balance allowed grows with time, reflecting increased mortality and hence a shorter period over which the value of the lender s position is likely to depreciate. Reverse mortgages have sometimes been associated with annuities. The option with fixed payments until death or exit from the home is similar to an annuity but for the state in which the borrower is still alive but has moved and therefore no longer receives payment. A 7 See Rodda, Herbert and Lam (2000). 8 The following discussion draws largely on Rodda et al. (2000). 6

8 lump sum payment can be converted into an annuity by purchasing an annuity from another provider, but in this case the HECM lender does not bear longevity risk with respect to payments made. The maximal loan balance at the time of origination is typically smaller for reverse mortgages than for conventional home equity mortgages. This balance increases with the borrower s age and decreases with the prevailing one-year treasury rate. Despite differences in mortality, men and women are offered the same interest rate and maximal loan balance; couples are offered the balance that would be offered to the younger spouse if single. As of August 2004 an 80 year-old homeowner could obtain lump sum proceeds of approximately two-thirds of property value; a 65 year-old could obtain approximately one-half of value. The maximal loan amount is a slightly increasing fraction of appraised value, up to a maximal property value that depends on average home prices in the state of residence. No other borrower characteristics, such as sex, income, or wealth, influence loan terms. HECMs are typically repaid all at once, when the borrower dies or moves out of the home for other reasons. Borrowers are not required to make any payments until the earlier of death or move out of the borrower or both borrowers if a couple. At this point, the borrower or their estate must repay the bank the minimum of the home s resale value (in an arm s length transaction) or the outstanding loan balance. The outstanding loan balance at termination date T on a loan that was originated at time 0 is: T 1 T 1 M T = F (1 + r t ) + m t T 1 t=0 t=0 s=t (1 + r s ), (1) where F represents up front costs incurred at loan closing, r t is the one month interest rate on treasuries at month t plus an annualized spread of 1.5 percent, 9 and m t is the cash taken out by the borrower in period t. m t can be a negative number (amortization), but such prepayment is very rare. Fixed rate loans are possible under HECM, but Fannie Mae only purchases adjustable rate loans, so as a practical matter all loans are adjustable. 9 Or the one year interest treasury rate in year t plus a larger spread if the rate adjusts annually rather than monthly. 7

9 Historical closing costs have been extremely large relative to conventional home equity loans, on average close to 6.8 percent of property value, and this has been cited as a major reason for the relative weakness of demand. Part of the reason for high closing costs has been a guarantee fee of 2% of appraised property value charged by the Federal Housing Administration ( FHA ), a subsidiary of HUD. FHA guarantees the mortgagee that in the event that the resale value at termination is less than the outstanding loan balance M T, FHA will pay the mortgagee the difference. Part of the interest rate (.5 percent per year) charged on the loans also goes to FHA insurance premiums. Both the up-front insurance and ongoing insurance premia paid to FHA are far larger than the insurance payments made on conventional loans. To date, rapid mobility and high rates of house price appreciation have left FHA with few claims to pay and with large reserves against future losses. Refinancing was very costly in the period for which we have data, so the only feasible way to extract increased equity from appreciation was to move. Recently, refinancing has become easier and cheaper and this change can be expected to change the economics of selection in this market. Technically, borrowers are required to perform a minimal level of maintenance and to pay property taxes. Practically, the maintenance requirement cannot be enforced after closing, because it would be unlikely for a court to force a senior citizen out of their home for failure to perform maintenance. HECM is not the only product that allows older homeowners to convert home equity to cash without moving. There are other reverse mortgage products on the market which have, to date, had smaller market share than HECM. The largest of these is Financial Freedom, which has larger costs but allows larger loan amounts for higher value properties. For seniors with large incomes, conventional home equity loans can work much like reverse mortgages. While these loans require payment of interest and some principal before moving, for several years a line of credit with an increasing balance can behave like a reverse mortgage. Reverse mortgages can be more attractive, despite their high fees, because home equity lines will only 8

10 provide a loan amount such that repayment is feasible without selling the home and without using annuitized income. For many seniors, the allowable loan size is thus small. Larger loans without sufficient income are possible, but failure to document sufficient income leads to higher interest rates. 3 A Model of Selection and Moral Hazard We now ask whether the HECM industry structure described above lends itself in theory to adverse or advantageous selection and whether moral hazard or its opposite seems more likely to arise. A large portion of the high costs associated with the HECM product stems from guarantee fees charged by FHA. For this reason, and because FHA bears the risk of default, we consider selection and moral hazard from the guarantor s perspective. Selection is thus adverse (advantageous) if the expected profits from guarantees on loans to individuals with characteristics associated with becoming a borrower are less (greater) than the expected profits from guarantees on loans to individuals with characteristics associated with not becoming a borrower. Guarantor profits on a loan to a borrower with characteristics x are, under some assumptions: π(x) = H (F a + fm T (x) a e (r M r)(t a) dt I(T > t )(me (r M r)(t(x) a) e (g r)(t(x) a) ) The first term of equation (2) represents the up-front guarantee fee, expressed as a fraction F of the initial home value H a. The second is the present value of the continuing fee income, taken to be a fixed fraction f of the outstanding loan balance. Here, r M is the interest rate on the reverse mortgage, r is the rate at which the guarantor discounts, a is the date at which the loan is funded, and T is the date at which the borrower terminates (through death, payback, or mobility). We assume the maximum fraction of home value m that can be drawn at the start of the loan is in drawn by the home owner at origination and that there 9 ). (2)

11 is no prepayment before T. The final term in equation (2) represents any losses that arise from the loan amount due exceeding home value at termination. g is the rate of real home price appreciation (an element of the set of characteristics x) and t = a + ln(m)/(g r M ) is the critical date at which the loan is first in default. We have assumed that g < r M, so that t is positive for 0 < m < 1. Profits are increasing in the termination date up to this critical date and decreasing in T thereafter. We have assumed in equation (2) that the initial loan balance is taken up front and that g, F, f, m, r M, and r are deterministic constants (g is assumed constant with respect to the loan amount, but may vary across borrowers, e.g. geographically). These are not merely simplifying macroeconomic assumptions. The existing literature on reverse mortgages emphasizes the disincentive to perform maintenance that arises under default, and g presumably grows with the level of maintenance. 10 While it is surely the case that g will vary with x through maintenance, it is not at all clear which characteristics will affect g and in which direction. This is because the liquidity provided by the reverse mortgage may generate more, not less, maintenance prior to termination. If default is not to occur, then concave utility implies that transferring money from the post-termination to the pre-termination move makes investment in the home more, not less, desirable. 11 This point should be clear on inspection of the consumer s problem, written below. As the direction of the distortion to maintenance induced by reverse mortgage debt is uncertain, we cannot know which characteristics will lead the magnitude of the distortion to be larger or smaller. The exogeneity of the loan-to-value ratio m, the up-front and ongoing fee rates F and f, and the interest rate r M may seem particularly troublesome. In a competitive market, we would expect relevant characteristics to be priced, so that each of these variables would take all the elements of x as arguments. However, the HECM market is not competitive. Pricing is determined by federal entities, so profit maximization may not be the objective. Further, even with profit maximization as a motive, the discussion below should make clear that the 10 See Miceli and Sirmans (1994) and Shiller and Weiss (2000). 11 Unless there is strong substitution between non-housing consumption and the quality of home repair. 10

12 appropriate changes in price and quantity terms with borrower characteristics are not easily identified. Given the industry s infancy, the fact that F, f, and r M r are constants given borrower age should thus not be surprising. m is a function of property value, but this function is nearly constant within age groups and states, as can be verified by experiments with AARP s online Reverse Mortgage Loan Calculator. The economics of selection and moral hazard would become more interesting and difficult if r and g were treated as stochastic rather than constants. However, we find the comparatively simple case discussed here sufficiently interesting and difficult to warrant our attention in what we understand to be the first treatment of selection and moral hazard issues with respect to mobility. To avoid intra-household complications, we consider only single borrowers. Singles represent a large majority of HECM borrowers to date. 3.1 Definitions of Selection and Moral Hazard Negative profits are possible only if the termination date is sufficiently large and the price growth rate is less than r M. For this reason, we consider selection to be adverse (advantageous) if (1) characteristics associated with long (short) stays before moving or dying are associated with reverse mortgage take-up and (2) borrowers tend to live in geographic areas with low (high) appreciation rates. 12 Moral hazard occurs when, holding characteristics constant, the act of borrowing leads to behavior associated with reduced profits to the guarantor. Because g is assumed exogenous conditional on location, we define moral hazard to occur if, conditional on characteristics, reverse mortgage borrowers are likely to move or die at a later date than non-borrowers. We focus on mobility, assuming away private information on mortality. The decision to take on reverse mortgage debt is difficult to analyze because it is discrete. As a proxy for reverse mortgage demand, we consider the gain in utility from adding reverse 12 Gyourko et al. (2004) explain how expected growth rates can differ across regions. 11

13 mortgage debt. For any given reverse mortgage size M, the larger the value of the derivative of lifetime indirect utility with respect to mortgage size, V/ M, the likelier we consider reverse mortgage take-up to be. We define adverse selection as a positive correlation across characteristics x between V/ M and the gain from waiting to move V/ T, evaluated at any arbitrary combination of T and M. Advantageous selection is defined as a negative correlation. Moral hazard arises if taking on additional reverse mortgage debt makes deferred mobility more attractive, i.e. if 2 V/( T M) > 0. We refer to the case where reverse mortgage debt makes mobility more attractive, 2 V/( T M) < 0, as the opposite of moral hazard. 3.2 Plausibility of Advantageous Selection and Moral Hazard We define indirect utility as an objective maximized over choice of the level of savings carried over from the period before moving to the period after. Here, we treat the periods before and after moving as single periods, to abstract away from intertemporal smoothing issues within these periods. The simulations below parameterize direct utility within these periods. Indirect utility is written as: V = max v (T a, w, y, H a, x) + µ(t ) + v + (A T, w +, y, e g(t a), x), (3) s + s.t. w =s a + M s +, (4) w + =f(s +, y, H a, M, T ) + h(t, M, H a e g(t a) ) (5) Indirect utility V is the maximized sum of three terms: indirect utility before moving v ; a disutility associated with moving that may be a function of the date of move, µ(t ); and indirect utility after moving, v +. v and v + map from five arguments to the real numbers. The first argument in v and v + is the length of the period in question. The period before moving has length T a and the period after has length A T. T is thus bounded above at A. We assume that length of life A is deterministic and known to both the borrower and the lender. As discussed below, the advantageous selection seen to date in this market 12

14 appears unrelated to more rapid mortality among borrowers. v + could, in principle, include a bequest motive. The second and third argument of indirect utilities v and v + relate to wealth spent in the period in question. Wealth for the period prior to moving consists of savings at period a, plus the reverse mortgage proceeds M, minus savings (or debt) carried over to the post-move period. We allow the rate of interest on s + to depend on income and collateral. Post-move wealth w + consists of an increasing function f of savings s +, plus housing wealth h. The wealth from savings function f is affected by income level and housing assets because if s + is negative, the borrowing rate will be affected by collateral. For example, a home equity loan at lower interest rates than credit card debt will only be available if home value is sufficiently large and if there is no reverse mortgage debt. h itself is a function increasing in home resale value, H a e g(t a) and decreasing in M and the time to repayment and resale T. For reverse mortgages in default at date T, the derivative of h with respect to each argument is zero. Income y is assumed annuitized and constant in real terms. The fourth argument of indirect utility relates to housing consumption. For the period prior to moving, this argument is direct housing consumption, fixed at H a. For the period after moving, indirect utility is negatively affected by the real price of housing after moving, e g(t a). The fifth argument of indirect utility is a vector of unobservable characteristics x that affect the shape of v and v +. Such characteristics include health status, gender, bequest strength, impatience, and taste for smoothing consumption. µ(t ) relates to the disutility of moving and to any health benefits that might arise from moving closer to care givers. If V is differentiable, then using the envelope condition on s +, we have: ( V f T = v 1 + µ v T + h ) T + gha e g(t a) h v + H a e g(t a) 2 ge g(t a) v 4 +, (6) V M = v 2 + ( h M + f M )v+ 2, (7) 2 V M T = v 12 + ( h M + f M ) ( ) v ge g(t a) v 24 + (8) 13

15 ( 2 f + T M + 2 h T M + ) ( 2 h M H a e g(t a) gha e g(t a) v +2 + s+ w T s + v 22 + ( h M + f ) M )v+ 22. Moral hazard arises if 2 V/( T M) > 0. The plausibility of moral hazard is reflected in the first expression in equation (8). v 12, the effect of length of stay prior to moving on the value of expenditures allocated to the pre-move period, must be positive. Moral hazard is not guaranteed. The second and third terms in equation (8) reflect the fact that additional time spent at home makes the reverse mortgage costlier if default is not planned. The added cost comes from the spread r M r. This consideration has the effect of making the critical cross-partial 2 V/( T M) more negative (barring very strong substitution between numeraire and housing demands and strong real home price appreciation). The fourth term reflects the fact that savings are likely to be diminished the longer is the time at home and the concavity of indirect utility in wealth. If default is planned, then extra time at home does not make reverse mortgage debt more costly, except to the extent that the borrower also has non-mortgage debt paying an interest rate that rises with M. Moral hazard is thus more likely to operate if default is feasible. We now see why moral hazard on the dimension of maintenance is not guaranteed. The structure of the maximization almost guarantees that adding reverse mortgage debt will encourage maintenance if default is not planned (by concavity of utility), but will discourage maintenance if default is planned (since there is no resale payoff to maintenance if the default option is sufficiently in the money ). Adverse (advantageous) selection arises if the values of the derivatives V/ M and V/ T are positively (negatively) correlated across borrower characteristics. These derivatives are given by equations (6) and (7). The effect of different characteristics on these derivatives are complicated and will be simulated for a particular parameterization below. From the guarantor s perspective, the correlation is most interesting conditional on a positive quantity of M. The possibility of advantageous selection can be seen by considering the correlation between v1 v 1 +, which increases the value of V/ T, and v2 v 2 +, which increases V/ M. 14

16 The first difference reflects whether time spent before moving is more or less pleasant than time after moving. This value should be large when consumers have adequate income and savings to remain in their home for a long time and when their second period wealth is relatively small, e.g. through a low level of housing wealth and a low growth rate g. By contrast, the second difference is likely to be large under the exact opposite circumstances. v2 v 2 + reflects whether money is more valuable before or after moving. By concavity, pre-move wealth should be useful when savings and income are low and post-move wealth should be less useful when the home value is large. Hence a negative correlation between V/ T and V M is plausible. More succinctly, house-rich, cash-poor older individuals can smooth consumption across periods both by taking on reverse mortgage debt and by moving to release any remaining home equity. Variation in risk aversion and discounting has ambiguous effects on the direction of selection. The stronger the taste for consumption smoothing (risk aversion) the more negative will be v1 v 1 + and the more positive will be v2 v 2 + for the majority of the elderly who have most of their financial wealth in home equity. This effect, which argues for advantageous selection, could be reversed if default is planned on the reverse mortgage or the reverse mortgage is large, so that the post-move period is poorer than the pre-move period. Clearly heavier discounters should find reverse mortgages relatively attractive. If we assume that µ(t ) < 0, so that moving is unpleasant, then heavy discounters should postpone moves. However, heavy discounting also makes the cash inflow from moving more attractive. Hence variation in risk aversion seems likely to feed advantageous selection in the absence of default but may feed adverse selection where default is planned. Variation in discounting has unclear effects on selection. 3.3 Numerical Examples of Selection and Moral Hazard We now turn to a numerical solution of the lifetime optimization problem given in (3). We conduct comparative statics to resolve ambiguities in selection and moral hazard for specific 15

17 parameterizations. The characteristics x that we consider are initial wealth s(a), annuity income y, and home value H a, using values meant to capture a reasonable range of single older homeowners based on the AHEAD survey. We choose this subset because it forms the bulk of the potential reverse mortgage market. A summary of all baseline parameters discussed below is given in Table 1. Consider a single woman of age a = 75 years who will die for certain at age A = 95 years and has no bequest motive. The woman is endowed with a fixed annuity income of $7,500 per year, a house with initial value H a = $140, 000, and very little initial liquid wealth s(a). Her lifetime utility is taken to be additively separable with a personal discount rate of 3%, equal to the constant riskless rate of interest on savings. We choose the instantaneous (annual) utility to be of the form u(c, h) = 1 1 γ c1 γ + ξ 1 η h1 η + µ 0 δ(t T ) + µ 1 θ(t T ), (9) where the disutility of moving, W 1 γ D µ 0 = F D 1 γ < 0 (10) applies only on the move date T, while W 1 γ [ ] B µ 1 (t) = F B p die (t) p die (T P B ) 1 γ > 0 for t > T P B (11) accrues every year after the move, and is welfare enhancing (detracting) after (before) date T P B. 13 In equation (9), c is other consumption, and h is service flow from housing consumption. To simplify, pre-move we take h to be a constant S H H a, where the service flow rate is fixed at 3%. Post-move, the agent chooses c and the rent level h that maximizes her 13 In equation 11, p die (t) is the probability of a single woman dying at age t. µ 1 is intended to capture the benefit of living near assistance from families or professionals when sufficiently frail (old). The costs and benefits of mobility µ 0 and µ 1 follow a trajectory such that absent financial considerations, the optimal move date would be at age 85, halfway between initial consideration and death, roughly matching the fraction of retirees that are observed to move before death. 16

18 utility U post move = A t=t +1 β t T u(c t, h), (12) subject to the budget constraint A W s(t ) + β t T y t=t +1 A t=t +1 ] β [c t T t + (1 + g H ) t T h. (13) Here, the utility from housing level h remains fixed, while the cost of achieving this utility is assumed to rise at the same rate as house prices. We find c = W S β Ω 1 + Ω h = W S β Ω where Ω = ξ 1/γ ( Sβ S α S β = β 1 βa T 1 β S α = α 1 αa T 1 α ) 1 1/γ α β (1 + g H ) (14) For the relative risk aversion coefficients, we fix γ η = 2, reflecting a moderate degree of risk aversion over non-housing and housing consumption. 14 The 2004 Consumer Expenditure Survey shows that housing comprises roughly 25% of total expenditures for older renters. From equations (14), this determines ξ = 0.1, which is the value we choose. We sidestep some important questions regarding what housing quality means and the difference in price and utility between living on one s own or in a nursing home, but our main results are robust to the precise value of ξ. We consider the optimal move date and consumption trajectory for our potential borrower under two sets of circumstances; (a) when she is unable to take on reverse mortgage debt and (b) when she has taken on reverse mortgage debt at t = a. To simplify in case (b), 14 See, for example, Barsky et al. (1997). 17

19 we assume that the reverse mortgage debt is taken as a lump sum at the maximum value allowed, viz., 5/7 of home value. The reverse mortgage balance accrues interest at a rate of 4.5%, and a large fixed fee of 6.8% of loan proceeds is paid at origination. We do not consider the alternative of a non-hecm home equity loan (HELOC) in case (a). If we did, we might estimate reduced value to taking on a reverse mortgage. However, for the borrower profile we are concerned with here, the bulk of her income is likely from Social Security, which cannot be pledged toward the debt service of a HELOC. The only other income source that would count toward the income test is interest payments from liquid wealth. Given that a HELOC s coupon rate is considerably greater than the interest rate on savings, the owner would only tap the HELOC once liquid wealth is consumed or if default were planned. This complicates the numerics of implementing a HELOC, and we leave it for later work. We use a grid search to maximize the retired homeowner s total utility, by choosing pre-move consumption trajectory {c t } and the move date T : max {c t}, T T β t u(c t, S F H a ) + β T U post move (s(t ), T ). (15) t=0 Given T and S(T ), U post move is fixed via equations (14). Equation (15) is solved for both cases of (a) no reverse mortgage, and (b) a maximal lump sum reverse mortgage at t = a. There two key results we are interested in to assess selection and moral hazard. First, how much does s(a) have to increase (or decrease) for a homeowner without a reverse mortgage to attain the same level of maximized utility as a homeowner with a reverse mortgage. We denote this compensating variation by CV, or the dollar value of a reverse mortgage. Second, we need the optimal move-out date and, in particular, the difference in the move-out with and without a reverse mortgage to investigate moral hazard and selection. The top panel of Figure 2 shows the optimal move dates with (squares) and without (circles) a reverse mortgage, as a function of annual income y. The solid line is the result for a home that is depreciating at 3% per year, while the dashed line is for appreciation of 2%. The bottom panel shows the corresponding dollar value of the reverse mortgage. 18

20 Moral hazard operates for sufficiently low income: borrowers remain in the home much longer than do non-borrowers. At higher income this diminishes, with both types postponing the disruption of moving until the beneficial utility from moving becomes positive. Figure 2 shows advantageous selection in that lower income homeowners move more quickly than higher income individuals when there is no reverse mortgage present, and these individuals value the reverse mortgage more than higher income individuals. This effect does not, however, operate once the reverse mortgage has been taken up. Further, we see that this form of advantageous selection is undermined by the prospect of default. The slope of the dollar value of the reverse mortgage is less steep with price growth of g H = 3%, where the mortgage balance exceeds the house value by year 7, than with +2% appreciation, where default only occurs at death (year 20). This is also borne out in the dollar value of the reverse mortgage: at high appreciation it is negative for sufficiently large income, while it remains positive for all incomes in the case where strategic default is possible. A pattern that emerges in all of the simulations is that the value of reverse mortgage take-up is much larger when default occurs than when it does not. In unreported simulations, we find advantageous selection on appreciation rates in the range of non-default. That is, once default is ruled out, the reverse mortgage has a more beneficial effect on welfare when the appreciation rate rises. In Figure 3, we consider variation of initial housing wealth, H a. Income is fixed at y = $7, 500, and the top and bottom panels show corresponding results for move-out date and CV, respectively. Again, we find moral hazard is operative, in that the reverse mortgage induces the owner to stay longer. Moral hazard is stronger in the case where default occurs, at the -3% appreciation rate. Ignoring very low home values (where transactions cost play a role), the reverse mortgagor stays until the benefit to moving becomes positive, and even staying somewhat longer in the default scenario. The non-mortgagor accesses home equity by moving earlier, and, the lower the appreciation, the earlier she moves. The discrepancy between a mortgagor and an non-mortgagor becomes larger the larger the home value because the non-mortgagor s access to larger wealth offsets the larger disutility from moving early. 19

21 Figure 3 shows that selection is strongly advantageous in H a. The dollar value of the reverse mortgage opportunity rises while exit dates decrease in H a. In Figure 4, the top and bottom panels, show respectively move-out and CV versus initial liquid wealth. Moral hazard is again operative, and selection is advantageous on s a. Wealthier individuals move later, but value the reverse mortgage less. For s(a) greater than about $20,000, the reverse mortgage is not selected when appreciation is high: the high cost of a reverse mortgage outweighs the marginal utility increase. For low appreciation, the CV remains positive because of strategic default. Introducing a HELOC for the non-reverse mortgagor may lower CV, but only for significant liquid wealth levels (as annuity income does not count toward the income test). This would shift the wealth level at which a reverse mortgage becomes undesirable to slightly lower levels, but not affect the benefit to a cash-poor individual by much. Summarizing these simulations, we find advantageous selection on observables H a, y, and s a in the sense that house-rich, cash-poor homeowners move more quickly in the absence of reverse mortgage debt and find reverse mortgages more attractive. However, conditional on reverse mortgage take-up, this selection does not operate, presumably because with a reverse mortgage, borrowers cease to be cash-poor. Moral hazard operates in that a reverse mortgage induces longer stays. Moral hazard is more severe when appreciation is lower in that the gap between mobility rates with and without the reverse mortgage grows. Further, with negative appreciation rates, selection becomes less strong in that the reverse mortgage is attractive to almost all borrowers when default is feasible. Selection is also weakened with lower appreciation in that borrower characteristics associated with reverse mortgage demand become associated with longer stays at home conditional on reverse mortgage take-up. 20

22 4 Empirical Evaluation of Selection and Moral Hazard The theoretical analysis and simulations suggest that advantageous selection and moral hazard are likely to arise in the reverse mortgage market. Advantageous selection seems likely because low non-housing wealth, high appreciation rates, and high housing wealth are all plausibly associated with both reverse mortgage demand and rapid mobility. Moral hazard seems likely to arise because endowing an individual with a reverse mortgage eases liquidity constraints in the period before moving. The prospect of zero cost to remaining at home should make moral hazard more likely when default is feasible. In Figure 1, we see that selection and moral hazard effects, in combination, lead to considerably more rapid mobility among HECM borrowers than AHS respondents. This effect is much stronger among women than men. This graphical depiction of mobility differences does not illustrate the roles of advantageous selection or the opposite of moral hazard. To evaluate selection and moral hazard empirically, we compare characteristics and realized exit from homes of HECM borrowers to those of older homeowners who are not reverse mortgage borrowers. Data on reverse mortgage borrowers comes from a survey of all loans issued through mid-2003 by HUD. A comparison group of older homeowners comes from the American Housing Survey ( AHS ). Only approximately one in ten thousand older homeowner AHS respondents is a reverse mortgage borrower, so the AHS is taken as a nonborrower comparison group. As in the theoretical discussion, we confine attention to singles; this group comprises just over two-thirds of reverse mortgagors. To test for the presence of advantageous selection, we ask whether predicted participation in the HECM program, based on observable characteristics, is associated with more rapid mobility, conditional on actual participation. Moral hazard is more difficult to identify than advantageous selection. We never observe the same individual s mobility with and without a reverse mortgage and characteristics are measured incompletely and with error. Finding that observed characteristics do not fully explain differences in mobility between the HECM and AHS samples thus does not imply 21

23 that the opposite of moral hazard is operative. Rather than trying to estimate a moral hazard component of mobility differences, we ask only whether the data are consistent with the model of moral hazard presented above. We thus ask whether the difference in the hazard out of homeownership for HECM borrowers relative to AHS non-borrowers is greater in markets where default seems unlikely than in markets where default seems feasible. We also ask whether advantageous selection works less strongly in these markets, by asking if characteristics associated with reverse mortgage demand are less strongly associated with exit rates where default is arguably more likely. 4.1 Data The HECM administrative data has information on all 77,007 HECM loans originated between the program s inception in 1989 and the start of this project in mid Included for each loan are the borrower s age, state of residence, appraised home value, income, and non-housing debts and assets as of loan closing. We also know the dates of loan closing and termination, if any. For a minority of the terminated loans, we have indicators for whether termination was due to death or to a move. The HECM data do not suggest that the speedy exit from homes on the part of borrowers relates to high mortality rates. Indeed, there is some suggestion of adverse selection on mortality. Among the terminated HECM loans for which a reason for termination is stated, approximately 25 percent state death. Because the number of loans terminated with the borrower alive and still in the home is small (less than three percent), we can evaluate the role of mortality in HECM exit speed by comparing this 25 percent mortality termination rate to mortality-based termination of homeownership spells in other data sets. Table 2 compares mobility and mortality rates across different data sets and suggests that mortality would be the cause of between one-third and one-half of terminations in a representative sample of the elderly. By conditioning our empirical estimates on gender, we control for the most important source of observable mortality heterogeneity. 22

24 The AHS is a biennial panel survey of approximately 55,000 US homes. The current panel has been observed from 1985 to 2003 with some additions and deletions. For each home-year observation, we learn whether the unit is owner-occupied, the age and family relationships of all residents, and whether any of the residents from the prior wave of the panel remain there. 15 We do not know why occupants move out of their homes, but do know the date at which the next occupant moved in. We deem this subsequent move-in date as analogous to the date of loan termination in the HECM dataset. In our hazard models, failure occurs at the date at which the subsequent tenant moves in to an AHS housing unit or when a HECM loan is terminated. We limit the sample to homes owned a single individual over 61 years old, as renters and younger homeowners are ineligible for reverse mortgages. Table 2 indicates that the combined mobility and mortality rates generating terminations in the AHS are, if anything, greater than the rates reported in other sources of data on the elderly. Hence comparison group data quality cannot explain the relatively rapid mobility of HECM borrowers. In addition to age and termination status for each each home-year in the AHS, we observe sex; self-reported income; an indicator for whether the respondent has $20,000 in nominal asset wealth; and the metropolitan area, if any, where the home is located. We infer the state of residence from the metropolitan area. Non-metropolitan homes are excluded. Outstanding mortgage debt is almost never recorded and hence we do not include this as a covariate. Summary data from the two datasets are reported in Table 3. The variable INV20K, indicating whether the individual has $20,000 in asset wealth or more, is constructed based on nominal assets from the continuous variable reported in the HECM data. Otherwise, economic values are deflated to be in 2005 dollars based on the non-shelter U.S. Consumer Price Index for all urban consumers. The summary statistics present averaged variables across panels for each observed older homeowner in the AHS as a separate observation. 15 For the years 1997 through 2003, this indicator variable is subject to mismeasurement and is augmented with an indicator for whether the respondent indicates having moved in before the prior survey year and another for whether the reported age is consistent with the prior response. 23

25 The HECM data is notable for the large number of zero values for income and non-housing wealth. Because these variables do not affect HECM loan terms, there is little incentive for the data collectors to record report these variables, and unfortunately non-housing wealth and income are reported as zero in the HECM data when they are missing. However, $20,000 in non-housing wealth is almost never reported positively when income is missing. Hence we assume that INV 20K is missing when income is unreported for summary purposes. The missing data is highly correlated with time: through 1995 income is almost always positive and IN V 20K is positive in two to three percent of cases. Thereafter, income is rarely reported and INV20K is positive almost never. For this reason, in several specifications, we confine the HECM data to loans closed prior to Tests of Selection and Moral Hazard Figure 1 shows plots of a Kaplan-Meyer survival estimates for four groups: women in the AHS, men in the AHS, women in HECM, and men in HECM. The vertical axis depicts the fraction of each group that survives, the horizontal axis depicts the length of time since first observation. In the AHS, this start time varies between 1985 and Starts later than the first year of the panel are possible because vacated homes may be subsequently occupied by single older homeowners. Start dates in the HECM dataset range between early 1989 and The program has grown with time, so the mean start date is substantially later in the HECM data (1999) than in the AHS data (1989). We see in Figure 1 that mobility is considerably more rapid in the HECM group than among the AHS households and that this effect is particularly true among the approximately 60 percent of each sample that are women. However, these plots do not condition on age, income, house value, or market characteristics. Hence we do not know if the more rapid mobility among HECM borrowers stems from advantageous selection or from the opposite of moral hazard. A first view of selection comes in Table 3. Income is lower among the HECM respondents 24

26 who report income than among AHS homeowners. Likewise, INV20K is significantly more frequently affirmative in the AHS dataset. Home values are significantly higher in the HECM sample, but some of this reflects real price appreciation and the later average observation time in HECM relative to AHS. The third set of columns of Table 3 shows that HECM borrowers housing values were also higher than AHS non-borrowers in the early 1990s when the home price boom had not yet started. The low incomes and wealth and high home values of the reverse mortgage borrowers are consistent theoretically with more rapid mobility Pooled Hazard Estimates One approach to determining the roles of selection and moral hazard in the rapid mobility of HECM borrowers is to see if the difference in mobility rates survives conditioning on observable borrower characteristics. Table 4 estimates hazard regressions, with columns (1) through (3) pooling the AHS and HECM data. We observed truncated spells in both data sets. The coefficients on each variable are the estimated effect of an increase in that variable on the log hazard rate out of the starting home. A positive coefficient indicates that increasing the variable speeds exit from the home and a negative coefficient indicates that the variable slows exit. For both datasets, we measure covariates as of the first observation of the individual. The estimates come from a Cox proportional hazard specification, but similar results arise if a simple exponential hazard, without a time-specific hazard component, is estimated. A problem with the data for hazard estimation is that we do not observe homeowners from the starting point of their stay in a home, but rather from an arbitrary date in the middle of their tenure, so the interpretation of the underlying hazard is difficult. The AHS data, unlike the HECM data, includes the date at which the respondent first moved into the home. Unreported repeated probit estimates of termination within AHS, with the original move date included and with respondent characteristics (including age) allowed to vary over the course of the panel, yield results essentially identical to those presented below. The first column of Table 4 confirms in numbers the graphical evidence of Figure 1. 25

27 Unconditionally, HECM participation multiplies the hazard out of homeownership by roughly the number e. Column (3) shows that this effect is diminished but still large and significant when covariates are included. State dummy variables, age, and age squared are included in the regression but not reported. The implication of the coefficient estimate of.768 on participating in HECM in column (3) is that all else equal, participation in HECM leads to a hazard out of homeownership that is more than twice as large as it would be for a nonparticipant. We find no significant effects of either investment wealth in excess of $20,000 or of total household income. Consistent with the theory, we find that home value is associated with more rapid mobility. In unreported specifications, we find that male mobility is more sensitive to covariates than female mobility. The sample in column (3) of Table 4 is much smaller than in columns (1) and (2), because log income is not reported by most reverse mortgagors. If the unconditional estimates of HECM participation are confined to the AHS sample and to the reverse mortgagors who report positive income, the estimated effect of HECM participation falls to a level between the unconditional and conditional values. This suggests that failure to report income may be associated with low income and hence more need to move, consistent with the theory. A report of zero income is also correlated with low home value, suggesting that a report of zero income is, in fact, consistent with low true income. Table 5 sheds some light on the sources of advantageous selection seen in Table 4. The same variables (particularly home value) that predict participation in HECM also predict more rapid mobility. The first column of Table 5 shows that log income and having $20,000 in non-housing wealth negatively predict participation and that home value is positively associated with participation. A second degree polynomial in age and many indicator variables for state of residence are also significantly associated with participation. We also find that single men are more prevalent in the HECM universe than in the AHS sample. In column (2) of Table 5, we find that all of income, wealth, home value, and being male have effects on termination in the pooled sample that have the same sign as their effect on HECM participation. 26

28 4.2.2 Hazard Estimates Conditional on Reverse Mortgage Status Analysis of the pooled sample is problematic for at least two reasons. First, covariates presumably operate differently on the hazard out of homeownership depending on mortgage status. In terms of the model presented above, V/ T depends on M. Second, the extent of mismeasurement may vary across the samples. An alternative approach to pooling the samples is to ask if advantageous selection works in the sense that characteristics associated with reverse mortgage participation are also associated with rapid termination, conditional on participation or non-participation in HECM. We do this in two ways: the first way is a two-step approach in which we first predict participation in a pooled AHS-HECM sample, and second use the estimate of predicted participation as a right hand side variable in separate survival analyses. The second way is to simply consider the effect of each variable on take-up in the pooled sample and mobility in the separate samples. The first column of Table 5, discussed above, provides results of a probit estimation for participation in HECM in the pooled sample. Columns (4) through (7) of Table 4 investigate the effects of predicted participation on mobility. In these specifications, we condition on age, because we are interested in selection on characteristics other than age, which is priced. Comparing columns (4) and (6) of Table 4, we find that the positive effect of predicted HECM participation on mobility comes entirely from the HECM sample. HECM borrowers who appear most likely to participate move more rapidly than borrowers with characteristics less typical of borrowers. Interpreting the coefficient of approximately.3 in the HECM sample, a one standard deviation increase of.2 in predicted participation from the mean of.72, with all other variables evaluated at their means, would be associated with an increased hazard of of approximately six percent. However, in the AHS sample, having characteristics associated with a high probability of HECM participation is not associated with rapid mobility. There, predicted participation has a negative but insignificant effect on the hazard. The same pattern observed in Table 4 is observed in Table 5. Column (3) shows high 27

29 housing value positively associated with both reverse mortgage take-up and with rapid termination among HECM borrowers. Income and INV20K have insignificant effects on the hazard among HECM borrowers: income has the right sign, with a positive effect on the hazard, but INV20K, which features very little variation within the HECM group, has the wrong sign. Column (4) of Table 5 shows that none of these covariates have significant effects on the hazard out of home in the AHS sample Do Selection and Moral Hazard Worsen With Reduced Appreciation? The fact that variables associated with participation in the HECM program are associated with more rapid mobility, and the related fact that the inclusion of covariates reduces the estimated effect of HECM participation in the pooled sample, imply that advantageous selection is at work. What cannot be known from these results is the source of the remaining positive effect of HECM on mobility. Plausible candidates for the residual excess mobility are (a) selection on the same observables that are imperfectly observed in the data; (b) selection on other, unobserved, characteristics; and (c) operation of the opposite of moral hazard. The simulations suggest that it is unlikely that endowment of a HECM leads to more rapid mobility, but our model allows for the possibility that under some specifications, the opposite of moral hazard could operate. We cannot prove or disprove a role for the opposite of moral hazard empirically. We show, however, that there is evidence consistent with the operation of moral hazard as described in the model. The variable LOWGROW indicates that the respondent lives in a state in which the historical appreciation rate on owner occupied housing (as estimated from 1976 through 2004 by the Office of Federal Housing Enterprise Oversight) has been in the bottom 15% of the sample. Differences in appreciation rates are persistent across regions, so lagged performance may indicate that the respondent has information concerning appreciation. Further, much of the house price index history is concurrent with our sample. Hence LOWGROW plausibly indicates borrower beliefs that default will at some point be feasible. The low point in the 28

30 distribution (the 15th percentile) was selected because price appreciation has been so strong and interest rates so low since the inception of the HECM program that default appears out of the question for reasonable horizons in most regions. Differences in appreciation rates at higher points in the distribution may play a role in mobility differences: several of the state dummies are significant predictors of both participation and mobility. Column (2) of Table 4 confirms the prediction that the benefits of advantageous selection may be offset by moral hazard considerations when default is feasible. The excess mobility of HECM borrowers is considerably smaller in low appreciation states than in states that have enjoyed greater home price appreciation, and where default is presumably less feasible. This is reflected in the significant negative coefficient on the interaction term between HECM participation and the indicator for living in a state with historically low appreciation. Columns (5) and (7) of Table 4 show that predicted participation has a smaller effect on exit in low return states in both the HECM and AHS samples. In neither case is the interaction effect significantly different from zero. It is thus possible that reduced differential HECM mobility in low appreciation states is not a result of moral hazard, but merely the fact that characteristics associated with being a reverse mortgage borrower have a smaller impact on mobility in low appreciation states than high appreciation states. For the critical selection variable home value, this is logical: with diminished appreciation, home equity is smaller for any starting value, hence so too is the financial incentive to move more quickly. Summarizing, we find that, as predicted, HECM participation has a smaller effect on exit rate in environments with historically low appreciation rates. This is consistent with the model s prediction that endowing an individual with a reverse mortgage has a more negative effect on mobility when default is feasible. We also find some evidence that the very characteristics associated with advantageous selection become less advantageous to lenders when default is feasible, again consistent with the theory. The fact that characteristics associated with borrowing have a negative (albeit insignificant) effect on mobility among non-borrowers clouds the interpretation of both of these findings as relating to moral hazard. 29

31 5 Conclusions Reverse mortgages have the potential to become a huge market worldwide. Simulations show substantial gains to house-rich, cash-poor older homeowners despite large fees. The reverse mortgage market resembles a conventional insurance market, suggesting that a reason for its small size is fear of adverse selection and moral hazard on the supply side. Large fees charged to HECM borrowers seem to be rooted in such fears, and must have a dampening effect on demand. In fact, to date, HECM borrowers have behaved in a way that has led to greater profits to lenders and the guarantor than might have arisen with population average behavior, at least on the critical dimension of mobility. Borrowers have moved out of their homes rapidly, so almost every resold home has retained value in excess of reverse mortgage principal and accrued interest. Our model suggests that the rapid mobility observed is attributable in part to advantageous selection. The intuition is that individuals with a taste for spending their home equity are likely to do so both by taking on reverse mortgage debt and by cashing out remaining equity by moving. Low liquid wealth and high home value generate rapid mobility in theory and in simulations, and these characteristics are significantly associated with HECM participation. Empirically, larger initial home values have been associated with more rapid mobility among HECM borrowers, consistent with the theory. We should note that the simulations we parameterize predict that increased mobility with increasing home values occurs among non-borrowers rather than borrowers, the opposite of what occurs in the data. While advantageous selection on observables explains a significant portion of the differences in mobility between HECM borrowers and non-borrowers, we cannot be certain what explains the rest. The logical candidates are advantageous selection on unobserved characteristics or the opposite of moral hazard. The empirical results are broadly consistent with our model of how moral hazard would be likely to work: when default is feasible based on historical appreciation rates, excess mobility is diminished. Selection on unobserved char- 30

32 acteristics, possibly including the parts of home value and wealth that are missed due to survey error, thus seems the likelier explanation for the residual mobility difference. Impatience, perhaps generated by large cash needs, might be one source of such unobserved heterogeneity. The fact that the difference in mobility rates between HECM borrowers and the AHS comparison group has been smaller in states with historically low home price appreciation rates presents some negative news for the future of the reverse mortgage industry. Rapid mobility is most attractive to the lenders and guarantor who bear reverse mortgage risk precisely when depreciation is likely to reduce home values below outstanding mortgage debt. If the generally high appreciation rates that have characterized the life of most HECM loans become negative, our results suggest that losses could be considerable. We cannot rule out the possibility that the opposite of moral hazard operates through financial pressure to move generated by HECM s interest rate spread over riskless savings, thereby causing part of the rapid mobility observed to date. The evidence supportive of moral hazard in low appreciation states is weakened by the fact that borrowers with characteristics similar to HECM borrowers appear to move more slowly in low appreciation states, independent of actual HECM participation. We cannot know from the data available whether borrower characteristics will become associated with less rapid mobility in states with historically high appreciation rates should appreciation rates fall in the future. We have not given much attention to the possibility of moral hazard on the dimension of home maintenance. Our model suggests that maintenance moral hazard may not be an equilibrium outcome in this market, because the inflow of cash generated by a reverse mortgage should increase the willingness of homeowners to invest in projects that pay off in part after they leave their home. We consider this an interesting direction for future research should data become available. Likewise, incorporation of uncertainty seems like a natural extension of our work. The data appear consistent with the adverse selection on mortality that might arise with asymmetric information. Of most immediate relevance, our results call into question the wisdom of recent policy 31

33 changes easing the refinancing of HECM loans. To date, reverse mortgage borrowers who have seen prices appreciate, such that their home equity remains large despite the presence of the mortgage, and who wished to spend some of that excess equity, have had little choice but to sell their homes. With easy refinance, residual home equity can be spent away, so some of the incentive to move can be expected to disappear. 32

34 References Aizcorbe, Ana M., Arthur B. Kennickell, and Kevin B. Moore, Recent Changes in U.S. Family Finances: Evidence from the 1998 and 2001 Survey of Consumer Finances, Federal Reserve Bulletin, January 2003, pp Artle, Roland and Pravin Varaiya, Life Cycle Consumption and Homeownership, Journal of Economic Theory, 1978, 18 (1), Barsky, Robert B., F. Thomas Juster, Miles S. Kimball, and Matthew D. Shapiro, Preference Parameters And Behavioral Heterogeneity: An Experimental Approach In The Health And Retirement Study, Quarterly Journal of Economics, May 1997, 112 (2), Bayot, Jennifer, As Bills Mount, Debts on Homes Rise for Elderly, New York Times, 2004, July 4, 1. Caplin, Andrew, Turning Assets into Cash: Problems and Prospects in the Reverse Mortgage Industry, in Olivia S. Mitchell, Zvi Bodie, P. Brett Hammond, and Stephen Zeldes, eds., Innovations in Retirement Financing, Philadelphia: University of Pennsylvania Press, 2002, p. chapter 11. Chinloy, Peter and Isaac F. Megbolugbe, Reverse Mortgages: Contracting and Crossover Risk, Journal Of The American Real Estate And Urban Economics Association, 1994, 22 (2), Cohen, Alma and Liran Einav, Estimating Risk Preferences from Deductible Choice, Manuscript, Stanford University. Davis, Morris A. and Jonathan Heathcote, The Price and Quantity of Residential Land in the United States, Finance and Economics Discussion Series , Federal Reserve Board

35 de Meza, David and David Webb, Advantageous Selection in Insurance Markets, RAND Journal of Economics, Summer 2001, 32 (3), Finkelstein, Amy and James Poterba, Testing for Adverse Selection Using Unobservables, Manuscript, MIT. and Kathleen McGarry, Private Information and Its Effect on Market Equilibrium: New Evidence from the Long Term Care Industry, working paper 9957, NBER Gyourko, Joseph, Christopher J. Mayer, and Todd Sinai, Superstar Cities, Working Paper, Wharton. Kutty, Nadinee, The scope for poverty alleviation among elderly homeowners in the US through reverse mortgages, Urban Studies, 1998, 35 (1), Mayer, Christopher, Reverse Mortgages and the Liquidity of Housing Wealth, Journal Of The American Real Estate And Urban Economics Association, 1994, 22 (2), Miceli, Thomas and C.F. Sirmans, Reverse Mortgage and Borrower Maintenance Risk, Journal of the American Real Estate and Urban Economics Association, 1994, 22 (2), Mitchell, Olivia S. and John Piggott, Unlocking Housing Equity in Japan, Journal of the Japanese and International Economies, 2005, forthcoming. Rodda, David, Christopher Herbert, and Hin-Kin Lam, Evaluation Report of FHA s Home Equity Conversion Mortgage Insurance Demonstration, Prepared for US Department of Housing and Urban Development, Abt Associates Sheiner, Louise and David Weil, The Housing Wealth of the Aged, NBER Working Paper 4115, NBER Shiller, Robert and Allan Weiss, Moral Hazard in Home Equity Conversion, Real Estate Economics, 2000, 28 (1),

36 Szymanoski, Jr. Edward J., Risk and the Home Equity Conversion Mortgage, Journal Of The American Real Estate And Urban Economics Association, 1994, 22 (2), Venti, Steven and David Wise, Aging and Housing Equity, NBER Working Paper Yaari, Menahem E., Uncertain Lifetime, Life Insurance, and the Theory of the Consumer, Review of Economic Studies, April 1965, 32,

37 Figure 1: Survival probabilities by sex and HECM participation Survival Probability AHS,male AHS,female HECM,male HECM,female Months from entry into panel 36

38 Figure 2: Optimal Move Date, Value of a Reverse Mortgage, and Income Optimal Move Date [yr] g H = 3% 2 w/o RM w/ RM y [$ 000] Dollar Value of RM [$ 000] g H = 3% y [$ 000] Notes: Top panel plots optimal move date after retirement, with (circles) and without (squares) a reverse mortgage. The bottom panel plots the dollar value of a reverse mortgage versus annual income y. Results are shown for two values of house price appreciation g H, while other parameters are fixed as in Table 1. In particular, H a = $140, 000, ξ = 0.1, and s(a) = $1,

39 Figure 3: Optimal Move Date, Value of a Reverse Mortgage, and Home Value g H = 3% 2 w/o RM w/ RM Optimal Move Date [yr] H a [$ 000] Dollar Value of RM [$ 000] g = 3% H H a [$ 000] Notes: The top panel plots optimal move date with (circles) and without (squares) a reverse mortgage. The bottom panel plots the dollar value of a reverse mortgage versus initial house value, H a. Results are shown for two values of house price appreciation g H, while other parameters are fixed as in Table 1. In particular, y = $7, 500, ξ = 0.1, and s(a) = $1,

40 Figure 4: Optimal Move Date, Value of a Reverse Mortgage, and Liquid Wealth Optimal Move Date [yr] g H = 3% 2 w/o RM w/ RM s(a) [$ 000] Dollar Value of RM [$ 000] g H = 3% s(a) [$ 000] Notes: The top panel shows the optimal move date after retirement, with (circles) and without (squares) a reverse mortgage. The bottom panel plots the dollar value of a reverse mortgage versus initial liquid wealth, s(a). Results are shown for two values of housing utility weight ξ, while other parameters are fixed as in Table 1. In particular, H a = $140, 000, y = $7, 500, and g H = 0. 39

41 Table 1: Baseline case parameters for the numerical solution of the optimization problem, Section 3.3. Description Symbol Baseline value Age of potential borrower a 75 Age at Death A 95 Age of Positive Move Benefit T P B 85 Numeraire/Housing Curvature γ = η 2 Housing Utility Weight ξ 0.1 Initial Wealth s(a) $1,250 Benefit/Disruption Factor F B = 3F D 50 Benefit/Disrupt Wealth W B = W D $30,000 Annual Income y $7,500 Initial House Value H a $140,000 Bequest Strength κ 0 House Price/Rent Appreciation g H = g R 0%/yr Personal Discount Factor δ 3%/yr Inflation Rate π 0 Real Interest Rate r δ Reverse Mortgage Rate r M r + 1.5%/yr Reverse Mortgage Fee r fee 6.8% Reverse Mortgage Loan Amount L RM 5 7 Ha Housing Service Flow S H 3%/yr 40

42 Table 2: Two-Year Mobility and Mortality Rates among Single Women Homeowners Aged 62 + in Several US Surveys Data Mortality Mobility Mortality or Mobility Mean Age AHS % 73.6 Berkeley Mortality % 74 SIPP mobility survey % 76 AHEAD % 78.8 AHEAD (Venti and Wise (2000)) 3.8% Berkeley Mortality % 78 Notes: Berkeley data is for women aged 73 or 77 in 1993 only. Venti and Wise use the entire AHEAD panel. Authors own calculations based on public survey data otherwise. Table 3: Summary Statistics by Dataset Variable Obs Mean Std. Dev Obs Mean Std. Dev Obs Mean Std. Dev AHS HECM HECM, pre-1996 INCOME 2,913 28,166 24,117 74,573 2,273 6,267 12,113 12,511 9,315 VALUE 2, ,914 94,532 73, ,247 86,483 11, ,573 60,941 LNINCOME 2, , , LNVALUE 2, , , INV20K 2, , , AGE 2, , , LOWGROW 2, , , ZEROINC 2, , , FEMALE 2, , , Pr(HECM) 2, , ,

43 Table 4: Cox Proportional Hazard Regressions: Exit on Actual and Predicted HECM Status (1) (2) (3) (4) (5) (6) (7) LNINCOME (0.019) LNVALUE 0.079** (0.025) INV20K (0.052) FEMALE ** 0.074** ** ** HECM 0.966** 0.994** 0.768** (0.032) (0.034) (0.038) (0.025) (0.028) (0.028) (0.062) (0.062) LOWGROW (0.067) (0.141) (0.115) Pr(HECM) 0.291** 0.317** (0.070) (0.074) (0.113) (0.121) Pr(HECM) LOWGROW (0.215) (0.293) HECM ** LOWGROW (0.071) State FE No No Yes No No No No Age Polynomial No No Yes Yes Yes Yes Yes Sample HECM,AHS HECM,AHS HECM,AHS HECM HECM AHS AHS Observations 77,514 77,514 14,268 10,932 10,932 2,851 2,851 Notes: Regressions estimate probability of exit at time t from first observation as a baseline function of time multiplied by e(xβ), where x is the vector of covariates and β are the coefficients listed in the table. ** Denotes significant at 1%. Standard errors in parentheses. Columns (1) and (2) include all observations for the HECM sample and all of the observations spells in the AHS panel. Columns (3) through (7) are confined to observations with positive income and home values reported. Pr(HECM) comes from the estimates presented in the first column of Table 5. 42

44 Table 5: Effects of Covariates on HECM Participation and on Exit From Home (1) (2) (3) (4) HECM Hazard Hazard Hazard participation LNINCOME ** ** (0.036) (0.017) (0.023) (0.036) LNVALUE 0.477** 0.149** 0.176** (0.030) (0.023) (0.033) (0.036) INV20K ** ** (0.051) (0.050) (0.080) (0.070) FEMALE ** ** ** (0.038) (0.024) (0.027) (0.061) Constant ** Time Time Time (1.281) Varying Varying Varying State FE Yes Yes Yes Yes Age Polynomial? Yes Yes Yes Yes Observations 17,042 14,268 11,417 2,851 Sample HECM, AHS HECM, AHS HECM AHS AHS Subsample Year<1996 1st obs NA 1st obs Notes: Standard errors in parentheses. ** Denotes significance at 1%. Column (1) presents a probit estimate of the effect of covariates on participation in the HECM program. Columns (2) through (4) present the effects on a Cox proportional hazard out of the current home. A positive coefficient indicates that a variable is associated with more rapid exit. Column (1) uses all HECM respondents and uses each home-individual respondent in AHS, with standard errors clustered on homes to allow for correlated disturbances within homes and individuals. Columns (2) and (4) confine the AHS sample to one observation per owner, with covariates determined in the first observation and the length of homeownership determined as described in the text. 43