Selection and Moral Hazard in the US Reverse Mortgage Industry

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1 Selection and Moral Hazard in the US Reverse Mortgage Industry Thomas Davidoff and Gerd Welke Haas School of Business UC Berkeley Highly Preliminary: comments encouraged March 25, 2004 Abstract Home equity plays the leading role in the wealth of most older Americans up until death and a large number of older Americans can be characterized as house rich, cash poor. If bequest motives are not strong, then reverse mortgages should be popular in that they allow a transfer of cash to homeowners from the period after their home is sold to the period before. A natural concern, however, is that the reverse mortgage market might be destroyed by adverse selection and moral hazard in the sense that borrowers might remain in their homes so long that any cash transfer of decent size will grow to an amount greater than collateral value by the time of departure. We show in a parsimonious model, in which an older person chooses both optimal consumption and the date at which they move, that reverse mortgage demand need not be correlated with longer stays in the home. Based on loan histories and the American Housing Survey, we find empircally that single women who have participated in the most popular US reverse mortgage program (HECM) depart from their homes at a rate almost 60 percent greater than observably similar non-participating older single women homeowners.

2 Home equity plays the leading role in the wealth of most older Americans. Based on the 2001 Survey of Consumer Finances, Aizcorbe, Kennickell and Moore (2003) show that 76 percent of household heads 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. A large fraction of home equity appears to be retained up to death. Sheiner and Weil (1992) report a mobility rate of approximately 4% among older single women based on the Panel Study of Income Dynamics, and a similar number arises in the Survey of Income and Program Participation. Combined with mortality rates, this suggests that something like 50% of 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. In the absence of very strong bequest motives, these facts suggest that a financial product that would allow consumption of home equity without requiring a move would be quite valuable to older homeowners. Artle and Varaiya (1977) implicitlt show that an older homeowner will typically be willing to pay an interest rate in excess of the rate on savings in return for the opportunity to take cash out of their home prior to moving. This is the logic behind the reverse mortgage market. Figure 1 illustrates the sequence of payments in a simplified version of a reverse mortgage. Payments need not be made until the (both) borrower(s) die or move out of the home. M 1 denotes a cash advance made at the time of loan closing. Should the homeowners die or move out of the home, they must pay principal and interest on M 1 as well as fixed costs F incurred at the time of closing but typically financed. Interest accrues at rate R RM 1. If the borrower stays in the home, they have the option of paying down some of the balance or drawing down a further cash advance; M 2 can be positive or negative. In no event is the amount owed greater than the property value at the time of resale. H denotes the value of the home at the time of loan closing and Π 1 is the realized rate of price inflation. Perhaps the most familiar form of contract to economists specifies that payments are constant as long as the homeowner remains in the home. This would conform with Figure 1 if we assumed that the homeowner in no event can live past period 2 and M 1 and M 2 are pre-specified to be equal. In fact, most loans under the dominant US program allow greater flexibility, as discussed below. If we assume that R RM is greater than the return available on savings to the borrower and that fixed costs are significant, then it is clear that demand for a reverse mortgage will exist only for homeowners whose marginal utility is greater while in the home than after moving or in death. High marginal utility in the home makes sense if the bequest motive is weak and the present value of additional expenditures incurred after moving while still alive (such as medical costs and rent on housing still consumed) 1

3 M 2 min((m 1 + F )R 2 M + M 2R M, HΠ 2 ) Stay [p] M 1 Move [q] min((m 1 + F )R M, HΠ) 0 Dead [1-p-q] min((m 1 + F )R M, HΠ) Figure 1: Reverse mortgage design. Loan balance is repaid by the borrower as late as the date of move out of the home or death. F denotes financed closing costs. do not exceed the value of the home. A natural concern for lenders, under the assumption that the rate of interest exceeds the rate of house price inflation in expectation, is that the borrower will live so long with such a low mobility rate that the present value of reverse mortgage payments will exceed the collateral value when the loan becomes due. Indeed, the famed Frenchwoman Jeanne Calmet, who lived to be 121 sold her apartment forward in her late eighties in what must have been a disastrous arrangement for reverse mortgagee Andre-Francois Raffray. 1 To focus on the question of whether we should expect reverse mortgagors to remain alive and in their homes longer than the rest of the population, we assume that the borrower has perfect information concerning events in the future. A fuller model of demand would of course incorporate uncertainty into the borrower s thinking. Given the infancy of the industry and the critical role of a government insurer, we take a partial equilibrium approach and do not consider strategic behavior on the part of lenders. In Section 2, we present a model of the timing of move out of an original owner occupied home and ask whether characteristics that increase demand for reverse mortgages can be expected to be associated with a later date of move out or death. If we believe that all relevant characteristics that are associated with increased reverse mortgage demand are also associated with lengthened optimal time to move, then we would expect to find empirical evidence that reverse mortgagors delay moving relative to the rest of the population. We find instead that in the absence of very strong assumptions, we can not rule out either the possibility that reverse mortgagors move out early relative to the rest of the population or move out late. Section 3 provides 1 As reported by the Associated Press on August 5,

4 empirical analysis showing that reverse mortgagors in the most popular US program leave their homes at a rate that far exceeds the rate for comparable older homeowners. A natural interpretation that arises is that moral hazard must be present in that the introduction of a reverse mortgage seems unambiguously to make a later move out date more attractive. Positive selection appears to operate in this market, however, in that the same people who should find reverse mortgages attractive should tend to find moving out of the home attractive in the absence of a reverse mortgage or the presence of a small mortgage. Throughout, we will focus on the structure of the Home Equity Conversion Mortgage, which is the largest reverse mortgage product in the US and enjoys a guarantee from the Federal Housing Administration. Other products are available in the US, notably the Financial Freedom reverse mortgage, sold privately and which allows larger loan amounts. The most popular way for older Americans to withdraw home equity in recent years appears to be through home equity loans or home equity lines of credit. These products require amortization during the life of the loan Home equity loans are one such product, but these require partial repayment prior to moving out of one s. A line of credit could be structured to postpone any out of pocket repayments on a fairly large balance for a number of years. Examination of the performance loans made for consumption smoothing purposes to older homeowners would be of interest if such data were easily available. Indeed, at present it appears that the only way that a HECM could be preferred to a home equity line would be if the anticipated stay in the home were close to 15 years or if income were very low. 2 We will not discuss maintenance moral hazard, which has been discussed elsewhere (Miceli and Sirmans (1994) and Shiller and Weiss (2000)), except to observe that moral hazard may not be a problem with the elderly, in the sense that with or without a reverse mortgage, older homeowners can be expected to do very little home maintenance. Indeed, Davidoff (2004) suggests that combining a reverse mortgage with a maintenance contract might generate Pareto gains to dynasties in which children might otherwise oppose a reverse mortgage. 1 The HECM Product The theoretical willingness of older homeowners to pay a spread above the riskless rate to borrow against future housing sale proceeds underlies the reverse mortgage industry, which dates to 1961 in the US and the early part of 20th Century in Europe. In the late 1980s, the US Department of Housing and Urban Development ( HUD ) 2 As noted below, the HECM has very high fixed costs but an interest rate typically lower than home equity loans. 3

5 devised a Home Equity Conversion Mortgage ( HECM ) program which is currently the dominant reverse mortgage product in the US. The program works roughly as follows, based on a program evaluation done for HUD by Abt Associates in Borrowers must be homeowners with very little or zero outstanding mortgage debt. Banks or mortgage brokers find borrowers, thereby earning upfront fees and the originators typically retain servicing rights. These lenders typically sell the cash flow rights associated with the loans to Fannie Mae. The loan cash flows are insured by the Federal Housing Agency against default. In exchange for the guarantee, FHA receives 2 percent of the property value at the time of loan closing and assesses a charge of 1 24 of one percent of the outstanding loan balance each month. The borrowers are obliged to make property tax payments and to perform minimal maintenance but maintenance requirements are presumably enforceable only before closing. 3 Otherwise, no payments are due until all mortgagors (a borrower and a spouse if one exists) have moved out of the home, dead or alive. There is no recourse to the lender for payments outside of the value of the home in the event that the resale value is below the outstanding loan balance. Because interest rates are likely to exceed the rate of house price inflation, loan-to-value ratios are fairly small and increase with age. Borrowers can receive payments in several forms. They may receive a single lump sum payment, a line of credit with an increasing maximum outstanding balance, monthly payments that last for a fixed period (term payments), or monthly payments that last as long as the borrower lives in the home (tenure payments). Borrowers may receive payments in a combination of any of these forms. The line of credit is by far the most popular option (and it includes lump sum payments as a subset). The amount that may be borrowed is decreasing in interest rates and increasing in borrower age. The interest rate on HECM loans may be fixed or adjustable, but almost all existing loan rates are adjustable as Fannie Mae will only purchase ARMs under HECM. The spread over the one-year treasury rate is typically near 1.5 percent. Closing costs on the 77,007 loans issued to date vary considerably, and the size of the loan has minimal explanatory power. 4 The median ratio of closing cost to property value is 6.8 percent. These closing costs, which may be financed, are large relative to conventional loans, particularly relative to home equity lines of credit which feature closing costs of zero in some cases. No payments are due until the borrower moves or dies. Absence of demand has led to the exit of many originators, 5 but the potential size 3 One would expect considerable legal difficulty in evicting an elderly mortgagor for failing to make sufficient repairs to their home. 4 The R 2 from a regression of closing cost on maximum loan amount is just.0008 and the coefficient on maximum loan amount has the wrong sign. 5 Other problems have plagued the industry. Some reverse mortgages were designed with shared appreciation features. Some reverse mortgagors under such SAM arrangements died within one or two years 4

6 of the market is huge. The 2000 US Census reports that there are approximately 17.5 million homes owned by households with heads over age 65. Hence the total originations of 77,000 to date in the decade of HECM operation represents a very small market share. Indeed, Mayer (1994) suggests that the HECM product should be attractive to at least six million older households. From the American Housing Survey, homeowners aged over 65 had homes that averaged values of $170,000 in If 10 percent of the value of these homes were subject to reverse mortgages, the outstanding balance would be approximately $300 billion. The next section explores the extent to which an increase in demand is warranted by life cycle considerations. 2 A Model of Ambiguous Correlation Between Length of Time at Home and Reverse Mortgage Takeup The purpose of this section is not to build a fully realistic model of the optimal time of move out. Developing a tractable and interesting model of move out is a separate work in progress. Rather, the discussion below is designed to illustrate that under differing sets of assumptions, neither of which seems out of bounds (except for in their simplification of the problem), it is possible to obtain either the result that reverse mortgagors should be expected to remain in their homes for a longer duration than similar non-mortgagors or the result that reverse mortgagors should be expected to leave their homes more quickly. Among the more obvious abstractions, we assume a certain date of death, an absence of shocks to health status, no choice over the level of housing consumption, existence of only a single asset in which to save with a constant return and a known path for housing prices. Under a different modelling structure, allowing for stochastic medical expenses that shock the taste for living at home and generate expenditures, we show in the Appendix that there appear to be large gains to taking on a reverse mortgage for a typical set of wealth variables. Our approach to finding how shocks affect both the time of moveout and the choice of whether to take out a reverse mortgage will be based on the premise that whether or not a reverse mortgage is taken out should be an increasing function of the optimal size of a reverse mortgage conditional on positive demand. We will differentiate a utility function with respect to demand for the reverse mortgage, with respect to optimal move date and with respect to different parameters to identify the optimal mortgage of origination but enjoyed large capital gains, so that the payments received relative to the debt owed were very small. This has led to legal conflicts. Perhaps for this reason, Fannie Mae does not purchase shared appreciation mortgages. 5

7 size. The presence of fixed costs and a spread over the interest rate on savings for reverse mortgages realistically imply a mass of zero demand that will not move with small parameter changes. 2.1 Optimal Move Out Date and Reverse Mortgage Demand Consider a single woman of age a who owns a home. Suppose that a reverse mortgage is the only way in which the woman can borrow money such that absent the reverse mortgage, sale of the home represents a liquidity shock. However, if she were interested, the woman could save at rate r. This is the basic setup of Artle and Varaiya (1977), but here we allow for choice over the date of the move and do not restrict the curvature of instantaneous utility. Suppose that the woman has a fixed income of y per year as well as assets worth s a. The home is currently worth HP 0 and prices are appreciating at a known rate π such that P t = P 0 e πt. Assume that the woman knows for certain that she will die at time A and that there is no bequest motive. If she moves out of her home, she must continue to consume housing, but the quantity consumed changes from H 0 to H 1, at which level housing remains until death. This housing is rented at a rate which is a constant fraction f of the housing price level. Moving out generates a cost in utility terms of η which may vary with time. 6 Assume that utility is additively separable across time and that u c > 0, 2 u c 2 < 0. Denoting by T the date at which the woman chooses to move out of her home, taking on a reverse mortgage in the amount M entails repayment after the move of Me (T a)r M. With additive separability assumed across periods, her utility maximization problem is: T max U = u(c t, H 0 )ω t dt + {c},t,m a A T u(c t, H 1 )ω t dt η(t ) (1) subject to s t 0 t. (2) ds(t) = dt(s t r c t + y + δ(t a)m + δ(t T )(H 0 P t Me (t a)r M θ(t T )fp t H 1 ). (3) In equation (3), δ(t T ) indicates infinite mass at the point t = T, whereas θ(t T ) takes on a value of one if t T and zero otherwise. ω t represents the weight that the utility function places on consumption at time t and might reflect diminishing health and discounting of the future. Note that there are at most two constraints associated with the positive wealth constraint (2); if ω is monotonic, lim ct 0 u (c t ) = and 6 That a psychological cost to moving exists seems beyond question. Venti and Wise (2000) cite an AARP report which shows a large majority of older people want to stay in their homes as long as they can. Adding a monetary cost should not affect the absence of clear results. 6

8 wealth is positive at times T and A, then positive consumption guarantees positive wealth at all times. Positive savings at time T are not necessary, but imply that the constraint on wealth accumulation (3) has the same value before and after move out. If savings are zero at time T then we have two different shadow values for money before and after move out, λ 0 and λ 1. Comparative statics on optimal moveout date and reverse mortgage choice becomes much simpler if we can eliminate the need to differentiate the utility function with respect to optimized consumption. To do this, we make the following assumptions: 1. Set the interest rate on savings to zero. 2. Fix housing H 1 and assume additive separability in u within periods such that housing is present in the optimization only through the budget constraint. 3. Assume no discounting. With these assumptions in place, we have the result that consumption is constant across time before and after the move date T. This implies in turn that the optimization over {c}, T and M is equivalent to a maximization over T and M where the woman has consented to be forced to consume a constant amount within the periods before and after the move. Note that if savings are positive at T, then there is no reverse mortgage demand. Hence, except for a knife-edge, marginal utility is different before and after T. The maximization problem can now be rewritten: max U = (T a)u(y+ s a + M T,M T a )+(A T )u(y+ H 0P a e π(t a) Me rm (T a) A T A T fh 1P a e π(t a) ) η T. (4) Optimal Move Date The first order conditions, if we are not at a corner where optimal T is before a or after A are (with a notational shortcut for the arguments of utility before and after the move): 0 = U T = A + B + C (5) A u(t ) u(t +) η (T ) (6) B (A T ) 1 u (T +) (T a) 1 u (T ) (7) C (πh 0 P a e π(t a) r M e r M (T a) fh 1 P a e π(t a) )u (T +). (8) Terms A and B reflect the utility lost by waiting to move due to deferring a switch from low utility (and high marginal utility) to high utility (and low marginal utility) 7

9 as well as the likely gain from deferring the cost of moving. η < 0 seems most likely negative as ill health may make a move out more palatable. Term C reflects the financial cost or benefit of a delayed move multiplied by the marginal utility of consumption after moving. The upside to waiting is that the home may appreciate in value before the move and that rental payments are deferred. The downside is additional reverse mortgage interest and the possibility of depreciation on the home. A rental rate in excess of (the here zero) interest rate less appreciation plus depreciation for an owner occupier are generally cited as the reason for high rates of owner occupancy despite the diversification problem. Among elderly single women, it seems less likely that depreciation is smaller during owner occupancy than under a landlord-tenant relationship. 7 If C is zero, and if there is positive reverse mortgage demand, then it is easy to see that η < 0 is necessary for an internal optimum for T Optimal Reverse Mortgage Balance and Date of Moveout Moral Hazard Assuming positive demand for the reverse mortgage, the first order condition is simply 0 = U M = u (T ) e r M (T a) u (T +). (9) Moral hazard will arise with respect to the reverse mortgage if, holding characteristics constant, increasing the exposure to the reverse mortgage tends to make staying in the home longer more attractive, that is, if U MT > 0. It turns out that this critical derivative is not easy to calculate. Differentiating U T with respect to M term by term, we learn the following: A M : The effect of the reverse mortgage on price adjusted marginal utilities is zero by optimality. Note moral hazard is more likely to be an issue if the reverse mortgage is constrained above such that this term is guaranteed to be positive. B M = (T a) 3 u (T ) + e r M (T a) (A T ) 3 u (T +). This sign depends on the sign of u (most likely positive), on T (larger T makes the reverse mortgage effect on optimal length of time more positive, on the existing size of the reverse mortgage (larger makes the reverse mortgage effect more positive) and on the reverse mortgage interest rate (larger makes the effect more negative). C M This effect has the same sign as the financial incentive to defer moving, because taking money away from the post-move life increases the benefit or cost of the financial effect by increasing post-move marginal utility. 7 See Davidoff (2004). 8

10 Moral hazard may thus occur or not, depending on assumptions. It is clear that moral hazard is more likely to occur in the event that the reverse mortgage balance is suboptimally low. In fact, this is likely to be the case for those who take on reverse mortgages due to the upper bound on borrowing (engendered in part by fears of moral hazard and adverse selection) as well as due to the very large fixed cost of obtaining a reverse mortgage discussed above, which guarantees that the only takers will be those for whom a large balance is attractive. 2.2 Adverse Selection To determine the effects of parameter changes on the optimal reverse mortgage demand and on the date of move out, we observe that for any parameter α, we can write the utility function as U(T, M, α). Differentiating the first order conditions with respect to α and denoting partial derivatives with subscrips, we obtain: Solving the two equations yields This implies that dt 0 = U T α + U T T dα + U dm T M dα, (10) 0 = U Mα + U T M dt dα + U MM dm dα = U T α + U T T U T M dt dα dm dα. (11) dt dα = U Mα + U T M. U MM dt dα ( U T T U T M U T M U MM ) = U Mα U MM U T α U T M. (12) Note that the term multiplying dt dα on the left hand side of (12) is positive if the maximization problem is concave, which is necessary for an interior optimum. The first term on the right hand side has the opposite sign as U Mα by concavity of u. The second term on the right hand side has the opposite sign as U T α if U T M is positive and the same sign if this moral hazard term is negative. By symmetry, we can obtain a clear prediction on the sign of dm dα so long as U T T is negative (a quasi-concavity requirement of an internal optimum). Assuming U T M is positive, this derivative is positive (negative) if U T α is negative (positive) and U Mα is positive (negative). The latter signs flip if U T M is negative. This discussion provides the basis for ambiguity in the net moral hazard and adverse selection likely to occur in the reverse mortgage market. When moral hazard is present, we will be able to detect a basis for adverse selection to the extent that the same characteristics that tend to add to the utility appeal of reverse mortgages also add to the utility appeal of staying longer. On the other hand, when there is the opposite of moral hazard (immoral hazard?), positive selection occurs to the extent that parameters 9

11 tend to have the same effect on the marginal utilities of delaying moves and the reverse mortgage. Conversely, in the presence of moral hazard, positive selection is a possibility when parameters tend to have opposite effects on the marginal benefit of the reverse mortgage and the marginal benefit of postponing the move out date. The same positive selection effect can also arise if U T M is negative but close to zero such that there is little utility complementarity either way. In this case, the own derivative terms dominate the analysis. The parameters of the maximization problem discussed below seem to have clear effects on the relevant marginal utilities Initial Savings and Adverse Selection It is clear that initial savings render a later move more attractive through terms A and B of U T. This is a result of a dimished gap in utility levels and marginal utilities preand post-move. By contrast, initial savings render the reverse mortgage less attractive for the same reason ofreduction of pre-move marginal utility pre-move relative to postmove. Assuming the moral hazard condition, this is a basis for positive selection. If the opposite of moral hazard holds, this is a basis for adverse selection Home value and Adverse Selection By almost opposite arguments as above, a large initial home value has exactly the opposite effect as initial savings, and hence U MH0 > 0 and U T H0 < 0. The conclusions regarding selection are the same Price Level, Inflation and Adverse Selection Housing inflation has a hard-to-sign effect on the benefit of a long stay in the home, but has a clearly positive effect on reverse mortgage demand as long as housing consumption after the move is small. This effect comes through a reduction in marginal utility after the move due to the trade down in housing. The level of house prices has a negative effect on duration so long as post-move housing consumption is small and the financial effect of a move due to inflation and the reverse mortgage are small, again through diminution of marginal utility after the move. Again, this works in the opposite direction for the appeal of a reverse mortgage Length of Life and Selection Increasing length of life A, holding a constant, or reducing a holding A constant, reduces the level of utility after the move by increasing the horizon over which constant resources are spent. This also increases marginal utility, engendering positive effects 10

12 on terms A and B. If there are financial gains (losses) to moving, these effects are augmented (diminished) by the increase in marginal utility in term C. Hence increasing length of life is likely, but not certain, to increase the date of optimal moveout. It certainly does so if moving costs are large such that optimal move out is only upon death. By contrast, again, the effect on the marginal utility of a reverse mortgage is negative. So again, in the event of moral hazard, length of life has a positive selection effect. There is certainly positive selection operative on those stuck at the never move corner, who now like a reverse mortgage less (these individuals, though, could only not take a maximal reverse mortgage if there is a bequest motive). These claims could be reversed if the optimal move occurs close enough to death Cost of Moving and Selection Holding η constant and assuming η < 0, an increase in moving costs clearly has a positive effect on the marginal utility of a late move out date. There is no direct effect on the desirability of a reverse mortgage. This combination of facts engenders positive or negative selection again depending on the moral hazard term U MT. 3 Empirical Results 3.1 Claims to be Evaluated From the discussion above, if moral hazard is a concern, we expect to see the following: 1. Conditional on all relevant covariates, reverse mortgage borrowers should remain in their homes longer than identical non-mortgagors. 2. If all covariates are not observed, unclear whether reverse mortgage borrowers should remain more or less long than observably similar non-mortgagors. 3. Reverse mortgagors should have less wealth conditional on housing and more housing conditional on wealth than non-mortgagors. 4. Low wealth conditional on housing and large housing conditional on wealth should be associated with more rapid movement out of homes. 5. Large price appreciation should be associated with reverse mortgage demand. The remainder of this section discusses the empirical evidence on these claims. 3.2 Data The analysis below relies on data from several sources. To compare the mobility rate of reverse mortgagors to non mortgagors, we merge two datasets. HUD has assembled 11

13 a database with some detail on the performance of all of the approximately 77,000 HECM mortgages issued since Included with each loan record are the date of loan funding, the assessed value of the home, the borrower s age and marital status, the state in which the property is located and the date of loan termination, if any. 8 We compare the rate of mobility among single women in this dataset, all 62 or older, with the rate of mobility among older single woman homeowners in the American Housing Survey (AHS). The AHS has the virtue of following homes over a sixteen year period, comparable with the years of HECM activity. Neither dataset allows differentiation between mortality and moving out while alive. A natural concern in matching mobility rates is that the AHS data might under- or over-report the rate at which older women exit from homeownership due to imperfect data collection. 9 To address this concern, we estimate mortality and mobility rates in three different datasets to see if AHS appears consistent with other datasets populated almost entirely by non-reverse mortgagees. 10 Table 1 compares mobility and mortality rates across datasets. The AHEAD dataset is an outlier for its low mobility rates among single women homeowners. The AHS features a combined mortality plus mobility rate that is slightly higher than the implied mortality plus mobility from the Berkeley Mortality Database and the SIPP mobility survey of The AHS mobility rate is overstated yet more if we consider that mortality rates are typically lower among homeowners than renters, as suggested by comparing the AHEAD mortality rates from 1993 to 1995 to those in the general population (mortality is nonlinear, so the comparison is imperfect). It appears that, if anything, the AHS overstates the speed of implicit loan termination. 3.3 Move Out Date and Reverse Mortgage Take Up Figures 2 and 3 show Kaplan - Meyer survival time and hazard rate estimates based on the AHS and HECM data. A failure date in the AHS data is listed as the earliest date at which a respondent who is not the original single woman occupant reports moving into a home, if this occurs at all. 11 A failure in the HECM data is the date at which the loan terminates, if the loan has terminated as of mid As noted above, HECM loans appear to terminate only very rarely for reasons other than a move or death We see that single women participating in HECM terminate the loans at a rate far in excess 8 Loans rarely terminate while the owner still lives in the property prepayment without a move represents roughly 2% of the roughly 50% of the minority of loans which have terminated. 9 Incorrect loan termination dates in the HECM dataset seems like less of a worry. 10 Given the penetration rate of substantially less than one percent, there is no concern that large population samples have a large number of mortgagees. 11 On average, this date is earlier than the date at which the respondent reports having purchased the home, biasing mobility rates up, not down in AHS. 12

14 Table 1: Two-Year Mobility and Mortality Rates among Single Women Homeowners Aged 62 + in Several US Population Surveys Data Mortality Mobility Mortality + 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 Figure 2: Kaplan Meier survival estimates, by hecm analysis time hecm = 0 hecm = 1 of the combined mobility and mortality rates in the AHS. This is consistent with the preliminary results in Rodda, Herbert and Lam (2000), but inconsistent with fears of moral hazard or adverse selection. With respect to the theoretical claims, either claim 1 is incorrect, or there are relevant covariates that must be taken into account. 13

15 Smoothed hazard estimates, by hecm Figure 3: analysis time hecm = 0 hecm = 1 Table 2 incorporates some covariates that, based on the discussion, might be expected to affect the date at which loans terminate or at which move out or death occurs. Here HECM is an indicator for participation in the HECM program. Age reflects age at entry into observation (a in the notation above), so there is an implicit assumption that changes in mobility rates follow the change in the baseline hazard. Table 3 provides summary statistics. Separate means are provided for each dataset. We find that the presence of covariates does not alter the conclusion that older women participating in HECM leave their homes much more rapidly than do similar women who are not participants. Older single women HECM borrowers move out at a rate approximately 60 percent greater than the rate for older single women in AHS. The effects of age is predicted by the model; advanced age (and hence a shorter remaining lifetime) renders moving more attractive (and death more likely). The shorter horizon also renders the reverse mortgage more attractive according to the model. Table 3 shows that increasing the average age of HECM borrowers is 3.5 years older than single women homeowners in AHS. Column (3) of Table 2 shows that there is no significant effect of log income on mobility. Unreported specifications confirm the same fact for levels. Unfortunately, many HECM borrowers are listed as having no income; this presumably reflects a legal restriction on using social security income to support loan payments. This lack of effect does not run counter to the model, which predicted an ambiguous effect of income on length of stay. We find dramatically lower incomes in the HECM sample, but this again may reflect definition. In the absence of an income control, we find a significant effect of house value on the hazard rate out of home ownership. A doubling of house value would be associated with an increase of approximately 20 percent in the hazard rate. As predicted by 14

16 Table 2: Regressions of Hazard Rates on HECM Participation and Covariates. Dependent variable is the estimated time-varying hazard rate under the Weibull distribution (1) (2) (3) (4) (5) (6) HECM 1.69** 1.77** 1.68** 1.56** 1.58** 1.52** AGE 1.05** (.063) (.066) (.086) (.062) (.089) (.001) ln Value ** 1.21** 1.16** ln Income 1.02 (.025) (.018) (.02) (.018) (.023) INV20K.993 State FE No No Yes No No Age polynomial No Yes Yes Yes Yes Yes (.010) Time dependence α 1.45** 1.46** 1.47** 1.38** 1.47** 1.47** (.009) *(.009) (.010) (.016) (.010) (.010) Observations 42,272 42,272 41,664 8,671 42,112 42,112 Notes: Z-statistics reported in parentheses - subtract one from the coefficient estimates to get something akin in magnitude to a t-ratio. These estimates come from a merge of the cross section of HECM loan performance with the American Housing Survey Panel from 1985 to State fixed effects are approximated in the sense that the state of residence in AHS is identified through the location of the central city of a metropolitan area. The polynomial in age contains five terms. INV20K denotes non housing assets are worth at least $20,

17 Table 3: Summary Statistics for Hazard Regression Covariates Variable Obs. HECM Mean HECM Obs. AHS Mean AHS AGE 41, , House Value 41, ,807 1,301 58,370 Income 41,004 2,841 1,299 12,047 House Value Total Assets 40, INV20K 41, the model, the value of the home is also positively associated with reverse mortgage demand. This is shown in the very large differences between HECM and AHS housing values. However, this difference overstates the true difference because the HECM dataset is on average newer than AHS and the bulk of originations have been made since the price boom starting in the mid- to late- 1990s. A clearer picture of housing value relates to wealth. We see that despite much larger housing prices and a run-up in the stock market, HECM borrowers are much less likely than AHS older woman homeowners to have $20,000 in savings (the discrete figure is all that is available in the AHS dataset). Figure 4 and shows the distribution of non-housing assets and the ratio of housing assets to these other assets in the HECM dataset and the AHEAD dataset, respectively. We see both less wealth and much more concentration of wealth in housing among HECM borrowers. This is hardly surprising given the program details which guarantee that it is a poor idea to take up the reverse mortgage when liquid assets are available. 3.4 House Price Appreciation and Reverse Morgtgage Take Up The model predicted (claim 5) that house price appreciation should be associated with reverse mortgage demand. This is verified by Figure 5, which plots the US states and territories with mean annualized appreciation on the horizontal axis and the difference between the state s share of all originated HECM loans and the state s share of all eligible US homeowners according to the 2000 US Census. We find a significantly positive relationship. It is also the case that high house price appreciation is associated with early exit from the home, as the model suggests is likely: a one percent increase in annualized state appreciation rate is associated with an eight percent increase in mobility rates. Given housing market equilibrium considerations, it would be unwise to attach causality. 16

18 Figure 4: Distribution of non-housing assets (horizontal axis) and ratio of housing to non ratio housing assets (vertical) in the HECM (top panel) and AHEAD (bottom panel) datasets hecm_assets h2atota:w2 total of all assets ratio

19 Figure 5: States disproportionate share of HECM borrowers (relative to share of older homeowners) and OFHEO House Price Appreciation dfrac mr 4 Conclusion There appears to be substantial positive selection (or the opposite of moral hazard) in the US reverse mortgage market to date, at least among the plurality of borrowers who are older women participating in HECM. There is clear positive selection on observables such as house value, age and price appreciation. However, even controlling for these observables, we find a significant positive correlation between HECM participation and the rate of departure from homes. The model presented in Section 2 makes it hard to believe that this relationship is causal in the sense that a HECM loan enables early move out. Rather, it appears that some borrower characteristics, such as health status, access to unreported assets, bequest motives, localized price conditions or an attachment to home equity (perhaps due to some precautionary concerns), are both unobservable and important determinants of reverse mortgage demand that are associated with early move out. At least in recent years, we might reason that reverse mortgages enable longer stays at home, but that the kind of people who want to cash out their housing wealth turn first to a reverse mortgage and relatively soon thereafter to disposal of the entire asset. The result has been that there have been very few losses paid out of the comparatively large reserves collected by the FHA as insurance against insufficient collateral. It will be interesting to observe whether the favorable selection observed to date continues in any deflationary periods. When default is likely to occur in the sense that loan balance exceeds amount due, a longer stay becomes more attractive with falling prices. 18

20 References Aizcorbe, Ana M., Arthur B. Kennickell, and Kevin B. Moore (2003) Recent changes in u.s. family finances: Evidence from the 1998 and 2001 survey of consumer finances. Federal Reserve Bulletin pp Artle, Roland, and Pravin Varaiya (1977) Life cycle consumption and homeownership. Journal of Economic Theory 18, Davidoff, Thomas (2004) Maintenance and the home equity of the elderly. Technical Report. Fischer Center Working Paper Heiss, Florian, Michael Hurd, and Axel Borsch-Supan (2003) Healthy, wealthy and knowing where to live: Trajectories of health, wealth and living arrangements among the oldest old. Working Paper 9897, NBER Mayer, Christopher (1994) Reverse mortgages and the liquidity of housing wealth. Journal Of The American Real Estate And Urban Economics Association (2), Miceli, Thomas, and C.F. Sirmans (1994) Reverse mortgage and borrower maintenance risk. Journal of the American Real Estate and Urban Economics Association 22(2), Rodda, David, Christopher Herbert, and Hin-Kin Lam (2000) 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 (1992) The housing wealth of the aged. NBER Working Paper 4115, NBER Shiller, Robert, and Allan Weiss (2000) Moral hazard in home equity conversion. Real Estate Economics 28(1), 1 31 Venti, Steven, and David Wise (2000) Aging and housing equity. NBER Working Paper

21 Appendices A Should There be Any Demand for Reverse Mortgages? A Stochastic Model In this section, we provide a somewhat different model of reverse mortgage demand, and ask whether such a mortgage would be attractive to a woman facing stochastic health conditions that simultaneously engender the need to move out of the home and a need for medical expenses We consider a 75 year old single woman homeowner. We endow this woman with assets and income that make a reverse mortgage appear moderately attractive on the surface. This seems natural given that we would like to know if there is a substantial fraction of the population that would benefit from a reverse mortgage, not whether all older households would gain. Thus she has a house valued at the 75th percentile among 75 year old women in the fifth Health and Retirement Survey (HRS) wave, or 140,000. She has income (which we assume is constant across time) and assets at the 25th percentile of women 75 or over with houses worth over 90,000. This yields an annual income of 15,000 and net non-housing wealth of 17,000. The woman maximizes lifetime utility which is a sum of subutilities over annual consumption and the terminal bequest subject to a budget constraint which forbids negative wealth. Savings earn a real interest rate of 3 percent and as a baseline there is no inflation. Interest accrues on the reverse mortgage balance at the real rate plus a typical spread of 1.5 percent. To facilitate computation, we assume that the entire loan balance is withdrawn at age 75. Given positive assets and the 1.5 percent spread, this assumes a greater loan balance due than would be the case under optimal behavior where liquid assets are run down to zero before a reverse mortgage line of credit is tapped. Thus welfare gains here will be understated. We assume that annuities beyond those which provides annual income are unavailable (the tenure payments option is like an annuity, but payments end when the owner moves out of the home). In the absence of a bequest motive and any possibility of moving out of the home, the value of taking on a reverse mortgage is equal to the loan amount. This is because repayment occurs only in states of the world (death) which someone with no bequest motive does not care about. Valuing the reverse mortgage is more complicated when, as in the real world, the individual may move out of the home and thus be required to repay the balance due before death. The balance due exceeds the loan amount in present value because of the interest rate spread and the upfront fee (assumed to be 6.8% of the loan value). Thus if frontloading consumption is not sufficiently important and if the probability of a move is relatively high the reverse mortgage can be unattractive 20

22 even in the absence of a bequest motive. A bequest motive can be expected to detract further from the value of a reverse mortgage to the borrower because even absent a move, repayment occurs in a state of the world where money is valued. For modeling purposes, at least two important assumptions must be made regarding what occurs after a move: changes to the subutility function and changes to the probability of survival. We might think that marginal utility (holding wealth constant) increases after a move because moves might be occasioned by increased medical and hence financial needs. Indeed, Heiss, Hurd and Borsch-Supan (2003) show that a common transition from one s own home is to a nursing home. A move generally will require new financial burden in that housing payments must be made relative to the assumption that there was no mortgage debt on the existing home. However, there may be a negative complementarity between consumption and the state of being in ill health. We thus assume a constant utility function while alive, regardless of where one lives, but we allow for the possibility of required expenditures up to $30,000 per year. 12 A second assumption concerns the probability of death conditional on being alive. We borrow mortality probabilities for ages 75 to 105 year old from Berkeley s mortality database. To speed computation we assume death occurs with 100 percent probability at the end of the year if the woman lives to be 105. However, we multiply these probabilities by 1.5 (up to a maximum of 100 percent probability) in states of nature where the woman has moved out of her home. This is consistent with the correlations among ill health, mortality and moving out of one s home found by Sheiner and Weil (1992) and Heiss et al. (2003). As is commonly done, we assume that utility is additively separable across time and that utility over consumption c in any period has the constant relative risk aversion form of c1 γ 1 1 γ. In particular, we assume that γ is equal to 2 so that utility is given by c. This seems moderately risk averse given the responses to questions in the Health and Retirement Survey concerning willingness to gamble different fractions of something that could be interpreted as either income or wealth. We assume that the bequest motive has the same curvature as the periodic utility function and is multiplied by some number κ. Discounting arises only from mortality probabilities. Hence, lifetime utility can be written as: U = 105 t=75 1 γ + m tκ w1 γ t+1 ). (13) 1 γ q t ( c1 γ t 12 In this version, medicaid is ignored. The consequences of the presence of medicaid for the attractiveness of a reverse mortgage are unclear and depend on medicaid s treatment of housing wealth. For a permanent move out of one s home and into a nursing home, most states would capture home equity before paying for the nursing home from medicaid funds. This suggests that the presence of medicaid makes HECM more, not less attractive in that the disutility of zero wealth is bounded. 21

23 Here q t is the probability as of age 75 that the individual will be alive. m t is the probability that the individual dies at age t conditional on surviving to date t 1. We assume that there is no discounting of future utility over consumption or bequests. other than a weighting of future utility by survival probabilities. It is clear that an increased discount rate will increase the value of a reverse mortgage because the reverse mortgage involves the transfer of funds from later to earlier periods. w t,wealth available at time t is constrained to be positive. w t s value is given by: w t = (w t 1 + RM t 1 c t + H t 1 X t )(1 + r), (14) RM t 1 represents transfers arising from the reverse mortgage program at date t 1 and H t 1 represents the sale price of the home if the widow moves out of her home at the end of period t 1. We assume that there is no real house price appreciation; relaxation of this assumption would predictably increase the value of the reverse mortgage to the borrower. X t represents required medical or housing expenditures that do not arise while the widow lives in the home she owns but do arise after she moves out. Reverse mortgage transfers RM are equal to the maximum loan amount of 100,000 (based on interest rates of November, 2003 and the results of AARP s Reverse Mortgage Calculator software) at age 75 and equal to the outstanding loan amount (the future value of RM plus fees of 6.8 percent, with interest accruing at the real interest rate plus the interest rate spread). We vary κ between 0 and 50. At a value of 50, the bequest motive is extremely strong. In the last year of life, an individual with such a large value for κ with $60,000 in wealth would consume $1500 and bequeath the remainder. Because repayment of the reverse mortgage is triggered by a move out of the home, the state space is fairly simple. At the age of 76, the individual may die, move or live in the same home. If the individual has moved, she may remain out of the home or she may die at age 77. If the individual has stayed through age 76, she may again stay, move or die. If she has died at age 77, she remains dead. These transition possibilities are repeated up to age 105. The probability of moving, based on the results of Sheiner and Weil (1992) and panel analysis of the American Housing Survey, is equal to 4.5 percent through age 85 and 8.5 percent per year thereafter. B Optimization Procedure and Results To solve the utility maximization problem subject to a positive wealth constraint, we solve the problem backwards. We allow wealth and consumption values between $1,500 and $300,000 in each period. We solve for the optimal level of consumption conditional on wealth at the maximum possible age of 105 under the assumption that the individual no longer lives in their home (this amount depends on the strength of the bequest motive). This yields a value function mapping wealth at age 105 to a terminal 22

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