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Sloan* CThomas J. Hoerger** tKand sDGabriel Picone*** L *Duke University **Research Triangle Institute ***University of South Florida L ` ` #GL Partial support for this study comes from a grant from the National Institute of Aging, "Effects of Public Subsidies on Use of LongTerm Care" (#R01 AG09468). We benefitted from helpful comments from participants at the Third Annual Health Economics Workshop at Johns Hopkins University and the National Bureau of Economic Research Summer Institute. We wish to thank Christoph Schenzler, David Van Dalfsen, and Teresa Waters for computational assistance; May Shayne and Jim Kinser for assembling information on state Medicaid policies; Friedrich Breyer, J.S. Butler, Peter Kemper, Liliana Pezzin, Willard Manning, and Joseph Newhouse for advice and comments on earlier versions; and Charlene Harrington, James Swan, Alvin Headen, Baldwin Kloer, Larry Corder, and Francis Pendergrass for providing unpublished data used in this study.'=0*0*0* =  X81Í ÍX(1Í ÍX(1Í Í(1Í ÍI. INTRODUCTION Inspired by Becker (1974, 1981), economists have returned to the classic idea that intrafamily decisions lie at the heart of many important aspects of economic behavior. Models of the family generally emphasize either altruism or strategic exchange as the major motivation for behavior. Models of altruism assume that family members provide services or transfers to one another because they care about each other. By contrast, strategic exchange models emphasize that family members exchange services for cash or inkind transfers. For example, a child may provide attention to a parent in exchange for bequests. The strategic exchange models generally allow for altruistic behavior; strategic effects arise when one family member can induce another to  xP exchange more services or transfers than the second member prefers to provide.X  xP ԍSee, for example, Becker (1974), Becker (1981), Kotlikoff and Spivak (1981), Cox (1987), Bernheim and Stark (1988), Bernheim et al. (1985), Pollak (1988), Becker and Murphy (1988), and Bruce and Waldman (1990). Both types of models have been used to analyze how public policies affect family decisions. Few areas offer greater potential for interaction between family decisions and public policy than longterm care for the elderly. Because their health deteriorates gradually or because of sudden health shocks, the elderly face an appreciable probability of not being able to care for themselves (Kemper et al., 1991). Care to enable disabled persons to function may be provided in a nursing home, or alternatively in the community with paid help, and/or unpaid help obtained from relatives and friends. There is little private insurance against such risk (Pauly, 1990). Rather, such care is primarily paid from savings of the elderly and their children, inkind transfers in the form of informal care, and from public sources of which Medicaid is by far the most important one. Savings and obtaining a subsidy from Medicaid are closely related in that an individual's income and wealth determine a person's eligibility for Medicaid and the amount of the subsidy if the person is determined to be eligible. Availability of Medicaid subsidies for longterm care (LTC) services may have decreased demand for private longterm care insurance, caused some elderly parents to make intervivos transfers to their children and others, decreased elderly families' savings, decreased the time relatives and friends spend in caring for the disabled elderly ("informal care") and increased their use of purchased longterm care services ("formal care") in the community. #=0*0*0*ԌThe purpose of this study is to investigate the effects of Medicaid and strategic behavior on (1) the probability of entering a nursing home, (2) amounts of formal and informal care provided elderly persons in the community, and (3) asset accumulation. To provide a conceptual framework for studying the interaction between Medicaid subsidies, strategic behavior, and family decisions, we present a twoperiod model motivated in part by Bernheim et al's (1985) strategic bequest model. Bernheim et al. argue that, by threatening disinheritance, parents can extract more attention from their children than the children would like to provide. Empirically, they find that the number of children's telephone calls and visits to their parents rises with parents' wealth. Testing for strategic effects is an important part of our empirical work. We measure childrens' attention by informal care provided to disabled parents, which plausibly has more value to parents than telephone calls or visits. We present our basic model in Section II. Extensions of the model are discussed in Section III. Section IV describes our primary data source, the National LongTerm Care Survey (NLTCS), and other data sources, and how we have adapted the data to our twoperiod model, followed by more detailed empirical specification in Section V. In Section VI, we present our empirical results. We find that Medicaid subsidies increase the probability of entry in the nursing home and use of formal care of elderly who remain in the community. However, Medicaid subsidies have not "crowded out" informal care provided by relatives and friends of the elderly. Nor has Medicaid reduced wealth accumulation by the elderly. Overall, we find little empirical support for the hypothesis that caregiving by children is motivated by the prospect of receiving bequests from their parents. We discuss our evidence on the strategic bequest motive in Section VII and present conclusions in Section VIII. 1dddddddd (1) 1dddddddd (1)  X` X` pX` pX` 4!II. CONCEPTUAL MODEL A. Outline of the Model In the sequential twoperiod model, there are two actors: a widowed parent and the parent's grown child. In period 1, the parent is healthy and chooses consumption and savings to maximize expected utility. Three states can occur in period 2. First, with probability , the parent will die (d). Second, with probability #, the parent will become cognitively unaware (u) in period 2. Because the parent is incapable of making dec'0*((Ԯisions, the child will decide whether to place the parent in the nursing home or leave her in the community. The child also decides optimal levels of formal and informal care in the community. To capture the asymmetry in preferences between parent and child, we assume that in the community the parent receives greater utility from informal care than formal care, whereas the child only worries about the total care received by the parent. In the third state, the parent will be cognitively aware (a), but with worse health than in period 1. Because she is aware, the parent will decide whether to enter the nursing home or not, and, in the latter case, how much formal and informal care to purchase. A key question is how much informal care the parent will be able to receive; in general, the amount will depend on both the parent's demand for informal care and the child's supply. If the parent can credibly threaten to disinherit her child, she may be able to extract more informal care than the child would like to supply. At the end of period 2, the parent dies. Any remaining assets are inherited by the child; such bequests give the parent utility. The parent solves her problem rationally through the use of backwards induction. The parent first determines optimal choices of nursing home, formal, and informal care in period 2, taking period 1's saving as exogenous. This produces optimal response functions that depend on savings and other variables. Given these functions, the parent chooses period 1 consumption and savings to maximize expected utility from both periods. One of the reasons Pauly (1990) gives for the nonpurchase of longterm care insurance is that parents fear that if they have such insurance, their children will be too quick to place them in a nursing home when they are no longer able to resist. If parents eschew such coverage, the children will face the full price of nursing home which will cause corresponding reductions in their bequest. Consequently, they will be more reluctant to place the parent in the nursing home. In this study, we formalize Pauly's idea, but here, instead of not purchasing private health insurance, the parent can make herself ineligible for a Medicaid subsidy for nursing home care by saving more. Consequently, she will be less likely to be institutionalized when and if she becomes cognitively impaired.  D %0*((  D B. SecondPeriod Decisions: Choices of Formal and Informal Care in the Community and Choice of Nursing Home Care In the second period, the decision is made whether the parent lives in a nursing home or in the community. If in the latter, a decision must be made about use of informal and formal care. 1. The Parent is Cognitively Unaware We distinguish between cases in which the parent is cognitively unaware and aware. In the first case, because the parent is unable to make decisions, the child decides whether to institutionalize the parent or leave her in the community and, if the latter, how much formal and informal care to purchase. To decide, the child compares his utility in the alternative locations. a. Community Location. Although the optimal choice of formal and informal care in the community at this stage is made by the child, the parent has different preferences than the child, and this difference may affect the parent's first period decision. If the parent remains in the community, her utility is given by  yP  1dddddddd (1) 1dddddddd (1)  ` ` # ,UuQ(Q) + UuI(I) + VuC(CK) 4!4!~ (1)  xPR where Q, total care in the community, is the sum of informal care (I) and formal care (F), CK is the child's consumption, U refers to utility from the parent's consumption and V is the utility from the child's consumption; the subscript u indicates the parent is cognitively unaware. In contrast, the child's utility is given by  yP ` ` # ,UuQ(Q) + VuC(CK)G4!4!~ (2) Although the child still receives utility from the total care received by the parent, the child receives no  xP additional utility from informal care. xP ԍSeveral points about these utility functions also apply to the other states. First, the utility functions are separable both between the two individuals' consumptions and between the two components of the parent's utility. The primary justification for this specification is tractability. As usual, assuming separability may affect the comparative statics in an important way. Second, the individuals are altruistic in that each cares about components of the other's utility. It is necessary for the child to care about the parent in order for an unaware parent to receive care because providing either formal or informal care will cost the child. Third, the assumption of separability imposes a special kind of altruism. By assuming that each individual cares about the other's utility from specific components of consumption rather than the other's total utility, we avoid the type of infinite regress that occurs when I care about your utility and you care about my utility.0*((ԌThe child spends the parent's savings (S) and the child's income (Y), which depends on his wage rate (w) and the amount of informal care (I) he provides, on formal care and consumption according to  yP  ` ` # ,S + Y (w,I) p FF CK = 0,4!4!~4!4!~ (3)  xP where pF is the price of formal care.  xPB Providing informal care reduces the child's income, with YI < O and YIIĠ<0. Substituting (3) into (2), maximizing over F and I, and suppressing obvious subscripts and superscripts, yields  b B xddddddx($ yP ` ( (4a) ă;func{{,U} over {,Q}~~p^F {,V} over {,C^K}~=~0}c P7Pc P7Pc P7P a65,6U,]5,:,t5UUQ pooFg5V2:Coo{K!0Bڐand   S xddddddjx($ yP ` ( (4b) ă<func{{,U} over {,Q}~+~Y_I {,V} over {,C^K}~=~0,}c P7Pc P7Pc P7P a65,6U,]5,:,b5UUQ YooIU5V :Coo{K0b,S  xPJ respectively. If both firstorder conditions are satisfied, pFĠ=-YI. Because the child views formal and informal care as perfect substitutes, the child provides informal care as long as its shadow price is less than the price of formal care. The child will purchase care until the parent's marginal utility from consumption equals the marginal utility of the child's foregone consumption. Effects of Public Subsidies. Two types of public subsidies may affect the mix of care in the community. First, a low income parent may receive a cash supplement equal to M, thereby shifting out the child's budget constraint. The increase in the budget constraint increases total care (Q). Because there is no change in  xP: the relative prices of formal and informal care (pF, -YI), the amount of informal care does not change. Therefore, only F rises as the cash transfer rises. The second subsidy consists of an inkind transfer by Medicaid to the recipient of  Q  units of formal care. The usual result for an inkind transfer holds: the parent will consume at least as much formal care as before, although the child will purchase less formal care privately. The amount of informal care provided will not change.z&0*((Ԍ xP Other comparative statics. With an increase in pF, formal care falls, informal care rises, and total care falls. If the parent's savings (S) do not affect Medicaid eligibility, an increase in S shifts the child's budget  xP  constraint out.X  xPx ԍTo simplify the theoretical analysis, we collapse parent's wealth and income. In fact, both income and wealth standards are applied for purposes of determining eligibility for Medicaid. We consider both standards in our empirical analysis. As with M, this increases formal care and has no effect on informal care.  xP Medicaid eligibility standards for community care subsidies consist of savings thresholds.t xP( ԍThere are also income thresholds which are considered in our empirical analysis.t Parents with savings below the thresholds are eligible for subsidies, while parents with higher savings are not. Consequently, formal care falls discontinuously when savings reach the threshold level. Above the threshold, savings have their usual positive effect on formal care. Since inkind transfers and cash subsidies do not affect I, the amount of informal care will not change as S crosses the savings threshold. b. Nursing Home Care. The child's utility from placing the parent in the nursing home is   " xddddbU-dd x(# yP ` * (5) ă"func{U_u^N (N bar)~+~V_u^N (C^K),}c P7Pc P7Pc P7PbUooNoo7ub(6bNb)bVoowNooY7ub(bCooKb)b,I.b"  xP where CKĠ=S+Y(w)pN N  and Y(w) is the child's income when he provides no informal care. We assume  xP that only a fixed quantity of nursing home care  N  can be purchased for the outofpocket expenditure pN N .x xP ԍOur data set contains no measures of the quantities of formal and informal care received by residents in nursing homes. As a result, there are no choice variables to be selected in the equation, but changes in exogenous variables affect the child's utility, conditional on selecting nursing home care. Increases in the child's income increase the child's utility if the nursing home is selected, while increases in price lowers utility. If Medicaid changes eligibility requirements, the amount of money the child can keep after paying for nursing home care changes. This amount, which we call residual wealth in the  xP nursing home, equals SpN N . The effect of savings on utility depends on whether the parent is eligible for Medicaid. To be eligible, the parent's savings must lie below the state's savings threshold, T. If the parent is on Medicaid, she pays her entire savings (minus a small allowance for personal consumption) for nursing home 0*(( care; Medicaid pays the remainder. In a sense, Medicaid coverage has a variable deductible equal to the parent's savings. c. Community Care vs. Nursing Home Care. To choose between sites for the parent, the child simply compares the maximum utilities calculated above. Consequently, a probit equation estimating the probability of entering a nursing home should include any variable which affects utility in one or both states. Variables only affecting utility in one of the states have definite signs in the equations, whereas variables affecting both utilities in the same direction have indeterminate signs, since it is impossible to tell which marginal effect is larger without placing further structure on the problem. Therefore, we predict that more liberal Medicaid eligibility for nursing home care, lower nursing home prices, and higher prices or lower subsidies for formal care in the community will increase the probability of nursing home placement. Variables affecting both utilities and having indeterminate effects are child's income and parent's savings. In one case, savings clearly reduces the probability of institutionalization, however. If savings are below the Medicaid threshold for nursing home care and above the threshold for community subsidies, increasing S only increases utility in the community, since higher savings in the nursing home simply translate into a higher deductible. We exploit this exception empirically by including separate terms for residual wealth in the nursing home and community in our equation estimating the probability of nursing home entry. 2. The Parent is Cognitively Aware If cognitively aware (a), the parent decides about her care. a. Community Location. When the parent selects formal and informal care in the community, she must consider how much informal care the child will supply. This issue was easily resolved in the cognitively unaware case since the child chose his utilitymaximizing level of informal care. Now, because of the asymmetries in preferences (see (1) and (2)), parent and child will prefer different levels of formal and informal care. Can the parent induce the child to provide more informal care than the child prefers? Or if the child provides his optimal level of informal care, can the child prevent the parent from buying too much formal care, thereby "squandering" the child's inheritance?%0*((ԌTo resolve these questions, we first examine extreme solutions which alternatively give each participant the full gains from trade. At the one extreme, the child provides his or her optimal level of formal and informal care. This outcome is supported as a Nash equilibrium by the child's threat to withhold informal care  xP if the parent purchases any level of formal care different than the child's optimal level. xP ԍWe assume that the parent does better with the child's optimal levels of care than she does spending all of her savings on formal care. This is not a very restrictive assumption. This outcome is identical to that in the unaware state and the same comparative statics apply. At the other extreme, the parent possesses superior bargaining power and captures all the gains from  xP` trade.[`  xP ԍThis is the outcome Bernheim et al. (1985) have in mind in their model of strategic bequests. They assume, however, that the parent must have more than one child for the threat of disinheritance to be credible. More realistically, even with one child, the parent's threat is credible since she can give to charity, another relative, or a formal caregiver. Although our model has only one child, we assume disinheritance is credible in order to incorporate the strategic bequest motive; as an extension, we discuss the case of more than one child.[ In this outcome, the parent achieves her optimal levels of formal and informal care by threatening to  xP disinherit the child if the child does not provide the parent's optimal level of informal care.  xPP ԍThis time we assume that the child is better off at the parent's optimal level of formal and informal care than he or she is when providing no informal care and being disinherited. In the optimal outcome for the parent, she receives more informal care and less formal care than when she is cognitively unaware. The first order conditions maximizing the parent's utility (1) differs from the firstorder conditions that maximize the child's utility. The firstorder conditions for the parent are:  0 T xdddddd> x($ yP `a w ' (6a) ă=func{{,U^Q} over {,Q}~~p^F {,V} over {,C^K}~=~0}c P7Pc P7Pc P7Pr a@65,pU,5,V:,5Uoo"vQUQ~pooF5V:Coo9{K0T and  "  xdddd)dd x($ yP `@ ` # (6b) ă@Vfunc{{,U^Q} over {,Q}~+~{,U^I} over {,I}~+~Y_I {,V} over {,C^K}~=~0}c P7Pc P7Pc P7Pr $an65,pU,5,U,5,:,5Uoo"vQUQ5UoovI6UIYoo<I 5V:Coog{K0@" ( 0*((ԌThe firstorder conditions for the child are (4a) and (4b); (4a) and (6a) are identical. Totally differentiating either equation shows that the locus of I and F satisfying the equation is negativelysloped. At the values of F and I which maximize the child's utility, equation (6b) will be greater than zero, implying that the locus of points satisfying (6b) lies above those satisfying (4b). Therefore, the parent will prefer more informal care and less formal care than the child prefers. To go beyond the extremes, we treat the problem as a simultaneous move, strategic bargaining problem. A natural way to introduce the bargaining process is to assume that the bargaining solution maximizes a weighted sum of the parent's and the child's utilities, where the weight on the parent's utility is #x{0ddddddd x(@ yP XX` ` # (7a) = = S over {S + Y(O, W)}c P7Pc P7Pc P7PrL: &S:S:YC:O:W :(:,o:)=$(#(# (#(# !'#$ and the weight on the child's utility is #x{pddddddd| x(? yO XX` ` # (7b). 3( 1- ) = {Y ( O,W )} over {S + Y (O,W)} c P7Pc P7Pc P7P(P1`)(,8)1:(:,:)q: yY OW:S:Yh:O :Wߢ$(#(#(#(# !'#$ If neither party has complete bargaining power, the parent and child will choose points formal and  xP informal care solutions for parent and child along the locus of points satisfying (4a).o  xPX ԍThe parent and child's indifference curves will be tangent at such points.o Thus, the parent will do at least as well in the community when aware as when unaware. The parent's bargaining power should increase with her savings level, since the threat of disinheritance becomes more distasteful to the child. Consequently, savings should have a larger effect on the informal care the parent receives than when she is unaware. b. The Nursing Home Decision. We assume that the parent has the same preferences over nursing home care  xP as the child.}  X xP$ ԍAn assumption more consistent with Pauly's (1990) analysis of strategic nursing home decisions is that the parent receives less utility than the child from being in a nursing home. This assumption would strengthen our conclusion below that cognitively aware parents are less likely to enter nursing homes than cognitively unaware parents.} Therefore, the parent receives the same utility from nursing care when aware as when unaware.@ @ 0*((!0'# p'#N @Ԍc. Community Care vs. Nursing Home Care. Because she receives more utility in the community and the same amount of utility in the nursing home, the parent is less likely to enter the nursing home when aware than when unaware. Similarly, an aware parent in the community should consume more informal care and less formal care than an unaware parent. By strengthening the parent's bargaining power, the parent's saving should have a negative effect on the probability of nursing home entry, relative to its effect in the unaware state. Looking only at aware parents, explanatory variables such as prices and Medicaid policies which have unambiguous signs on the probability of entering a nursing home in the unaware state should have the same sign, but not necessarily the same magnitude, as in the aware state. 3. Summary of Comparative Statics Results from the comparative statics analysis for period 2 decisions are summarized in Table 1. 4. The Parent Dies If the parent dies (d) before the second period, her savings pass to the child. E. FirstPeriod Decisions  xPP In period 1, the parent chooses saving (S) and consumption (C1) to maximize expected utility, subject to  xP the constraint that the parent's wealth, A, equals S+C1. Substituting for C1, the firstorder condition for saving is   i   xixddipNAdd x()2  yP  (8) L func{ stack { stack{ tT ԩ`{,U_1} over {,C_1}~+~# {,(0_u)} over {,S}~+~(1~~~~#) {,(0_a)} over {,S}~+~ {,V_d} over {,S}~=~0, #linespace 4#  tT where~0_i~=~max[U_i^Q (I_i (S)~+~F_i (S))~+~U_i^I (I_i (S))~+~V_i^C (Y(w,I_i (S))~+~S~~p^F ~F_i (S)), #linespace 4# U_i^N ({N bar})~+~V_i^N (S~+~Y(w)~~p^N {N bar})].}}}c P7Pc P7Pc P7P$tTlUoos1pCook1(oosu )oSC $(z $1 $):(oosa/)SSVoosdS$0h$,tTwhereooi'maxE[|UooYQooih(Iooi(2S)Foo i< (s S ) )3 Uoo YIoo i (+ Iooh i ( S )Q )~VooYCooid(Y(Jw,Ioo)iH(S))?SpooBFFooi(GS)),bUooNooq7ib(bNb) bVooW Noo9 7i b( bS0 bY b( bwW b)bpooNKbNb)b]1b.$, ,{$,, $ $z $ ,R,$,0,h$z   b b bKK KK($#;0 $' $#q0r$0)^L   This condition has the usual interpretation in a saving model: the parent equates the marginal utility of foregone consumption in period 1 with the expected marginal utility of savings in period 2. An important policy question is whether Medicaid subsidies increase or decrease savings. Unfortunately, comparative statics on S yield generally ambiguous predictions because (1) S has zero or positive effects onq& 0*(( residual wealth in the nursing home, depending on whether the parent is eligible or ineligible for Medicaid; (2) the parent may be placed in the nursing home if unaware but remain in the community if aware; the two  xP  locations have different marginal utilities; and (3) derivatives of ,0i/,S with respect to the exogenous variables  xP are not easily signed because the secondperiod optimal response functions (Iu(S), Fu(S), etc.) implicitly include such variables. Nevertheless, the model clearly indicates that variables which influence second period decisions will also affect the firstperiod savings decision. III. EXTENSIONS OF THE MODEL A. Multiple Children The model can easily be modified to include the case of multiple children. Bernheim et al. (1985) argue that children will provide more informal care in the presence of siblings since the parent's threat of disinheritance is more credible. This argument suggests that more children increase informal care to aware parents, but, except for the effect of more children on the time price of care, more children should have no effect on care provided unaware parents. B. A Living Spouse The presence of a living spouse will affect the model in several ways. Presumably, the spouse, not the child, will decide whether to admit a cognitively unaware parent to the nursing home. The spouse will probably place greater weight on the parent's preference for informal care than the child places, and therefore more willingly provide such care. Consequently, the probability of nursing home entry should fall. Second, because most persons in our sample are 75 or older, most spouses will be retired and have no children at home. Thus, the spouse's cost of providing informal care may be less than the child's, thereby increasing provision of informal care and lowering the probability of entering the nursing home. Indeed, the cost of providing informal  xP care may be so low that -YIĠX@ xP ԍSome of the sample persons who were institutionalized in 1989 responded to the 1984 community survey. We could have used the housing wealth on those persons available for 1984. But since there were so many replacements in 1989, we would have lost quite a number of observations.> The spouse's nonbequeathable income is for the survey month. Higher housing wealth and spouse's nonbequeathable income should reduce the probability of institutionalization. e. Other Variables. We also included: number of ADLs and a binary variable for being cognitively unaware in 1989 to measure functional states; gender; and age. 2. Supply a. Discount Medicaid Obtains. To account for rationing of Medicaid patients by nursing homes on account of the discount Medicaid obtains, we calculated how much the nursing home could expect to receive if the patient never qualified for Medicaid. We then calculated the nursing home's projected revenues taking into account when the patient would become eligible for Medicaid and the Medicaid payment levels to nursing homes in the state. The difference between the first and second measures is the Medicaid discount. Our hazard model estimated the probability that the person is alive during each period. b. Other Supply Variables. We include several other supply variables: number of nursing home beds per 1,000 state population for bed availability; binaries for blacks and Hispanics to measure possible discrimination; and number of ADLs and a binary for unaware persons to measure homes' willingness to accept functionally impaired patients. More beds should improve Medicaid recipients' access to nursing homes; cet. par., being0*(( black, unaware and having more ADLs should decrease nursing home willingness to accept an elderly person for admission. B. Hours of Formal and Informal Care Provided to Elderly in the Community The dependent variables for our empirical analysis of formal and informal care are hours of help for ADLs and IADLs provided to the elderly person during the week before the survey. We defined two alternative measures of informal care: hours of help provided by anyone, including spouses and unpaid volunteers, and hours of help provided by children or childreninlaw. For formal care, we used hours of care paid by someone. The sample includes all persons in the community in 1989 stratified on the basis of cognitive impairment. Alternatively, we used a binary variable for impaired persons when we analyzed the two samples together. The specification of the formal and informal care equations was the same as the equation for the probability of entry into the nursing home with these differences. First, residual wealth in the nursing home and nursing bed ratio variables were excluded. Second, we combined housing and nonhousing wealth into a single variable. Third, we included the number of IADLs the person had at the survey date and a binary variable for persons who lived in communities with more than 50,000 population (urban). We used a twostage procedure to estimate the formal and informal care equations. In the first, a bivariate probit was estimated for the decision to live in the community versus a nursing home and to use any informal or formal care. With consistent estimates of the parameters of the two selection processes and the correlation of their error terms, we calculated a Mills ratio which was used to estimate informal and formal care equations in the second stage with the Mills ratio as a regressor (see, e.g., Connelly, 1992). As discussed below, results using this procedure were often not robust. Alternatively, we estimated equations of I and F with Tobit analysis without taking sample selection into the community into account. `"0*(( C. Nonhousing Assets The dependent variable for our empirical analysis of savings was the family's nonhousing assets in 1989. We limited the analysis to nonhousing assets because housing assets are illiquid and comparatively difficult to adjust to optimal values. Also, Medicaid excludes the home as a countable resource under several circumstances. The sample for our analysis of savings behavior was limited to persons who were not cognitively impaired in 1984 and were in the sample in both 1984 and 1989. Although the comparative statics analysis did not yield unambiguous hypotheses, conceptually, all exogenous variables from period 2 should appear in this equation for the period 1 decision. The explanatory variables, defined for 1984, were: predicted probability of being dead by 1989; predicted probability of being cognitively impaired in 1989; black; nonbequeathable income of sample person and spouse; housing assets; nonhousing assets; composition of nonhousing assets (savings accounts, bonds, stocks, etc.), measured by binary variables indicating whether or not such assets were in the portfolio; binary variables identifying persons who would have been immediately eligible for Medicaid in 1984 if they entered a nursing home, persons who would never be eligible for Medicaid in a nursing home, again using 1984 standards, because their nonbequeathable income was too high, and persons who would be immediately eligible for Medicaidsubsidized formal care in the community. Families immediately eligible could look forward to paying zero net prices for care. Those never eligible would know that they would have to pay for much or most of their care outofpocket. We included other exogenous variables defined for 1989: married; number of children; private nursing home price; and nursing home beds per 1,000 state population. To account for the impact of unanticipated health shocks on wealth, we included variables for the number of admissions to nursing homes that occurred between 1984 and 1989 and the number of admissions to hospitals during 19889. The NLTCS did not obtain hospitalizations for earlier years. To estimate the probability of dying between 1984 and 1989 or being cognitively impaired in 1989, we estimated a probability function with probit, conditional on levels of variables defined for 1984. The dependent variables were one if the person died before the 1989 survey and one if the person was cognitively impaired in 1989.'0*((  KFVI. Results A. Levels of Nursing Home, Formal and Informal Care Cognitively unaware persons were four times more likely to be in a nursing home than the cognitively aware (Table 2). In fact, cognitively aware persons had a low probability of being institutionalized, 0.06. Cognitively unaware persons received six hours of formal care weekly while cognitively aware persons received two hours of such care. Cognitively unaware persons received three times as much informal care from all sources than did cognitively aware. Children were twice as likely to provide informal care when the parent was cognitively unaware, and when they did, they provided more of it. B. Nursing Home Choice Regressions Our model predicts that the probability of choosing to enter a nursing home rises as residual wealth in the nursing home increases and falls as the parent's residual wealth in the community increases. The first prediction is strongly supported in both univariate and bivariate probit regressions (Table 3). Residual wealth in nursing home coefficients are statistically significant at the one percent level in the regressions based on the entire sample, and at least at the five percent level in the two subsamples. Admission elasticities, evaluated at the observational means, are 0.2 at the highest and in the univariate regression for the entire sample, about one fourth of this. A $10,000 increase in residual wealth in the nursing home raises the probability that a cognitively aware person would be admitted by 0.01. The corresponding increase in the probability for cognitively unaware is 0.02. Effects are small, but residual wealth has a greater effect for the cognitively unaware than for the cognitively aware. In our model, the child makes the choice when the parent is cognitively unaware. In the bivariate probit regression, residual wealth has a larger effecta change in 0.03 in the probability for a $10,000 increase in residual wealth. Coefficients on residual wealth in the community, measured by nonhousing wealth, have anticipated negative signs, but they are statistically insignificant. We attribute lack of significance to multicollinearity. When the sample is limited to persons who would qualify for Medicaid immediately on entry to the nursing home, more precise results on the coefficient on the wealth variable were obtained.%0*((ԌThe price of formal care in the community has the anticipated positive effect on the decision to enter a nursing home, and the coefficient is statistically significant at the 10 percent level or better in both the univariate and bivariate regression with the aware and unaware samples pooled. More generous Medicaid subsidies for home health care in the community, which measures  Q , have no statistically significant effect on nursing home entry. The effects may be insignificant because the subsidies are small; the mean expected subsidy per week for our 1989 sample was only $1.41, with a range from zero to over $40. We measured the price of informal care by the number of children of the elderly person, categorized by distance from the parent. As anticipated, availability of nearby children clearly lowers the probability of institutionalizing parents, much more so for cognitively unaware than aware parents. As expected, higher amounts of spouse's nonbequeathable income decrease the probability of institutionalization. Likewise, coefficients on housing assets are negative. Housing assets may capture omitted heterogeneity in unmeasured preferences for house ownership. Our model predicts that a low price of informal care leads to a lower probability of being in a nursing home. Our measure of this price, number of children by travel time from parent, in fact exerts a negative impact on this probability. But if less informal care were provided to unaware parents on average, one would expect the effect of nearby children to be greater for such parents. In fact, unaware elderly receive more such care (Tables 2 and 3), and the coefficient on the number of children within 30 minutes of the parent is larger for the unaware than for this aware. A plausible interpretation is that when children live near the parent, the effect of the productivity increase of informal care dominates any strategic effects associated with being unaware. We entered "cognitively unaware" on both demand and supply sides of the bivariate model. The coefficient on cognitively unaware is significant on both sides. We anticipated that the coefficient would be positive on the demand but negative on the supply side. Overall, the findings on the supply variables indicate supplyside limitations to entry. Of greatest interest are the roles of the supply of nursing home beds and the discounts that Medicaid obtains from nursing homes. In states with more nursing home beds per person over age 75, the elderly were more likely to enter, suggesting important supply constraints. Surprisingly, however, the Medicaid discount does not have significant'0*(( negative effects on entry. In fact, the coefficient is positive and significant in the bivariate probit analysis. The results on number of ADLs and the cognitively aware binary variable imply that nursing homes are more willing to accept functionally impaired persons. C. Formal and Informal Care Regressions Estimated equations for formal and total informal care and for informal care provided by children are shown for the total community sample (Table 4) and separately for cognitively aware and unaware elderly (Table 5). We initially estimated these equations with the twostage sample selection procedure mentioned in Section V and alternatively with Tobit not correcting for sample selection. Results from the twostage procedure sometimes were implausible (e.g., standard errors were implausibly low) and were not robust to changes in equation specification. We therefore present estimates based on both approaches in Table 4 when we were able to obtain plausible estimates with the sample selection procedure. In Table 5, only conditional Tobit estimates are presented. 1. Informal Care The price of formal care has no effect either on the total amount of informal care the respondent received or on informal care provided by the elderly person's children (Table 4). The coefficients are negative, the opposite of what our model predicts. These results, viewed in combination with those for formal care, where the price has an unexpected positive and insignificant effect, do not necessarily mean that these choices are not influenced by price. First, if the price of informal care is below the price for formal care within the relevant range of hours, the gross price would have no effect. Unfortunately, the NLTCS did not provide sufficient information on the wage of potential caregivers (with the exception of the primary caregiver) to allow one to make inferences about the price of informal care. Second, we have used the wage of aides employed by nursing homes for the gross price of formal care. Many households may face a far different price, even if they use personnel in this skill category.  xP#  Our model predicts that the Medicaid subsidy  Q  should affect formal but not informal care if the parent is unaware. The subsidy's effect is positive and almost statistically significant at conventional levels (12 percent) in the formal care equation, but the subsidy has a negative impact on informal care and in one'0*(( regression, the effect is almost significant. These results suggest, if anything, some crowding out of private effort as a consequence of this public subsidy which, considering the substantial differences among states, is meaningful. Bernheim and coauthors (1985) hypothesized that wealthy parents receive more attention from their children because the payoff in terms of a subsequent bequest is higher. Also, parents with more children should receive more attention because the threat of disinheritance is more credible. Using data on numbers of visits and telephone calls by children to their parents, they found empirical evidence in support of their theoretical  xP framework.   xPH ԍUsing the same data source and additional years of data, Hurd and Wang (1991) found little evidence of strategic bequest motives. Also, see Hurd (1989, 1990). Cox (1987) found that patterns of intervivos' transfers are consistent with the hypothesis that children exchange services for transfers from their parents. This hypothesis is closely related to the strategic bequest. However, Cox only observed transfers to recipients; he did not observe services provided by the recipient.  Our results on informal care, another measure of attention, are relevant to their work in two respects. First, the pattern of decreasing attention with distance of children from parents suggests that some of the effect of children can be attributable to time prices. Second, wealthier parents get less informal care from the children than poorer parents, a result clearly inconsistent with the strategic bequests model. The strongly significant negative effect for informal care provided by children when the parent is cognitively aware (column 1 of Table 5) is particularly telling, because it provides the best opportunity for children to impress their parents. Having a spouse reduces informal care provided by children much more when the elderly person is unaware. Again, time price is much more influential when a higher quantity of care is provided to the recipient, as in the unaware case. 2. Formal Care The number of children living within 30 minutes of the parent has an important negative impact on formal care hours. Other children do not make a difference. Married elderly demand much less formal care. Having children nearby lowers demand for formal care by both aware and unaware. The effect is stronger for the unaware. From our model, one would have expected use of formal care by the unaware to be particularly sensitive to relative factor prices, and, more importantly, to the Medicaid subsidy (Table 1). But`"x0*(( our results do not show this. The negative effect of marital status is appreciably greater for the aware than the unaware, but the exchange relationship hypothesized to exist between parents and children does not plausibly extend to spouses. The Medicaid subsidy has a positive effect on formal care levels, although the effect is never significant. The price of formal care only has the anticipated effect on the cognitively aware's formal care, but the coefficient is not statistically significant. Assets do not affect use of formal care by either the aware or the unaware. D. Nonhousing Assets Three issues are particularly important in our analysis of nonhousing assets. First, how does the probability of being in each of the three statesdead, cognitively aware, cognitively unawareaffect savings? Second, does the prospect of receiving a Medicaid subsidy in the event of a catastrophic expense affect savings? Third, to what extent do health shocks affect wealth of the elderly? Three Tobit regressions are shown, two based on the entire sample of persons who reported the levels of financial assets in both 1984 and 1989 and were cognitively aware in 1984 and a third limited to persons who were in the community in 1989 (Table 6). Cognitively aware elderly with at least one ADL/IADL impairment face substantial probabilities of an adverse outcome within a five year period. In our sample, 33 percent of the cognitively aware respondents to the 1984 survey died before 1989. Another 18 percent were cognitively impaired by 1989. Although statistical significance is lacking, the signs on the coefficients for both adverse outcomes are consistently negative, implying that the marginal utility of wealth is lower for persons in poor health, a result in agreement with other empirical evidence (Viscusi and Evans, 1990). The coefficient on the probability of being unaware implies that a .01 increase in the probability leads to a $607 or $546 decrease in nonhousing assets on average, conditional on positive nonhousing assets. The answer to the second question is that Medicaid does not crowd out savings, at least as measured by nonhousing assets. Persons who would have satisfied the state Medicaid program's income and asset standards immediately on entry in 1984 saved less, but those who would never have qualified in 1984 because their nonbequeathable income exceeded the state's income ceiling for Medicaid eligibility saved even less on average. We included several exogenous determinants of use of care in the second regression. The theory does not yield'0*(( unambiguous predictions about these variables' direction of effect on savings. None of these variables have statistically significant impacts on nonhousing assets' accumulation in either direction. To the extent that the bequest motive is an important determinant of savings by the elderly, one would expect that the number of potential heirs, measured here by the number of children, would affect wealth. We find no effect. In regressions not reported, we split the number of children into the distance groups used in other parts of our analysis. No effect of the number of children was detected in that analysis either. The answer to the third question is that health shocks, at least those associated with admissions to a nursing home, do have appreciable impacts on wealth. Judging from the coefficients on the number of nursing home stays during 198489, each stay decreases nonhousing assets by about $20,000 on average. With persons who were in the nursing home in 1989 excluded (column 3), the estimated effect falls substantially and loses statistical significance. Admissions to a hospital do not affect savings, but, unfortunately, the NLTCS only recorded hospital admissions for the year before the ٚinterviews. VII. ARE STRATEGIC EFFECTS IMPORTANT? Our empirical analysis provides three major tests of the types of strategic effects described by Bernheim and coauthors (1985). First, our strategic model suggests that having more children leads to a lower probability of entering the nursing home, less formal care, and more informal care. The empirical results are consistent with these hypotheses. However, the results may be confounded by the childrens' locations, which will affect their supply of care. This appears to be the case, as nearby children have much larger marginal effects on nursing home entry and care in the community. Moreover, the number of children (and their locations) also has significant effects in the equations for the unaware only. The strategic model predicts that, cet. par., the number of children will not affect the amounts of care provided since an unaware parent cannot disinherit her children. Thus, the observed significant effects again suggest that the number of children affects the supply of care independently of any strategic effects. The second strategic test comes from the coefficients on unaware in the pooled equations. The strategic model suggests that unaware parents will be more likely to be placed in the nursing home and receive less informal care and more formal care in the community than aware parents. While unaware parents are more'0*(( likely to be placed in nursing homes as expected, they actually receive more informal care and less formal care than aware parents. We noted above that being unaware might increase the marginal productivity of all types of care. While it is not possible theoretically to say how the relative productivities change across settings and between formal and informal care, it seems plausible that there would be a larger increase in productivity in nursing homes. Thus, a change in productivity associated with being unaware in consistent with both the  xP observed increase in the probability of entering the nursing home and the greater use of informal care.*X xP( ԍThe negative effect for formal care is still somewhat of a puzzle. The same productivity argument applies to ADLs and IADLs; like unaware, these variables increase the probability of entering a nursing home and informal care, but they also increase formal care.* This is not to say that strategic effects are necessarily nonexistent: had the unaware parents become aware for an instant, they might have been disappointed in the amount of informal care they had been getting. However, the positive productivity effect on informal care appears to far outweigh any negative strategic effect. Perhaps our cleanest test of strategic effects is the coefficient on total wealth in the informal care equation for cognitively aware parents. The strategic model predicts that children will provide more informal care to rich parents because they have more to lose through disinheritance. Our result shows that richer parents actually receive less informal care than poorer parents. Because this result directly contradicts Bernheim and coauthors' finding that rich (but not necessarily disabled) parents receive more telephone calls and visits, we examined our estimate in greater detail. A potential criticism of our specification is that we have not fully controlled for the supply of care from children, so that a parent's wealth may be correlated with omitted variables. For example, a parent who knows her child is unusually reluctant to provide informal care may need to hold larger stores of wealth to induce him to provide  xP  any care at all.X  xP! ԍAs our discussion of comparative statics on the savings decision indicates, having such a child will produce ambiguous effects on savings. Also note that the number of children has no effect on savings in our wealth equation. To correct for this endogeneity, we used a twostage approach. We first estimated wealth as a function of education and other exogenous variables in the model and then reestimated the informal care equation with the fitted value of wealth. Education was included because it is correlated with wealth, but@0*((  xP logically independent of the childrens' supply function. xPX ԍBernheim and coauthors used lifetime income as an instrument for wealth. This instrument is not on the NLTCS. The coefficient on the fitted wealth variable appears in column 2 of Table 6; for comparison, the coefficient on wealth, treated exogenously, from Table 4 appears in  xP  column 1. Wealth has an even stronger negative effect in column 2.h   xP ԍOther coefficients (not shown) are virtually unchanged from Table 4.h Bernheim and coauthors distinguish between bequeathable and nonbequeathable wealth under the presumption that children only respond strategically to bequeathable wealth. In column 3, we divide wealth into its bequeathable and nonbequeathable components and estimate the Tobit equation assuming bequeathable wealth is exogenous. Column 4 repeats the analysis under the assumption that bequeathable wealth is endogenous. In both equations, both types of wealth have negative effects on informal care; the coefficient on bequeathable wealth is appreciably more negative when this variable is considered to be endogenous. Thus, our finding that informal care falls as the parent's wealth rises is quite robust. Do our results rule out the strategic bequest motive? Perhaps strategic effects do not become important until a parent amasses a sizable fortune. Most of the elderly in our sample were quite poor, but this is the lot  xP of most disabled elderly persons.  xP ԍWe compared estimated wealth from the 1989 NLTCS with wealth from other samples. Adjusting for inflation, the NLTCS wealth estimates are similar to those from the National Channelling Demonstration data, also a survey of the disabled elderly (Garber and MaCurdy, 1990, p. 180). Disabled elderly in both the NLTCS and Channelling data bases tend to be poorer than elderly without functional impairments. Because a relatively few large estates will naturally account for a disproportionate share of all bequests, the strategic bequest motive could still be an important determinant of overall bequests, despite our results, but not of the informal care children provide elderly parents. It is perhaps reassuring that children are willing to provide substantial amounts of informal care to even poor, unaware parents, probably out of a sense of altruism. VIII. CONCLUSION This study has presented and tested a model which analyzes the effects of family behavior and government policy on longterm care for the elderly. Some Medicaid subsidies, such as those reflected in the present value of the amount of nonhousing wealth elderly can retain if they enter the nursing home, affect@0*(( choice of living in a nursing home versus in the community. Also, greater availability of Medicaid subsidies of care in the home increases the amount of formal care the elderly receive. However, we find no indication that these public subsidies have decreased relatives' and friends' willingness to provide informal care to the elderly. This result is consistent with past research (see, e.g., Tennstedt et. al., 1993, and Wiener and Hanley, 1992). Strategic effects arise in the model because children make longterm care decisions when a parent is cognitively unaware, whereas the parent makes decisions when she is aware. However, the empirical results indicate that strategic effects are not an important determinant of longterm care decisions. Family members are an important source of longterm care. This result suggests that altruism motivates much of informal care and points the way to future research studying variation in altruistic attitudes amongst potential caregivers. 0*(( GREFERENCES  zP XAbowd, John M., and Farber, Henry S. "Job Queues and the Union Status of Workers." Industrial and Labor  zP$ Relations Review 35 (April 1982):354-67.(#  zP XBecker, Gary S. "A Theory of Social Interactions." Journal of Political Economy 82 (1974):1063-93.(#  zPL XBecker, Gary S. A Treatise on the Family. Cambridge, MA: Harvard University Press (1981).(#  zP XBecker, Gary S. and Murphy, Kevin M. "The Family and the State." Journal of Law and Economics 31 (April 1988):1-18. (# XBernheim, B. Douglas and Stark, Oded. "Altruism Within the Family Reconsidered: Do Nice Guys Finish  zP Last?" American Economic Review 78 (December 1988):1034-45.(#  zP( XBernheim, B. Douglas, Shleifer, Andrei, and Summers, Lawrence. "The Strategic Bequest Motive." 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American Economic Review 80 (June 1990):353-74.(# XWiener, Joshua M., and Hanley, Raymond J. "Care for the Disabled Elderly: There's No Place Like Home," in  zPl Stephen M. Shortell and Uwe E. Reinhardt, eds. Improving Health Policy and Management: Nine  zP! Critical Research Issues for the 1990s, Ann Arbor, MI: Health Administration Press, 1992:75110.(# D'0*((Ԍ     #X\  P6G;P#Table 1. Comparative Statics Results: Period 2 Part A. Formal and Informal Care in the Community ` ` # , Parent IsG Parent Is ` ` # UnawareG Aware4!4!~ X` 4!X` 4!` ` # ,F7IGFRI X` 4!X` 4!  xP pF` ` # ,7+GR+* X` 4!X` *4!S` ` # ,+70**EAmbig.R+ X` *4!X` *4!W` ` # ,+7;**EG+PAmbig. X` *4!X` *4!M` ` # ,+70;**EG+PR+  Q *** ` ` # ,70;**EGPR+ X` *4!X` m [*4!**` ` #m m +n.a.[[6n.a.**EG PR+ Part B. Probability of Parent Being in a Nursing Home  xP X` m [*4!X` m z [*74!pF` ` #m m + +[[6;**EG77M+P  xP SpN ` ` #m m + +[[6;**EG77M+ W` ` #m m + +[[6;**EG77M+ M` ` #m m + z z 3[[6;**E 77M  Q  ` ` #m m + z z 3[[6;**E 77M X` m z [*74!X` m / [*74!` ` #m m + n.a.[[6;**EG77M _____________________ * Assumes that the substitution effect dominates the income effect associated with the price change. **  includes children's and parent's wealth. See eq. 7a in text. n.a. = not applicable. *** Result for formal care represents the amount of formal care purchased from family funds. Total formal care consumption, F +  Q , rises. `" 0*((  xP    X` m / [*74!X0P8X@X0P8X@X#[2PG;QP##X\  P6G;P#Table 2. Means of Dependent Variables  @ Cognitively[ Cognitively @ Aware [ Unaware uTotal XX330 Probability of entry into nursing homeBAB0.06BOBI]0.27BiBQw0.14 Formal care*BAB2.26B)M(0.21)BI]5.98B1g(0.25)BQw3.53 Informal care* TotalBA10.40B)M(0.51)B\30.68B1g(0.78)Bv17.32 Kids onlyBAB3.68B)M(0.28)B\17.96B1g(0.56)BQw8.60   *Hours per week in the community sample. Numbers in parentheses are fraction of noncensored values. !0*0*0*  X   X ,       X330X < #X\  P6G;P##&a\  P6G;#{&P##Xj\  P6G;[hXP##G\  P6G;{P##X\  P6G;P# Table 3. Nursing Home Choice  <<:Pe  z  QD   QD Bivariate Explanatory Variables<<: Univariate Probit e  z  QD   QD Probit  <<:PCognitivelyeCognitively Demand<<: All P Aware e Unaware   z All   xP X < X  `"30InterceptB A2.78aBT3.36aB i2.04aB!`"3.45a B A(0.60)BT(0.96)B i(0.78)B!`"(0.53)  xP Residual wealth inBAB0.066aBUU0.060bB j0.069bB "`"0.18a nursing home ('0000$)B A(0.021)BT(0.030)B i(0.033)B!`"(0.030) Residual wealth inB A0.028BT0.025B i0.023B!`"0.0090 community ('0000$)B A(0.028)BT(0.023)B i(0.027)B!`"(0.021)  xP Price of formal careBAB0.06cBUU0.058B j0.062B "`"0.13a ($ per hour)B A(0.032)BT(0.049)B i(0.042)B!`"(0.039) Expected Medicaid subsidy forB A0.00025BUU0.013B i0.0082B "`"0.005 home health ($ per week)B A(0.0054)BT(0.0084)B i(0.0072)B!`"(0.0087)  xP No. of children w/inB A0.28aBT0.17aB i0.33aB!`"0.30a 30 minutes awayB A(0.029)BT(0.051)B i(0.037)B!`"(0.031) No. of children 31 toB A0.015BT0.075B j0.036B!`"0.009 60 minutes awayB A(0.058)BT(0.072)B i(0.079)B!`"(0.069)  xP No. of children moreB A0.048cBT0.073cB i0.037B!`"0.042 than 60 minutes awayB A(0.025)BT(0.042)B i(0.032)B!`"(0.031)  xP MarriedB A0.24cBT0.41cB i0.18B!`"0.30b B A(0.12)BT(0.22)B i(0.15)B!`"(0.13)  xP$ Housing assetsB A0.19aBT0.18aB i0.21aB!`"0.26a ('0000$)B A(0.021)BT(0.034)B i(0.028)B!`"(0.028)  xP Spouse's nonbequeathableB A0.21aBT0.17aB i0.22aB!`"0.21a income ('00$ per month)B A(0.029)BT(0.058)B i(0.034)B!`"(0.029)  xPD No. of ADLsBAB0.33aBUU0.29aB j0.34aB "`"0.33a B A(0.018)BT(0.030)B i(0.024)B!`"(0.022)  xP X  `"30X X !`"0000Cognitively unaware@BAB0.45aSXXh!!B "`"0.42a @B A(0.079)S()XXh()!!B!`"(0.10)  xPd Age@BAB0.0070SBUU0.016cXXhB j0.0026!!B "`"0.017a @B A(0.0055)SBT(0.0090)XXhB i(0.0073)!!B!`"(0.0057)  xP Male@BAB0.080SBUU0.32bXXh 0.060!!  QD 0.22b @B A(0.089)SBT(0.14)XXhB i(0.11)!!B!`"(0.094) Supply  xP Intercept@ S XXh !!B!`"1.69a @()S()XXh()!!B!`"(0.46)  xP Discount ('0000s)@BAB0.044SBT0.0003XXhB i0.089!!B "`"1.05a @B A(0.040)SBT(0.053)XXhB i(0.063)!!B!`"(0.23)  xP4! Nursing home beds per@BAB0.010aSBUU0.0063cXXhB j0.013a!!B "`"0.012c 1,000 persons  age 75@B A(0.0023)SBT(0.0036)XXhB i(0.0031)!!B!`"(0.0067)  xP" Black@B A0.91aSBT1.16aXXhB i0.80a!!B!`"2.06a @B A(0.11)SBT(0.22)XXhB i(0.13)!!B!`"(0.30) Hispanic@BAB0.41SXXh!!B!`"0.024 @B A(0.30)S()XXh()!!B!`"(1.21)  xP% No. of ADLs@SXXh!!B "`"0.28a @()S()XXh()!!B!`"(0.059)  xPt' Cognitively unaware@SXXh!!B "`"0.75a @()S()XXh()!!B!`"(0.25) loglikelihood@Bc?853.58SBwR341.4XXhB g501.59!!B/!`"858.32 N@B>4,235SB$Q2,549XXhB f1,686!!B `"~4,235    xP, aStatistically significant at the one percent level, twotail test.  xP- bStatistically significant at the five percent level, twotail test.  xP|. cStatistically significant at the ten percent level, twotail test. *Wealth other than housing and spouse's nonbequeathable income. See text for discussion.D/"D1D1D1,,   3'3'Standard'3'3StandarderJet III  , # X X !`"0000X\8$*#X\  P6G;P#Table 4. Informal and Formal Care   \\G  Informal Care Tobits t Informal Care with Selection ** Formal Explanatory Variables\\G  Total 88] Kids Only t  Total $$ Kids Only ** Care Tobit X\8$*XP, t',33XP, t',33XPd, &t'$,,00000  xP InterceptKBrPK37.69addbBN,b76.05a  |B |30.99a&&B&t'88.66a$,$,B,,90.32a K(7.27)ddbB,c(9.58)  |BE }(8.67)&&B&t'(17.97)$,$,B,,(10.27) Price of formal careKBPL0.81ddbB,c0.85  |BE }0.61&&B&t'0.69$,$,B,,0.65 ($ per hour)KBPL(0.51)ddbB,c(0.68)  |BE }(0.53)&&B&t'(0.72)$,$,Ba,,(0.69) Expected Medicaid subsidyKBPL0.17ddbB,c0.017  |BE }0.13&&B&t'0.099$,$,B,,0.22 for home health ($ per week)KBPL(0.12)ddbB,c(0.16)  |BE }(0.13)&&B&t'(0.16)$,$,Ba,,(0.15)  xP No. of children withinKBPM2.87addbB,d5.56a  |B} ~1.98a&&B!'t'5.08a$,$,Ba,,4.01a 30 minutes awayKBPL(0.36)ddbB,c(0.46)  |BE }(0.38)&&B&t'(0.84)$,$,Ba,,(0.60) No. of children 31 toKBPM0.76ddbB,d0.8  |B} ~0.41&&B!'t'0.84$,$,B,,0.38 60 minutes awayKBPL(0.85)ddbB,c(1.01)  |BE }(0.86)&&B&t'(1.04)$,$,Ba,,(1.31)  xP No. of children moreKBPL0.28ddbB,c1.22a  |BE }0.31&&B&t'1.16b$,$,B,,0.30 than 60 minutes awayKBPL(0.38)ddbB,c(0.50)  |BE }(0.38)&&B&t'(0.57)$,$,Ba,,(0.54)  xPH MarriedKBPM9.52addbBN,b24.10a  |B} ~7.84a&&B&t'27.61a$,$,Ba,,8.87a K(1.59)ddbB,c(2.21)  |BE }(1.68)&&B&t'(3.76)$,$,Ba,,(2.38)  xP Total assetsKBPL0.066ddbB,c0.15c  |BE }0.08&&B&t'0.26b$,$,B,,0.014 ('0000$)KBPL(0.059)ddbB,c(0.087)  |BE }(0.069)&&B&t'(0.11)$,$,Ba,,(0.079)  xPh Spouse's nonbequeathableKBPM0.90addbB,d0.36  |B} ~0.71a&&B!'t'0.53c$,$,Ba,,0.39 income ('00$)KBPL(0.17)ddbB,c(0.25)  |BE }(0.17)&&B&t'(0.29)$,$,Ba,,(0.26)  xP No. of ADLsKBPM4.19addbB,d2.14a  |B} ~5.59a&&B!'t'4.03a$,$,B,,4.81a K(0.36)ddbB,c(0.46)  |BE }(0.38)&&B&t'(0.47)$,$,Ba,,(0.51)  xP No. of IADLsKBPM6.95addbB,d5.85a  |B} ~5.92a&&B!'t'6.95a$,$,B,,3.42a K(0.32)ddbB,c(0.43)  |BE }(0.55)&&B&t'(0.97)$,$,Ba,,(0.46)  xP Cognitively unawareKBPM7.46addbB,d9.68a  |B} ~9.08a&&B&t'13.07a$,$,Ba,,5.90a K(1.29)ddbB,c(1.67)  |BE }(1.34)&&B&t'(1.87)$,$,Ba,,(1.90)  xP AgeK0.066ddbB,d0.54a  |B} ~0.055&&B!'t'0.52a$,$,B,,0.58a K(0.085)ddbB,c(0.11)  |BE }(0.087)&&B&t'(0.14)$,$,Ba,,(0.12)  xP8 MaleKBPM2.92bddbB,c7.20a  |B} ~4.35a&&B&t'7.91a$,$,Ba,,4.47b K(1.38)ddbB,c(1.91)  |BE }(1.46)&&B&t'(2.29)$,$,Ba,,(2.03)  xP BlackKBPL0.43ddbB,d0.83  |BE }2.34c&&B&t'2.70$,$,B,,1.60 K(1.27)ddbB,c(1.70)  |BE }(1.34)&&B&t'(1.80)$,$,Ba,,(1.79) HispanicKBPM0.96ddbB,c6.63  |B} ~3.83&&B&t'3.45$,$,Ba,,8.67 K(4.59)ddbB,c(6.06)  |BE }(4.72)&&B&t'(6.44)$,$,Ba,,(7.93)  xP UrbanKBPL2.32cddbB,c1.82  |BE }2.43b&&B&t'2.17$,$,B,,0.74 K(1.18)ddbB,c(1.56)  |BE }(1.22)&&B&t'(1.63)$,$,Ba,,(1.64)#%%%,, XPd, &t'$,,00000X\8$*Table 4. Informal and Formal Care (Cont.)   \\G  Informal Care Tobits t Informal Care with Selection** Formal Explanatory Variables\\G  Total 88] Kids Only t  Total $$ Kids Only ** Care Tobit X\8$*XP, t',33XP, t',33XPd, &t'$,,00000  xP %K30.15addbB,c31.24a  |&&$,$,BF,,33.16a K(0.46)ddbB,c(0.68)  |()&&()$,$,Ba,,(0.89)  xPx KddbB,c20.97a  |B* }35.66a&& ()K()ddbB,c(3.65)  |BE }(3.65)&&() log likelihoodKByPH11275.0ddbB,`6113.4  |&&$,$,Bh+,4848.2  xP` R2KddbB,d0.35  |B} ~0.30&&  xP  R 2KddbB,d0.34  |B} ~0.29&& FKddbB,c68.82  |B* }29.00&& d.f.Kddb17, 2172  |17, 1108 N3,611K2,971ddb2,190*  |1,126*&&3,611    xP aStatistically significant at the one percent level, twotail test.  xP bStatistically significant at the five percent level, twotail test.  xPP cStatistically significant at the ten percent level, twotail test. *Number with positive values. $%%%,, '3'3StandarderJet III3'3'StandarderJet III(  , #%       XPd, &t'$,,00000X <l  QD #X\  P6G;P# QD Table 5. Informal and Formal Care: Cognitively Aware and Unaware (Tobit)  <<: Informal Care: Kids Onlye  Formal Care <<: CognitivelyP Cognitivelye Cognitivelyl l { Cognitively Explanatory Variables<<:  Aware P  Unaware e  Aware l l {  Unaware  X <l X p"30  xP InterceptB@46.35aBpV74.97aB k54.98aB!"155.39a B A(8.69)BpV(17.47)B]l(8.57)B!"(23.94) Price of formal careB A0.83BpW0.38B]l0.076Bq""2.27 ($ per hour)B A(0.59)BpW(1.27)B]l(0.56)B9""(1.60) Expected Medicaid subsidy forB A0.18BpW0.015Bm0.17Bq""0.19 home health ($ per week) B A(0.21)BpW(0.24)B]l(0.15)B9""(0.29)  xP` No. of children w/inBAB4.19aBpX5.78aB]l2.68aB9""5.20a 30 minutes awayB A(0.44)BpW(0.78)B]l(0.55)B9""(1.22) No. of children 31 toBAB0.41BpX1.71B]l0.47Bq""2.45 60 minutes awayB A(0.87)BpW(1.89)B]l(1.10)B9""(2.98)  xP No. of children moreB A0.48BpW1.81bBm0.37Bq""0.24 than 60 minutes awayB A(0.43)BpW(0.91)B]l(0.45)B9""(1.22)  xP MarriedB@15.50aBpV31.36aB k10.24aB9""2.42 B A(2.13)BpW(3.83)B]l(2.09)B9""(5.12)  xP Total AssetsB A0.22aBpX0.073Bm0.056B9""0.27 ('0000$)B A(0.080)BpW(0.16)B]l(0.060)B9""(0.22) Spouse's nonbequeathableBAB0.39BpX0.087Bm0.084B9""0.87 income ('00$)B A(0.26)BpW(0.41)B]l(0.23)B9""(0.54)  xP No. of ADLsBAB0.63BpX3.53aBm2.44aBq""7.82a B A(0.45)BpW(0.76)B]l(0.46)B9""(1.01)  xPP No. of IADLsBAB5.17aBpX5.33aBm3.45aBq""2.50a B A(0.41)BpW(0.72)B]l(0.41)B9""(0.95)  xP AgeBAB0.32aBpX0.59aBm0.36aBq""1.04a B A(0.10)BpW(0.194)B]l(0.090)B9""(0.26)  xPp MaleB A2.77BpV11.04aB]l1.61B9""7.91c B A(1.71)BpW(3.41)B]l(1.69)B9""(4.56) BlackBAB1.56BpW1.89Bm0.17Bq""5.99 B A(1.44)BpW(3.26)B]l(1.43)B9""(4.31) HispanicB A6.5BpW5.87B]l2.69B!"19.64 B A(5.65)BpV(10.54)B]l(6.83)B!"(16.72)  xP  UrbanB A2.90bBpX0.013B]l0.48Bq""5.43 B A(1.36)BpW(2.89)B]l(1.33)B9""(3.84)  xP %BA20.38aBpW38.11aBBl21.42aB""46.19a B A(0.65)BpW(1.16)B]l(0.73)B9""(2.01) log likelihoodB>2877.8BpT3123.0Bdi2788.7B@!"1943.8 NB>1,948BpT1,023Bdi2,383B@!"1,228    xP$ aStatistically significant at the one percent level, twotail test.  xP% bStatistically significant at the five percent level, twotail test.  xPH& cStatistically significant at the ten percent level, twotail test. '%D1D1D1,,  , X     X p"30X  XX@  #X\  P6G;P#Table 6. Nonhousing Wealth   QDI  QDI D  All  Community D  1. ^  2. @@w  3.   xP  X@X,@30X,@30X!33InterceptBG78.8aBb118.5aB !}87.5a BG(17.7)Bc(36.2)B !}(18.8) Probability of dyingBG18.4Bc18.7B !}40.8 BG(27.5)Bc(28.0)B !}(62.4) Probability of beingBG60.7Bc54.6B !}23.2 unawareBG(58.2)Bc(59.6)B !}(29.8)  xP Nonhousing wealth, 1984B5I1.47aBe1.47aBE!!1.45a BH(0.14)Bid(0.15)B !!~(0.15)  xP` Housing wealth, 1984B5I0.55aBe0.57aBE!!0.58a BH(0.10)Bid(0.11)B !!~(0.11)  xP Savings accts., money marketBH40.4aBNd40.1aB !~49.3a funds, CDs had in 1984BH(9.4)Bid(9.7)B !}(10.0) Bonds had in 1984BH11.1Be9.3B !~10.2 BG(18.3)Bc(18.9)B !}(19.4)  xP Stock had in 1984BH26.7cBNd26.6cB !~26.8c BG(14.5)Bc(15.1)B !}(15.2)  xP No. of nursing homeBG19.1aBc20.6aB !!~9.1 stays, 198489BH(6.7)Bid(7.0)B !}(12.1) No. of hospitalBH2.6Be7.1BE!!0.35 stays, 198889BH(4.3)Bc(43.5)B !!~(4.82) Medicaideligible at entryBH4.8Bid5.9B !!~4.7 to nursing home, 1984BG(10.0)Bc(10.4)B !}(10.6)  xPP Not Medicaideligible withinBG30.9bBc33.6bB !}34.6b 10 years of entry, 1984BG(13.1)Bc(13.9)B !}(13.8) Immediately eligible forBG15.5Bc14.6B !}15.7 Medicaid formal care, 1984BG(10.2)Bc(10.4)B !}(11.0) MarriedBH3.9Bid3.1B !!~2.4 BH(9.1)Bid(9.5)B !!~(9.6) Spouse died, 198489BH5.7Bid6.8B !!~5.3 BG(12.3)Bc(12.7)B !}(12.9) X!33X, !00030Price of formal careG ,,dBe4.5 } ($ per hour)G(),,dBid(7.3) }() Private nursing homeG ,,dBe0.42 } priceG(),,dBid(2.02) }() Dif. private and MedicaidG ,,dBe2.50 } price ('000s): year 1, 1989G(),,dBid(2.66) }() No. of childrenG ,,dBid0.25 } G(),,dBid(1.56) }() Nursing home beds per 1,000G ,,dBe0.018 } persons  age 75, 1989G(),,dBid(0.27) }() BlackG ,,dBc31.6 } G(),,dBc(57.7) }()  xP# Total nonbequeathableGB5I0.032a,,dBe0.032a }BE!!0.031a income ($ per year)GBH(0.010),,dBid(0.010) }B !!~(0.010)  xP% %GBH92.2a,,dBNd92.8a }B !~93.5a GBH(3.0),,dBid(3.2) }B !!~(3.3) log likelihoodGBD5,955.0,,dB8`5,825.3 }B!z5,590.3 NGBE1,008,,dBc989 }B !}876    xP* aStatistically significant at the one percent level, twotail test.  xP+ bStatistically significant at the five percent level, twotail test.  xP, cStatistically significant at the ten percent level, twotail test.,&P-P-P-  X, !00030X8#X\  P6G;P#Table 7. Informal Care: Cognitively Aware (Tobit)  ;L88\r Endogenous ;L88\r Beq., ;ExogenousLEndogenous88\ Exogenousr Exogenous ; TotalL Total88\Beq., Nonbeq.r Nonbeq. ; Assets L Assets 88\ Assets r Assets  X8XPd,@ 0000  xP@ Total assets=BA>0.22aPPMBN0.82adda@@w ('0000$)=BA>(0.078)PPMBN(0.20)dda()@@w()  xP Total bequeathable=PPMddaB,b0.13@@wB} x0.94a assets ('0000$)=()PPM()ddaB,b(0.089)@@wB} x(0.26)  xP` Total nonbequeathable=PPMddaB,b0.63a@@wB} x0.11 assets ('0000$)=()PPM()ddaB,b(0.23)@@wB} x(0.27)    xPH aStatistically significant at the one percent level, twotail test.  xP bStatistically significant at the five percent level, twotail test.  xP cStatistically significant at the ten percent level, twotail test.