The supply of children's time to disabled elderly parents.

Sloan, Frank A. ; Picone, Gabriel ; Hoerger, Thomas J. 等

I. INTRODUCTION

In recent years, economists have become increasingly interested in intergenerational transfers of both time and money.(1) Such transfers may be motivated by altruism or exchange. Models of altruism assume that a person's utility depends on the consumption or utility of other family members and her own consumption. For example, children may supply unpaid ("informal") care to aging parents because their utility increases when their parents are happier. One of the most striking predictions of models of altruism is that public subsidies tend to crowd out transfers by altruistic individuals, especially if the subsidy is financed by taxing the altruistic individual (Becker [1974]).

In exchange models, there is typically altruism, but one family member, such as a parent, can induce a relative, such as a child or "kid,"(2) to provide more services or money than the relative would normally provide by threatening to withhold a bequest. To the extent that this is so, one would plausibly expect more care and attention to be provided to wealthy parents. When there is more than one kid, more care should be provided because the threat of disinheritance is more credible when there is competition between kids for bequests. In a well-known article, Bernheim, Shleifer, and Summers [1985] (hereafter referred to as BSS) found empirical support for the strategic bequest motive, based on an observed positive relationship between children's visits and telephone calls to elderly parents per child (as the measure of attention) and bequeathable wealth per child (as the measure of the financial motivation for providing such attention). One might expect this result to extend to decisions about direct provision of help ("informal care") that kids may provide to parents. The marginal benefit of such care is plausibly greater than the benefit derived from a visit or telephone call.

In a recent article, however, we found no evidence that the strategic bequest motive is an important determinant of the amount of informal care kids provide or a related decision - whether or not to place the parent in a nursing home (Sloan, Hoerger, and Picone, [1996]). We focused on the distinction between cognitively aware parents who can threaten to disinherit their kids and cognitively unaware parents who cannot disinherit and examined whether this distinction had any effect on the probability that the parent entered a nursing home or on amounts of formal and informal care received if the parent remained in the community. Any strategic effects were swamped by the greater marginal benefit of care to the parent when the parent was cognitively unaware. Moreover, among the cognitively aware, richer parents actually received less informal care, contrary to the strategic model's predictions. Unfortunately, in past research on intergenerational transfers of time and money, it was not possible to control for the wealth, wage, and other characteristics of kids. To the extent that kid's wealth and wage were positively correlated with parent's wealth, which was observed, the parameter estimates on parent's wealth may be negatively biased. Although parent's wealth and kid's wealth and wage rates are plausibly positively correlated, they have opposite effects on the supply of kid's time, according to the strategic bequest model. That is, potential bequests from a parent may be less attractive to rich kids and therefore induce less care.

We test the strategic bequest model using information on elderly parents and their children from two linked surveys, the 1989 National Long-Term Care Survey (NLTCS) for elderly individuals and the Survey of Informal Caregivers (SIC) for a subsample of the elderly's children. Using these data, we can include explicit measures of kid's wealth and wage rates, thereby avoiding the possible bias introduced by a correlation between parent's and kid's wealth and wages. Also, the data sets provide information on several pertinent health, cognitive, and functional status variables which are not typically observed in surveys of financial status. In particular, the measure of cognitive status allows us to distinguish between parents who are not in a position to bargain with their children because of their cognitive deficits versus parents who do not have these deficits.

Section II presents the conceptual framework for our empirical analysis. Section III describes the data and section IV our empirical tests of the strategic bequest hypothesis. Results, shown in section V, do not provide empirical support for this hypothesis. Further discussion of findings and conclusions are found in section VI.

II. ANALYTIC FRAMEWORK

Initially, assume that there is one parent and one kid. The parent's utility depends on the total care she receives (Q), the amount of informal care she receives from the kid (I), and the kid's consumption ([C.sup.K]). Total care equals the sum of informal care and paid or formal care (F); that is, Q = F+I. But the kid's utility only depends on Q and [C.sup.K]. Thus, the parent's utility is given by

(1) [U.sup.Q](Q) + [U.sub.I] (I) + [V.sup.C]([C.sup.K])

while the kid's utility is given by

(2) [U.sup.Q](Q) + [V.sup.C]([C.sup.K]).

Two aspects of this utility framework are worth emphasizing. First, both the parent and the kid are altruistic in the sense that each one's utility function includes components of the other's consumption.(3) Second, preferences differ in that the kid is mainly concerned that the parent is cared for; by contrast, the parent attaches a special value to care from her kid. This difference will result in the parent wanting to receive more informal care than the kid is willing to provide. This aspect of our specification is similar to BSS's assumption that both the parent and the kid receive utility from their interactions, but the interactions mean more to the parent.

The family's overall budget constraint applies to the parent and kid and incorporates the price of formal care ([p.sup.F]), the kid's income [Y(I, W)], which rises with the kid's wage (W) and falls with the amount of informal care provided, and the parent's exogenous level of wealth or savings (S). Thus, the budget constraint is

(3) Y(I, W) + S - [p.sup.F] F - [C.sup.K] = 0.

Implicit in the budget constraint is a monetary transfer of S- [p.sup.F] F from the parent to the kid. If S- [p.sup.F] F [greater than] 0, this transfer can be interpreted as a bequest. For simplicity, we assume that the parent dies at the end of the period. However, S - [p.sup.F] F need not be positive; the kid may spend more than S to purchase formal care.

The effects of the differing preferences between the kid and parent can easily be seen by substituting the budget constraint for the kid's consumption [C.sup.K] and taking the first-order conditions. First, if the kid maximizes utility over F and I, the first-order conditions are

(4) ([Delta][U.sup.Q]/[Delta]Q) - [p.sup.F] ([Delta][V.sup.K]/[Delta][C.sup.K]) = 0

for formal care and

(5) ([Delta][U.sup.Q]/[Delta]Q) + [Y.sub.1]([Delta][V.sup.K] / [Delta][C.sup.K]) = 0

for informal care.

Assuming an interior solution, (4) and (5) together imply that the kid provides informal care up to the point where its opportunity cost is just equal to the price of formal care (i.e., [p.sup.F] = [Y.sub.1]). All subsequent care is purchased in the formal sector.

In contrast, when the parent maximizes her utility function, the first-order conditions are

(6) ([Delta][U.sup.Q]/[Delta]Q) - [p.sup.F]([Delta][V.sup.K]/[Delta][C.sup.K]) = 0

and

(7) ([Delta][U.sup.Q]/[Delta]Q) + ([Delta][U.sup.1]/[Delta]I) + [Y.sub.I]([Delta]V/[Delta][C.sup.K]) = 0.

Equations (4) and (6) are identical. The difference between (5) and (7) is that the latter contains an extra term reflecting the parent's preference for informal care. Compared to the kid, the parent prefers to receive more informal care. Figure 1 shows the loci of points satisfying the respective first-order conditions for the parent and kid. As mentioned above, the first-order condition for formal care is the same for both the parent and the kid. The parent's curve for informal care lies above the kid's curve.

Solving the respective first-order conditions leads to two polar cases, which can both be interpreted as Nash equilibria under the proper circumstances. The first case occurs when the parent unilaterally chooses F and I to satisfy (6) and (7). This case is supported as a Nash equilibrium by the threat that the kid will be disinherited if he does not provide the level of care desired by the parent (P in [ILLUSTRATION FOR FIGURE 1 OMITTED]). Such a threat is at the heart of the strategic bequest model of BSS. The second Nash equilibrium occurs when the kid makes the decision unilaterally (point K). Such a decision could occur if the parent is mentally unable to make decisions. Because the loci of points satisfying the first-order condition for formal care is shared with the parent and is downward-sloping, point P obviously involves more informal care and less formal care than point K.

Multiple equilibria pose problems since comparative statics cannot be applied; moreover, the multiplicity problem is likely to grow even greater if the parent's and kid's decisions about informal care are made jointly. A reasonable way to provide structure for empirical analysis is to assume that the outcome of the joint decision depends on the relative bargaining strength of the parent and kid, and to focus on outcomes which lie on the loci of points satisfying the shared first-order condition for formal care between points P and K. Such points are pareto efficient since, by the definition of the first-order condition, both the parent's and the kid's iso-utility curves are horizontal when they pass through the formal care loci.(4)

Three factors affect the relative bargaining power of the two parties. First, as emphasized by BSS, a parent's threat to disinherit a kid may be more credible if the parent has another kid to give her money to. Consequently, parents are likely to receive more informal care when they have more than one kid. Second, disinheritance is not a credible threat if the parent is cognitively unaware, since the legal system requires mental competence for changes in bequests. Absent this threat, the quantity of informal care provided will be largely determined by the kid. Therefore, cognitively unaware parents should receive less informal care than the cognitively aware. Finally, a rich parent should have better bargaining power than a poor parent, holding the kid's income constant, since the kid has more to gain by pleasing the rich parent. A natural way to formalize this aspect of the bargaining power argument is to assume that the bargaining solution maximizes a weighted sum of the parent's and kid's utilities, where the weight on the parent's utility is

(8) [Theta] = S / [S + Y(0, W)]

and the weight on the kid's utility is

(9) 1 - [Theta] = Y(0, W)/[S+ Y(0, W)].

The weights represent each party's share of the family's budget in the absence of informal care. This specification produces a unique solution which lies somewhere along the formal care loci between points P and K (as mentioned above, such a point will be Pareto efficient).(5) Qualitatively identical results can be derived from a Nash-bargaining model of the family (see McElroy and Homey [1981]) where the threat points are characterized by selfish preferences and neither informal care nor financial transfers occur.(6)

Using comparative statistics analysis on the weighted bargaining solution, we evaluated the effects of changes in [p.sup.F], S, W, [Theta], and in-kind public subsidies of personal care [Mathematical Expression Omitted] (Table I). To provide additional insight, we also present comparative statics for the polar cases where the parent and the kid make unilateral decisions. The polar case where the kid decides is especially relevant for our empirical [TABULAR DATA FOR TABLE I OMITTED] analysis, because we can examine how much informal care the kid provides when the parent is cognitively unaware.

Unless otherwise indicated, the following results apply to the bargaining solution. We first examined the effect of an increase in the parent's relative bargaining power, [Theta]. This increase may occur for exogenous reasons, such as the presence of siblings competing for bequests, or if there is a redistribution of wealth which favors the parent but keeps total family wealth constant. Such a redistribution produces a pure bargaining effect, since there are no income effects. An increase in [Theta] moves the equilibrium along the formal care loci away from K and towards P in Figure 1. Therefore, informal care rises and formal care falls. When the parent's saving, S, increases, informal care rises, while there is an ambiguous change in formal care. Increased saving has two effects. First, it strengthens the parent's bargaining position, thereby boosting I and lowering F. At the same time, assuming that informal and formal care are both normal goods, the income effect associated with higher S increases the quantity of both.(7)

An increase in the kid's wage produces three effects on informal care. First, the substitution effect reduces informal care as the opportunity costs of providing such informal care rise. Second, the increase in the kid's base income increases his bargaining power

relative to the parent; this effect lowers I. Finally, there is a positive income effect which tends to increase 1.(8) Thus, the net effect of the kid's wage on informal care is ambiguous. In contrast, an increase in the kid's wage unambiguously raises formal care.

Two types of government subsidies for formal care are possible. Subsidies which lower, but do not eliminate, the out-of-pocket cost of formal care have the same effect as a reduction in [p.sup.F]. With an in-kind subsidy of [Mathematical Expression Omitted] units of personal care, total formal care, [Mathematical Expression Omitted], will rise, even though F, falls. But somewhat surprisingly, informal care rises. This appears counterintuitive to our usual expectation that public subsidies crowd out private effort. In fact, however, crowding out is very much a part of our model; it is just that it is formal care purchases, not informal care, which is crowded out.

This is most easily understood for the polar case where the kid makes decisions unilaterally. Recall that the kid provides I up to the point where its shadow price just equals the [p.sup.F]; it is cheaper to buy subsequent units of care in the formal care market. Receiving the in-kind subsidy does not change the point where -[Y.sub.I] = [p.sup.F], so the equilibrium level of I does not change. Privately-financed purchases of formal care, F, are crowded out, even though total purchases, [Mathematical Expression Omitted], rise due to the income effect associated with the subsidy. Hence, the in-kind subsidy has no effect on informal care in this polar case. In the bargaining solution, the income effect associated with the subsidy actually increases [I.sup.9]. Finally, an increase in the price of formal care, [p.sup.F], should decrease the amount of formal care and increase informal care.(10)

III. DATA

The U.S. Census Bureau conducted the NLTCS in 1982, 1984, and 1989. Criteria for inclusion in the sample were that the respondent be at least age 65 and receive help with one or more Activities of Daily Living (ADLs) or Instrumental Activities of Daily Living (IADLs) for a period of at least three months. ADLs are limitations requiting help with basic personal activities, such as eating and bathing. IADLs are limitations in other, less personal activities, such as shopping and doing laundry. Of the elderly persons originally screened, 15% satisfied the criteria for being disabled. The response rate has been very high (around 95%). The 1989 NLTCS, which we used, contained 5,708 respondents, with 1,354 residing in nursing homes. Advantages of the data are (1) information on a national sample of individuals who have a high probability of using long-term care services, (2) inclusion of detailed information on health and functional status, income and wealth, receipt of cash and noncash transfers, relatives of the respondent (both those living in the same household as respondents and elsewhere), and use of various services by respondents, and (3) release of geographic state identifiers.

The Survey of Informal Caregivers, part of the 1989 NLTCS, was designed to obtain information on the amount and kind of care that a caregiver provides to the disabled person living in the community. The survey also asked about some problems commonly associated with caregiving, including mental stress and living and work situations of the caregiver, and about income and assets of the caregiver. To be selected for the SIC, the caregiving respondent had to be related to the disabled elderly person and had to have provided the most help to the person with ADLs (in hours) during the week before the interview of all of the caregivers related to the disabled elderly individual. If there was a tie, the caregiver who was listed first by the interviewer was selected. If no relative provided such help with ADLs, the caregiver providing the most help with IADLs was selected. Ties were broken in the same manner as with ADLs. A total of 1,006 persons responded to the SIC; of these, 366 were spouses of the disabled elderly persons, 324 were kids, and 316 were others (siblings, in-laws, and other relatives). We only selected kids because the focus of our study was on parent-kid relations and informal care. Because of missing values, the 324 observations were reduced to the 261 used in our study.

The mean number of hours of care per week provided by the primary caregiver was 28.6 (Table II). Parents with a kid who was the primary caregiver received almost no informal care from their other kids. In total, the disabled elderly in this sample received 31.3 hours from all sources of informal care and 4.1 hours of formal care. By contrast, all disabled elderly persons in the NLTCS community sample received 17.1 hours of informal care of which 7.4 hours came from children. The number of formal care hours was about the same for the total sample as for the subsample we analyzed.

Data on state Medicaid program characteristics - eligibility standards and Medicaid expenditures - came from several published sources (U.S. Department of Health and Human Services [1987]; Budish [1989]; and Neuschler [1987]). Information on the probability of receipt of Medicaid home health benefits and per capita Medicaid home health expenditures in 1989 came from unpublished Medicaid program data (Health Care Financing Administration Form 2082). Our measure of the gross hourly price of formal care came from an unpublished survey of nursing home wage rates of aides by state conducted for the American Health Care Association. To obtain information on the wages of children, we used data on individuals between ages 25 and 65 from the 1989 Current Population Survey (CPS).

[TABULAR DATA FOR TABLE II OMITTED]

IV. EMPIRICAL SPECIFICATION

Variables Related to the Strategic Bequest Hypothesis

The dependent variable was the number of hours that the primary caregiver spent helping the sample person with ADLs and IADLs during the week preceding the interview. The key explanatory variables for testing the strategic bequest hypothesis relate to the wealth of the parent and kid, cognitive status of the parent, and factor prices.

In our model parent's wealth has a positive effect on informal care, and this effect will be greater when the threat of disinheritance is more credible. To test this hypothesis, we included the total wealth of the parent as an explanatory variable, and we interacted this variable with binaries for only child and for parent cognitively unaware.

We measured parent's wealth as the sum of housing and nonhousing wealth. Both forms of wealth are bequeathable. We imputed missing values of nonhousing wealth using Tobit estimates from a regression of parent's wealth on their income, marital status, education, age, race, and housing wealth. When income was missing, we set the income variable to zero and included a binary variable for income missing. We used this approach to avoid imputing a variable for nonhousing wealth based on imputed values of income.(11)

We measured the kid's wealth as nonhousing wealth. No information on the kid's housing wealth was provide by the NLTCS or SIC. When the SIC provided no information on the kid's nonhousing wealth, we imputed values for this variable based on the kid's income, education, age, gender, and occupation. We used Tobit analysis because of the concentration of values of nonhousing wealth at zero. The SIC did not provide information on the caregiver's wealth when the caregiver lived with the elderly person. Fortunately, information was obtained on the variables we used to impute the kid's nonhousing wealth; thus, we could predict values of nonhousing wealth for such persons.(12)

We distinguished between parents who were cognitively unaware and therefore would not be likely to disinherit their kids and cognitively aware parents who had the mental capacity to threaten to disinherit their kids. The NLTCS administered the Short Portable Mental Health Status Questionnaire (SPMSQ), which was developed by Pfeiffer [1975]. The SPMSQ, which consists of ten questions, such as "what is today's date?" and "who is the President of the United States now?", is widely used in aging research (Kasper [1990]).

We defined cognitively impaired disabled elderly persons as (1) those who answered fewer than seven out of ten questions on the SPMSQ correctly or (2) those who could not respond to the questionnaire and required a proxy respondent. The validity of a proxy report as an indication of cognitive functioning may be questioned. However, Kasper [1990] argues persuasively for accepting proxies as an indication of cognitive impairment (p. 92). To the extent that cognitively impaired elderly are less able to impose their preferences for informal care on their children, we expect to find that such persons receive less informal care than others. Cognitive impairment was included as a binary variable and in an interaction term with parent's wealth. The price of informal care was measured by the kid's hourly wage. Since we had no direct measure of the kid's wage, we developed an imputed measure using CPS data. We regressed, separately for males and females, the hourly wage on a number of personal characteristics - race, marital status, educational attainment, age, number of children less than or equal to age 15 who lived in the household, and variables for the person's industry (12 industry groupings) and occupation (six broadly defined occupations). To correct for selection into employment, we performed a Heckman correction. The estimated selection and hourly wage equations are available from the authors on request.

We included two measures of the price of formal care: the hourly wage paid aides in nursing homes in 1989 by state and the expected weekly per capita home health subsidy provided by the state's Medicaid program in 1989.

The Medicaid variable was defined as the product of (1) a binary variable for Medicaid eligibility, (2) the probability of receiving any home health benefit from Medicaid if a recipient, and (3) the Medicaid subsidy for home health care per recipient and per week. Medicaid provides an in-kind subsidy of care; little or no patient cost-sharing is imposed.

We used the income and asset standards for Medicaid eligibility to define the binary variable for Medicaid eligibility. We used 1989 income and asset standards by state for 1987 from Neuschler [1987] inflated to 1989 dollars. The probability of receiving any home health benefits was measured by the fraction of elderly Medicaid recipients in the state in 1989 who received any home health benefits from Medicaid in that year. Our calculation did not account for the fact that many Medicaid-eligible persons do not actually apply and receive benefits; data on the pool of Medicaid eligibles were not available.(13)

Other Explanatory Variables

We controlled for other factors that plausibly affect the supply of kid's time to parents. For the parent, we controlled for number of kid's siblings, parent age, number of ADLs the parent needs help with, binary variables for, according to the child, (1) whether the parent yelled when upset and (2) whether the parent could be left alone. For the kid, we included variables for gender, marital status, and whether the kid said his/her health status was "fair" or "poor." Finally, we included a binary variable which was set to one if the kid said there was another potential caregiver for the parent.(14)

Estimation

We estimated the equation for informal care ordinary least squares (OLS) as well as regression corrected for selection. For the selection equation, we used information from the NLTCS roster on all children of the disabled elderly person (10,897 observations). Each child of each parent was a separate observation. In the majority of cases, no kid was selected as a primary caregiver or no primary caregiver was interviewed, given the NLTCS criteria for a primary caregiver interview (e.g., caregiver must be a relative). The selection equation included explanatory variables also included in the informal care equation with these differences. Variables for parent's marital status, the number of children the kid had who were 15 or younger, and number of kid's children by age missing (binary) were included in the selection equation but not the informal care equation. Included in the latter but not the former equation were: kid's nonhousing wealth and health; parent yells and cannot be left alone; and other potential caregiver. In most cases, variables were excluded from the selection equation because data were unavailable on these variables for the entire NLTCS sample. In a few cases, the specification was guided by results of preliminary empirical analysis showing no effect.

V. RESULTS

Selection Equation

Several explanatory variables are statistically significant determinants of selection into a primary caregiving role (Table III): number of kid's siblings (-); parent age (+); parent single (+); number of ADLs (+); kid male (-); kid age (+); kid married (-); and number of kid's children by age missing (-).

Informal Care Equation: Basic Specification

Informal care regressions are presented with and without the selection correction (Table IV). Although positive, implying negative selection, the coefficient on the Mill's ratio is not statistically significant. The two sets of parameter estimates are very similar. Therefore, we only discuss the estimates without the selection correction.

Overall, the empirical evidence yields very little evidence in support of the strategic bequest model. In our version of this model, prices of formal and informal care affect amounts of informal care provided. In particular, the kid's wage was hypothesized to have a negative impact on informal care when the kid makes the care decision unilaterally and to have an ambiguous effect when the parent is involved in decision making (see Table I). In fact, the coefficient on the kid's wage variable is negative and statistically significant at the 5% level. A one dollar increase in the kid's hourly wage decreased informal care provided by the primary caregiver by 1.8 hours per week on average. This is the only result that supports the strategic bequest model. Admittedly, the observed kid's wage effect could also be consistent with a simple time allocation model with no strategic behavior.

The other measures of strategic bequest behavior have no effect on the amount of informal care provided. The effect of parent's wealth in the case of cognitively aware parents with more than one child is given by the coefficient on the parent's wealth variable. Parent's wealth has a negative, but statistically insignificant effect on informal care rather than the positive effect predicted by the strategic bequest model. The coefficient on the interaction term between parent wealth and the binary for cognitively unaware parents is positive, but insignificant, rather than negative as our model predicted. The effect of the interaction of parent's wealth and the binary for an only child is positive and insignificant whereas a negative coefficient would have supported the notion of competition for bequests. The effect of kid's wealth on informal care is negative, as anticipated, but the standard error of the estimate is almost as large as the coefficient on this variable. The home health subsidy also has a negative impact on informal care, but this coefficient is not quite statistically significant at the 10% level. Logically, the subsidy should have a greater impact on formal than informal care. The formal care price has no effect on informal care.

Other explanatory variables were included to represent other effects rather than to provide empirical tests of our model. Of these variables, parent ADLs (+), parent yells when upset (+), parent cannot be left alone (+), kid male (+), and kid married (-) have statistically significant effects at the 5% level. All of these coefficients are plausible with the exception of the coefficient on kid male for which a negative coefficient was expected.(15) The coefficient on kid male was negative in the selection into caregiving equation. Apparently, males [TABULAR DATA FOR TABLE III OMITTED] who select into primary caregiving of elderly parents are a unique group of males. Other potential caregivers logically include other relatives of the parent. Although negative, this coefficient is not much larger than its standard error.

In preliminary analysis, we included a variable for the product of parent's wealth and the binary identifying parents who yelled when upset. Possibly, the threat of disinheritance is greater when the parent yells. We dropped the variable after finding no empirical support for this possible relationship.(16)

[TABULAR DATA FOR TABLE IV OMITTED]

Alternative Specifications of the Informal Care Equation

Because these results differ so sharply from BSS, who found support for the strategic bequest model, we estimated alternative specifications of the informal care equation which more closely resembled those in BSS's study. First, we expressed parent wealth on a per kid basis, dropping observations in which there was only one kid. BSS argued that the threat of disinheritance is only credible when there is more than one kid. Coefficients on the variables most closely related to the strategic bequest model are shown in column I of Table V. We obtained a positive coefficient on the interaction between parent's wealth per kid and the binary identifying cognitively unaware parents. However, our model led us to expect a negative coefficient on this variable since the threat of disinheritance disappears when the parent is cognitively unaware. The coefficient on the kid's wage remained about the same as in the basic specification. TABLE V Informal Care Equation: Alternative Specifications (Results on key variables)(*) Exogenous Endogenous Explanatory Wealth Wealth Variables (1) (2) Parent's wealth per kid ('00005) -0.33 0.84 (0.96) (2.76) Parent's wealth per kid x parent 1.76(b) - parent cognitively unaware ('00005) (1.11) (-) Parent's wealth per kid x only kid ('00005) 0.58 - (1.00) (-) Parent cognitively unaware 8.05(b) - (5.04) (-) Only kid -4.98 - (6.66) (-) Kid's nonhousing wealth ('00005) -0.43 -0.91 (0.33) (0.59) Kid's wage -1.83(a) - (0.57) (-) Formal care price -1.09 - (1.71) (-) Medicaid home health subsidy -0.60 - (0.43) (-) a Statistically significant at 1% level (two-tail test). b Statistically significant at 10% level (two-tail test). * With the exceptions noted in the text, the specification of the first regression is the same as the second regression in Table 4. In the second regression, we included variables for parent ADLs, parent yells when upset, parent cannot be left alone, kid male, and kid married in addition to those shown.

Second, we treated parent wealth per kid as an endogenous variable. BSS argued that the parent's bequeathable wealth is endogenous because, for one, the parent will take account of the children's propensity to supply attention in deciding how much wealth to accumulate. We used these instrumental variables: income the parent received during the previous month from pensions, annuities, and public cash transfers (nonbequeathable income) and parent's education expressed as binary variables. We also dropped the kid's wage, prices of formal care, and other variables which BSS did not include in their analysis.

The coefficient on parent's wealth per kid became positive, but not statistically significant. The coefficient on kid's wealth is negative, as expected, and nearly statistically significant at the 10% level. The increase in size and significance of kid's wealth is due to the more limited specification in which the kid's wage variable is absent, not the change from treating parent's wealth per kid as an endogenous rather than as an exogenous variable.

VI. DISCUSSION AND CONCLUSIONS

The NLTCS is an excellent source of information on disabled elderly persons. It combines detailed information on income and wealth with information on health, functional, and cognitive status of such persons. The Survey of Informal Caregivers, a subsample of the NLTCS, provides information on a national sample of elderly persons' caregivers not available from other sources. In particular, the survey provides data on kid's nonhousing wealth and variables, such as education, needed for predicting a market wage. Other national surveys tend to either emphasize financial status or health, functional, and cognitive status. To our knowledge, no survey provides as complete information on parent-child pairs. The disadvantage of the NLTCS-SIC is the small number of such pairs.

Our main purpose was to determine whether a model of strategic behavior explains provision of informal care by children. Only two results are consistent with the strategic bequest model, the results on kid's wage rates in Tables IV and V and the result on kid's wealth in the specification in which parent's wealth per kid is treated as an endogenous variable in Table V. Other pertinent coefficients are far from attaining statistical significance at conventional levels, with the exception of the home health subsidy.

Our failure to find empirical support for strategic bequests as a motive for caregiving does not reflect a general failure to explain variation among elderly persons in amounts of informal care received. Several other variables have statistically significant impacts on the dependent variable and, judging from the magnitude of the coefficients, have important impacts on the amount of informal care received.

Particularly in view of the very selected sample and the sample size of primary caregivers, it is important to examine results of other studies in light of our findings about the impact of the strategic bequest motive. Unfortunately, although there is a rich body of literature on caregiving to the elderly, few empirical studies include measures of prices, wealth, and public subsidies.(17)

As mentioned above, BSS found that richer parents received more telephone calls and visits. Their study suffers from the potential bias of unobserved correlations between parent's and kid's wealth as well as with other omitted variables, such as the kid's wage rate and the parent's functional status. Rich parents may have relatively rich kids, and rich kids may be less likely to respond to the threat of disinheritance. The only other study to include both parent's and kid's wealth is by Boersch-Supan et al. [1992]. They used data from a single state (Massachusetts) to test an altruistic model and, as in our study, found that parent's wealth had an insignificant effect on informal care. They included a variable for parent's income which to some extent duplicated the wealth variable since some of the income flowed from wealth; this variable had a significantly negative effect which tends to contradict the strategic bequest model.

This apparent contradiction may stem from the difference in dependent variables between the studies. That is, the strategic bequest motive may be an important determinant of the number of telephone calls and visits a parent receives,(18) as in BSS,(19) but have little effect on the amount of informal care received, as in the other studies. The distinction here would seem to be between concern or attention, which is responsive to the parent's wealth, and actual care for the disabled parent, which is not responsive. From the standpoint of public policy, attention provided by children in the form of care of disabled parents is much more important.

ABBREVIATIONS

BSS: Bernheim, Shleifer, and Summers NLTCS: National Long-Term Care Survey CPS: Current Population Survey SIC: Survey of Informal Caregivers SPMSQ: Short Portable Mental Health Status Questionnaire ADLS: Activities of Daily Living IADLS: Instrumental Activities of Daily Living OLS: Ordinary least squares

1. See, for example, Becker [1981], Kotlikoff and Spivak [1981], Cox [1987], Bernheim and Stark [1988], Pollack [1988], Becker and Murphy [1988], Bruce and Waldman [1990], Altonji et al. [1992], and Cox and Rank [1992]. For a recent review of this literature, see Seater [1993].

2. The latter terminology comes from Becker's Rotten Kid Theorem. See Becker [1981].

3. Thus, although we follow Becker [1974] in referring to the grown child as a "kid," our kid is not "rotten" (completely selfish).

4. The weighted bargaining solution has been used in empirical models of bargaining. See, e.g., Danzon and Lillard [1983] and Lillard and Viscusi [1990].

5. Since both individuals share the same first-order condition for formal care, maximizing the weighted sum of their utilities will also produce the same first-order condition, implying that the solution will lie on the same formal care loci.

6. Selfish preferences at the threat point mean that if the parent and kid fail to reach a cooperative agreement, then each only cares about his or her own consumption. This is equivalent to the parent and kid disowning one another if they fail to reach a bargaining solution and is similar in spirit to the threat of disinheritance in BSS's model. However, BSS focused exclusively on the threat of disinheritance by parents and did not consider kids' threats to deny attention. In addition, BSS did not address the issue of multiple equilibrium.

7. This income effect is not present when the kid makes unilateral decisions. In this polar case, the kid purchases informal care up to the point where its cost, - [Y.sub.I], equals [p.sup.F]. Any additional care which is consumed is bought in the formal care market. Since an increase in S has no effect on [Y.sub.I] or [p.sup.F], I does not change.

8. Again, the income effect vanishes if the kid makes decisions unilaterally. In this polar case, an increase in wage has an unambiguously negative effect on informal care.

9. It is important to note that this result depends on there being an interior solution for both F and I. If it is optimal for the kid to provide only I, the in-kind subsidy will crowd out informal care.

10. This assumes that the substitution effect associated with the price change dominates the income effect. Given the relatively low levels of formal care in our sample, which generalizes to the disabled elderly population in the U.S., the magnitude of the income effect is likely to be small.

11. Income of parents was missing in 3.1% of cases.

12. Forty-eight percent of primary caregivers lived with parents.

13. The Medicaid Form 2082 data, used to construct this variable, contain some inconsistencies in numbers of recipients and expenditures. Fortunately, the variance in true spending appears to be very large, both in absolute terms and relative to any likely error. In 1986, over half of total Medicaid home health expenditures was incurred in just five states (Feder [1991]). According to our calculations, 75% of elderly persons in our sample were ineligible for Medicaid because their income/assets were too high; for such persons, our variable was measured exactly.

14. As a referee pointed out, some of these variables also relate to the strategic behavior hypothesis, although they may play other roles as well. For example, the present discounted value of a bequest of an older parent is higher, ceteris paribus, because such persons have a lower life expectancy. Also, a parent needing help with more ADLs may be in a more vulnerable bargaining position.

15. See, e.g., Dwyer and Coward [1991] for evidence on caregiving by gender.

16. In his Nobel lecture, Becker [1993] developed a model in which the parent tries to make the kid feel guilty. His model predicts that only parents without a bequest motive would do this. We do not test such a model here, but it represents a potentially interesting extension of our analysis.

17. See e.g., Boersch-Supan et al. [1992], Kemper [1992], and Wolf and Soldo [1991].

18. BSS found no effect of parent's wealth on the number of letters written. They explained this lack of findings by noting that wealth increases visits and telephone calls. Given a lot of parent-child contact, they argued that the number of letters written would logically diminish.

19. However, empirical tests by Sloan and Zhang [1994], using data from the 1992 Health and Retirement Survey, found no empirical support for the strategic bequest model using telephone calls and visits as the dependent variable.

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