Upstream intergenerational transfers.

• Author: Sloan, Frank A.

1. Introduction

   Intergenerational transfers, both of money and of time, have long interested economists and other social scientists. From a policy perspective, transfers from adult children to parents are important. Historically, families in all countries have provided the most important safety net for elderly persons. Although this safety net has become somewhat more limited in recent years, especially in developed countries (Norton 2000), partly in response to the growth of public assistance, understanding the motives for support of elderly persons remains an important topic. (1) Several motives for such transfers have been proposed. These include altruism, exchange, provision of self-insurance within families, and, in the sociological literature, reciprocity. (2) In an altruistic model, a donor derives utility from increased welfare of others. The exchange model assumes that the motive for helping others is to receive something in return. In the insurance model, the motive for transferring "upstream" is to provide elderly parents with insurance against uncertain dates of death. Reciprocity means that people feel obligated to return favors of others. The vast majority of studies have gauged motives based on income of the transfer recipient. In particular, the altruism model predicts that (i) the probability of transfer and (ii) the amount transferred conditional on a transfer is negatively related to the recipient's income (Becker 1981; Cox 1987). Moreover, this model predicts that a decrease of one dollar in the recipient's income, together with an increase of one dollar in the donor's income, results in a one-dollar reduction in transfers between them (Altonji, Hayashi, and Kotlikoff 1997), assuming that donors do not update their expectations of that person's future income based on the recipient's current income (McGarry 2000). (3)

   In the most cited empirical study of exchange, Bernheim, Shleifer, and Summers (1985) infer support for the exchange motive from a positive relationship between the number of contacts with parents and parents' bequeathable wealth. This finding, however, is not supported by empirical evidence from other recent studies (e.g., McGarry and Schoeni 1995; Sloan, Hoerger, and Picone 1996; Sloan, Picone, and Hoerger 1997; Perozek 1998). More fundamentally, a negative relationship between recipient income and transfers is consistent with an exchange model as well as altruism. In a study of intergenerational transfers in Malaysia, Lillard and Willis (1997) find evidence in support of exchange. (4) Their evidence for the exchange motive is that people are more likely to transfer money and transfer more to other people when they received time help from others. Although the results are interesting, this behavior can also be explained by double-sided altruism (Stark and Falk 1998).

   In this study, we formulate a model to provide a framework for empirical analysis in which a middle-aged child transfers both money and time to an elderly parent based on altruism. The goal of our study is not to test alternative motives. We use an altruistic model to examine substitution between financial transfers and time transfers using data from the Health and Retirement Study. Rather than focusing on a single type of transfer, as many other studies have done, we investigate determinants of several types of transfers from adult children to elderly parents: coresidence with parents, living distance from noncoresident parents, money transfers, time spent doing chores, time spent performing tasks for parents limited in activities of daily living, and frequency of contact with parents. Assessing several kinds of transfers permits an assessment of the breath and depth of the private safety net for the elderly, at least from the perspective of one adult child. By investigating several transfers, we can not onl y determine whether the results of one type generalize to others but also study trade-offs between various types of transfers.

   We find that, holding child wealth and other factors constant, parents who were financially worse off relative to their children receive more financial help. However, this help tends to be very limited in magnitude, hardly providing a safety net for very needy elders. Child time prices matter to the extent that higher-wage children donate more money to their parents. The effect of the child's time price on provision of time to parents tends to be negative. Parents residing in nursing homes receive less time and attention from children. Taken in combination with empirical evidence from other studies, this result suggests some crowding out of private effort by the major public program that finances nursing home care, Medicaid. Section 2 presents our model and comparative statics results. Section 3 describes the data, empirical specification, and estimation methodology. Section 4 discusses our empirical results. In section 5, we compare our results with those from previous studies and discuss implications of our findings.

2. Conceptual Framework

   The Model

   Consider two individuals, an altruistic middle-aged adult (M) and her elderly parent (P). Child utility is a function of her parent's well-being. M can improve her parent's utility by providing financial support, paying her parent's medical or nursing home bills, and/or providing services to her parent, such as help in dressing and eating or by visiting. The parent lives on wealth accumulated when young. She also receives financial transfers from M and enjoys help provided by M. In addition, the parent may be subsidized by the government, either in kind or with money. M is the decision maker. The parent affects M's decisions through the value she places on her own consumption and services provided by M. Utility functions for M and P are given by

   V = V([c.sub.m], U), U = U ([c.sub.p],s,g), (1)

   where V is M's utility, [c.sub.m] is her consumption, U is her parent's utility, [c.sub.p], is the parent's consumption, s is the time transferred from M to P, and g is the government in-kind transfer to P. (5) One reason s differs from g is that P may value services received from a child more than those from the government in that companionship and demonstration of affection from the child to the parent is jointly supplied with help. (6) The utility functions have the following properties:

   [V.sub.1] > 0, [V.sub.2] > 0, [U.sub.1] > 0, [U.sub.2] > 0, [U.sub.3]> 0,

   [V.sub.11] > 0, [V.sub.12] > 0, [V.sub.22] > 0, [U.sub.11] > 0, [U.sub.22] > 0, [U.sub.33] > 0.

   Subscripts refer to arguments in the functions. The marginal utility of M's consumption increases as P's utility increases ([V.sub.12] > 0). Consumption of M and her parent's well-being are complements. Intuitively, if P is doing well, M is happier. The child allocates her time between work and care. Budget constraints are

   [C.sub.m] [less than or equal to] [y.sub.m] + w(L - S) - T for M, and

   [C.sub.p] [less than or equal to] [y.sub.p] + T for P, (2)

   where [y.sub.m] and [y.sub.p] are M and P's wealth, respectively; w is M's wage rate; L is the total number of hours that M can supply to labor market; and T is the financial transfer to P from M. We assume, for simplicity, that services that M provides P do not have a perfect market substitute. These are services, either in the form of informal care or just companionship that parents prefer to be provided by their children rather than by someone they hire (see Cox 1987). Exogenous government transfers of money to P are included in [y.sub.p]. (7)

   Assuming nonsatiation, the budget constraint for P becomes an equality. Thus, P's consumption is completely determined by transfers from M and P's wealth. Government transfers are taken as given. M sets financial transfers, time transfers, and her own consumption to maximize Equation 1 subject to Equation 2. First-order conditions for time and financial transfers are

   [V.sub.2] [U.sub.2] - [wV.sub.1] = 0 for time transfers, (3)

   [V.sub.2] [U.sub.1] - [V.sub.1] = 0 for money transfers. (4)

   Optimal levels of time and financial transfers are set at the point where the increase of M's utility from P's increased utility equals the decrease in M's utility from a decrease in her consumption due to the time transfer. Combining the two equations,

   1/w [U.sub.2] = [U.sub.1].

   The parent's marginal utility from receiving one dollar from the child ([U.sub.1]) equals the parent's marginal utility of receiving the time transfer worth of a dollar measured in terms of M's wage. If the equality does not hold, welfare of both can be improved by reallocating financial and time transfers.

   Comparative Statics Analysis

   Using comparative statics analysis, we assess effects of exogenous changes in M's wealth and wage rate, P's wealth, and the government in-kind subsidy to P on M's optimal choice of financial and time transfers. To determine effects of these exogenous changes, we differentiate Equation 2 and Equation 3 with respect to [y.sub.m], w, [y.sub.p], and g (Table 1).

   Signs of the effects of M's and P's wealth and M's wage on T and s depend on the sign and magnitude of [U.sub.12]. The analysis is simplified if (i) P's consumption and time provided by M are complements ([U.sub.12] > 0); (ii) the magnitude of [V.sub.2] [U.sub.12] is small, which holds if M is not very altruistic ([V.sub.2] is small); and/or (iii) consumption and time transferred to P is not too strongly complementary.

   First, when M becomes wealthier, she transfers both more money and more time to her parent. Second, increasing M's wage rate increases the money transfer from M to P. The effect of increasing M's wage rate on time transfers, however, is ambiguous. There are two offsetting effects. When M's wage rate increases, she is wealthier than before. For this reason, she transfers more money to P. But when M's wage rate increases, her opportunity cost of time also increases. This reduces the amount of time provided to her parent. Third, when the...