Delaying inter vivos transmissions under asymmetric information.

• Author: Cremer, H.

1. Introduction

   In today's societies, most bequests occur when children-heirs get close to retirement age. In many respects, this is quite late. Most individuals, if they could choose, would like to keep their parents alive and healthy as long as possible but at the same time to benefit from what the parents intend to bequeath them at a much earlier stage of their life cycle. We talk here only of planned transmissions and not of accidental bequests that arise from the combination of early death and precautionary saving.

   There are two ways to avoid too late transmissions. First, children could borrow from the financial market against the expectation of their future bequests. Second, altruistic parents could make early transfers through inter vivos gifts at the time their children need them the most. One indeed finds children borrowing upon the anticipation of bequests and parents financing their children's start in life. Parents generally do it first by providing children with human capital (Becker and Tomes 1986). Yet, we know that using a forthcoming inheritance as a collateral requires the formal consent of parents; consequently, the bequest is then effectively equivalent to an inter vivos gift. We also know that in reality most financial transfers from parents to children accrue through bequests (see, e.g., Joulfian 1992) rather than through gifts.(1)

   The fact that bequests are much more important than earlier transmissions can be explained by nonaltruistic inheritance motives - precautionary motives already alluded to, but also strategic motives implying that parents keep their estate as long as they live to bait their children into giving them attention, care, love, etc. (Bernheim, Shleifer and Summers 1985). Even allowing for these nonaltruistic motives, we believe that there might be another reason to postpone inter vivos gifts, that is, parents want to make sure that their children don't behave like "rotten" or "spoiled brats" who shirk at their expenses and waste their talents.

   This argument, developed by Becker (1991), Lindbeck and Weibull (1988), and Bruce and Waldman (1990), can rely on moral hazard or adverse selection. In a recent paper (Cremer and Pestieau 1996), we assumed that parents are not perfectly informed about the earning abilities of their children. They want to avoid having the more gifted child behave as if he were the less gifted one in order to obtain a large transfer. To do so, the parents make later gifts so as to discipline their children and provide them with incentives to reveal their true capacity. In this paper, we study the implications of an alternative source of asymmetric information, namely moral hazard. Children have a perfectly observable ability, but the amount of effort they supply is not observable. As it will appear, even though earlier gifts are more attractive because of liquidity constraints, parents will postpone some of their transfers until they observe their children's actual incomes.

   The work by Chami (1996) and Chami and Fischer (1996) constitutes a notable (albeit remote) precursor to our analysis. Chami (1996) compares two settings: one with precommitment by parents and one where parents have the "last word." He shows that the former dominates the latter. In our paper, commitment is assumed at the outset. Chami and Fischer (1996), on the other hand, study the relationship between nonmarket transfers and transfers operated through insurance markets. The desirability of nonmarket arrangements is shown to depend on the degree of altruism.

   The rest of this paper is organized as follows. In the next section, the basic model is introduced along with notation. Then a full information solution where the parents observe their children's levels of effort is derived. In the fourth section, we contrast the choice of effort by children who either cooperate or not at the level that parents would choose. The general problem is dealt with in the fifth section.

2. The Basic Model

   We consider a family consisting of one parent and two children. Each child i's income [I.sub.i] is a random variable with two possible values [I.sup.L] and [I.sup.H], where [I.sup.L] [less than] [I.sup.H]. The probability of [I.sup.H] depends on the child's effort level e, and it is denoted by p(e) with p[prime](e) [greater than] 0, p[double prime](e) [greater than] 0 and 0 [less than or equal to] p(e) [less than or equal to] 1. The random variables [I.sub.1] and [I.sub.2] are independent and have the same distribution when both children choose the same effort level ([e.sub.1] = [e.sub.2]). As soon as the [I.sub.i]'s are realized, they are observable to parents and children. However, parents do not observe the children's effort levels.

   Two kinds of transfers are available. First, there are inter vivos gifts [g.sub.i] made before I is realized (and observed), that is, when the child starts his active life. Consequently, one necessarily has [g.sub.1] = [g.sub.2] = g. Second, there are bequests [b.sub.i], made much later at the time [I.sub.i] is known. Because of that difference in timing and usual market imperfections, bequests are less valuable than gifts of an equal amount. To express this property, we assume that a transfer of [b.sub.i] increases the child i's income by [Gamma][b.sub.i] with [greater than] [less than] 1. The parameter [Gamma] thus reflects liquidity constraints as well as the rate of interest. Both intergenerational transfers are restricted to be nonnegative...