INTERPERSONAL ALLOCATION CONTINUOUS WITH INTERTEMPORAL ALLOCATION: BINDING COMMITMENTS, PLEDGES, AND BEQUESTS Julian L. Simon* The ultimate human mystery may not be anything more than the claims on us of clan and race. (Arthur Miller, Timebends: A Life, New York: Harper and Row, 1987). Christmas came early for shoppers on a South Side street Thursday when an unidentified man handed out $1,200 worth of $10 bills. Police later took the man...into custody when he returned to a savings and loan institution to withdraw $2,000 more from his account. Authorities said the sidewalk philanthropist had a history of mental problems and would be placed under mental observation. (Chicago Daily News, Dec. 25-26, 1971, p. 1). In his survey of "The Expanding Domain of Economics," Hirshleifer wrote that gifts and bequests are a "scandal" for economic theory (1985, p. 55), a "difficulty [which] can be resolved only in the light of bioeconomic considerations" (p. 55). Within the framework offered here, however, gifts and bequests present no greater difficulty than does intertemporal allocation of lifetime resources within a given individual's lifetime, which economists routinely deal with theoretically. The core of the issue is to explain how "one", or the "self", allocates the available resources for consumption among (a) the current person, (b) future self-persons who are legally and physically the same individual who is allocating, and (c) other individuals at present and in the future. Quote marks are around "one" as in "one should", and the equivalent "self" as in "self-interest," because the definition of the unit for which they stand is the very heart of the explanation. The key intellectual obstacle is that economists consider the legal-physical individual throughout her/his lifetime, or just a disconnected single chunk of that life, to be the appropriate entity for analysis. The mechanism which overcomes this obstacle is to consider the future periods of the given individual's life -- future "self-persons" -- on the same footing as other individuals. That is, instead of a one-dimensional point for the maximizing unit, or even the two-dimensional individual who allocates intertemporally, this scheme envisages a three-dimensional space; the interpersonal 'distance' dimension replaces the concept of altruism. This is the main point of the paper: to argue that other individuals with whom we are close should not be considered as distinct from us but rather as part of our "identity" to greater or lesser degrees. The analytic apparatus and the particular examples analysed are presented as devices to show the general value of this way of thinking as well as for their technical value. The model suggested here aims not only to remove a theoretical difficulty, but also to adjust the economist's thinking more closely to reality. The individualistic asset- maximizing model apparently leads some economists to assume that human nature is like the model's assumptions. For example, a panel of six "expert" economists on average made very poor predictions about outcomes to laboratory experiment on a prisoner's dilemma game; theory led them to expect no cooperation and their overall predictions ranged from 0% to 30% cooperation, whereas the outcomes averaged between 40% and 60%; it is also interesting that economics graduate students exhibited less cooperation - about 20% than did non-economists (Marwell and Ames, 1981). The individualistic model also leads to puzzlement about such phenomena as gifts (Camerer, 1988), and behavior in catastrophes (Hirshleifer, 1987), which do not puzzle non- economists. My aim is to make gift-giving or "altruism" as "rational" in the context of economic theory as is inter-temporaral intra- personal allocative saving and spending. The paper does not deal with the consequences of various amounts of altruism, as do Becker (1981, Chapter 8), Becker and Barro (1988), and Mulligan (1993), who seek to understand how non-selfish activities fit into the larger scheme of human behavior. Nor does the paper discuss the causes of altruism; Mueller, for example, attempts to explain such behavior in a backward-looking fashion in the context of behaviorist learning theory<1>, and H. Simon (1990) offers a model of the genetic and social-learning causes of altruism. Rather, the paper offers intellectual machinery intend to be a consistent framework to help make understandable otherwise-puzzling choices, and especially their timing (such as timed transfers). For Becker's purpose a one-period framework suffices, although he discusses dynamics in passing. In contrast, my point is that either intertemporal transfers and time-discounting cannot be integrated and made understandable within economic thoery or interpersonal transfers discounting can be so made, along with intra-personal transfers over time. ELEMENTS OF THE ANALYSIS<2> These are the elements used in the analysis: 1) The mental states of a single legal individual at a given moment or during a given period comprise the basic entity, here called the "temporal person." The "I" or "me," of which one is conscious at any moment is part of the "current person" or "present person"; it is one particular time-dated or "temporal" person in the individual's lifetime. By contrast, in William James's system (1890/1963, Chapter XII), as also in the systems of Schelling (1984a,b), Elster (1986), and Thaler and Shefrin (1981), there are several "selves" at a given moment operating within (in Schelling's terminology) a single legally-unique and physically-distinct "identity." 2) The sequential temporal persons may be thought of as distinct from each other just as individuals are ordinarily thought of as distinct from each other. This analogy between (on the one hand) the feelings of kinship between "oneself" and other legally-distinct individuals, and (on the other hand) the feelings of kinship between different temporal persons within a given individual's lifetime, is central to the point of view of this paper. 3) The feeling of sympathy between one and another of the individual's temporal self-persons -- and especially between the current person in operation and any future temporal self-person - - may be measured by a discount factor of the ordinary kind. Time discounting will be assumed to be a common characteristic of human behavior, though it might be absent or even negative in a given situation. 4) The discount from the current person to any future self- person typically is considerably greater than the discount between a pair of the individual's future self-persons that are separated by the same length of time. This is the key assumption that makes "self-control" appear "rational," as will be seen in examples to come; without this assumption, self-control behavior does not make sense in conventional terms. This assumption is supported by considerable evidence derived from questionnaires and laboratory experiments with animals and humans; in support of this assumption; see e.g. Ainslie (1975) for evidence from animal experiments showing that reward potency declines with delay at a rate greater than exponential, and Ainslie and Haendel (1983) and Ainslie and Haslam (1992) for a review of other evidence. 5) The feeling of sympathy between the current person and another individual may also be measured by a discount factor. The sympathy discount weight for another individual is likely to be small relative to the discount weights among an individual's temporal persons, except perhaps the weights for close beloved persons, but they may be of the order of the weights for the individual's temporal persons many years in the future. Operationally, one is likely to divide one's assets less evenly between another individual and one's current person (in the form of one's legal identity) than between one's current person and one's person next year, say. The strength of kinship feeling to other individuals is likely to be affected systematically by relationships of blood, geography, common views, caste, ethnicity, religion, and extent of interaction (emphasized by Hume; see Mulligan, 1993, Chapter 2) among others. The inter-individual structure of discount factors could be estimated for some scientific purposes by examining such phenomena as the relationship of charitable giving to geographic distance (or number of people living in between the donor and the donee), the closeness of blood relationship (even identical twins as compared to fraternal twins), and the number of newspaper stories about countries at different geographic distances and having different degrees of ethnic and religious kinship from the reference point. One would also expect people to exhibit more sympathy -- and even bequests in wills, say -- for animals such as gorillas that are relatively close to us biologically than for animals that are relatively further away, or are commonly pets compared to those species that are not commonly pets. A survey of the importance of preserving various species confirms this: "The 20 top-ranked animals are all mammals, relatively large birds, or relatively large turtles...Almost all of the 20 bottom-ranked animals are obscure rodents, snakes, insects, or snails" (Coursey, 1994, p. 10), and this ranking squares with government expenditures on preserving the various species (Coursey, p. 11). A similar propensity is exhibited in such public policy as U. S. immigration laws that have favored persons who live in countries from which much of current native stock was originally drawn. Adam Smith masterfully explored this basic idea and mapped the typical relative strengths of sympathy toward individuals at different distances from us. Every man...is first and principally recommended to his own care; and every man is certainly, in every respect, fitter and abler to take care of himself than of any other person. Every man feels his own pleasures and his own pains more sensibly than those of other people. The former are the original sensations--the latter the reflected or sympathetic images of those sensations... After himself, the members of his own family, those who usually live in the same house with him, his parents, his children, his brothers and sisters, are naturally the objects of his warmest affections. They are naturally and usually the persons upon whose happiness or misery his conduct must have the greatest influence. He is more habituated to sympathize with them: he knows better how every thing is likely to affect them, and his sympathy with them is more precise and determinate than it can be with the greater part of other people. It approaches nearer, in short, to what he feels for himself.<3> The proof of Smith's observation may be seen on the front pages of the newspaper. For example, on May 24, 1971, The Jerusalem Post had as its main and highest headline "Elrom found murdered in Istanbul flat," a story about an Israeli Council- General. Lower and smaller was "1,000 feared dead in quake," a story about a Turkish earthquake. And down toward the page in much smaller type was "70 dead in plane crash," about a Yugoslav airliner. Sidgwick (1907) noted the similarity between the interpersonal and the intertemporal sympathies, as did Sen more recently (1977), and Elster (1984, p. 71) who wrote: "The absolute priority of the present is somewhat like my absolute priority over all other persons". Derek Parfit makes the same point - that "our later selves are properly to be seen as rather like other people" (Williams, 1984), though Parfit takes seriously the idea of psychological continuity (1984, Chapter 10). The scheme presented here uses a weighted set of discount factors representing a pre-existing set of attachments which "explain" the allocations, and which one might even infer from external evidence. This scheme supports a quantitative formalization which can make sense of binding decisions as well as allocational behavior that involve both intertemporal and interpersonal dimensions. The basic descriptive equation used here is formally the same as the literature on utility functions that include the utility of others (see e. g. Becker, 1981, Chapter 8), and one may consider it as a development within that tradition. If so, the new technical contribution of this paper is the analysis of pledges and bequests that hinges upon the combination of the analysis of intertemporal binding commmitments, developed in J. Simon (1990), with the familiar-looking multi-individual utility function. Underlying the approach given here, however, and also Smith's view, I believe, is a different vision of the phenomenon than the vision embodied in that literature on altruistic utility functions. That literature seems to envision decision-making based on a cool assessment of costs and benefits, and well- thought-out maximizing intentions. In contrast, the vision here is more that of a mother bear instinctively defending her cubs, or a mother sparrow feeding her young. Some research in the laboratory describes such a state: 1. Krebs obtained subjects' opinions on various subjects and then showed the subjects supposed questionaire responses by confederates, varying the extent of agreement between confederates and subjects. The subject then observed the confederate performing tasks with various degrees of success, or participating in roulette where the outcome was either money winnings or electric shock. "When the confederate was perceived as similar, the observers demonstrated more physiological response (increased heart rate and the like) as a function of the outcome experienced by the confederate. Also, when the confederate was perceived as similar, subjects were more likely to sacrifice some of their own reward for the confederate, when given an opportunity to do so" (Krebs, 1975, as described by Baron, 1988, p. 409). 2. In Milgram's experimental work on pain induction, subjects who were remote from their "victims" were willing to administer much more punishing electric shocks than were subjects in closer proximity to the "victims" (1975, Table 2). The approach presented here also differs from the Becker- type formulation in that it emphasizes the similarity of sentiment toward an individual's own future persons and the present and future persons of other individuals. Becker does view them as formally symmetrical, but he uses such language as that "other selves" are included in his utility function, (letter of February 1, 1990), and the notion of a discount factor is limited to the reference individual's intertemporal decisions. And the term "altruism" suggests a distinction that I wish to do without. Placing interpersonal and intertemporal allocation on the same footing, which is the key element in this paper, makes the term "altruism" as unnecessary when talking of allocation to other individuals as when talking of allocation to future periods of the same individual. Further discussion of the difference in viewpoints may be found below. This framework also supports systematic understanding of such phenomena as pledges and bequests that cannot be understood without the conjunction of the intertemporal and interpersonal dimensions plus the non-exponential discount-factor structure while remaining squarely within the received body of economic theory without invoking auxiliary psychological elements. The issue addressed here is not whether a person is "really" different persons over time, but whether it is useful to treat the legal individual as if s/he is different over time in a fashion similar to the differences among legal individuals at a particular time, so as to better understand behavior toward other individuals. THEORETICAL APPARATUS The individual is assumed to maximize the present value of the expected (positive) pleasures and (negative) pains experienced by the present and future self-persons, and by other individuals with whom s/he feels sympathy, discounted and summed. (1) max Vt,i=0 = Gt,i=0 - Bt,0 + d'Gt+1,0 - d'Bt+1,0 + d''Gt+2,0 - d''Bt+2,0 ... + ej=1Gt,j=1 - e1Bt,1 + d'e1Gt+1,1 - d'e1Bt+1,1 ... + ej=2Gt,j=2 - e2Bt,2 + d'e2Gt+1,2 - d'e2Bt+1,2... j=n m k = S1 ei,j S1 d (G - B ) i=0,j=1 h=0 t+h;i,j ( t+h;i,j t+h;i,j) subject to F1 < alpha, F2 < beta... where Vt,i=0 = present value of the expected relevant experiences for the reference individual i=O evaluated at time t i,j = index of an individual, the decision-maker (i=O) or another individual (j = 1,2 ... ) G = a positive event, a "good" or "pleasurable" experience B = a negative event, a "bad" or "painful" experience d = a time-discount weight, where d < 1 for the normal cases discussed here. ei,j = sympathy weight for the self-person i or for another individual j where ei = 1 and ej < 1. F1, F2, etc. = lifetime endowments of time, strength, and other elements affecting the quantities of pleasure and pain, and alpha, beta, etc. are constants. Let us first exercise this machinery for the case of an intra- individual choice that involves the idea of pre-commitment. Consider that an individual will make either one or two choices among three alternative courses of action: The first choice consists of the option (a1) of binding oneself at time t=-T to accept a future negative event (or series of events) at t=0 in order that a positive event (or series of events) will occur at t<0, t=0, or t>0; the alternative option (a2), not making a binding commitment, leads to a second choice between options (b) and (c). The valuation of option (a1) is made as follows: (2) V(a1)t=-1 = -Bt=0dk + Gt=1dk+1 + Gt=2dk+2 + Gt=3dk+3... where k = a constant > 1, and where all other goods and bads, those unconnected with this option, are considered to net out to an arbitrary reference point of zero for notational convenience. Option (b), which becomes open at t=0 if option (a1) is not chosen earlier, consists of choosing the negative event at hand in order to obtain the positive event(s); it is valued at the moment it might be chosen as follows: (3) V(b)t=0 = -Bt=0 + Gt=1dk + Gt=2dk+1 + Gt=3dk+2... Option (c), which also becomes open at time t=0 if option (a1) is not chosen earlier, consists of choosing against the negative event; the option is valued as of t=0 (4) V(c)t=0 = 0 The choice of interest here is between (a1) and (a2), whether or not to make a binding commitment. The value of (a2) is the greater of the values of (b) and (c), that is, the alternative which will be chosen if (a1) is previously not chosen; the conditional choice between (b) and (c) will depend upon the values of the right-hand-sides of eqs. 3 and 4 as of t=0. If (c) would be chosen, its value as of t=-T would be zero because its value as of t=0 is zero. If (b) would be chosen over (c) conditional upon (a1) not being chosen, then there is no need for a binding commitment; the same course of action would be arrived at anyway. It is only if (c) would be chosen over (b) that there is a role for a binding commitment. In order that the choice of (a1) be 'rational,' then, two conditions must hold: i) (c) must be seen as preferable to (b) as of t=0, and ii) (a1) must be seen as preferable to (c) as of time t=-T (at which time c has a value of zero, as explained above). That is, the ordering (of the right hands sides of) eq. 2 > eq. 4 (valued as of t=-T), and eq.4 > eq. 3, is necessary if a binding commitment is to make sense. Please notice that equations 2 and 3 contain exactly the same goods and bads on their right-hand sides. They therefore can only differ in sign if the discount factor for the first period has an exponent k greater than unity, that is, if the discount from the present to the next period is greater than forward discount factors.<4> This is the idea at the heart of Strotz's analysis, expressed here in a simple and transparent fashion which points to a wide variety of applications. My earlier paper (1990) illustrates this machinery with Schelling's vivid example of a woman about to give birth who arranges beforehand for attendants not to give her anesthetic while in labor even if she requests it. Also discussed there are Christmas Club saving, which is very similar to the birth-anesthesia situation; life-cycle savings, which can be explained more neatly and more in consonance with standard theory with this system than with self-control theories<5>; ordinary purchases on credit, most of which (especially minor purchases) are better explained by a kinked (or faster than exponential) discount structure than by credit-market constraints; and a variety of assorted behavior such as binding religious vows, and the pathological killer who sends messages to the police saying "Please catch me". INTERPERSONAL ALLOCATIONS Now we move to the individual's decisions about allocation among that individual and other individuals. Again, such decisions are not the exception, just as intra-personal self-binding decisions in the case of credit purchases are the rule rather than the exception. Rather, every individual who lives in a family and is part of a community makes such allocations as a matter of course. The conceptual framework employed here obviates the age-old question about whether an act of giving by one individual to another should properly be labeled "altruism," or whether instead one is "really" being "selfish" by making oneself feel good. An individual's discount weights vis a vis other individuals may be considered a full description of the individual in this connection, assuming that the individual's behavior corresponds to his/her discounts vis a vis other individuals. In this scheme, there is no place for intentions, and hence there are no false intentions. Revealed preferences, comprise the entire system. Because the reader is likely to wish to see the model in operation as soon as possible, reflections on the meaning of the model are deferred until the Discussion section of the paper. The analysis concentrates on three illustrative issues: (a) the charity pledge, because it illustrates extension of the technical innovation offered here, (b) the bequest in the context of life-cycle savings, because it illustrates generalization of the basic idea, as well as itself being an important issue theoretically, and (c) predictions about the effects of changes in a person's expected lifetime or the set of interpersonal connections. Pledges Charities routinely suggest that donors pledge gifts for future payment if they do not wish to make an immediate donation. And many persons do just that. In 1992, 14,665 Harvard College alumni pledged and paid at a later date, whereas 18,864 paid immediately with check, credit card, or securities (Hokanson, 1993). What explains the pledges? Surely it is not mainly that the pledger is reducing cost through future discounting. The greatest number of the gifts to Harvard are sufficiently small that the difference between the current amounnt and the discounted amount is very small (perhaps even small relative to the time cost of two transactions - pledge and payment, rather than just immediate payment). And if the pledger wishes to reduce the value of the gift by the discount amount, s/he can simply do so by giving a bit less in the present (and the amount less will not much affect the amount of "honor" or satisfaction obtained from the gift). The explanation that follows views the phenomenon as similar to buying on credit or "with no money down," which involves just one individual's persons in several periods, in that both phenomena work with contractual binding. A pledge is also similar to foreswearing anesthesia, and to the case of Ulysses, both of which also use the mechanism of self-binding. Imagine a good of any one of these illustrative types: (a) the harvest from a designated plot in the owner's garden either this year or next year; (b) an opportunity to spend an afternoon viewing a lovely picture in the possession of its owner, for an hour either now or tomorrow at the same time; and (c) a given nominal sum of money (the appropriate discounting is contained within the analysis) either this period or next period. Because the good in question is the same according to its physical description in each period, it is written without distinguishing period subscripts; rather, the enjoyment of it is attached to the period in which it occurs. Now consider three alternative possibilities: I) consumption of such a good by the owner in both periods; II) a gift by the owner so that another individual consumes the good in the present period, and the owner consumes it in the next period; and III) consumption by the owner in the present period, and by the receiver of a gift in the next period. That is, (6) VIi,t=0 = Ui,t=0(G) + dkUi,t=1(G) where U(G) = utility of experience G (7) VIIi,t=0 = et=0Uj,t=0(G) + dkUi,t=1(G). Please notice that e has now been given a period subscript because in the current analysis it may differ between periods. (8) VIIIi,t=0 = Ui,t=0(G) + et=1d?Uj,t=1(G) where the question-mark indicates that the relative size of the discount factor that the decision-maker applies for the other person is not known to us - whether it is larger or smaller than dk. For analytic convenience, let us suppose that the present values to the contemporary self-person of the reference individual i are the same for alternatives I and II. But the contemporary self-person is willing to choose III over I, pledging her/himself to make good on the gift in the next period. That is, (9) VI = VII, VIII > VII, and VIII > VI, The aim of the analysis is to make clear why this preference-and-choice system might exist - that is, why the present person might choose now to consume in the present period rather than to give in the present period, yet choose now to give in the next period rather than consume in the next period - and then to draw from the analysis conclusions that may illuminate other decisions. In order for that alternative III to come about, the owner must bind him/herself to carry it out; without a pledge, alternative III will seem, when the second period arrives, as II seems now, and the gift-transfer alternative will not come about; that is, without a commitment, III's higher present value than the present value of II or I will not be attained. This is analogous to self-binding decisions of the Strotz- Ainslie-Schelling nature analyzed in the previous section. Comparison of III to either II or I shows that either the one-period time-discount factor on j's utility (written d? because it is unknown) is higher than dk for i's utility, or the interpersonal discount et=0 is greater in the present period than et=1 in the next period (as seen in the present), or the differences are such that the multiplicand of the two discount factors d and e is greater in III than in II. That is, either d? > d1+k or et=1 > et=0 or both. I shall now show why this inequality is true. Assume that (10) Ui,t=1(G) = Ui,t=0(G), and Uj,t=1(G) = Uj,t=0(G) (all as assessed when they would take place) Subtract II from I (eq. 7 from eq. 6) to get (as also by definition) (11) Ui,t=0 = et=0Uj,t=0 Now subtracting I from III (eq. 6 from eq. 8), substituting Ui,t=0 for Ui,t=1, and substituting the l.h.s. of eq. 11 for the r.h.s which (after the substitution) appears in the subtraction of III from I, we get (12) d?et=1 > dket=0 If (12) is true, then either d? > d1+k or et=1 > et=0 or both. (Because of the confusing nature of the algebra with subscripts, the steps are presented in detail in the appendix.) To put the matter differently, if we think of the two periods as points on an east-west horizontal time scale and the two persons on a vertical north-south "social" scale, we may think of the present value of a point on that surface as a height above the base. We do not know whether the other-person-next-period point in the height surface is higher than the other two points that enter into the equations because of the slope in the time dimension, or because of the slope in the interpersonal dimension, or both. But such knowledge is not vital, at least for the present analysis. If we were to to assume - as may be reasonable - that e remains the same from period to period, then the driving element in the analysis is the difference in d functions that the decision-maker holds for him/herself and for the other person. Given the empirical evidence on the sharp immediate- period discount for animals and humans, it would not be surprising if the discount from the present to (say) the next period is less sharp for the other person's function than for one's own function, following which the function for oneself might be at the same rate (or at a slower rate) than for the other person. This can account for the greater willingness to (commit to) transfer goods to another person in future periods than in the present. The solicitor of the pledge can read from this analysis a rationale for soliciting a pledge rather than an immediate gift. And the giver of the pledge can read in the analysis the rationale for binding her/herself to the future gift. Hence they agree that a pledge should take place. The analysis is in this respect quite parallel to the self-binding activities described in the first part of the article. That is, the alternative of making the gift in the future has a higher present value than not making it, or than making it now. Please note the role of the formal pledge to increase the extent to which the commitment is binding. Politicians' promises have quite the same rationale. Bequests and Lifetime Savings Assuming (a) diminishing returns, (b) a discount factor less than unity (i.e. a discount rate greater than zero), (c) no risk aversion, (d) no bequest motive, and (e) correct assessment of life expectancy on average, we would expect people to run out of money before death, rather than leaving bequests. But instead we do find bequests, on average. Various plausible explanations have been offered (see e.g. Modigliani, 1988; Kotlikoff, 1988). But an explanation that is conformable with standing theory would seem preferable to an ad hoc theory. The basic present-value eq. 1 suggests that bequests be seen as part of that function, in which case there is no longer reason to think that consumption in the early periods in the life-cycle consumption plan will be at a running-out level. But first we should ask: Why do not people give the bequests as immediate gifts? Uncertainty about the length of one's life, and the possible "need" for consumption funds, i.e. a "precautionary motive," have been suggested. As others have pointed out, an individual can avoid this set of problems by purchasing an annuity. Yet the usage of annuities is rare. The structure of discount factors offers a plausible explanation. The present person first makes an allocation plan which includes a gift to another individual. A planned gift can be of sufficient size to overcome the tilt of consumption toward the present, and make the present period's consumption less than E/n, where E is the lifetime endowment and n the expected number of future periods of life -- as is observed to be the case. The next step is that the present person observes that actually giving the gift now is less attractive than postponing the giving until at least next period, by exactly the same logic as was shown formally for pledges. The process then repeats each period until death, at which point the bequest is realized. The fact that a person makes a will is not evidence that the person intends to hold onto the gift all throughout his/her life; a will is a precaution against death before plans have been completed, among other possibilities. The mode of thinking described here is not distinguishable in behavior from the desire to hold onto assets because of the power they bestow over the prospective recipient. But the explanation offered here is more parsimonious, and is wholly consistent with standard economic theory, which should make it relatively attractive. Effects of Changes in Conditions: The model can help understand, and make predictions about, the allocations that will be made when the claimant periods/persons or their weights are changed exogenously. Here are several examples: 1. If the individual's life expectancy is shortened (lengthened), the allocations to the present and future persons, and to other individuals, will be increased (decreased). If you learn that you may expect to die next month, you are likely to give away some of your books today, and treat family and yourself to a fancy dinner. 2. If there is an increase or decrease in the set of individuals whom you feel a responsibility to assist, you will allocate less to each prior claimant. That is, if your prodigal brother-in-law, whom you despise but feel obligated to help, re-appears in your life, he will get some of your endowment, and others and yourself will get less. This sort of change is a "move through social distance" (a phrase of Ainslie's) akin to the move through temporal distance that we experience in our lives . 3. A change in the expected lifetime or the number of interpersonal connections is likely to change work effort. For example, the model predicts increased work on the part of the parents when the number of children increases, because the wealth of the present person is decreased thereby (since more is being allocated away from the present person). And indeed, there is considerable evidence for this hypothesis in data on hours worked per year by both parents, and moonlighting (see review in J. Simon, 1988). The mechanism is simply that an additional "claimant" in the utility function decreases the amount the earner spends upon him/herself. This diminished wealth implies greater work effort. (Becker's analysis does not imply such behavior, so far as I can see, because the earner's "social income" is increased by the additional child, and there would therefore seem to be no motive for increased work. This model may be seen as focusing on the production of utility whereas the Becker-type model focuses on the "consumption" of utility.) DISCUSSION 1. Viewing the unit of consciousness as composed of continuously extended rings of "interest" or "sympathy" or "empathy" around the core of the self-person, in close analogy to the notion of continuous successive temporal persons, illuminates many phenomena in everyday life. For example, it is not surprising or irrational when an individual endangers or sacrifice her/his life to save the life of her/his child. This way of thinking also mitigates or eliminates the theoretical problem that "In the supply of public goods, far less free-riding actually occurs than traditional theory predicts" (Harrison and Hirschleifer, 1989, p. 201). Hirshleifer defines as follows: "[S]omeone is non-self-interested to the extent that he or she attaches utility to the impact of events upon the bodies or psyches of other parties" (1985, p. 55). And he says that if the economist allows a person's "ends in life [to] include the well-being of others [so that] their interests become his "self-interest'", this becomes "an evasion that robs the concept of self-interest of any distinguishable content" (p. 55). Whether the concept is "robbed" or not I shall not try to say. But I hope this paper shows that such an inclusion does not get in the way of useful analysis, but rather is crucial for some analyses. Perhaps I can best bring out this point by comparing the situation to the individual's various periods of life. The periods are treated separately in personal planning, as indicated by the different discount factors applied to them. And as I show at length in my previous paper (1990), much analysis is facilitated by assuming that the period-persons are different, each of them bearing much the same relationship to the current person as do other individuals. But including the "ends" of those future self-persons in one's current planning does not "rob the concept of self-interest of...content." Again, the sharp line between oneself and others is replaced in this analysis by a continuum. In a related view, John Donne wisely says that each person's death diminishes "me" -- not eliminates, or leaves untouched, but reduces me to some degree. And Adam Smith's earlier quote orders the degree of attachment in the typical case. In the extreme mystic vision a person is one with all humanity -- present, future, and past (though one cannot allocate to the past). This might be the vision of the saint who keeps no worldly goods. Floyd Allport came to much the same view in the study of social psychology. As with the concept of the 'group', we...find that the very notion of a 'thing', instead of being distinct and absolute, is shifting, ambiguous in denotation, misleading as to its singularity, overlapping, relativistic, and blurred. Our understanding of 'group' realities depends, therefore, on our finding some suitable substitute for our present concept of an entity or thing. But since a 'thing' and what it does, that is to say, the events in which it is involved, has long been one of the very pillars of our notion of causality, this realization leaves us baffled as to where to turn (1965, p. 30). Even though, as Hirshleifer puts it, "in the domain of the family no- one can seriously deny that benevolence plays an overwhelming role" (1985, p. 57), analysis using the concept of individual self-interest gets along just fine. This should demonstrate that self-interest need not be defined as narrowly as Hirshleifer demands it be. This is not to say that for some purposes economic analysis using narrow self-interest may not help us sort out what happens within a family, but rather that in most situations ordinary family caring can be acknowledged without causing difficulty. Indeed, most of a main breadwinner's purchasing power is not spent on his/her own bodily and mental needs. Rather, it is spent upon other members of the family, future self-persons and future family members' self- persons, other "gifts", and the government. There is nothing particularly "natural" about an individualistic focus for analysis. Indeed, Hayek talks about "instincts of solidarity and altruism" (1989, p.12), and asserts that one of the problems of development is to discipline such instincts. "[C]ontinued obedience to the command to treat all men as neighbours would have prevented the growth of an extended order" (p. 13). If we were to apply the unmodified, uncurbed, rules of the micro- cosmos (i. e., of the small band or troop, or of, say, our families) to the macro-cosmos (our wider civilization), as our instincts znd sentimental yearnings often make us wish to do, we would destroy it. Yet if we were always to apply the rules of the extended order to our more intimate groups, we would crush them. So we must learn to live in two sorts of worlds at once. (p. 18, italics in original). This implies that if economics wishes to apply its logic to both impersonal markets and personal relationships, it ought to adapt its mode of analysis to the context --either a) markets or b) the current person's allocation -- rather than simply applying the machinery developed for analysing markets to kin-like situations. 2. An observation about the family conveys the flavor of the analysis offered here: Parents spend less on children's clothing than on their own, even after children are old enough not to outgrow clothes. This suggests that the children's "utility" is discounted relative to the parental allocators', though of course a myriad of other explanations of this phenomenon are possible. (Why, in a traditional household, does the wife spend more for clothes than the husband? I think that many other issues, on which I dare not speculate, come into play here.) 3. A nice illustration of the close analogy between (a) other individuals, and (b) the given individual's future persons, is shown by the fact that what economists suppose to be altruistic behavior is often enforced by community norms or even the law, indicating that it is not exceptional. For example, the traditional male breadwinner is legally required to allocate assets to his wife and children even if divorced. And ethics require a variety of contributions of time, energy, and money to the welfare of neighbors and co-workers in need. The commonality between the intertemporal and interpersonal situations also is illuminated by the interventions of the law in the dispositions of an individual's assets over time. Social Security is a leading example; one is required to make provision for one's future self-persons. (It would be interesting to compare what the law requires in private-scheme countries such as Chile.) Another example is unemployment insurance. Also relevant are laws regulating the wearing of seatbelts and motorcycle helmets, under- age drinking, housing codes enforceable with respect to (say) wiring safety even in owner-occupied homes, and involuntary commitment to the hospital (paid for by the person being committed) if a person does not take care of oneself properly, or even if - sin of sins - one is not prudent in guarding one's money. 4. Concerning the principle "Charity begins at home" as a precept: There are advantages to the public at large if individuals focus their charitable attention close to home rather than further from home. This is analogous to a decentralized economic system, which takes advantage of people's extensive knowledge of both nearby resources and needs, and people's ability to monitor the workings of businesses that they observe firsthand either as owners or as consumers. Similarly, charity close to home can be more efficient than charity farther away due to one's ability to know which individuals and organizations have the need for more resources -- that is, which ones are suffering from lack of resources -- as well as which individuals and organizations make effective use of the resources which they receive, rather than wasting them. You can know much more about a family which belongs to your lodge, whose main breadwinner has just died and whose talented child cannot afford violin lessons, than you can about a family a thousand or 10,000 miles away whom you have never met. And you can check that the local family is not spending what they receive on expensive mail solicitations to obtain even more money, most of it going to the professional fundraisers. You cannot easily obtain the same information about Greenpeace or the Hunger Project; even their annual reports are hard to interpret.<6> Does a close-to-home policy mean that richer communities give "too little" aid to poorer communities? Yes, there is such a danger. Assets are not distributed evenly or at random, and the person "closest to the home" of a wealthy person is not likely to be the person in greatest need of charity. This is the rationale underlying Combined Charities, United Way, and their like. But even these omnibus organizations concentrate on local charities. It is an interesting question how far afield such a umbrella charity collector should go, and in what proportions relative to distance. Furthermore, the improvement of communications all over the world means that now it is easier to have firsthand or good secondhand knowledge of needs and capacities much farther away than in the past. The key isssue is not geographic propinquity. Closeness on other dimensions such as religious or ethnic characteristics can fill the same role. And it is easier to get good information about people related to you in such ways than it is about complete strangers. In this fashion it is possible to avoid confining your loyalties and resources to well-off people geographically close to you. Shoveling the next-door neighbor's snow is not efficient, so the pattern has evolved to doing your own sidewalk except in an emergency. 5. Differences in concern about animals that more or less closely resemble us -- gorillas, say, as compared to moles -- suggests an instinctive basis for allocational weights. 6. Paragraph 1 above points to an important distinction between public and private allocation. Hayek's point that in order to develop a modern extended society we must learn to deny our instinctive urges to favor those close to us pertains to public allocation. A moral government treats all individuals alike. But an individual putatively does best by not treating all persons alike, as in charity begins at home. (Bentham's utilitarianism often falls into confusion by failing to make this distinction.) 7. Individuals often recommend or implore other individuals (such as parents urging their children) to make gifts to third persons. This is consistent with the idea that there is a lesser discount in the reference person's mind between the second individual and the third than there is between the reference individual and the second individual, though the connection is not logically tight. (There also is an analogy here to politicians freely disposing of other people's tax moneys in welfare programs.) 8. The framework suggested here could give economics a better image with the public. The individualism model contrasts "greed" and selfishness versus altruism. It invites glorification of the state, which supposedly acts non-selfishly, "idealistically". But in the model described here, private economic maximization seems kindly and loving and cooperative because it takes full account of allocation beyond the legal individual. It does away with the idea of "contributing" to an abstract society in order to feel like a good person, instead includes such acts as part of the standard behavior. 9. It might be fruitful to study some cases in which convicted persons (such as spies) accept longer prison sentences for themselves in exchange for shorter or no prison sentences for spouses; the interpersonal discount factor may be surprisingly small. Such cases would be particularly illuminating because the currency of one's time is not subject to the complication - attendant on money - that one person has more of it than another and therefore has a lower marginal utility for it. And such cases may be quite analogous with a person allocating prison time (or other restriction on freedom such as a commitment to work) among present and future time periods, e. g., I'll work a month for you next year if you'll free me from a week's work now so I can be with my beloved, or finish my book. 10. It might be fruitful to systematically compare the probabilities of death of a person who might save the life of another, and of the savee, in various relationships - father and son, lifeguard and anonymous swimmer, passerby and anonymous swimmer, and so on. 11. One wonders: Are there normative extensions to this model? The answer is negative, I believe. It may be that explicit consideration of the structure of discount factors across individuals and through time may improve the consistency of allocation, the way explicit financial planning may help a person attain one's temporal allocation goals. But anything beyond that would require bringing additional constraints into the model which have not yet been required by the discussion until now. 12. The interpretation of human behavior that is involved in the analysis here matters for both behavior and feeling. First note Hutcheson's analysis of the cause of giving: ... whence the conjunction of interest between the parent and child? Do the child's sensations give pleasure or pain to the parent? Is the parent hungry, thirsty, sick, when his children are so? No; but his naturally implanted desire of their good, and aversion to their misery, makes him be affected with joy or sorrow from their pleasures or pains. This desire then is antecedent to the conjunction of interest, and the cause of it, not the effect: it then must be disinterested. (Hutcheson, 1725/1738/1991, p. 279) Then he analyses it philosophically: Is there then a natural disposition in every man to love his like, to wish well not only to his individual self, but to any other like rational or sensitive being? and this disposition strongest, where there is the greatest likeness in the more noble qualities? If all this is called by the name self-love; be it so: (Hutcheson, 1725/1738/1991, p. 279) But the concept of altruism as self-interest is not just a matter of tautology, as Hutcheson suggests it is; it also affects the outlook of people who come to believe it, as this quotation from the autobiography of a Japanese young man shows: I finally put my doubts to Matsue Yaichiro. I thought he was probably the most sincere of the students at the academy. I asked him this question: "I recognize your sincerity. When you speak of devoting your life to the country and to the service of our people, do you do this without any thought of self at all, without any idea of bringing honor to your own name? I wish you would reveal your true feelings to me." Matsue laughed aloud and said, "Doesn't everybody think about his own reputation? Isn't that why people do what they do? My reputation means everything to me." That was his reply. On hearing it I was startled: was it that way even with him? "Well," I asked, "what about Iichiro-san?" He was emphatic in his answer: "Why, Iichiro-san is even more concerned with fame than we are." When he saw how disappointed I was, he tried to reassure me. "It's best not to worry too much about unnecessary matters like this," he said. "A man is born in the world, achieves something, and builds a fine reputation; then he dies. That is enough. You shouldn't worry any further." But these reassurances didn't console me in the slightest. I thought to myself that it was elegant and splendid to die for one's country and for one's people. But if you did so just to build up your own fame, wasn't it only another form of egoism? So-called "idealists" of this sort seemed to me no better than butchers who labeled dog meat as lamb. In fact, if this was really true of Iichiro-san, shouldn't he be exposed too? As a result of all this I became dogmatic and arrogant. I despised not only my fellow students, but even my teacher. And then, by extension, all the great heroes, the men of high purpose of former and present times: they too became objects of my contempt. After a while I began to examine myself as well. ... If I were to despise my fellow students, I had no choice but to go on to despise myself. Right. I too was despicable. As a result I was without hope, deep in melancholy, and unable to sleep or eat. (Toten, 1982, pp. 14-15.) This idea can lead to people reducing the coefficients on the social relationships in the belief that there is no moral basis for having relatively high coefficients of giving to others; this might explain the attitudes of economists, so different than other groups in this respect (though philosophers were not studied), as reported by Marwell and Ames (1981). SUMMARY Gifts and bequests have seemed anomalous in economic theory. The paper offers a framework within which such allocations cause no more difficulty than does intertemporal allocation of lifetime resources within a given individual's lifetime, which economists routinely deal with theoretically. The essence of the matter is to place on the same footing the allocation of the available resources for consumption among (a) the current person, (b) future self-persons that are legally and physically the same individual who is allocating, and (c) other individuals at present and in the future. That is, instead of a one-dimensional point for the maximizing unit, or even the two-dimensional individual who allocates intertemporally, this model envisages a three-dimensional surface, the interpersonal "distance" dimension replacing the concept of altruism. The key intellectual obstacle is that economists conventionally take the legal-physical individual throughout her/his lifetime, or just a disconnected single chunk of that life, as the entity of analysis. A key element in both purely intertemporal allocations, and in (at least some) mixed intertemporal-interpersonal allocations, is the assumption (first used by Strotz in this connection) that the allocational discount factor between the current conscious "person" and future "self- persons" within the same individual is greater than the discount factor between equal-length forward periods within the same individual. A related element is that the discount also is greater between the current conscious person and other individuals than among other individuals at different psychic distances from the current self-person. Applying a conventional present-value framework to evaluate utility, as seen at various decision- making moments, then makes sense of the phenomena under discussion. In comparison to analyses which require additional assumptions about individual psychology, this mode of analysis has the advantage that it sticks strictly to the conventional concepts of economic analysis rather than requiring concepts which are not conformable with standard theory. Also, it does not need to distinguish between "self-forced" plans and much ordinary economic behavior, and it thereby points up that "self-control" situations are not abnormal. The paper views temptation, regret, sacrifice and similar phenomena as cases of externalities, and it uses conventional theory to deal with them. This conceptual framework obviates the age-old question about whether an act of giving by one individual to another should properly be labeled "altruism", or whether instead one is "really" being "selfish" by making oneself feel good. An individual's discount weights vis a vis other individuals may be considered a full description of the individual in this connection, assuming that the individual's behavior corresponds to his/her stated discounts vis a vis other individuals. In this scheme, there is no place for intentions, and hence there are no false intentions. 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James Coleman and Gary Becker, co-organizers of the continuing seminar, were most helpful, and other participants also made many useful comments. I appreciate valuable criticisms, ideas, and citations from George Ainslie, Dennis Mueller, and two anonymous readers of the paper. **ENDNOTES** <1>: I agree with Mueller that much such behavior can best be understood by seeing it as driven rather than as chosen, though I would guess that much of it is hard-wired genetically in humans as it is in animals, rather than being entirely learned. I concur with the viewpoint expressed by Frances Hutcheson in point 12 in the DISCUSSION section. <2>: This section draws upon Simon (1990). Anyone familiar with that piece should skip the next two sections to the section on INTERPERSONAL ALLOCATIONS. <3>: Smith continues: This sympathy, too, and the affections which are founded on it, are by nature more strongly directed towards his children than towards his parents... The earliest friendships, the friendships which are naturally contracted when the heart is most susceptible of that feeling, are those among brothers and sisters. Their good agreement, while they remain in the same family, is necessary for its tranquillity and happiness. They are capable of giving more pleasure or pain to one another than to the greater part of other people... The children of brothers and sisters are naturally connected by the friendship which, after separating into different families, continues to take place between their parents. Their good agreement improves the enjoyment of that friendship--their discord would disturb it. As they seldom live in the same family, however, though of more importance to one another than to the greater part of other people, they are of much less than brothers and sisters. As their mutual sympathy is less necessary, so it is less habitual, and, therefore, proportionably weaker. The children of cousins, being still less connected, are of still less importance to one another; and the affection gradually diminishes as the relation grows more and more remote... ...A father is apt to be less attached to a child who, by some accident, has been separated from him in its infancy, and who does not return to him till it is grown up to manhood. Among well-disposed people the necessity or conveniency of mutual accommodation very frequently produces a friendship not unlike that which takes place among those who are born to live in the same family. Colleagues in office, partners in trade, call one another brothers, and frequently feel towards one another as if they really were so... Even the trifling circumstance of living in the same neighbourhood has some effect of the same kind. We respect the face of a man whom we see every day, provided he has never offended us... The same principles that direct the order in which individuals are recommended to our beneficence, direct that likewise in which societies are recommended to it... The state or sovereignty in which we have been born and educated, and under the protection of which we continue to live, is, in ordinary cases, the greatest society upon whose happiness or misery our good or bad conduct can have much influence. It is accordingly by nature most strongly recommended to us... Every independent state is divided into many different orders and societies, each of which has its own particular powers, privileges, and immunities. Every individual is naturally more attached to his own particular order or society than to any other. His own interest, his own vanity, the interest and vanity of many of his friends and companions, are commonly a good deal connected with it: he is ambitious to extend its privileges and immunities--he is zealous to defend them against the encroachments of every other order or society (Smith, 1759/1976, pp. 359, 360, 361, 362, 366, 371, 372, 376). <4>: I hold no brief for any particular shape of discount function - including the exponential - for any particular set of periods in the future. The kinked shape used here is purely for convenience in discrete analysis. I have been persuaded by the writings of Herrnstein (1981) and Ainslie and Haendel (1983) that the hyperbolic function makes the most sense for many animal and human experiments, and that the "matching law"... I am even willing to agree that negative time discounting fits some facts, e. g. "Deliver it tomorrow instead of today, because I can't find a place to put it today" or "I'll enjoy it more after I finish the day's work", and even across persons, "You take it; I've gotten too old to use it" or "It's more fun to watch you do it than to try to do it myself". Securities markets do give us some general ideas about time-discount factors of one sort, but we need not assume them to hold in all circumstances of life. (See Loewenstein and Elster for an authoritative collection of writings on the subject of the discount factor in relationship to individuals' decisions. Willingness to admit a wide variation of time discounts makes easier the analogy to relationship discounts. I (and Adam Smith, almost surely) do not assume a fixed relationship between kinship or geography and degree of sympathy, but assume instead that there are tendencies in those respects, and that sympathy is not independent of kinship or other measures of social distance. And there may even be negative sympathies for some relationships - e. g. a parent torturing a child, as there may be negative time- discounts in some cases. But this need not fall into circularity by defining social distance by degree of exhibited sympathy as long as objective factors have some predictive power. <5>: Deily and Reed (1993) offer an interesting theory that takes explicit account of the stock of willpower and the cost of using it. But that theory seems less applicable to the important everyday problems of saving, credit, charity pledges, and the like than to such behavior as eating and drinking. <6>: But you can be sure that many such charities transfer much less than half of what they receive to the supposed objects of charity; the occasional exposes of these frauds are sickening. page 4 /article9 interper/February 10, 1995