This paper considers several alternative explanations for the fact that households with higher levels of lifetime income (‘the rich’) have higher lifetime saving rates (Dynan, Skinner, and Zeldes 1996; Lillard and Karoly 1997). The paper argues that the saving behavior of the richest households cannot be explained by models in which the only purpose of wealth accumulation is to ﬁnance future consumption, either their own or that of heirs. The paper concludes that the simplest model that explains the relevant facts is one in which either consumers regard the accumulation of wealth as an end in itself, or unspent wealth yields a ﬂow of services (such as power or social status) which have the same practical eﬀect on behavior as if wealth were intrinsically desirable.

This paper was published in the volume Does Atlas Shrug? The Economic Consequences of Taxing the Rich, Harvard University Press, 2000, Edited by Joel B. Slemrod:

I am indebted to Sidney Carroll, Elizabeth B. Carroll, and Elizabeth I. Carroll for many of the insights in this paper. Any errors are my own.

1 Introduction

The saving behavior of the wealthy has received remarkably little academic attention in the past twenty years or so. This is probably largely attributable to a relative lack of good data: The Survey of Consumer Finances is virtually the only publicly available source of detailed data on wealthy households, and even the SCF has only a few hundred really wealthy households in each triennial wave. Despite recent neglect, the topic is an important one for scholars of saving behavior, for at least two reasons. First, wealthy households should provide a powerful means of testing whether the standard model of consumer behavior, the Life Cycle/Permanent Income Hypothesis, is adequate as a universal model of saving and consumption. This is an application of the general scientiﬁc principle that models should be tested under extreme conditions; if they do not hold up, a new model (or an extended version of the old one) is called for. The second reason for studying the wealthy is that they account for a large share of aggregate wealth. In fact, some understanding of the saving behavior of the wealthy is probably indispensable to any credible attempt to account for the magnitude of aggregate wealth.

Although the primary source of evidence in this paper will be the four Surveys of Consumer Finances conducted in 1983, 1989, 1992, and 1995, the inevitable limitations of those data will be apparent. The paper therefore also relies to a considerable extent on unorthodox kinds of evidence, ranging from information in the annual Forbes 400 tabulation of the richest American households, to quotations from and about the very rich, to the results of a “focus group” meeting with a set of wealthy individuals who were directly asked their reasons for saving.

The paper begins by considering whether the standard model of household consumption and saving decisions, the Life Cycle model, provides an adequate description of the behavior of wealthy households. I argue that the Life Cycle model, or at least the traditional incarnation in which the decision-maker saves mainly to ﬁnance his own future consumption, cannot simultaneously explain both the behavior of the median household and the behavior in the upper tail of the wealth distribution. The next section of the paper considers whether a “Dynastic” model, in which the wealthy save mainly for the beneﬁt of their heirs, performs better. While the Dynastic model can explain some observations, and probably does roughly apply to some households, I argue that it still does not explain some important facts about the saving behavior of the wealthy. Furthermore, the Dynastic model conﬂicts with the self-reported motives for saving that many wealthy people voice. Finally, I consider a model in which the wealthy save because, either directly or indirectly, they obtain greater pleasure from possessing an extra dollar of wealth than they would get from an extra dollar of consumption. Following Max Weber 1905 as interpreted by Zou 1994 and Bakshi and Chen 1996, I call this the “Capitalist Spirit” model. I argue that a direct wealth accumulation motive is indispensable in explaining at least some of the observed behavior of the very wealthy.

2 Can the Life Cycle Model Explain the Behavior of the Wealthy?

A provocative recent paper by Hubbard, Skinner, and Zeldes 1994 (henceforth, HSZ) argues that an expanded version of the Life Cycle model in which uncertainty is modelled realistically can generate patterns of wealth accumulation that are roughly consistent with average data from household surveys, and amounts of aggregate wealth that are similar to observed aggregate household wealth in the U.S. If such a model really did produce roughly correct predictions for household wealth holdings, there would be little need to study the very wealthy in detail, since they would merely be scaled-up versions of everyone else.

Behind the scenes of the HSZ model, however, all is not well. While it is true that the model can predict approximately correct average values for wealth or the wealth-to-income ratio, it achieves this average by making large but oﬀsetting errors in predicting the underlying distribution of wealth. Speciﬁcally, the HSZ model predicts, at most ages, that the household with median wealth actually holds substantially more wealth than the median household in SCF data holds and, at the same time, the model greatly underpredicts the amount of wealth held by the households at the top of the wealth distribution.

Figure 1 presents data on the age proﬁle of the ratio of total wealth to permanent income for the median household in a stochastic Life Cycle model very similar to that of Hubbard, Skinner, and Zeldes.² The ﬁgure also presents data on the age proﬁle of the actual median household’s wealth/permanent income ratio from the 1992 and 1995 Surveys of Consumer Finances (dashing lines) during the working lifetime.³ The ﬁgures make clear that the HSZ model substantially overpredicts the wealth of the median household in the SCF data.⁴

How, then, can the HSZ model produce overall averages that resemble the means of the SCF data? The answer lies in the wealth holdings of the top few percent of the distribution. The solid line in ﬁgure 2 shows, for each age group, the average ratio of wealth to permanent income for households at the 99th percentile (by age) in the HSZ model. The dashing line shows the corresponding calculation using the actual data from the 1992 and 1995 SCFs. Clearly, the richest SCF households own enormously more wealth, in relation to their permanent income, than the richest consumers in the HSZ model.

Taken together, Figures 1 and 2 show that the stochastic Life Cycle model under HSZ parameter values matches the aggregate and average data only because it makes two oﬀsetting errors: overestimating the wealth of the typical household and underestimating the wealth of the richest households.

These simulations indicate that even the extended Life Cycle model misses some crucial features of household behavior. However, the model’s overprediction of the wealth of the median household is easily rectiﬁed; Carroll 1992, 1997 argues that the model captures the main features of the behavior of the median household very well if consumers are assumed to be slightly more impatient than HSZ assume, and if the income process is modiﬁed to include the beneﬁts of aggregate productivity growth (HSZ assume that households expect, and experience, zero aggregate productivity growth over their lifetimes).

If assuming that consumers are somewhat more impatient can make the stochastic Life Cycle model match the behavior of the median household, a natural question is whether assuming that consumers are somewhat more patient can make the model match the richest households. If so, then it might be possible to argue that the only modiﬁcation needed to make the stochastic Life Cycle model match the facts is to assume that consumers with higher lifetime incomes are also more patient. Figure 3 examines this possibility by showing the pattern of wealth over the working life of consumers who are the same as the consumers in the baseline HSZ model except that they have a time preference rate of zero rather than the baseline HSZ time preference rate of 3 percent annually. While the age/wealth proﬁle is certainly higher than in the standard HSZ model, it remains far below the proﬁle for the consumers in the top 1 percent of the SCF data. Plausible modiﬁcations of other parameter values also fail to raise the model proﬁle to the level found in the data. In other words, the richest households are saving more than can be justiﬁed even in a version of the Life Cycle model that allows for very patient consumers with a strong precautionary saving motive.

The evidence presented thus far has concerned the saving behavior and wealth proﬁles of consumers during the working period of life. The Life Cycle model has another set of testable implications for behavior in the latter stages of life, after retirement. In particular, according to the standard Life Cycle model, even patient consumers want to spend all of their wealth before they die. Of course, an uncertain date of death makes this diﬃcult to achieve on one’s own. However, there is a ﬁnancial instrument which accomplishes exactly the goal implied by the model: annuities. One test of the rough accuracy of the basic Life Cycle model is therefore whether the wealth of retired households is largely annuitized.

Carrying out such a test requires some methodology for calculating annuity wealth. I assume that the annuity is ﬁxed in real terms (primarily because the largest form of annuity income, Social Security, is inﬂation-adjusted). I assume a real interest rate, and use the mortality tables from HSZ to construct the expected present discounted value of a one-dollar per year annuity as:

where $Λi$ is the probability of surviving from year $i − 1$ to year $i$ and $R = 1 + r$ is the gross interest rate (I assume $R = 1.03$ but results would be similar for other plausible interest rates). The wealth value of the observed annuity income YANN at age a is then $Γ a$ YANN $a$ .

Using this method, and including home equity among annuitized wealth, the mean household over age 65 has approximately 55 percent of their wealth in annuitized form. However, among the richest 1 percent of households, the mean annuitization rate is only 10 percent.

This evidence on annuitization is suggestive, but hardly conclusive. Annuity markets are likely far from perfect; as in other insurance markets, adverse selection may distort the market suﬃciently to make inference hazardous. Furthermore, annuities are the perfect ﬁnancial vehicle to counter only one kind of risk, mortality risk. If other kinds of risk are important, it is no longer obvious that even selﬁsh Life Cycle consumers should annuitize most or all of their wealth. For example, if there is a small probability of a very expensive medical problem, it may be important to have access to a large chunk of nonannuitized wealth in order to pay the bills (assuming that no health insurance will fully cover every possible medical catastrophe or every potentially desirable experimental treatment).

An extreme assumption would be that annuity markets are so imperfect that, for practical purposes, we can assume that annuities cannot be purchased. This assumption would obviously vitiate the argument that the failure of the wealthy to annuitize their wealth proves that they are not Life Cyclers. However, in the absence of annuities the Life Cycle model has other implications. In particular, it implies that selﬁsh Life Cycle consumers, even patient ones, will eventually begin running down their wealth as they age. Figure 4 shows that by age 80 or so the HSZ model implies that consumers should be dissaving at a fairly substantial pace (the simulations here follow HSZ’s assumptions about mortality rates, which they derived from actuarial data, with the modiﬁcation that they assume that death occurs for certain at age 100 if it hasn’t happened yet). However, Figure 5 shows the actual average age proﬁle of wealth across the four SCF surveys. Although wealth accumulation slows, or perhaps halts, around age 65, there is no noticeable decumulation of assets for consumers in the top percentile of the wealth distribution.⁵

Of course, nothing in economics requires us to believe that the only purpose of saving is to ﬁnance one’s own future consumption; that is merely a hypothesis of the basic Life Cycle model. One natural idea is that the wealthy do not run down their assets because they want to leave bequests to their children. This thought leads to the next model.

3 The Dynastic Model

In the 1995 issue of the annual Forbes 400 count of the richest Americans, there are at least 11 households containing descendants of Pierre du Pont (died 1817). This might seem to be compelling evidence that at least some of the very rich have a powerful bequest motive. On the other hand, apparently no members of the 400 trace their wealth to Robert Morris, reputed to be the wealthiest man in America at the time of the Revolutionary War. And Andrew Carnegie gave away over 90 percent of his fortune before he died. Furthermore, the fact that large bequests to children do occur does not prove that provision of such bequests is the primary motivation for accumulation.

This section of the paper considers a particular model of bequests proposed by Barro 1974. The dynast alive at time $t$ is assumed to solve the intertemporal maximization problem:

where $Ct$ corresponds to the lifetime consumption spending of the generation living at time $t$ , $W$ is the dynasty’s wealth, $Y$ is the (noncapital) income earned by that generation, $R$ is the intergenerational interest rate, and $β$ is the discount factor. The implications of this equation for macroeconomics spawned the large literature on Ricardian equivalence in the 1970s and 1980s. More recently, Altonji, Hayashi and Kotlikoﬀ 1992 have tested the Dynastic model with household-level data from the Panel Study of Income Dynamics and rejected its strong implication that only dynastic resources should matter for any individual family’s consumption. The typical PSID family, however, is not particularly wealthy, so those results do not necessarily imply that the Dynastic model is a poor one for the wealthiest families.

Although intuition suggests that the dynastic model might be interchangable with other models in which leaving a bequest yields utility, in fact the model has distinctive implications, such as Ricardian equivalence, that need not follow from other models of bequests. As a result, the economic literature has drawn a distinction between Dynastic models like the one speciﬁed in equation 3 and “Joy of Giving” models in which the bequest yields utility directly. For example, the Dynastic model implies that the size of the bequest should be a function of the ratio of the parent’s lifetime income and the child’s lifetime income; that parents should give larger bequests to poorer children; and that childless wealthy people should leave no bequests. All of these implications of the Dynastic model have been tested in population-representative datasets and none has received consistent empirical support. This section provides evidence that the Dynastic model is also a poor description of the behavior of the richest households.

To begin with some very informal evidence, Kennickell, Starr-McCluer, and Sunden 1995 report some results from a “focus group” session on saving motivations that was convened as part of the preliminary work in designing the questions for the 1995 SCF.⁶ The eight members of the group were all wealthy individuals,⁷ mostly in their 50s. Participants were asked “Thinking about your reasons for saving, what sorts of reasons are most important to you?” In the entire course of a three hour conversation of saving behavior, however, providing a bequest was not mentioned once as a reason for saving.⁸

A group of eight individuals is obviously too small a sample to convincingly demonstrate the general absence of a bequest motive among the wealthy. Somewhat more persuasive evidence is provided in the results of survey questions on the 1992 SCF. Respondents were asked to list their ﬁve most important reasons for saving. As shown in Table 1, only three percent of the general population, and two percent of the wealthy households, indicated that providing an inheritance was the most important reason to save. ⁹ Furthermore, only 5 percent of the total population and 4 percent of the wealthy households indicated that providing an inheritance was among their top 5 reasons for saving. (The diﬀerences between the wealthy households and the general population are not statistically signiﬁcant here.)

Another obvious test of the model is to see whether the childless elderly tend to dissave more than those with children. This hypothesis has been tested using population-representative data; Hurd 1986 found that in the population as a whole, there is no tendency for elderly with children to decumulate faster than those without. Unfortunately, even when the data from the four SCFs are combined, the number of childless, elderly, wealthy households is too small to permit reliable estimation of age proﬁles of wealth (only about ten percent of elderly couples are childless).

Another option is to consider what childless elderly people say about their saving and spending behavior. Respondents to the 1992 and 1995 SCFs were asked whether their spending was greater than, equal to, or less than their income over the past year, and how spending usually compared with income. The results are presented in Table 2.¹⁰ The childless elderly were less likely to say that they dissave than those with children, by this crude measure, either as a general rule or in the current year in particular. Of course, it is possible that some of the “spending” of the elderly with children consists of inter vivos transfers to those children. The real problem for the Life Cycle model is the testimony of the childless, wealthy elderly, essentially none of whom say that their spending exceeds their income. This is all the more impressive given the comparatively small fraction of their income that is annuitized.

Given the paucity of publicly available data on the very wealthy, it is not surprising that the economic literature contains almost no empirical studies that shed any light on the behavior of the childless wealthy elderly (although there have been several studies that have examined the behavior of non-wealthy childless elderly households, and have found that they do not dissave; see, e.g., Menchik and David 1983 and the references therein). I was able to ﬁnd only one study that contains even tangential information on the subject, a paper by Auten and Joulfaian 1996 which uses a proprietary dataset compiled by the Internal Revenue Service on 1982 decedents who paid estate taxes. From ﬁgures in their Table 1, p. 62 it is possible to calculate that the mean wealth of the childless decedents was virtually identical to that of those with children - hardly what would be expected if those with children had a powerful dynastic saving motive which the childless (presumably) do not share.¹¹ Furthermore, those with children actually contributed slightly more to charity during their lifetimes than the childless. Again, a dynastic motive would suggest the opposite. Finally, Auten and Joulfaian found no signiﬁcant eﬀect of children’s income on the size of charitable bequests. This ﬁnding is consistent with evidence by Wilhelm 1996 who found little support for the altruism model’s implication that the size of bequests in families with more than one child should be related to the relative lifetime income of the children. Instead, Wilhelm found roughly equal bequests in about 80 percent of bequests.

4 The Capitalist Spirit

This section presents a model in which wealth enters consumers’ utility functions directly, and argues that such a model is both consistent with the available data on the saving behavior of the wealthy and plausible on grounds other than its consistency with these facts. Zou 1994 and Bakshi and Chen 1996 have recently noted that Max Weber 1905 long ago argued that the pursuit of wealth for its own sake was the ‘spirit of capitalism,’ and so I will call this the ‘Capitalist Spirit’ model.

4.1 The Model

Consider a consumer with lifetime wealth $wT$ . Suppose the utility function for lifetime consumption is a standard CRRA utility function, $1−ρ u (ct) = c1−ρ-$ , and suppose the consumer also obtains utility from wealth in a modiﬁed Stone-Geary form,

The problem can be solved analytically if we choose $ρ = 2$ and $α = 1$ . If we set $γ = 1$ the solution is

The essential insights from this model carry over when the model is extended to many periods and when labor and capital income are incorporated: consumers with permanent income below a certain threshhold will behave like standard Life Cyle consumers and will try to spend all their assets before death, while consumers with permanent incomes above the threshhold will save at ever increasing rates as lifetime income rises.

The idea that bequests (charitable or otherwise) are insigniﬁcant for most of the population, but become increasingly important in the upper reaches of the lifetime income distribution, has been informally expressed by several previous authors. Indeed, Modigliani 1986 himself has argued that, to the extent that bequests must be included in the Life Cycle framework, they should be incorporated in precisely this “luxury good” manner. There is also a growing body of empirical evidence in support of the proposition. Dynan, Skinner, and Zeldes 1996 examine data from several micro datasets and ﬁnd consistent and strong evidence that households with higher lifetime income leave larger bequests; Lillard and Karoly 1997 ﬁnd similar results.

In theoretical terms, the value added in this paper relative to the previous literature is simply the proposal of a speciﬁc and simple functional form for the consumer’s utility function which captures the informal idea that rich people save more in a way that is at least roughly consistent with the empirical evidence marshalled above. But such consistency may not be a high enough standard.

4.2 Informal Evidence

The essence of Joan Robinson’s complaint about utility theory was that it is possible to construct a utility function to justify any conceivable behavior: Just assume that the behavior in question yields more utility than its alternatives. Any postulated utility function, or proposed modiﬁcation to a standard utility function, should therefore be defensible on grounds other than its ability to match the facts it was created to match. This section argues, using a variety of informal evidence, that most qualitative descriptions of the behavior of the wealthy, both by the wealthy themselves and by outside observers, can be interpreted at a fundamental level as implying that wealthy people derive utility either directly from the ownership of wealth or indirectly, either from the activities that lead to wealth accumulation or from a ﬂow of services that is closely tied to the ownership of that wealth.

The ﬁrst important argument about the plausibility of the Capitalist Spirit model concerns the assumption that the marginal utility of consumption decreases sharply with the level of consumption. What matters critically here is really the assumption that there is an alternative way to employ wealth whose marginal utility decreases more slowly than that of consumption (and hence will be a luxury good relative to consumption). It is important to recall that the kind of consumption treated in the model is for strictly nondurable goods and services. Carroll and Inhaber 1992 note that “luxury” goods that are generally associated with the wealthy such as art, estates, jewelry – even sports teams – are almost all assets. Indeed, beyond a certain level of wealth it becomes diﬃcult to imagine how one could spend even the earnings on one’s wealth on nondurable goods and services for personal enjoyment. For example, recent press accounts have estimated Bill Gates’s net worth at $40 billion. Assuming a ten percent annual rate of return, Gates would have to spend $4 billion a year, or over $10 million a day, on nondurable goods and services simply to avoid further accumulation.

The proposition that the marginal utility of consumption approaches zero as the level of consumption rises is also lent credence by statements of wealthy people themselves. Andrew Carnegie, Cornelius Vanderbilt, and other fabulously wealthy people refer to their “surplus” wealth, and of determining when one has “enough” wealth. H.L. Hunt, then the richest man in the world, once said that “for practical purposes, someone who has $200,000 a year is as well oﬀ as I am.” Similar statements (appropriately adjusted for inﬂation) have been attributed to William Henry Vanderbilt and John Jacob Astor, two 19th century plutocrats.

One of the appealing features of the idea that rich people eventually reach near-satiation in their consumption of nondurables is that this means one need not assume a towering and obsessive greed lies behind their continuing accumulation. If ‘greed’ is deﬁned as a desire to possess wealth for its own sake, even a modest amount of greed will suﬃce, so long as greed does not diminish with wealth as fast as the marginal utility diminishes with consumption. Or, to put the idea more concretely, if ownership of extra houses, yachts, artwork, or, for that matter, corporations has even a modest intrinsic appeal, eventually that appeal is likely to exceed waning lure of an extra dollar of nondurable consumption. Of course, this is merely another way of saying that ownership of these kinds of wealth yields utility directly, as the basic Capitalist Spirit model assumes.

And, among the 19th century plutocrats, according to historian Frederic Cople Jaher 1980,

To the extent that these quotations express the general truth about the motivations of the wealthy, the Capitalist Spirit model can be said to apply directly. However, the view that all wealthy people are motivated solely by a love of wealth for its own sake is surely extreme. A variety of other plausible, and apparently very diﬀerent, motivations are commonly proposed, ranging from job satisfaction to status-seeking to philanthropic ambitions to power-lust. The remainder of this section argues that, from a modelling standpoint, these other common ideas–diﬀerent though they may be from a psychological perspective–are essentially indistinguishable from each other and from the basic Capitalist Spirit model in terms of their implications for individual behavior. The argument, therefore, is that if any of these several proposed motivations is correct, the Capitalist Spirit model constitutes an appropriate mathematical model of the behavior of the wealthy.

Perhaps the most obvious example of a psychologically very diﬀerent model which would be behaviorally indistinguishable from the wealth-in-the-utility-function model is the idea that the wealthy enjoy doing their jobs well, and that they view the accumulation of wealth as the principal measure of job performance. This idea appears frequently both in the statements of the wealthy themselves and in commentary by others on the behavior of the wealthy. Two particularly direct statements are:

A closely related idea is suggested by the work of Robert Frank 1985, who has argued that an intrinsic component of human nature is a tendency to judge oneself by comparison with others. If for some wealthy people wealth is the metric of comparison, the utility function should contain not the absolute level of their wealth but some function of the relationship of their wealth to that of others. Bakshi and Chen 1996, Cole, Mailath, and Postlewaite 1992, and Zou 1994 have also argued that wealth matters because it is an index of social status.¹² For practical purposes of analysis of household-level data, however, either of these ideas is virtually indistinguishable from the proposition that wealth enters the utility function directly, and both ideas should produce essentially identical results in a model of saving (although they might have diﬀerent implications for optimal tax policy; see the discussion below and the paper by Frank in this volume).¹³

It is also possible that wealthy people continue accumulating because greater wealth yields some other beneﬁt that is more diﬃcult to measure, such as power. In particular, the view that wealth brings power is commonplace among both the wealthy themselves and observers of the wealthy. (The idea that power is desirable appears to be taken for granted.)

This last quotation raises a ﬁnal idea that crops up frequently in the statements of the wealthy themselves: that the purpose of accumulating wealth is ultimately to enable the wealthy person to pursue philanthropic activities, or to establish institutions to carry out such activities. While such an evidently self-serving interpretation should be subject to considerable skepticism, there are many prominent examples of philanthropy that bear out the proposition. The Ford Foundation, the Rockefeller Foundation, Carnegie-Mellon University, Duke University, Johns Hopkins University, the Getty museum, and a host of other prominent institutions owe either their existence or a substantial part of their endowments to the muniﬁcence of wealthy individuals (often, although not always, manifested through bequests). Morally, socially, and psychologically this motivation for wealth accumulation is very diﬀerent from pure greed. However, if more wealth allows one to establish a larger foundation or endow more institutions, the implications for saving behavior are again virtually indistinguishable from the idea that wealth enters the utility function directly.

5 Death and Taxes

Assuming that the Capitalist Spirit model provides a roughly correct description of the behavior of wealthy households, a natural question to ask is what the model implies about the relationship between accumulation behavior and taxes. ¹⁴ Returning to the parameterized version of the model in which $ρ = 2$ and $α = γ = 1$ , if bequests (or wealth) are taxed at rate $τ$ then the equation for optimal consumption becomes:

Figure 7 shows the eﬀect on consumption if bequest taxes are increased from 40 percent to 80 percent. Consider ﬁrst the curve labelled $τ = .4$ , which shows the optimal amount of consumption for consumers facing a 40 percent bequest tax if bequests are not constrained to be positive. The actual consumption function, of course, is the minimum of the 45 degree line and this curve. The point of intersection of this curve and the 45 degree line, labelled $ω1$ , reveals the level of lifetime wealth at which consumers begin to leave positive bequests.

When the bequest tax is raised to 80 percent, the amount of consumption shifts up, as indicated in the curve labelled $τ = .8$ . The point at which consumers begin leaving bequests, $ω2$ , is substantially higher than when the tax rate was 40 percent.

Hence, it is useful to think of the eﬀects of raising the bequest tax by considering three categories of consumers. The ﬁrst are those with lifetime wealth less than $ω1$ . They leave bequests under neither tax regime, so their behavior is unaﬀected by the tax increase. The second region is those consumers with lifetime wealth between $ω1$ and $ω2$ . These are the consumers who would leave bequests if the bequest tax were only 40 percent, but prefer to consume all of their lifetime wealth when the bequest tax rises. Finally, consumers with lifetime wealth greater than $ω2$ will leave bequests even when the bequest tax is 80 percent. However, at any level of lifetime wealth the size of the bequests they leave is reduced by an amount equal to the gap between the two consumption curves. It is simple to show that as lifetime wealth goes to inﬁnity the fraction of lifetime wealth bequeathed approaches 100 percent even with the higher bequest taxes. This is the region of the model presumably corresponds best to the circumstances of fabulously wealthy people like Bill Gates.

Because the eﬀect of taxes on consumption depends on the distribution of consumers across the diﬀerent levels of lifetime income, the aggregate eﬀect of bequest taxes in this model is impossible to judge in the absence of evidence (or assumptions) about the distribution of lifetime income (and information about the parameters of the model). If most bequests come from people with $ω1 < wT < ω2$ , then an increase in the bequest tax could reduce bequests almost to nothing. If, on the other hand, most bequeathed wealth comes from consumers with very large amounts of lifetime income, increasing the bequest tax might have very little eﬀect on either consumption or (pre-tax) bequests.

In principle, it should be possible to tease out estimates of the relevant parameter values from available data on wealth, consumption and income, using methods like those employed in an impressive recent paper by Gourinchas and Parker 2002. Those authors assume a “residual value function” that characterizes the utility experienced during the last part of life that is mathematically very similar to the “bequest utility” function postulated in the model here. Gourinchas and Parker assume that the coeﬃcient of relative risk aversion for the residual value function is the same as for the period utility function, and they do not incorporate a Stone-Geary term like my $γ$ , but their estimation methodology could easily be adapted to estimate those two additional parameters. Having estimated those parameters, they could then perform simulations to gauge the predicted impact of changes in bequest taxes on consumption.

6 Conclusions

A variety of evidence, both qualitative and quantitative, strongly suggests that people at the top end of the wealth and income distributions behave in ways that are substantially diﬀerent from the behavior of most of the rest of the population. In particular, it is diﬃcult to explain the behavior of these consumers using the standard Life Cycle model of consumption. A leading alternative to (or perhaps just an extension of) the Life Cycle model is the Dynastic model in which the decisionmaker cares about the utility of his descendants. The Dynastic model, however, has problems of its own, starting with the testimony of many wealthy households who say that providing an inheritance is not a principal motivation for saving and ending with the fact that childless wealthy old people do not appear to dissave. I argue that the simplest model capable of ﬁtting all the facts is a model in which wealth either enters the utility function directly as a luxury good, or wealth yields a stream of services that enter the utility function in ways that would be formally virtually indistinguishable from a model in which wealth enters the utility function directly.

In a way, the model reconciles Fitzgerald and Hemingway. Fitzgerald was right that rich do not behave simply as scaled-up versions of everyone else. They choose to save more and to accumulate faster because they can “aﬀord” the luxury of doing so. But Hemingway was right to suggest that the rest of us would probably behave the same way, if only we had more money.

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