It's a classic story, often told: Two of America's most famous writers
are sitting in a cafe in Paris back in the 1920s. "Let me tell
you about the very rich," says F. Scott Fitzgerald, with undisguised
envy. "They're different from you and me."
"Yes," replies Ernest Hemingway, taking a long pull from
a thick Havana and pausing still longer for effect. "They have
This familiar bit of conversation is amusing and perhaps insightful.
It's also pure fiction, in the best sense of the word. The novelists
didn't share these thoughts over drinks in Paris, Madrid or anywhere
else. Fitzgerald wrote the first phrases in a 1926 short story and
Hemingway replied a decade later in an article published in Esquire.
(As for Hemingway's glib retort: He borrowed it from Mary Colum, an
Irish literary critic.)
But as long as we're dealing in fiction, why not bring an economist
to the table? John Maynard Keynes, for example, was a worldly contemporary
with a deep interest in wealth accumulation.
"What exactly do you mean by 'the very rich,' Francis?"
he might ask. "Are you talking about the income-rich? Or do you
really mean wealthaccumulated savings resulting in high net
worth? And Ernest, why would you guess it is that they have more moneysimilar
incomes but higher propensities to save? Or are you speaking of Old
Money, inherited wealth?"
There's no evidence that Keynes was such a boor. He would have had
such thoughts, perhaps, but he wouldn't have mucked up a perfectly
good anecdote. Still, economists before and after Keynes have pondered
wealth at least as obsessively as novelists, and some of the finest
minds in the field have struggled to explain what seems on its surface
a rather simple phenomenon: Some people save much more money than
And a lucky few end up building, in their lifetimes and beyond, vast
fortunes that others only dream of. In the United States, the richest
1 percent of the population held nearly 35 percent of all personal
wealth in 1998 (up from 29 percent in 1989), according to the Federal
Reserve Board's Survey of Consumer Finances (SCF), whereas the poorest
40 percent had just 1 percent of all wealth. (See "Beyond
Rich and Poor".) Economic theory has, to its great frustration,
been unable to explain such high levels of wealth concentration.
The discussion is not purely academic (or literary). Wealth inequality
and the mechanisms behind savings accumulation have obvious policy
relevance: An end to dividend taxation and the permanent abolition
of the estate tax are two central and very controversial elements
of the Bush economic plan. But while policymakers debate the trade-offs
inherent in tax policies that may diminish or increase inequalityand
might encourage or impede economic growtheconomists say the
relationships are still unclear. In particular, the mechanisms that
explain the savings behavior of the very rich remain enigmatic.
There is hope. Recent work by economists has begun to unfold the mysteries
that surround the economics of wealth accumulation, and some of the
most fruitful such efforts are those of Minneapolis Fed adviser Mariacristina
De Nardi, an assistant professor at the University of Minnesota. De
Nardi released two papers in 2002 that explore the mechanisms behind
wealth distribution, and each draws successively closer to a full
"Before looking at how taxes affect inequality," said De
Nardi, "we have to understand how that inequality comes about,
and construct a model that we think does a good job of matching the
main features." De Nardi's models do exactly that, providing
a near perfect fit to the empirical realities of U.S. wealth distribution.
The economic reasoning behind her models, therefore, appears to provide
a solid explanation of how wealth is accumulated. Her models are based
on conventional theory, but they merge elements of two prevailing
(but inadequate) models into a distinctive and powerful fusion that
casts new light on the wealth of the very rich.
A wealth of history
As the title of Adam Smith's best-known work attests, a clear explanation
for wealthits accumulation and distributionhas long been
a Holy Grail for economists. A nation's aggregate wealth, after all,
sets its standard of living and determines its capacity to raise that
standard through investment.
In the early 20th century, economic studies of wealth focused on savings
behavior, noting that the rich tended to save a much higher portion
of their income than those with less net worth. Keynes himself considered
excessive saving to be a problem, and he hoped to pump up spending
in order to bring the world economy out of the Great Depression. This
Keynesian analysis of the Depression has been much debated by economists,
but Keynes' recitation of motives for saving remainsknowingly
or nota touchstone for most.
In his General Theory of Employment, Interest and Money
(published in 1936, also the year of Hemingway's article), Keynes
argued that bequests were a primary motive for saving and a major
source of wealth, and he also concluded that the rich were, indeed,
different in their propensity to save. It was a "psychological
law," he wrote, that as people's incomes increased, so did the
share of their income that they saved.
Keynes also listed "precaution" as a savings motive. It
was the need "to build up a reserve against unforeseen contingencies."
In the absence of insurance markets to buffer against all possible
eventualitieshospitalization, loss of a job, divorcerational
people will save for a rainy day. Such buffers are needed to survive
what Shakespeare called the "slings and arrows of outrageous
fortune." Theoretical economists phrase it somewhat differently:
Stochastic shocks modeled with a Markov process characterized by a
transition probability matrix. Less poetry, perhaps, but far more
analytical traction. And the Bard had something similar in mind, no
doubt, when Hamlet referred to "the thousand natural shocks that
flesh is heir to."
Virtually all economic modeling of wealth accumulation now incorporates
some element of uncertainty and risk aversion that allows for precautionary
savings, and economists find this motive is most important for individuals
in early stages of life, and for those with lower incomes. But precaution
doesn't explain savings behavior later in life or saving by the richwhich
is to say, it doesn't explain the greatest part of aggregate wealth.
The full answer lies elsewhere.
"Foresight" is another reason to save a portion of one's
income. In Keynes' rather convoluted words, foresight savings "provide
for an anticipated future relation between the income and the needs
of the individual or his family different from that which exists in
The same concept had been explored earlier by Irving Fisher in his
theoretical work on optimal allocation of resources over time. But
it was Roy Harrod who developed it in 1948 and gave it a pithy, if
inelegant, name: "Hump saving"the accumulation of
wealth during peak earning years.
It remained for Franco Modigliani to elaborate both motives, particularly
foresight, into what he called the life-cycle hypothesis. Modigliani's
seminal theory, published in 1954, was an intricate mathematical modeling
of the straightforward idea that people accumulate savings during
their earning years so that they can consume those savings during
retirement: They "squirrel away" wealth during the summer
so that they'll have something to consume in the depths of winter.
Or as Modigliani put it in 1985 on the day he won the Nobel economics
award for his theory: "I sometimes think that my work on this
subject was colored by [my] savings bank.
Their motto was,
'save it when you need it least; have it when you need it most.'"
The life-cycle hypothesis was intuitively appealing and theoretically
powerful. Among other things, it helped resolve the so-called Keynes-Kuznets
paradox. Simon Kuznets had found in 1942 that Keynes' "psychological
law" of higher savings rates among the rich appeared to be contradicted
by the data: Despite huge income increases in the United States, personal
savings as a share of national income had not increased. The life-cycle
hypothesis showed that there was no necessary connection between a
nation's aggregate savings rate and individual propensities to save.
The relationship was far more complex, demonstrated Modigliani, involving
a nation's age structure and population growth rate.
There was just one problem with the basic version of the life-cycle
theory: It didn't work, at least not in its simple, unsophisticated
form. Like the Fitzgerald-and-Hemingway-in-Paris story, it sounded
good but didn't describe reality. It's true that individuals show
clear "humps" in labor earnings over their lifetimes, but
the data don't exhibit a similar hump for wealth accumulation. Nor
do people necessarily save more during their peak earning years and
less in retirement, according to the empirical studies. Moreover,
it didn't explain the highly unequal distribution of wealth seen among
people of similar agesafter all, if Joe and Bob are at roughly
the same point in their life cycle, shouldn't they have accumulated
approximately similar levels of wealth? The data showed that wasn't
Exhaustive attempts to explain actual saving patterns with Modigliani's
basic life-cycle hypothesis proved entirely unsuccessful. Reviewing
these efforts, his close collaborator Albert Ando, along with Arthur
Kennickell of the Federal Reserve Board, wrote, "We started with
one of the most elegant theories in economics, and we could not find
a way to fit abundant bodies of data into its neat framework."
The role of bequests
One of the fundamental tenets of the life-cycle hypothesis is that
people "dissave" during retirement: They spend in old age
what they saved in middle age. And assuming that, on average, people
make fairly good guesses about how much they'll need between the time
they retire and the time they die, a basic inference of the life-cycle
theory is that not a lot should be left over. Whatever bequests are
made to children will be largely accidental and financially trivial.
Thus the bumper sticker: "We're spending our children's inheritance."
That, too, turns out to be untrue, at least in the aggregate. In perhaps
the most damning refutation of life-cycle theory, economists Laurence
Kotlikoff and Lawrence Summers showed in 1981 that as much as 80 percent
of current U.S. wealth was inherited and concluded that "the
pure life-cycle component of aggregate U.S. savings is very small.
American capital accumulation results primarily from intergenerational
transfers." Modigliani responded that the true figure for estates
as a percentage of U.S. wealth doesn't exceed 25 percent and argued
that the Kotlikoff-Summers' estimate reflects "mainly definitional
differences." But even so, he conceded that bequests "play
an important role
in the very highest income and wealth brackets."
Bequests, in fact, are the basis of the other major school of thought
regarding saving and wealth accumulation. Developed mathematically
by Gary Becker and Robert Barro in separate 1974 papers, this theory
holds that parents seek to provide for their children even after they
die, an altruistic impulse that leads them to curtail current consumption
and accumulate wealth that they intend to leave as an inheritance
for their offspring.
Often called the dynastic model, this hypothesis of wealth accumulation
for bequest purposes suggests not that people try to smooth consumption
over their lifetimes, but that they perceive their welfare as being
directly related to the well-being of their children.
In truth, that's the dynastic model in its most altruistic form. Other
versions put a less favorable light on the bequest impulse. One thought
is that people feel a "joy-of-giving" or "warm glow"
by building an estate and bequeathing it. Not entirely altruistic,
perhaps, but still generous. Another variant is the "strategic
bequest" motive: Parents use their accumulated savings as a bargaining
chip with their children"visit me, call me, let me see
the grandkids or I'll write you out of the will." Whatever lies
beneath the bequest motive, though, the bottom line is roughly similar:
People accumulate wealth with the express intent of giving it to their
The dynastic model, too, has clear intuitive appeal. But like the
life-cycle theory, it also has largely failed the empirical test.
At the simplest level, surveys by the Federal Reserve and other agencies
find that very few individuals, whether wealthy or not, mention building
an estate for their heirs as an important reason for saving. Just
5.1 percent of the sample surveyed in the Fed's 2001 SCF, for example,
said that "for the family" was one of their top reasons
for saving money.
More damaging, perhaps, is that mathematical models of dynastic savings
behavior are notably unsuccessful at generating wealth distribution
patterns that resemble the actual U.S. distribution of wealth. A 1994
dynastic model by S. Rao Aiyagari, for example, fell far short of
generating as much inequality in wealth distribution as actually exists
in the United States. In 1992, the richest 1 percent of the population
held 28 percent of the country's wealth, but Aiyagari's best dynastic
model could generate just 4 percent of wealth for the top 1 percent.
(See "Understanding the U.S.
Distribution of Wealth," Quarterly Review, Spring
1997, for a fuller description of these results.) More egalitarian,
perhaps, but a bad explanation of the facts.
Indeed, the best life-cycle models do a better job than pure dynastic
models at replicating reality. Mark Huggett's 1996 study of life-cycle
models was able to generate almost 14 percent of total wealth for
the richest 1 percent. But his model, too, was inadequate in explaining
the level of wealth held by the very rich. "The model economies
with earnings uncertainty," noted Huggett, "[generate] a
little less than half the wealth held by the top 1 percent in the
Seeking a better fit
If the dominant theories have proven inadequate, what then is the
likely explanation? What does account for savings behavior by the
very rich, and what theoretical models can better fit reality? According
to De Nardi, the answer lies in a blend, a model that nests elements
of dynastic theory within those of the life-cycle hypothesis, and
which then adds a few crucial features.
De Nardi begins with a model economy in which individuals save a portion
of their earnings during their working years and then spend those
savings during retirementstandard life-cycle stuff. But her
model also allows individuals to make bequests of two sorts: planned
bequests of financial/physical capital and also the transmission of
human capital or productivity (through education, training or pure
inborn talent) from parent to child.
Actual U.S. Wealth Distribution
Compared with Distributions Generated by Models
PERCENT OF TOTAL WEALTH HELD BY THE:
Actual U.S. Wealth Distribution (1989 Survey of Consumer
Combined life-cycle/ dynastic model with intergenerational
transmission of bequests and productivity
De Nardi (2002)
Combined model with bequests and entrepreneurs
De Nardi-Cagetti (2002)
The art of theoretical modeling is to develop a structure of interrelated
equations sufficiently nuanced to capture the essence of the economic
theory being explored without introducing such complexity that those
equations can't be solved. Simplifications make the model workable,
but they cannot be so unrealistic as to render it irrelevant. Art
is created when an abstraction from reality actually makes a model
The most crucial and innovative simplification in De Nardi's model
relates to strategic interaction between child and adult, a critical
issue in bequest economics. "I can be lazy because I expect a
lot of money when my parents die," might be one child's response
to the prospect of a fortune to come. The parent's strategic reaction:
"I'd sooner spend my savings now than breed sloth and entitlement
into my child."
Economic models have difficulty modeling such interaction because,
like real personal relationships, these strategic responses go back
and forth indefinitely, so the equations that represent them are very
"computationally intensive"they require so much effort
to solve (with current technology) as to render them unmanageable.
De Nardi solves the dilemma by building in partial observability.
In her model, children can't directly see their parents' assets, but
they can observe their parents' productivity at one period of time,
and from that infer the size of bequest they're likely to receive.
It's an inventive element that introduces intergenerational transfers
into a life-cycle model. And it makes all the difference.
In her paper "Wealth Inequality
and Intergenerational Links" (Staff Report 314.), De Nardi
builds the model and takes it for a ride. "I start with an experiment
in which the model is stripped of all intergenerational links,"
she wrote, "an overlapping generations model with life-span and
earnings uncertainty." This first experiment, then, is the base
life-cycle model that allows for just two reasons for wealth accumulation,
the precautionary and foresight (or retirement) motives.
She runs the numbers and generates a wealth distribution to be compared
alongside actual U.S. wealth distribution figures. Data for the United
States from the 1989 SCF show that the richest 40 percent of Americans
hold 93 percent of the nation's wealth. (Or conversely, the poorest
60 percent hold just 7 percent.) De Nardi's base model generates 90
percent for the top 40. Not bad. And it implies, as De Nardi puts
it, that "saving for precautionary purposes and saving for retirement
are the primary factors for wealth accumulation at the lower tail
of the distribution."
But for the very rich, the base modellacking intergenerational
linksexplains very little. The richest 5 percent actually hold
53 percent of all wealth, according to the 1989 SCF, but De Nardi's
model gives them barely half that, just 27 percent. The top 1 percent
hold 29 percent of wealth in reality, but the model generates only
7 percent. The base model is clearly missing a major part of the upper
crust's picture. Whatever makes them different remains unexplained.
It's when De Nardi introduces the bequest motive that the model proves
its worth. The version in which parents derive utility from giving
bequests to their children generates 95 percent of total wealth for
the richest 40 percent of the population, close to the 93 percent
in actual data. The top 5 percent get 37 percent of wealth, far closer
to their reality, and the top 1 percent double their holdings from
the base model to 14 percent of total wealth.
When De Nardi adds in the productivity transmission feature, the model
does still better, generating 42 percent of wealth for the top 5 and
18 percent for the top 1. The results aren't a perfect match, but
De Nardi's full model does considerably better than previous formulations
by others at replicating wealth distribution patterns in the United
States, and it therefore better explains the crucial relationships
that underlie savings behavior, especially for the rich.
"Households that either have high lifetime income or receive
large bequests, or both, choose a higher saving rate, build up large
estates, and keep a significant amount of assets even at advanced
ages," wrote De Nardi. "These households, therefore, are
more likely to leave large bequests when they die."
To test the broader relevance of her model, De Nardi also uses it
to analyze wealth distribution in Sweden, an economy in which the
richest 1 percent hold 17 percent of wealth and the richest 5 percent
hold 37 percent, considerably lower than comparable U.S. figures.
On the other hand, a much larger portion of the Swedish population,
30 percent, has zero or negative wealth, three times the U.S. figure.
Applied to the Swedish economy, the simple life-cycle model generates
a far less unequal wealth distribution than in reality. But De Nardi's
full model, including financial bequests and inheritance of productivity,
does a significantly better job of matching reality: It generates
10 percent for the top 1 percent and 34 percent for the top 5; the
share with zero or negative wealth is 33 percent, close to actual
"One contribution of the paper," said De Nardi, "is
to show that voluntary bequests are indeed important to explain wealth
concentration. If all bequests were accidental, there wouldn't be
much more concentration in wealth than in labor earnings." And
her model also clearly demonstrates that transmission of productivity
(or human capital) from parent to child also plays a part in wealth
generation. "I found that these are two important features to
explain why there are these rich families," she said, "but
they don't go all the way to explain what we observe in the data."
Going all the way
Working with Marco Cagetti, an economist at the University of Virginia,
De Nardi then explores another dimension of wealth generation: entrepreneurship.
The data show that entrepreneurs, defined as those who own and manage
their own businesses, are few in number but rich in wealth. Just 8.7
percent of the U.S. population are entrepreneurs, but they hold 39
percent of total U.S. wealth. And roughly two-thirds of the wealthiest
1 percent of Americans are entrepreneurs. So an understanding of the
motives and constraints facing those who are (or would be) entrepreneurs
should help to illuminate further overall wealth holding patterns.
In "Entrepreneurship, Frictions
and Wealth," (Working Paper 620), De Nardi and Cagetti build
a life-cycle model similar to De Nardi's earlier version, but pared
down to accommodate the extra feature of occupational choice: the
decision of whether to become an entrepreneur or remain a worker.
In the De Nardi-Cagetti model, individuals facing this choice must
have the inclination and ability to be an entrepreneur, of course,
but they also need capital. And that capital is availablein
their model as in the real worldonly if they've saved it themselves,
acquired it as a bequest or used their own wealth as collateral for
a larger loan. The entrepreneurial borrowing constraint, based on
work by Fed adviser Timothy Kehoe and University of California, Los
Angeles' David Levine, is a key element in this new model.
"The evidence," wrote De Nardi and Cagetti, "suggests
that entrepreneurs face borrowing constraints
and that the
possibility of becoming entrepreneurs
is related to the level
of own wealth." The borrowing constraint is likely to lead potential
entrepreneurs to save, they argue. "The need to accumulate assets
in the presence of such constraints may also generate high savings
rates among entrepreneurs (or households planning to become entrepreneurs)."
The De Nardi-Cagetti model without entrepreneurs fits the data
poorly. The richest 40 percent have just 84 percent of wealth, not
93 percent as in reality. The top 5 percent own a fifth of all wealth,
as opposed to the actual 53 percent. And the model generates just
5 percent of wealth for the top 1 percent.
But once credit-constrained entrepreneurs are introduced, their model
works extremely well, particularly for the hard-to-explain very wealthy:
The top 5 percent hold 55 percent of wealth in the model vs. 53 percent
in fact; the top 1 percent have 28 percent of wealth, close to the
29 percent found in actual data.
What of bequests? This model is not centrally focused on voluntary
bequests, as was De Nardi's first, but it too finds that they are
essential to fitting the model to reality. If Cagetti and De Nardi
exclude voluntary bequests from this modelleaving only the entrepreneurial
spirit to explain wealth distributionthe fit to data is markedly
poorer. Their explanation: "Younger people are bequeathed less
wealth, and in the presence of borrowing constraints, this means that
young potential entrepreneurs have less resources to start and increase
their businesses. Both effects reduce capital accumulation in the
economy [and] the concentration of wealth decreases."
With this paper, then, De Nardi and Cagetti have found that bequests
are a necessary but insufficient explanation of current patterns of
wealth distribution. Their fuller model "has a more simplified
life-cycle structure," acknowledged De Nardi, "but it has
occupational choice. And in that framework we find that we do an excellent
job of matching the wealth concentration that we observe in the data.
So that was the other ingredient that we needed to get all the way
De Nardi and Cagetti's efforts extend and generalize related work
by other leading economists. Vincenzo Quadrini, for example, has focused
on the importance of entrepreneurship to wealth accumulation in an
environment with "infinitely lived" households, an abstraction
that economists often use quite effectively, but which doesn't model
the life cycle and hence does not allow for a realistic treatment
of intergenerational transfers.
Ana Castañeda, Javier Díaz-Giménez and José-Víctor
Ríos-Rull have developed a model that, like De Nardi's, blends
elements of life-cycle and dynastic theory, but it does not allow
for occupational choice, thus omitting the role of entrepreneurs.
(Intriguingly, they also seem to make an implicit reference to the
Fitzgerald/Hemingway debate: "[W]e can account for the earnings
and wealth inequality observed in the U.S. without having to model
the poor and the rich as being different," they wrote. "Instead,
the poor and the rich can be thought of as being essentially the same
type of people, that have been subject to a different set of circumstances.")
De Nardi and Cagetti's framework, by contrast, models explicitly both
occupational choice and intergenerational links, thus allowing for
the analysis of a number of key policy questions that have remained,
until this point, largely unresolved.
If the art of economic modeling is prudent abstraction, then the
test of a model is how faithfully it can reproduce key elements of
reality. Over the last six or seven years, economists have made considerable
progress in this regard. But a model's ultimate value rests in its
ability to explore different realities. Theoretical models
are essentially economic laboratories. They allow economists to alter
certain variables, holding others constant, and measure changes in
outcomes. Economists can rarely perform real-world experiments, so
models are used for in vitro simulations, with computers as test tubes,
data for chemicals and equations to catalyze the reaction.
The De Nardi-Cagetti model appears particularly valuable precisely
because many of the critical processes are not imposed from without
but rather generated endogenously by the model economy, just as in
life. Policy variables such as tax rates, lending constraints and
subsidies can then be studied in a credible fashion.
"Our policy experiments in this framework are still at the very
initial stages," said De Nardi, of her work with Cagetti. But
their early findings are quite revealing. "Our preliminary results
indicate that if you were to eliminate estate taxation
would go up, but not terribly so. To give you an idea, the richest
1 percent before we eliminate estate taxation hold about 28 percent
of total net worth. If we were to eliminate the estate taxation, they
would go to 29 or 30 percent."
The main reason for such a minimal change, De Nardi suggests, is that
while legal tax rates on estates are quite high, the effective rate
is far lower, about 10 percent, because of tax avoidance efforts by
those with large estates. Abolishing the tax would therefore have
a smaller impact than predicted by looking at the official rate. Still,
De Nardi is struck by the result. "We were quite surprised to
find an effect this small to eliminating taxation," she said.
On the other hand, repealing the estate tax would raise investment
and gross domestic product, forecasts the model, because those with
large estates would be encouraged to save and invest still more. The
boost wouldn't be large, according to initial estimates, but significant
nonetheless. An increase in estate tax rates, by contrast, would have
a strongly detrimental effect on the numbers of entrepreneurs, their
business size and their investment, according to preliminary calculations.
At this point, De Nardi said, these findings are more suggestive than
conclusive. They've established the theoretical framework, built the
right laboratory. And now, with Cagetti, she has put forth a broad
set of research objectives: to explore fully the influence of borrowing
constraints and bequests on entrepreneurial decisions, capital accumulation
and inequality; to estimate the economic costs and benefits of taxing
capital income, entrepreneurial income and estates; and to gauge the
effect of entrepreneurial choice on overall business cycle fluctuations.
It's an ambitious research agenda. Given both the historical debate
over determinants of wealth accumulation and the current controversy
on tax policy and economic growth, it also stands as an especially
important and timely one. "We hope," said De Nardi, "that
others will find our work useful."