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 more money.”

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 wealth—accumulated savings resulting in high net worth? And Ernest, why would you guess it is that they have more money—similar 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 do others.

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 inequality—and might encourage or impede economic growth—economists 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 answer.

“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 wealth—its accumulation and distribution—has 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 remains—knowingly or not—a 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 eventualities—hospitalization, loss of a job, divorce—rational 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 rich—which is to say, it doesn't explain the greatest part of aggregate wealth. The full answer lies elsewhere.

Planning ahead

“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 present.”

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 ages—after 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 the case.

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 heirs.

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 U.S.”

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 retirement—standard 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:
MODEL	TOP 1 PERCENT	TOP 5 PERCENT	TOP 20 PERCENT
Actual U.S. Wealth Distribution (1989 Survey of Consumer Finances)*	29	53	80
Dynastic model Aiyagari (1994)	4	15.6	44.6
Life-cycle model** Huggett (1996)	11.1-13.8	33.8-40.4	72.3-80.2
Combined life-cycle/ dynastic model with intergenerational transmission of bequests and productivity De Nardi (2002)	18	42	79
Combined model with bequests and entrepreneurs De Nardi-Cagetti (2002)	28	55	79
* The Aiyagari and Huggett models used 1992 data to simulate the 1992 distribution of wealth, while De Nardi and Cagetti used 1989 data to simulate the 1989 distribution. Since wealth distribution differed only slightly in 1989 and 1992, this table, for simplicity, displays only the earlier year. ** Huggett's results show a range because he explored several versions of his life-cycle model with different levels of risk aversion, earnings volatility and borrowing constraints.

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 more relevant.

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.

Getting results

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 model—lacking intergenerational links—explains 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 data.

“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 available—in their model as in the real world—only 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 model—leaving only the entrepreneurial spirit to explain wealth distribution—the 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 there.”

Close relatives

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.

Considering policy

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 … inequality 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.”