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Chance helps the rich get richer, simulation study finds

July 22, 2011
Courtesy of the University of Minnesota
and World Science staff

Few would dis­pute that pure luck plays at least some role in bus­i­ness or in­vest­ment suc­cess. But does chance fa­vor the con­centra­t­ion of wealth in the hands of a few, or does it tend to lev­el the play­ing field?

It turns out luck helps the rich get richer, con­sist­ently push­ing wealth to­ward a few, say three re­search­ers who de­vised a com­put­er sim­ula­t­ion to an­a­lyze the ques­tion. The pro­gram was de­signed to iso­late the ef­fects of chance from oth­er fac­tors by be­hav­ing as though luck were the only fac­tor in the suc­cess of an in­vest­or or en­tre­pre­neur.

The Uni­vers­ity of Min­ne­so­ta group sim­ulated the per­for­mance of a large group of in­vestors who started with equal amounts of mon­ey and real­ized a re­turn of some per­cent­age each year. But that per­cent­age was a ran­dom draw tak­en from a pool of pos­si­ble re­turns, so any­one’s per­for­mance could vary wildly from year to year.

The simula­t­ions con­sist­ently re­sulted in dra­mat­ic con­centra­t­ion of wealth over time, the group found. The rea­son: With com­pound­ing cap­i­tal re­turns, some in­di­vid­u­als will have a string of high re­turns and, giv­en enough time, will ac­cu­mu­late an overwhelming share of the wealth. This seems to be a fun­da­men­tal fea­ture of economies where wealth is pri­marily gen­er­at­ed from re­turns on in­vest­ment, for ex­am­ple, through busi­ness own­er­ship and growth, the re­search­ers said.

“Pre­dic­tions from this mod­el about how wealth is dis­trib­ut­ed were more ac­cu­rate than pre­dic­tions from clas­sic eco­nom­ic mod­els,” said Jo­seph Far­gione, one of the re­search­ers. The study ap­pears in the July 20 is­sue of the jour­nal PLoS One.

The mod­el pre­dicts that the rate at which wealth con­centrates de­pends on the varia­t­ion among in­di­vid­ual re­turn rates. For ex­am­ple, when varia­t­ion is high, it would take only 100 years for the top 1 per­cent to in­crease their share of to­tal wealth from 40 per­cent—a re­cent lev­el in the Un­ited States—to 90 per­cent.

Healthy economies sup­port di­verse en­tre­pre­neur­ial ef­forts, driv­ing eco­nom­ic growth, the re­search­ers noted. But con­centra­t­ion of wealth re­duces di­vers­ity, and with it the most likely growth rate for a coun­try’s econ­o­my. “The im­plica­t­ion is that na­tions with di­verse economies should tend to out­com­pete on the world stage those with large con­centra­t­ions of wealth, such as monar­chies, or es­tab­lished democ­ra­cies that have al­lowed their wealth to con­centrate,” said co-author Clar­ence Leh­man.

The rate of wealth con­centra­t­ion bore no rela­t­ion to the av­er­age eco­nom­ic growth, the team found, and it oc­curred re­gard­less of boom-bust cycles or wheth­er wealth is split be­tween two off­spring each genera­t­ion. As wealth con­centrates with a few in­di­vid­u­als, the growth of the econ­o­my will de­pend more and more on the re­turns of those few, mak­ing the econ­o­my less re­sil­ient to dis­rup­tions in their in­vest­ments, the re­search­ers said.


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Few would dispute that pure dumb luck plays at least some role in investment success. But does chance favor the concentration of wealth in the hands of a few, or does it tend to level the playing field? It turns out luck helps the rich get richer, consistently pushing wealth toward a few, say three researchers who devised a computer simulation to analyze the question. The program was designed to isolate the effects chance from other factors by behaving as though luck were the only factor in investment success. The University of Minnesota group simulated the performance of a large group of investors who started with equal amounts of capital and realized returns annually over years. But each year an investor’s return was a random draw taken from a pool of possible return rates, so anyone’s performance could vary wildly from year to year. The simuations consistently resulted in dramatic concentration of wealth over time, the group found. The reason: With compounding capital returns, some individuals will have a string of high returns and, given enough time, will accumulate an overwhelming share of the wealth. This seems to be a fundamental feature of economies where wealth is primarily generated from returns on investment, for example, through business ownership and growth, the researchers said. “Predictions from this model about how wealth is distributed were more accurate than predictions from classic economic models,” said Joseph Fargione, one of the researchers. The study appears in the July 20 issue of the journal PLoS One. The model predicts that the rate at which wealth concentrates depends on the variation among individual return rates. For example, when variation is high, it would take only 100 years for the top 1 percent to increase their share of total wealth from 40 percent—a recent level in the United States—to 90 percent. Healthy economies support diverse entrepreneurial efforts, leading to high economic growth. But concentration of wealth reduces diversity, and with it the most likely growth rate for a country’s economy, according to the researchers. “The implication is that nations with diverse economies should tend to outcompete on the world stage those with large concentrations of wealth, such as monarchies, or established democracies that have allowed their wealth to concentrate,” said co-author Clarence Lehman. But while the rate of wealth concentration was increased by high variation among individual investors’ returns, it bore no relation to the average economic growth, the team added. The findings also indicated that wealth concentrating regardless of economic cycles of growth and recession and regardless of whether wealth is split between two offspring every generation. As wealth concentrates with a few individuals, the growth of the economy will depend more and more on the returns of those few, making the economy less resilient to disruptions in their investments, the researchers said.