EVER since Thomas Piketty, a French economist, published his monumental best-seller “Capital in the 21st Century” last year, his work has come under attack on theoretical and statistical grounds. The latest assault* comes from an unsurprising source: the libertarian Cato Institute.

The argument centres on Mr Piketty’s use of the expression “r > g”, where r is the return on capital and g is the growth rate of the economy. Mr Piketty argues that the growth rate of developed economies has been slowing, but that the return on capital is relatively undiminished. Since capital is concentrated in the hands of the wealthy, a long period in which returns exceed the growth rate will lead to widening inequality. This can be countered only by higher taxes.

The authors, who work for Research Affiliates and Efficient Frontier Advisors, two investment funds, accept that the growth rate of the developed world has slowed, largely for demographic reasons. Where they differ from Mr Piketty is over the impact on investment returns.

The wealthy have indeed enjoyed very good returns on financial assets over the past 30 years. Bond yields have plunged (and prices risen) from the double-digit yields seen in the early 1980s; equities have followed a more volatile but still profitable path. The annualised real return of a typical portfolio (60% in American equities and 40% in Treasury bonds) between 1982 and 2014 was 10.2%.

But yields in the developed world are now so low that future returns from bonds are likely to be much reduced. Research by the London Business School shows that periods of low interest rates are also associated with lower-than-normal equity returns. So to go back to Mr Piketty’s expression, g may have fallen, but so has the future rate of r.

In addition, the authors argue that the French economist did not allow for factors that reduce the net return to investors: taxes, fund-management charges and lavish lifestyles. They apply a rough-and-ready check by looking at the fortunes of members of the Forbes 400, an annual list of the world’s wealthiest people, first compiled in 1982. The 69 families (out of 297) that are on both the earliest and latest lists have achieved an annual real return of 8.4%—not bad, but well behind the indices. Once you include dropouts (based on the generous assumptions that their wealth fell to just $1 below the cut-off point in the year they were relegated and then matched the survivors’ subsequent performance), the average return falls to 6.5%. If they continue to underperform to the same extent in a world of lower yields, their real wealth may not grow at all.

Indeed, the authors point out that the rapid turnover of the Forbes 400 suggests that inherited wealth is unstable. Three-quarters of the families in the original list no longer appear on it.

Of course, dropping out of the Forbes 400 hardly indicates a descent into penury. But family wealth tends to dissipate over time. The Astors, Vanderbilts and Carnegies were among the wealthiest families of the late 19th century; not one of their descendants makes it onto the modern list. Indeed a Vanderbilt family reunion held in 1973 failed to find a single millionaire among the 120 present.

Much of that decline may have been because of the high tax rates that applied after the second world war. But even in the modern era of lower taxes on the rich, the erosion has continued: there were 13 Rockefellers and 25 DuPonts on the original Forbes list. Only one (David Rockefeller) appeared in 2014. A more comprehensive survey by the authors leads them to conclude, “Descendants halve their inherited wealth—relative to the growth of per capita GDP—every 20 years or less.”

None of this negates the idea that inequality has increased overall. But the authors argue that three trends have occurred simultaneously. First, there has been a big gain for the already wealthy from a probably unrepeatable rise in asset values. Second, new wealth has emerged in the form of successful entrepreneurs in the technology industry such as Bill Gates or Steve Jobs—a healthy phenomenon.

Third, there has been a big change in income inequality, driven by the high rewards given to corporate executives who make up three-fifths of the top 0.1% of American earners. As the authors note, there is little correlation between executive compensation and the creation of wealth for shareholders. So they suggest that, instead of higher taxes, a more fruitful way of tackling inequality would be for shareholders to pay more attention to corporate governance.

* “The Rich Get Poorer: The Myth of Dynastic Wealth”, by Robert Arnott, William Bernstein and Lillian Wu, to be published in the Cato Journal, Volume 35, Number 3.

Economist.com/blogs/buttonwood