This machine cuts and sorts $2,000 worth of $20 bills to be bundled and shipped to their destinations from the Bureau of Engraving and Printing. (Marvin Joseph/The Washington Post)

The “endless inegalitarian spiral” may be coming for us sooner than we think.

In his best-selling 2014 book “Capital in the Twenty-First Century,” French economist Thomas Piketty warned that if the already rich were able to accumulate wealth faster than economies were able to grow, inequality would skyrocket in the coming decades, potentially destabilizing societies in the process.

Wealth, after all, is self-perpetuating. You put cash in a savings account, and it grows. You buy a home, and its value (typically) appreciates. You invest in the stock market and see an annual rate of return.

Work, on the other hand, isn't like that. If you don't have wealth and want to make money, you have to keep working. If the economy is strong enough, your wages will grow, and eventually you'll be able to build up some wealth of your own. And if your wages are increasing more quickly than wealth is growing, there's a chance that someday, you could catch up with the person who started off with a million-dollar trust fund.

Conversely, if your wages are growing more slowly than wealth is increasing, you'll never be able to catch up. You can work as hard as you want and save as much as you want, but you'll never close the gap with that lucky trust-funder. To use a baseball analogy, not only did they start on third base, they're also running faster than you are.

But inquiries into how fast wealth grows relative to the economy have been hampered by a lack of good, complete, comparable long-term data on the rates of return for various assets: stocks, bonds, real estate and the like. You'd want this to know what you'd expect a “natural” rate of return to be in an economy such as ours: How much would you expect home prices to appreciate over time? What about the expected return on the stock market over the decades? How about government bonds?

Now a working paper, written by Federal Reserve Bank of San Francisco economist Òscar Jordà and others, purports to calculate just that: “The Rate of Return on Everything.”

After compiling this first-of-its-kind data set, Jordà's team makes a startling conclusion: If anything, Piketty's book underestimates the historical rate of return on wealth. “The same fact reported [by Piketty] holds true for more countries and more years, and more dramatically,” the researchers conclude.

Wealth accumulates faster — much faster — than economies can keep up. If this is true, it means that in coming years, wealth inequality could grow even faster than Piketty feared.

The gap between wealth accumulation and economic growth has been a constant feature of the world's most advanced economies for nearly the entire period from 1870 to 2015, the researchers found. They compiled a database of the annual rate of return on four major types of wealth: government bonds, treasury bills, stocks and residential real estate.

Their key contribution relates to that last piece: real estate. To get comparable data going back 150 years for 16 countries, they combined two recently compiled long-term data sets: one on house prices and another on rents.

Add up the returns on everything, plot the average rate over time for all 16 countries in the data set, and you get a chart that looks like this:

You can see there have been a few shocks to the overall returns on wealth over the past century and a half — rates fell dramatically during the two world wars, as well as during the 1970s oil crisis and, most recently, the 2007 global financial crisis.

But overall, if you were a typical investor and you wanted to buy a representative chunk of the wealthy world's economy, you could expect an annual rate of return of about 6.28 percent.

You can think of that as the “natural” rate of return in an advanced economy: If a person invested $100 into a representative slice of one of those economies, she'd have $106.28 at year's end.

Now let's compare that with the rate of overall economic growth.

With the exception of wartime, when instability rattles stock markets (or shuts them down completely) and bombs literally destroy housing wealth, the rate of return on wealth has been considerably higher than the growth rate of the major economies. Overall, if the average annual return on wealth since 1870 has been 6.28 percent, average annual economic growth works out to just 2.87 percent.

“The weighted rate of return on capital was twice as high as the growth rate in the past 150 years,” the authors conclude.

Now, many economists point out that this isn't necessarily a problem. There are many factors, such as inheritance taxes and depreciation, that can chip away at the value of capital over time. Ultimately, “more capital will erode the economy-wide return on capital,” as one of Piketty's critics put it in 2014.

But the numbers compiled by Jordà's team don't appear to bear that out. They note that the total value of capital assets in the economies they studied, relative to GDP, roughly doubled between 1970 and 2015. But over that period, the return on those assets was relatively stable. More capital did not erode the economy-wide return on capital.

The implication is that Piketty may have been correct after all with his dire prediction of accelerating inequality in the decades to come, perhaps even more correct than he realized.

Regardless, the data set compiled by Jordà's team should help economists further refine their understanding of the issue — and what it means for all of our pocketbooks.