Are America’s rich getting richer? They’re certainly making much more than ever before. Every official income measure we have shows that America’s most affluent are upping their incomes at a much faster clip than everyone else.

How fast? Between 1980 and 2010, notes an analysis of IRS tax data this past spring by economists Emmanuel Saez and Thomas Piketty, incomes for America’s top 1 percent more than doubled, after inflation, to an average $1.02 million.

Average incomes for the nation’s top 0.1 percent, over that same span, more than tripled, and at the tippy top of America’s economic summit — the top 0.01 percent — average incomes more than quadrupled, to $23.8 million in 2010.

And what about the rest of us? After inflation, average incomes for America’s bottom 90 percent actually fell — by 4.8 percent — between 1980 and 2010. Americans in this 90 percent averaged $31,337 in 1980, only $29,840 in 2010.

We have to go back to the late 1920s, right before the Great Depression, to find an income divide this wide between America’s rich and everybody else.

Income stats tell us how much people make. Wealth stats, by contrast, tell us how much people have. The two, common sense tells us, ought to be related. If incomes are becoming much more unequal over time, then the distribution of our national wealth ought to be becoming much more unequal, too.

But that doesn’t seem to be the case, at least not according to the best official wealth stats we have, the household wealth data collected by researchers at the Federal Reserve Board.

Last week, the nonpartisan Congressional Research Service released an analysis of the latest Federal Reserve raw wealth data. This new analysis shows no significant expansion in the gap between the wealth of the awesomely affluent and the rest of America over the last two dozen years.

In 2010, the new Fed data indicate, America’s top 1 percent held 34.5 percent of the nation’s household wealth, almost exactly the same share of the nation’s wealth that the top 1 percent held in 1995 and not all that much more than the 30.1 percent share America’s top 1 percent held in 1989.

The income and wealth numbers, in other words, just don’t add up. How could the top 1 percent share of America’s household wealth be holding relatively steady over the same span of time that top 1 percent incomes have been soaring and bottom 90 percent incomes have been sinking?

We have ourselves here a paradox pure and simple. What could explain it?

One explanation might be that the Federal Reserve hasn’t done a comprehensive enough job counting the wealth of the wealthy. Indeed, Federal Reserve researchers do acknowledge that they don’t take into account — for privacy reasons — the wealth of anyone appearing in the annual Forbes magazine list of America’s 400 richest.

In 2010, Forbes reports, this top 400 collectively held a rather awesome $1.37 trillion in wealth. But even if the Federal Reserve had taken this wealth into account, the top 1 percent share of U.S. wealth would have increased by not much more than a percentage point, not enough to solve the inequality paradox.

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So what else could explain our inequality paradox?

Maybe the rich are simply living over-the-top, throwing their excess income away on expensive food and frolic. But wasteful consumption can’t explain the inequality paradox either. Do the math. Deep pockets in America’s top 0.01 percent could shell out $5,000 every single day of the year and still have 93 percent of their annual incomes left to spend.

So what can explain the disconnect between the extraordinary income gains of the rich and the modest rise in their share of national wealth?

The London-based Tax Justice Network has an answer. The world’s super rich, the international group has just reported, are stuffing — and concealing — phenomenal quantities of their cash in secret global tax havens.

The Network’s new global tax-dodging study, the most detailed ever conducted, “conservatively” computes the total wealth sitting in these havens, as of 2010, at $21 trillion. That total could plausibly run as high at $32 trillion.

“Almost all these hidden assets are owned by the world’s wealthiest individuals,” note Tax Justice Network analysts, a reality that means that all previous studies “exploring economic inequality have systematically underestimated the wealth and income enjoyed by the world’s wealthiest individuals.”

The lead researcher on the Tax Justice Network’s new research, James Henry, formerly served as the chief economist at the prestigious McKinsey corporate consulting group. In the Network’s new report, The Price of Offshore Revisited, he mines a wide range of public and private sector data sources to gauge capital flows in and out of “offshore” secrecy jurisdictions all around the world.

These havens, notes Henry, host over 3.5 million paper companies, thousands of shell banks and insurance companies, and “tens of thousands of shell subsidiaries for the world’s largest banks, accounting firms, and energy, software, drug, and defense companies.”

This vast web, aided and abetted by weak and poorly enforced government regulations, has enabled, notes Henry, fewer than 100,000 people — just .001 percent of the world’s population — to “control over 30 percent of the world’s financial wealth.”

Americans make up, according to various previous surveys of the world’s ultra rich, almost a third of the world’s super wealthy. That would put the American share of unrecorded offshore private assets as high as $10 trillion.

Add this $10 trillion to the wealth of America’s top 1 percent and the inequality disconnect between wealth and income largely disappears. The top 1 percent share of the nation’s household wealth, a steady one-third according to the Fed Reserve data, jumps to the neighborhood of nearly one half.

Paradox solved. The distribution of wealth in the United States has become more top-heavy at a ferociously fast rate, just like the distribution of income.

Now we have a much bigger problem to solve: ending the march to ever greater inequality, narrowing that vast gap between wealthy tax dodgers and the rest of us. Shutting down tax havens might make a great place to start.