Trader Peter Tuchman smiles as he works on the floor of the New York Stock Exchange Tuesday, March 5, 2013. Five and a half years after the start of a frightening drop that erased $11 trillion from stock portfolios and made investors despair of ever getting their money back, the Dow Jones industrial average has regained all the losses suffered during the Great Recession and reached a new high. (AP Photo/Richard Drew)
(Richard Drew/AP)

Up isn't down, black isn't white, and higher taxes on the rich don't do nothing about inequality. The question, though, isn't whether they do anything — it's how much they actually do.

The answer might be less than you think. That, at least, is what William Gale, Melissa Kearney and Peter Orszag found when they simulated what raising the top tax rate would do to inequality as measured by the Gini coefficient. It turns out that increasing the top rate to 50 percent would only reduce the Gini, where 0 is perfect equality and 1 is perfect inequality, from 0.574 to 0.571. We would still be the 99 percent.

Or would we? The problem, as Marshall Steinbaum of the Washington Center for Equitable Growth points out, is that this looks at what happens when we raise taxes on the top 1 percent, but then tries to answer that by looking at a measure, the Gini coefficient, that doesn't tell us a whole lot about the top 1 percent. It is better at showing us what is going on at the middle of the income distribution than at the tails. So the way this has been set up all but guarantees that it will say taxes can do less about inequality than they really can.

But, again, the question is how much less. "It is not clear to me," Orszag told me, that this "materially changes the conclusions." And, in fact, it doesn't. They reran the numbers and found that the top 1 percent's share of income would only decline from 16.4 to 15.6 percent if you raised the top tax rate to 50 percent and redistributed that money to people at the bottom. That is a 5 percent reduction in inequality, as opposed to the 2.4 percent drop that the Gini coefficient picked up. Not nothing, but not a big enough difference that they would call it anything other than "small relative to overall inequality." Or, to put that in historical perspective, they say it would "leave in place between 82 and 97 percent of the increase in inequality since 1979." (The answer depends on whether you use 2007 or 2011 as your point of comparison for inequality).

But let's step back for a minute. It is easy to get lost in this back-and-forth over how much raising taxes on the rich would really reduce inequality. Maybe it would be only a little, or maybe it would be a little more than that. In any case, though, it would be making the rich a bit less so, and, if we redistributed that money to the bottom, helping the people who need help the most. Specifically, they estimate that hiking the top rate to 50 percent would let the government boost the bottom 20 percent's after-tax incomes by $2,650. That sounds like a pretty substantial policy.

If anything, this makes the case for raising taxes on the rich that much stronger. Think about it like this. The government, in all likelihood, is going to need more revenue to deal with the strain that the baby boomers' retirement will put on the budget. So how should we get it? Well, if higher taxes on the rich don't even hurt them enough to make much of a dent in inequality, then that sounds like a good place to start. The government gets some of the money it needs, and the rich are still, well, rich. In other words, there is plenty of room for taxes to go up at the top before we have to worry about them hurting the economy.

The fact that this is such an obvious starting place is why, Orszag told me, it was the only one they looked at. "The middle class is now being defined as 99 percent of the population," he said, so "it is not an uncommon proposal to say we are only going to raise the top tax rate." If we wanted to redistribute our way out of at least a little more of our extreme inequality, they said it would probably require raising "tax rates on capital gains and dividends or ... accrued wealth." After all, the top 0.1 percent receive almost half of them — in total. Even then, though, the rich have gotten so much richer that they'd still probably be a whole lot richer than they used to be, say, a few decades ago. Something has changed in our economy — whether that's technology or globalization or deregulation or all of the above — and it's harder to tax it away than it sounds.

But that doesn't hurt the case that we should still try.