Why won’t Mitt Romney release his tax returns? Some commentators have begun floating the suggestion that he paid very, very low tax rates while amassing enormous wealth. The Obama campaign released an ad today taking this further, claiming Romney’s use of offshore accounts and his low rate on investments should make you “wonder if some years he paid any taxes at all.”

How likely are these scenarios?

I surveyed several experts on the question. The answer: While they cautioned that this is necessarily speculative, since Romney won’t release his returns, it’s likely he paid significantly lower rates in previous years. They said the possibility that he paid next to nothing in any given year couldn’t be ruled out completely, though they said it was unlikely.

“For a person of that amount of wealth with good advisers, you would expect somebody like that to be well advised enough to minimize the tax consequences,” George Yin, a professor of tax law at the University of Virginia, tells me.

The experts said a key unknown is how Romney might have done this — and whether he resorted to aggressive tax sheltering, which could be very damaging.

“To the extent he was able to shift investments offshore, again presumably in compliance with the law, but in the views of some members of the public as aggressive sheltering, that would be a potential political problem for him,” said Yin, who in the mid-1980s was a GOP appointee to the Senate Finance Committee and has given money to candidates in both parties.

Yin said he obviously didn’t know if this were the case, but described it as a “reasonable possibility.”

The experts also said Romney may have reduced his tax rate significantly through more standard tax planning techniques and through offsetting capital gains with capital losses. These are typical methods that many people use but could still be politically difficult to explain, the experts said, depending on how substantially they reduced his overall tax rate on the money he actually made.

“This is the kind of thing people do all the time, but people will look at the percentage paid in tax, not the mechanics of how that percentage was paid,” Roberton Williams, a senior fellow at the nonpartisan Tax Policy Center, told me. “It’s not likely that he paid no taxes, but it is possible that he paid a much lower tax rate in earlier years than in 2010.”

In 2010, the year for which they released a return, the Romneys paid a 13.9 percent tax rate on $21.6 million in income, much of which was from lower-tax capital gains.

Asked what the likelihood was that Romney paid substantially lower tax rates than that in previous years, Daniel Shaviro, a professor of taxation at New York University, said: “His extreme reluctance to release the returns makes you wonder — it becomes the natural expanation.”

Shaviro, who supports Obama but is a nonpartisan tax analyst, said the question would then be this: “Did he get there just by selling losing stocks, or did he get there with aggressive tax shelters?”