Andrew Johns (IRS) & Joel Slemrod (Ross School of Business, University of Michigan) have posted The Distribution of Income Tax Noncompliance on the Michigan website.  Here is the abstract:

New research by OTPR Director Joel Slemrod and IRS employee Andrew Johns looks at income tax noncompliance by income group. It makes use of newly available data for tax year 2001 from the IRS’s most recent comprehensive study of individual income tax noncompliance, the National Research Program. The study finds that, when taxpayers are arrayed by their “true” income, defined as reported income adjusted for the underreporting estimated by the IRS tax gap methodology, the ratio of aggregate misreported income to true income generally increases with income, although it peaks among taxpayers with adjusted gross income between $500,000 to $1,000,000, and is lower than the peak ratio for individuals with income above $1,000,000. In sharp contrast, though, the ratio of underreported tax to true tax is highest for lower-income taxpayers. This contrast in results reflects the fact that under a graduated tax schedule a given percentage reduction in taxable income corresponds to a higher percentage reduction in tax liability the lower is a taxpayer’s income. Much, but not all, of the distributional pattern of noncompliance is related to the fact that on average high-income taxpayers receive their income in forms that have higher noncompliance rates.

The paper is extensively discussed in Forbes:  Rich Cheat More on Taxes, New Study Shows:

A new study based on unpublished IRS data shows the rich are different when it comes to paying taxes: They hide more of their income.

The previously unreported study estimates that taxpayers whose true income was between $500,000 and $1 million a year understated their adjusted gross incomes by 21% overall in 2001, compared to an 8% underreporting rate for those earning $50,000 to $100,000 and even lower rates for those earning less. (The "net misreporting rate" as the IRS calls it, includes both underreported income and inflated deductions.)

In all, because of their higher noncompliance rates, those with true incomes of $200,000 or more received 25% of all income, but accounted for 40% of net underreported income and 42% of underreported tax in 2001, the new analysis finds.

From Portfolio.com: