I ran across this 2007 paper in the Economic Journal by Naomi Feldman and Joel Slemrod. The authors used an interesting method to identify people who might have shortchanged the IRS. In particular, they look at (unaudited) IRS tax returns and calculate the ratio between charitable giving and reported taxable income. Their assumption is that that the "true" ratio should be relatively constant across households who receive their income in the form of wages/salary from an employer and those who earn their income from a small business or farming (that is, there is little reason to believe a salaried employee is more or less generous toward charities than a business owner; this is an assumption they test and discuss in detail in the paer). Of course, the crucial difference here is that salaried employees have their incomes directly reported by their employer to the IRS, which isn't always true of people who earn income in other ways.
From the paper:
“We find that the implied amount of noncompliance on non-wage-and-salary income is substantial and that it varies among these sources of income as well as between positive and negative values of each type of income. On average, reported positive self-employment, nonfarm small-business and farm income must be multiplied by a factor of 1.54, 4.54 and 3.87, respectively, in order to obtain true income.”
elsewhere they write:
“Farm income is estimated to have a compliance rate of 25.9% and Schedule E income has an estimated coefficient of 4.54, which corresponds to the lowest compliance rate in this study – 22.0%.”