Mark J. Mazur (Director, Research, Analysis, and Statistics, IRS) & Alan H. Plumley (Technical Advisor, Office of Research, Analysis, and Statistics, IRS) have published Understanding the Tax Gap, 60 Nat’l Tax J. 569 (2007).  Here is the abstract:

The Tax Gap is defined as the difference between the amount of tax imposed by the Tax Code and the amount that is reported and paid with timely filed returns. For the federal government, the gross tax gap is estimated at $345 billion for Tax Year 2001 (after the collection of late and enforced payments, the net tax gap is estimated at $290 billion for Tax Year 2001). This paper explains the concept of the tax gap, discusses how it is estimated, and points out some limitations with the estimates.