Richard Winchester (Thomas Jefferson) has posted The Gap in the Tax Gap: What Congress Should Do About It on SSRN.  Here is the abstract:

According to the most recent official estimates, $54 billion in taxes go uncollected each year because individuals underreport their employment tax liabilities. That portion of the tax gap is largely the result of self-employed individuals who underreport what they truly owe. The government’s official report on the tax gap gives substantial attention to only one reason why this is the case: the fact that sole proprietors simply do not report amounts they receive from third parties who are not required to either report the transaction to the government or withhold tax on the payment. However, self-employed persons understate their employment tax liabilities in other ways that are not reflected in the official tax gap estimates. The law permits them to artificially understate their employment tax liabilities when they do not operate their businesses as sole proprietors. This is possible because the employment tax laws operate in an inconsistent way across business forms. This article describes the defects in the law, estimates the magnitude of lost employment tax revenue, and offers a legislative proposal for reform.