Mark Thoma points to a study by Yuriy Gorodnichenko, Jorge Martinez-Vazquez and Klara Sabirianova Peter, which looked at household level data (they use the gap between household expenditures and reported earnings as a proxy for tax evasion) to see how tax reform influenced tax evasion and real income, finds that though tax evasion decreased under the flat tax, it did little to increase real income for taxpayers. They conclude that a flat tax can produce a revenue increase where under-reporting of income is widespread. They write,
"Utilizing difference-in-difference and regression-discontinuity-type approaches, we find that large and significant changes in tax evasion following the flat tax reform are associated with changes in voluntary compliance and cannot be explained by changes in tax enforcement policies. We also find the productivity response of taxpayers to the flat tax reform is small relative to the tax evasion response. Finally, we develop a feasible framework to assess the deadweight loss from personal income tax in the presence of tax evasion based on the consumption response to tax changes. We show that because of the strong tax evasion response the efficiency gain from the Russian flat tax reform is at least 30% smaller than the gain implied by conventional approaches."
Mark Thoma sums up the debate nicely,
"The lack of a significant productivity response undercuts the main supply-side argument that cuts in taxes produce increased growth in output that generates a partial offset (some even argue a more than full offset) to the revenue lost from the tax cut. So many supply-siders have switched to the compliance argument for the US, but I doubt this effect would be large, and certainly not large enough to pay for the tax cut, and compliance can be increased in other ways such as closing loopholes and better enforcement of existing tax law."
Austan Goolsbee examined the effects of the increases in the marginal tax rate by the Clinton administration in the early nineties and found little evidence of any distortion of incentives among the rich tax payers.