The case for a flat tax (the same tax rate for everybody, no matter how much income you earn) has been based on two main ideas: the first, is the increase in economic efficiency obtained by reducing the deadweight loss from taxes; the second and more sophisticated argument, is that by reducing tax rates, one would increase production incentives for high income people, thus increasing productivity, growth and revenues.
The Flat Tax has been implemented in many transition countries after the fall of the communist regime, from small states like the Baltic countries to Russia. The latter, has been the object of a study by economists Yuriy Gorodnichenko (University of California, Berkeley), Jorge Martinez-Vazquez and Klara Sabirianova Peter (both of Georgia State University). In an article published this month in the Journal or Political Economy they show that a flat tax reduces tax evasion but that its impact is insignificant on productivity. The estimates on tax evasion are hard to get, but the atuhors, by looking at the gap between reported consumption and income through survey data, create a reasonable framework for such analysis.
The policy conclusion are quite straightforward: tax evasion is reduced by this type of taxes (so confirming the first type of argument) but real income is not affected. The next question is: does the benefit from lower tax evasion (more compliance) compensate the effect of a hypoethetical tax cut on high income earners?