From the conclusion an NBER Working Paper "Myth and Reality of Flat Tax Reform: Micro Estimates of Tax Evasion Response and Welfare Effects in Russia":
The 2001 Russian flat rate income tax reform (flat rate of 13%, see chart above) has often been heralded as a success story and has been credited with large increases in tax revenues and an improved business climate. Although it has been difficult to differentiate between myth and reality with the Russian experience, many other transitional countries have followed suit with flat rate income tax reforms, and an increasing number of countries around the world are considering the adoption of a flat rate income tax.
In this paper we focus on the impact of the flat income tax rate on tax evasion, an issue that was, and continues to be, a major problem in Russia as well as in many other transition and developing countries. We argue that the flat tax reform was instrumental in decreasing tax evasion and that, to a certain extent, greater fiscal revenues for Russia in 2001 and several years beyond can be linked to increased voluntary tax compliance and reporting (see chart above).
The most significant reduction in tax evasion was for taxpayers that experienced the largest decrease in tax rates after the flat rate income tax was introduced. We also find that this decline in tax evasion was likely due to changes in voluntary compliance as opposed to greater enforcement effort by the tax administration authorities.