It seems obvious that the higher the tax rates, the more people will try to find ways to evade them. Employees usually few means to evade, as the employer is obliged to furnish payroll data to tax authorities. But self-employed people have much more latitude. One could thus expect that their numbers and/or reported income to vary with the tax rate.
Åsa Hansson uses a tax reform in Sweden to look at this. And our intuition is confirmed: the taxable income of small business owners is twice as responsive as that of employees. The reason is that self-employed people can more easily shift their income into categories that are easy to shelter from taxes. Indeed, gross income of small business owners does not seem to be responsive to tax rates.
Regarding the propensity to become self-employed, Åsa Hansson produces another study that shows a negative relationship between self-employment and marginal or average tax rates. That is counter intuitive, but has been found occasionally in other studies (although not systematically). Would there be something special about Sweden? The particularity is that taxation in Sweden is neutral in that the source of income does not matter, and one cannot play with gains and losses to exploit differences in marginal rates. To me, that makes the results even more puzzling. One would then expect to see no shifting of income in Sweden (but, say, in the US) and no correlation between tax rates and self-employment (while it would be positive in the US). Unfortunately, Hansson offers no convincing explanation for the results.