More evidence that redistribution must go from the rich to the poor

If the main objective of the evaluation of a tax reform is to give empirical content to the redistributive effects of different tax systems before and after the reforms, a formal expression of the concept of redistribution is required. Redistribution is defined here as the shift of income which occurs in the post-tax distribution from high to low incomes. Hence, it can be measured by comparing the pre-tax Lorenz curve with the post-tax concentration curve. Our measure of redistributive effect is therefore defined as: Π [ ] RS = − ∫ L p L p dp XT X − 2 0 1 () () (2) where the superscript of ΠRS refers to Reynolds and Smolensky (1977) who applied this measure to the US tax system, and L p xf x dx X y ( ) ( ) = ∫ µ 0 0 1 ≤≤ = p p Fy and ( ) (3) L p x t x f x dx t X T y − = − − ∫ ( ) ( ( )) ( ) µ( ) 1 0 0 1 ≤≤ = p p Fy and ( ) (4) are, respectively, the Lorenz curve of pre-tax income ( x ) and the concentration curve with respect to pre-tax income of after-tax income ( x tx − ( ) ), with: p : the population shares of the pre-tax distribution f x( ) : the density function of x F x( ) : the distribution function of x µ : mean income (pre tax) t x( ) : the tax liability corresponding with taxable income x t : the average tax rate.