IMPACT OF TAXES AND TRANSFERS

More documents

Recommendations

Info

Enami, Lustig, Aranda, No. 25, November 2016 1.1.1. Equalizing, Neutral, and Unequalizing Net Fiscal Systems: Conditions for the One Tax Case In this section, we review conditions that allow us to determine whether a fiscal system with only a single tax is equalizing, neutral, or uneqaulizing. Concentration and Lorenz Curves When the post-tax income Lorenz curve lies everywhere above the pre-tax income Lorenz curve, that is L X-T (p) ≥ L X (p), the tax is equalizing (and vice versa). Equation 3 implies that the post-tax income Lorenz curve lies completely above the pre-tax income Lorenz curve if and only if the concentration curve of taxes lies completely below the pre-tax income Lorenz curve. 5 (4) L X-T (p) ≥ L X (p) ‹=› C T (p) ≤ L X (p) for all p, and with strict inequality for some p In other words, the distribution of post-tax income is less unequal than the pre-tax income distribution if and only if the tax is distributed more unequally than the income to which it applies, or put another way, if and only if the concentration curve of taxes lies completely below the pre-tax income Lorenz curve. This condition is shown on figure 1, which features the Lorenz curves for pre-tax and post-tax income and the concentration curve for taxes. In other words, if the average tax rate t(x) is increasing with income everywhere, then taxes are distributed more unequally than pre-tax income. Thus, an everywhere progressive tax will always be equalizing. Given equation 4, it is easy to see that the condition for a tax to be unequalizing is C T (p) ≥ L X (p). This condition will occur if t(x) decreases with income, that is, if taxes are regressive everywhere. However, just like in the case of progressive taxes, it is not necessary for taxes to be regressive everywhere to be unequalizing. Finally, in the case of a proportional tax--that is, 5 This is true because if 0 g 1, the weights by definition sum to one. Hence L X (p) must lie between C T (p) and C X-T (p) by necessity. 8
Enami, Lustig, Aranda, No. 25, November 2016 when T(x)/x is the same for all x--the distribution of post-tax and pre-tax income will be exactly the same and C T (p) = L X (p). Figure 1. Lorenz Curve of Pre-Tax Income and Post-Tax Income and Concentration Curve of Tax In sum, incomes are less unequal after a tax than before the tax if and only if the tax is distributed more unequally than the income to which it applies. Incomes are more unequal after a tax than before the tax if and only if the tax is distributed more equally than the income to which it applies. A proportional tax will have the same distribution as the pre-tax income and leave the distribution of income unchanged. A poll tax, which taxes all individuals by the same absolute amount, will feature a concentration curve coincidental with the diagonal, that is, it will be very unequalizing. 6 6 Although not impossible in principle, taxes in absolute terms (that is, per capita) rarely decline with income in the real world. If such a tax were to exist, its concentration curve would lie above the diagonal and be extremely unequalizing. 9
Page 1 and 2: ANALYTIC FOUNDATIONS: MEASURING THE
Page 3 and 4: ANALYTIC FOUNDATIONS: MEASURING THE
Page 5 and 6: Enami, Lustig, Aranda, No. 25, Nove
Page 7: Enami, Lustig, Aranda, No. 25, Nove
Page 59 and 60:
Enami, Lustig, Aranda, No. 25, Nove
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
show all

IMPACT OF TAXES AND TRANSFERS

Create successful ePaper yourself

Delete template?

Save as template?