Haughton and Khandker
15 Table 15.1 Progressivity Illustrated Case 1: Progressive tax Case 2: Proportional tax Percent Income of total (1) 1 2 3 4 5 All
(2) 1,200 2,000 3,200 4,400 9,200 20,000
(3) 6.0 10.0 16.0 22.0 46.0 100.0
Tax paid (4) 80 150 270 450 1,050 2,000
Percent Percent of income of total (5) 6.7 7.5 8.4 10.2 11.4 10.0
(6) 4.0 7.5 13.5 22.5 52.5 100.0
Tax paid (7) 120 200 320 440 920 2,000
Percent Percent of income of total (8) 10.0 10.0 10.0 10.0 10.0 10.0
(9) 6.0 10.0 16.0 22.0 46.0 100.0
Case 3: Regressive tax Tax paid (10) 200 300 400 500 600 2,000
Percent Percent of income of total (11) 16.7 15.0 12.5 11.4 6.5 10.0
(12) 10.0 15.0 20.0 25.0 30.0 100.0
Source: Authors’ creation. Note: Data are hypothetical.
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The case of a proportional tax is shown in columns (7)–(9). In this case, everyone pays the same proportion of their income in taxes. And in columns (10)–(12), we present an example of a regressive tax. In this example, although tax payments are higher in absolute terms for the rich than for the poor, the proportion of income paid to taxes actually falls as one moves from poorer to richer individuals. The same information can be shown in the form of histograms; those in figure 15.1 are based on the three cases set out in table 15.1. It is easy to see at a glance that the first tax is progressive, the second proportional, and the third regressive. Sahn and Younger (1999) also make heavy use of graphs in their study of fiscal incidence in Africa. There is some loss of information when data are aggregated into quintiles (or deciles) as done here. A solution is to graph the results in greater detail, as is done in figure 15.2 for the hypothetical income numbers underlying the summary statistics in columns (2) and (4) in table 15.1. To construct figure 15.2, we first sorted all the individuals in the sample from poorest to richest, using income per capita as our welfare measure. Then we graphed the cumulative percentage of income on the vertical axis, against the cumulative percentage of individuals on the horizontal axis. This gives the Lorenz curve—the heavy curve in figure 15.2—which was discussed in more detail in chapter 6, “Inequality Measures.” This serves as a point of reference, along with the diagonal representing the line of perfect equality. We then added a tax concentration curve, which graphs the cumulative percentage of tax paid on the vertical axis. Note that the individuals are still sorted by income (and not by tax per capita). The concentration curve for the income tax shown in figure 15.2 is farther from the line of perfect equality than the Lorenz curve. In other words, tax payments are distributed more unequally than income, which means that the tax is progressive.