CHAPTER 15: The Effects of Taxation and Spending on Inequality and Poverty
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While the Kakwani measure indicates the progressivity of a tax, it does not serve as a good guide to the impact that a change in the tax would have on income distribution or poverty. For instance, a tax on salt may be highly regressive, but its abolition might do little to help the poor because the tax is so small. The Reynolds-Smolensky measure of the redistributive capacity of a tax solves this problem. A popular version of this measure is given by the following: RS2 = GY – GY–T where GY is the Gini coefficient for pre-tax income and GY-T the Gini coefficient for post-tax income. In our example RS2 = 0.387–0.378 = 0.0096 > 0, which is— • Positive, indicating a progressive tax, because the after-tax distribution of income (as measured by GY–T) is more equal than its pretax distribution (as measured by GY); and • Relatively large, indicating that this tax has considerable redistributive potential. In other words, this tax is a good candidate for serious efforts to make the tax code more progressive. The redistributive capacity of a tax depends both on its progressivity and on the tax rate. It can be shown that RS2 ≈ (t/(1–t)) K, where t is the average tax rate relative to pretax income.1 In our example, the tax rate averages 10 percent, so we have (0.1/(1–0.1)) × (0.086) ≈ 0.0096.
Review Questions 2. Household A has an income of 4,000 and pays tax of 300. Household B has an income of 20,000 and pays tax of 1,400. This tax is
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A. Proportional. B. Progressive. C. Regressive. D. None of the above.
3. A concentration curve for a tax is computed by
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A. Sorting households by tax/capita and graphing the cumulative percentage of tax against the cumulative percentage of households. B. Sorting households by expenditure per capita and graphing the cumulative percentage of tax against the cumulative percentage of households. C. Sorting households by expenditure per capita and graphing the cumulative percentage of tax against the cumulative percentage of expenditure. D. Sorting households by tax/capita and graphing the cumulative percentage of tax against the cumulative percentage of expenditure.
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