Progressivity, vertical and horizonal equity

Transcription

1 Progressivity, vertical and horizonal equity Abdelkrim Araar, Sami Bibi and Jean-Yves Duclos Workshop on poverty and social impact analysis in Sub-Saharan Africa Kampala, Uganda, November 2009 Progressivity and equity Kampala 1 / 11

2 Checking the progressivity of taxes and transfers Progressivity and poverty Concentration curves Checking the progressivity of taxes and transfers Tax Redistribution (TR) Income Redistribution (IR) Checking the progressivity of taxes and transfers The measurement of progressivity Progressivity and equity Kampala 2 / 11

3 Progressivity and poverty How do the poor benefit from the redistribution of national wealth? Do the poor benefit more than the non poor from different types of monetary and in-kind transfers? Is the tax burden on the poor relatively low? Studying the progressivity of taxes and transfers can help answer these questions. Progressivity and equity Kampala 3 / 11

4 Concentration curves An important descriptive and normative tool for capturing the impact of tax and transfer policies is the concentration curve. Suppose pre-tax incomes (gross incomes) X are ranked in ascending order such that: X 1 X 2... X n. Suppose that taxes T j (or transfers) are ranked according to the size of their associated gross income. The concentration curve of a tax T at percentile p is: C T (p = i/n) = i j=1 T j n j=1 T j Progressivity and equity Kampala 4 / 11

5 Concentration curves Table 1: Illustrative Example i p i X i T i L(p i ) C(p i ) Progressivity and equity Kampala 4 / 11

6 Concentration curves The concentration curve shows the proportion of total taxes paid by the bottom p proportion of the population. L(p) and C(p) line L(p) C(p) Percentiles (p) Progressivity and equity Kampala 4 / 11

7 Concentration curves When the concentration curve of a tax is below the Lorenz curve, the poor pay less taxes than the non-poor, relative to their income: the tax is said to be progressive. When the concentration curve of a transfer is above the Lorenz curve, the poor receive more transfers than the non poor, relative to their incomes: the transfer is progressive. What about inequality of net income N? There is a close link between the progressivity of taxes and transfers and inequality in net income. If a tax is progressive, then the net income share of the poor will be higher than the poor s share of gross income. Progressivity and equity Kampala 4 / 11

8 Concentration curves The concentration curve of net incomes N is: C N (p = i/n) = i j=1 N j n j=1 N j We can thus compare the concentration curve ofn to the Lorenz curve for X to assess the net progressivity of the tax and transfer system: C N (p) L X (p) = µ T µ N [L X (p) C T (p)]. Progressivity and equity Kampala 4 / 11

9 Concentration curves When reranking is not observed, we also find: L N (p) L X (p) = µ T µ N [L X (p) L T (p)]. Progressivity and equity Kampala 4 / 11

10 Checking the progressivity of taxes and transfers There are two approaches to making progressivity comparisons: Tax Redistribution : TR approach Income Redistribution : IR approach. Using Lorenz and concentration curves, the following rules can be used to check progressivity. Progressivity and equity Kampala 5 / 11

11 Tax Redistribution (TR) 1. A tax T is TR-progressive if: L X (p) C T (p) > 0 for all p ]0,1[. 2. A transfer B is TR-progressive if: C B (p) L X (p) > 0 for all p ]0,1[ 3. A tax T1 is moretr-progressive than a tax T2 if: C T2 (p) C T1 (p) > 0 for all p ]0,1[ 4. A transfer B1 is moretr-progressive than a transfer B2 if: C B1 (p) C B2 (p) > 0 for all p ]0,1[ Progressivity and equity Kampala 6 / 11

12 Income Redistribution (IR) 1. A tax or a transfer T is IR-progressive if: C N (p) L X (p) > 0 for all p ]0,1[ 2. A tax or a transfer T1 is moreir-progressive than a tax (and/or a transfer) T2 if: C N1 (p) C N2 (p) > for all p ]0,1[ Progressivity and equity Kampala 7 / 11

13 Checking the progressivity of taxes and transfers The measurement of progressivity Quantifying progressivity Indices of progressivity Redistributive Equity The measurement of progressivity Progressivity and equity Kampala 8 / 11

14 Quantifying progressivity 1. Lorenz and concentration curves may cross. 2. It may be useful to provide summary quantitative indices of progressivity. Progressivity and equity Kampala 9 / 11

15 Indices of progressivity Musgrave and Thin (1948) propose to measure progressivity by the ratio of Gini equality of net income to Gini equality of gross income: 1 I N 1 I X This ratio will be greater than one if the tax is progressive. Progressivity and equity Kampala 10 / 11

16 Indices of progressivity The Kakwani index of progressivity is based on thetr approach and equals twice the area between the Lorenz curve and the concentration curve of a tax. This is also the difference between the concentration index of the tax (IC X ) and the Gini index of gross income: IC T I X Progressivity and equity Kampala 10 / 11

17 Indices of progressivity The Reynolds-Smolensky index of progressivity is based on their approach and equals twice the area between the concentration curve of net incomes and the Lorenz curve of gross incomes. This is also the difference between the Gini index of gross income and the concentration index of net income: I X IC N Progressivity and equity Kampala 10 / 11

18 Indices of progressivity L(p) & C(p) Lorenz Curve & Concentration curves Percentiles (p) 0.5(Kakwani Index) 0.5(Reynolds Smolensky Index) R-S Index = µ T µ N (Kakwani Index). (1) Progressivity and equity Kampala 10 / 11

19 Indices of progressivity Example: Calculating progressivity indices Rank i X i T i N i Total I X = 0.25 //I N = 0.19 //IC T = 0.43 // IC N = 0.19 Musgrave and Thin index = (1 I N )/(1 I X ) = 1.08 Kakwani index = IC T I X = 0.18 R-S index = I X IC N = 0.06 Progressivity and equity Kampala 10 / 11

20 Redistributive Equity Does redistribution compress the distribution of post-tax incomes? (Vertical equity) Are equals in pre-tax incomes treated equally by the tax system? (Classical horizontal equity) Does the redistribution re-rank households? (Horizontal equity as non reranking). Progressivity and equity Kampala 11 / 11

21 Redistributive Equity Ranki X N A N B N C Average I X = 0.148;I N = Progressivity and equity Kampala 11 / 11

22 Redistributive Equity VE: HE: RE: Case A: Ranki X N A N B N C Average Vertical equity, since inequality has decreased. Horizontal inequity equals zero since equals are treated equally. Reranking inequity equals zero since no re-ranking is observed. Progressivity and equity Kampala 11 / 11

23 Redistributive Equity VE: HE: RE: Case B: Ranki X N A N B N C Average Vertical equity, since inequality has decreased. Horizontal inequity since equals are treated unequally. Reranking inequity equals zero, since no re-ranking is observed. Progressivity and equity Kampala 11 / 11

24 Redistributive Equity VE: HE: RE: Case C: Ranki X N A N B N C Average Vertical equity, since inequality has decreased. Horizontal inequity equals zero, since equals are treated equally. Reranking inequity since some households are re-ranked. Progressivity and equity Kampala 11 / 11

25 Redistributive Equity Ranki X N A N B N C Average One can use the following decomposition of the redistributive effect on inequality: I X (ρ) I N (ρ) = I X (ρ) IC N (ρ) }{{} Vertical equity (I N (ρ) IC N (ρ)). }{{} Reranking Progressivity and equity Kampala 11 / 11

26 Redistributive Equity Observed & Expected PC Net Income Gross and Net Per Capita Incomes Canada 1994 line_45 Observed E(N X) PC Gross Income in 1994 Progressivity and equity Kampala 11 / 11