1. Measurement of Income Inequality and Redistribution Ivica Urban Institut za javne financije Croatian Quants Day, Zagreb, 9 April 2010

2. The distribution of income “Capitalism has solved the problem of production, but failed to solve the problem of distribution.” Economics: not an easy science – many diverging views on how to organize society Egalitarians, interventionsts, socialists, libertarians...

3. Libertarians “There is no problem of ‘distribution’ at all.” “On the free market, everybody earns income in accordance with services provided to consumers.” Example: Ice-cream producer

4. Egalitarians “There is too much of inequality around, as a result of market process.” “It is an unfair situation and the government must be called to redistribute income.” Redistribution: taking from ones and giving to others If the “ones” are higher-income, and the “others” are lower-income people → reduction of income inequality

5. Socialism Abolishment of private property Central planning of production and income distribution No economic and political freedoms But still, we can hear: “It was a just society, everybody had a job, noone was left behind...”

6. Today, we’re all egalitarians! Modern democracies: huge “social security” systems A massive income redistribution apparatus: taxes, benefits and regulation How to estimate the impact of government?

7. Lorenz curves Income units Cumulative shares of units p Incomes X Cumulative shares of income L X (p) 0.00.0000 #1#10.1500.0097 #2#20.2800.0253 #3#30.31000.0448 #4#40.42000.0838 #5#50.52500.1326 #6#60.63000.1910 #7#70.73500.2593 #8#80.88000.4152 #9#90.910000.6101 #101.020001.0000

8. Gini coefficient = double the area between the Lorenz curve and the line of absolute equality

9. Income redistribution X = income before fiscal action T p = amount of pth tax B q = amount of qth benefit N = income after taxes and benefits N = X - Σ T p + Σ B q

10. Income redistribution Pre-fiscal income XLX(p)LX(p) Taxes T Benefits B Post-fiscal income N LN(p) LN(p) 00 500.0111120500.03 800.0317120600.07 1000.0421120800.10 2000.08431201000.16 2500.13541201100.22 3000.19641201500.28 3500.26751202000.36 8000.421721203000.50 10000.612141204000.68 20001.004291208001.00

11. Income redistribution Pre-fiscal income X Taxes T Benefits B Post-fiscal income N Net fiscal gain B-T (B-T) / X 5011120501092.19 8017120601031.29 1002112080990.99 20043120100770.39 25054120110660.27 30064120150560.19 35075120200450.13 800172120300-52-0.06 1000214120400-94-0.09 2000429120800-309-0.15

12. Horizontal equality / inequality

13. the principle of horizontal equality: “equals” should have equal treatment people with equal incomes should obtain equal net fiscal benefits

14. Horizontal equality / inequality

16. NKDE-2D Normal Kernel Density Estimation in 2 dimensions: h n = optimal bandwidth S = sample covariance w i = sample weights N = n x w i, n = number of observations

17. Conditional density Normal KDE in 2 dimensions, to obtain estimates of f(x,y), from which f(y|x) are calculated using:

18. 18 Measurement model Utility of income function U(y) with inequality aversion parameter ε: Equally distributed equivalent income (income that, if obtained by every individual, would deliver the same welfare as actual income):

19. Measurement model