1 Income Inequality in the US

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1 1 Income Inequality in the US We started this course with a study of growth; Y = AK N 1 more of A; K; and N give more Y: But who gets the increased Y? Main question: if the size of the national cake Y increases (growth), does everyone get a bigger slice? bigger than they had before? bigger relative to others? does growth trickle down? 1.1 The facts Shares of National Income going to various income groups, Upper and lower limits of various quintiles. How has median houshold income changed? how has average income changed? distribution getting more skewed? Between , and , all income groups except the top 20% (the top two deciles) have su ered declines in the share of national income going to them. The income share of the upper 1% in 1989 was equal to that of the bottom 40%! Demographic composition (see Table attached); importance of education Demographics of the richest 1% and poorest 20% (see Table attached) Moving from Incomes to Wealth: wealth inequality in the US; wealth measured by net worth (assets - liabilities): top 20% held 85% of U.S household wealth in 1989; the average net worth of the top 20% was $ 840,000; the bottom 20% had a net worth of $-14,000; the average net worth of the top 1/2 of 1% was $ 12.5 million!. Top 1% holds around 48% of US household wealth. Growth in average net worth: between ; the top 20% saw a 88% rise in their net worth, while the bottom 20% saw a $10,000 fall. Which are the main assets and liabilities of most Americans? In 1989, there were 93 million households in the US; so each percent represents just under 1 million households. 1

2 1.2 Measuring Income Inequality Lorenz Curve It depicts the total number of households on the horizontal axis and their total wealth holdings on the vertical axis. To construct the Lorenz curve, households are rst arrayed in ascending order by wealth. Then the total cumulative total wealth is calculated, beginning with the poorest household and ending with the richest household. These values are plotted for each household on the diagram, and then connected to construct the Lorenz curve. Any point on the curve shows that the poorest x% of households own y% of all wealth in the society. The 45 0 degree line represents perfect equality (the poorest x% of the households hold exactly x% of the wealth); if all wealth belongs to 1 household, then the Lorenz curve traces the lower and right-hand borders of the diagram (perfect inequality). Why must the Lorenz curve touch both ends of the 45 0 line? Inequality is greater the farther the Lorenz curve bends away from the 45 0 line of perfect equality (the larger the shaded area A): Gini coe cient A Gini = A + B = area btw curve and 450 line area under 45 0 line Gini is a number between 0 and 1. when is the Gini coe cient 0 or 1? The greater is the concentration of wealth, the closer is the Gini index to unity. The Gini index is a shorthand (summary) measure of inequality. for highly unequal countries, Gini lies between 0.5 and 0.7, while for countries with relatively equitable distributions, the Gini is around ; how has the US Gini changed over time? Socialist countries (e.g. Poland, Bulgaria, Hungary) tend to have lowest post-tax income Gini s. 2

3 Recent 1996 data reveal that Latin America as a whole has the highest Gini (0.5), followed by sub-saharan Africa, East Asia, high-income countries (U.S ~ 0.43), and former Eastern Europe (0.25). 1.3 Development and Inequality in cross-section Kuznets Curve In poor countries, economic growth would initially raise the gap between the rich and the poor. Only as economies became richer would the gap close. So, inequality rises in the early stages of development of a country and then it falls, once the country has grown su ciently. Kuznets curve: plot income inequality against per capita GDP (for various countries) on the horizontal axis, shape of an inverted-u (i.e., \): According to Kuznets, increases in income inequality is a natural outcome of the growth process (initially). 2 Income Distribution and Macroeconomics example of Phillipines and Korea Galor-Zeira model. Simple model with one message: where one starts o in life, matters a lot for one s own future, and the future generations in that lineage. Illustrates how income inequality perpetuates over time. one good; two technologies for producing this good. one uses skilled labor and capital; capital is xed. Wage rate in this skilled sector is w s : Formal sector. other uses unskilled labor, wage rate w n. w s >> w n agents live for 2 periods; second period they may leave bequest to their children 3

4 in the rst period, person receives a inheritance and then decides whether to get education (acquire skills) or work as an unskilled worker; real world analogy if he chooses to acquire skills when young, he becomes a skilled worker when old; otherwise, he is an unskilled worker in both periods. agents endowed with 1 unit of labor in each period. minimum amount h needs to be invested to get any returns from education; threshold; real world education agents only consume in the 2nd period of life u = c b 1 all agents are identical when born; what will create a di erence will be the inheritance they get from their parents. agents pay higher interest rate (i) when they borrow and get less (r) when they lend; credit market imperfection; i > r old agent s problem: an old agent with wealth y subject to the constraint that max c;b u = c b 1 c + b = y Solution is : max u = (y b) b 1 b b = (1 ) y Then indirect utility: U = (y b ) b 1 = (1 ) 1 y = "y 4

5 utility is linear in wealth if a person inherits x and chooses not to acquire skills, then as an adult, he gets [(x + w n ) (1 + r) + w n ] his utility will be: his bequest will be: U n (x) = " [(x + w n ) (1 + r) + w n ] b n (x) = (1 ) [(x + w n ) (1 + r) + w n ] if a person inherits x; where x h; and chooses to acquires skills using h part of his x; remainder he lends; then as an adult his wealth is [(x h)(1 + r) + w s ] his utility is: and his bequest is U l s(x) = " [(x h)(1 + r) + w s ] b l s(x) = (1 ) [(x h)(1 + r) + w s ] if a person inherits x where x < h; and chooses to invest in education, he borrows (h x) ; his adult wealth is [(x h)(1 + i) + w s ] his utility is and his bequest is U b s (x) = " [(x h)(1 + i) + w s ] b b s(x) = (1 ) [(x h)(1 + i) + w s ] when will all individuals prefer to work as unskilled? [(x + w n ) (1 + r) + w n ] > [(x h)(1 + r) + w s ] or, (2 + r) w n > w s h(1 + r) 5

6 This is unrealistic; so assume the opposite: Assumption (2 + r) w n w s h(1 + r) if this condition is true, then some people will choose to get education. when will a borrower (a person with inheritance less than h) invest in education? when or, U b s (x) = " [(x h)(1 + i) + w s ] U n (x) = " [(x + w n ) (1 + r) + w n ] x w n(2 + r) w s + h(1 + i) i r this means that individuals who inherit x > f will invest in education; individuals with su ciently high inheritance will choose to be skilled; others will stay unskilled. Suppose you come into a period with inheritance x t : How much will you leave for your children? 8 < b n (x t ) = (1 ) [(x t + w n ) (1 + r) + w n ] if x t < f x t+1 = b b : s(x t ) = (1 ) [(x t h)(1 + i) + w s ] if f x t < h b l s(x t ) = (1 ) [(x t h)(1 + r) + w s ] if x t h picture how to draw this picture? stable: if the line cuts the 45 0 line from above; unstable if the line cuts the 45 0 line from below In the long-run, agents converge to one of two steady states; rich families that get education generation after generation (get x s ) and poor ones that remain unskilled forever (get x n ) Message: where one starts o in life, matters a lot for one s own future, and for the future of later generations in that lineage. all persons who inherit less than g and more than x n will bequeath less than they inherit; the process continues until they converge to x n : f 6

7 2.0.2 Why too much inequality may be harmful for growth? 1. A country with highly unequal incomes has large numbers of poor; poor cannot borrow to nance education; therefore, higher inequality leads to less education for the poor and hence prevents them from growing out of their poverty; overall growth su ers; also uneducated (unskilled) work force does not contribute to national output that much. 2. Political instability: more inequality leads to more crime, coups, assassinations, rapid changes of government etc.; investments become more risky; leads to reduced investment domestically. 3 The median voter Consider an electorate that is distributed uniformly along the idealogical spectrum a 2 [0; 1] from the left to the right. Two candidates, 1 and 2; candidate with the most votes wins. Each voter casts her vote for the candidate that is closest to her idealogical position. The candidates know this and care only about winning. Simple majority is needed to win. One man, one vote. Is it possible to make a prediction about the idealogical position the two candidates would choose to stand for? At every point on the line, there is a voter who most prefers that value of a; point A has a voter who most likes a = 0:3: Suppose candidate 1 were to consider announcing that she stands for a = 0:3 [if elected, she would implement a tax rate of 0.3]. Candidate 2 considers announcing a = 0:5: How many people have most preferred tax rates that are greater or equal to a = 0:5? 50%. Why? For all these agents, a = 0:3 is further from their most preferred position than a = 0:5 is. a = 0:3; if elected, would hurt them more than if a = 0:5 were elected. Hence they all vote for a = 0:5; since this is at least 50% of the people, a = 0:3 cannot win! In fact, any candidate that positions herself between a = 0:3 and a = 0:5 will win. 7

8 Equilibrium: both candidates will announce they stand for a = 0:5; political equilibrium; appeal to the median voter; in this example, the one exactly in the middle. how does politics a ect macroeconomic policy making? a highly unequal democratic society has a poor median voter who all candidates attempt to win over Politics of inequality: highly unequal democratic societies are likely to vote for large income redistributions through the tax system; the rich get taxed heavily, enterprise su ers, welfare budgets will go up; such scal policies may harm future growth. 8