## Chapter Study Outline

19.1 The Distribution of Earnings

• The earnings distribution function, f(w), can be thought of as a relative frequency histogram in which the value of f(w) represents the proportion of workers in the population who earn precisely the wage w.
• Because f(w) represents the relative frequencies, the area under the curve is equal to one.
• In the United States, the earnings distribution has a pronounced right skew, so the average earnings exceed the median earnings.
• The cumulative distribution of earnings, F(w,) represents the proportion of workers who earn w or less.
• By taking the logarithm of earnings, the resulting distribution, g(v) (where v ≡ ln(w)), for the United States has virtually no skew.
• Recently, economists have increased their use of expected discounted lifetime earnings, which is equal to a worker’s current earnings plus the expected discounted value of his or her future earnings.
• An increase in inequality implies that the earnings distribution become more spread out
• The 90-10 ratio measures the spread between the earnings of those workers located at the top and bottom deciles of the earnings distribution and is often used to capture the gap between the rich and the poor.
• The Lorenz curve is given by y = L[x], where x represents the percentage of households in a group and y denotes the percentage of the group’s combined earnings.
• The Lorenz curve begins at the origin because the earnings that accrue to nobody are zero.
• The Lorenz curve ends at (100 percent, 100 percent) because 100 percent of the group’s earnings necessarily accrue to someone in that group.
• The Lorenz curve increases in x because earnings are positive.
• The most unequal earnings distribution occurs when all but one person’s earnings are zero.
• The most egalitarian earnings distribution occurs when everyone earns the same amount.
• The Gini coefficient, which lies between zero and one, is a frequently used inequality measure that is calculated using the Lorenz curve.

19.2 Superstars

• The superstar phenomenon arises whenever small ability differences are magnified into huge earnings differentials.
• The superstar phenomenon is ubiquitous in the entertainment industry, medicine, CEOs, and the legal profession.
• Earnings that are directly proportional to workers’ abilities are key to the absence of superstars.
• Rosen (1981) demonstrates that two distinct forces can lead to a nonlinear ability-earnings relationship.
• The willingness to pay for the good or service provided by the worker rapidly increases with ability.
• The worker’s market share increases rapidly with ability.
• This nonlinear relationship causes a symmetric innate ability distribution that leads to an earnings distribution with a pronounced right skew.

19.3 Earnings Inequality: The Evidence

• The level of income inequality in the United States was relatively steady from 1955 to 1979 and then increased rapidly during the 1980s.
• The increase in income inequality slowed during the early 1990s and increased rapidly again from 1998 through 2007.
• Men and women experienced sizable income inequality increases from 1963 through 2005 though the wage gap between men and women decreased.
• Empirical work has shown that residual inequality, earnings inequality within narrowly defined worker group, increased.
• Developed economies typically have lower levels of inequality than developing countries, but developed countries witnessed striking increases in inequality during the 1980’s and 1990s.

19.4 Explaining the Evolution of Inequality

• The supply-demand-institutions (SDI) framework is the principal theoretical tool that economists use to model changes in the relative earnings of different worker groups.
• In the SDI framework
• Skilled and unskilled workers supply their labor inelastically.
• The initial proportions of skilled and unskilled workers in a population are exogenously given.
• The demand for skilled and unskilled labor is governed by the standard negatively sloped marginal revenue product schedules.
• According to the supply-demand interpretation of the model, competitive forces ensure that demand for labor equals the supply of labor for both skilled and unskilled workers.
• According to the institutions interpretation of the model, labor-market regulations and institutional impediments tend to throw a wrench in the competitive machinery so that the demand and supply of labor may not be equal.
• Over the last 40 years, the U.S. labor force has experienced a pronounced skill upgrade so that more of the labor force is more skilled than ever before.
• This change should have narrowed the skilled-unskilled wage gap.
• The skilled-unskilled wage gap in fact increased over this period.
• The increase in the skilled-unskilled wage gap can be explained by an increase in demand for skilled labor.
• Three different avenues could have increased the supply for skilled relative to unskilled labor in the past 40 years.
• shift in the industrial fabric of the U.S. economy away from manufacturing toward services
• increased openness to international trade in the United States
• technological advances that led to skill-biased technological change

19.5 Institutional Factors and the SDI Framework

• In addition to supply and demand factors, institutional changes have a profound influence on the degree of earnings inequality.
• In the United States, earnings inequality is enormously affected by
• decline in the real value of the minimum wage
• increased use of performance pay
• decrease in union power
• Observed residual inequality levels can partially be accounted for by compositional effects as an increasingly large portion of the U.S. labor force is made up of female and minority workers.
• Empirically, economists have found that different economic forces have been at work in different parts of the earnings distribution.