## INCOME INEQUALITY & DUALISM

François Nielsen
Department of Sociology
University of North Carolina Chapel Hill

### What Is Inequality?

Inequality is a property of the distribution in a population of some (presumably valued) resource such as income or wealth but also cattle, wives (in a polygynous society), and articles published by scholars in scientific journals.  The distribution of such quantities is typically highly skewed, with a long tail to the right.
One can conceptualize inequality with the Lorenz curve.  Take the example of income.  Imagine that all income-receiving units (IRUs) are ranked by income from the smallest to the largest, and calculate the cumulative share of income accruing to each category of the populations from poorest to richest, as in the following table.

 Income Category Share of Total Income (%) p = Cumulative Share of Population (%) L = Cumulative Share of Income (%) Top 20% 42.7 100 100.0 4th 20% 24.4 80 57.3 3rd 20% 17.1 60 32.9 2nd 20% 11.1 40 15.8 Lowest 20% 4.7 20 4.7 Total 100

The Lorenz curve is the plot of the cumulative income share L against the cumulative population share p.

### Can One Measure Inequality?

Yes.  One common measure of inequality is the Gini coefficient.  The Gini coefficient (or "Gini index" or "Gini ratio") G is calculated from the Lorenz curve as the ratio
G = Area A/(Area A + Area B)
Note that (Area A + Area B) is the area of a triangle, given by 100*100/2=5000.
The Gini coefficient for the 1983 U.S. family income distribution is given by the following calculations.

 Area A + Area B 100*100/2 = 5000 Area 1 20*4.7/2 = 47 Area 2 20*(4.7+15.8)/2 = 205 Area 3 20*(15.8+32.9)/2 = 487 Area 4 20*(32.9+57.3)/2 = 902 Area 5 20*(57.3+100)/2 = 1573 Total Area B 3214 Area A 5000 - 3214 = 1786 Gini Coefficient 1786/5000 = 0.36 or 36%

Thus the Gini coefficient in this example is 1786/5000 = 0.36 or 36%.
In the Lorenz curve the 45 degrees line represents a situation of perfect equality.  (Why?).
In general, the closer the Lorenz curve is to the line of perfect equality, the less the inequality and the smaller the Gini coefficient.

Countries differ in the inequality of their income distribution.

Note how the Lorenz curves of different countries can intersect; this means that 2 societies with the same Gini ratio can have different Lorenz curves (i.e., more inequality "at the bottom" versus more inequality "at the top").  Thus the Gini coefficient is not a complete description of the income distribution.

The following table shows the distribution of family wealth in the U.S. in 1983.  You may want to calculate the Gini coefficient as an exercise.

 Income Category Share of Total Wealth (%) p = Cumulative Share of Population (%) L = Cumulative Share of Wealth (%) Top 20% 78.7 100 100.0 4th 20% 14.5 80 21.4 3rd 20% 6.2 60 6.9 2nd 20% 1.1 40 0.7 Lowest 20% -0.4 20 -0.4 Total 100

Inequality tends to be greater for wealth than for income.  (Why?).

The fifteen wealthiest people in the world in 2005

### Are There Other Ways to Measure Inequality?

Yes.  Other more or less sophisticated measures of inequality include the following
1. Share of total income accruing to the top 20% of IRUs; this is 42.7 for U.S. family income distribution in 1983; share of the top 10%, or 5% are also used; the larger, the more unequal the distribution
2. Share of total income accruing to the bottom 40% of IRUs; this is 15.8 for U.S. family income distribution in 1983; the larger, the less unequal the distribution
3. Gap in constant \$ between income of the 90th percentile and income of the 10th percentile; often used by economists; advantage is that knowledge of very top and very bottom incomes does not need to be accurate
4. Gini coefficient calculated form individual IRU data (as opposed to grouped data).  The formula is
1. G = (2/(μ*n2))Σi=1 to ni*xi - (n+1)/n
where xi is income, i is the rank of income xi (i=1 for smallest income, i=n for largest), and μ is the mean income.
5. Theil coefficient (or "information theory" or "entropy" measure) calculated from individual IRU data.  The formula is
1. T = [(1/n)Σi=1 to n(xi*log(xi)) - μ*log(μ)]/μ
where log denotes the natural logarithm.
6. Varlog (variance of the logarithms of income) calculated from individual IRU data.  The formula is
1. V = (1/n)Σi=1 to n(zi - z.)2
where zi = log(xi) and z. denotes the mean of the zi
7. The coefficient of variation calculated from individual IRU data.  The formula is
1. C = sX
where sX is the standard deviation of the xi and μ is the mean of the xi
Income inequality measures may or may not have certain desirable properties such as
• scale invariance: inequality is invariant to proportional increases or decreases in everyone's income (e.g., as may happen with inflation)
• principle of transfer: any transfer from an individual with a lower income to an individual with a higher income represents an increase in inequality, and vice versa
Only G, T, and C satisfy both properties.  For a detailed discussion see Allison (1978).
There is a substantial literature analyzing the properties of inequality measures with respect to social welfare.

### What is Dualism?

In this context dualism is the amount of income inequality generated by the difference in average income between two distinguishable categories of IRUs in a society.
Examples are
• inequality generated by the difference in average income between IRUs in the traditional /agricultural versus modern /urban sectors of a developing economy
• inequality generated by the difference in average income between black and white households in the U.S.

### How is Dualism Measured?

One measure of dualism is simply a special case of the Gini coefficient, in which the number of IRUs is reduced to 2.  Then the Gini coefficient can be calculated as
D = |p - L|
where p is the percentage of IRUs in the poorest category and L is the percent income share of IRUs in the poorest category.  The symbol |  | denotes the absolute value.
The relationship of dualism to the Lorenz curve and the Gini coefficient is shown in the following exhibit.

Historically the concept of dualism was emphasized in a famous article by economist Simon Kuznets (1955) that initiated a stream of research on the relationship of income inequality with economic development.  Kuznets thought that dualism generated by income differences between traditional/agricultural and modern/urban sectors was a principal reason for the high level of income inequality in developing countries.  The following exhibit shows sector dualism figures for countries of the world around 1970.

### The Big Picture: Inequality Trends and Sociocultural Evolution

Is U.S. society today more or less unequal than it was 200 years ago?  How do modern industrial societies compare with simple societies, such as hunters and gatherers?
Sociologist Gerhard Lenski has proposed a typology of human societies based on subsistence technology, and the nature of the environment of the society.  The basic typology (simplified) is

 Type of Society Main Technological Innovation Approximate Date of Appearance Hunting & Gathering (primordial) Horticultural Plant Cultivation 8,000 BC Agrarian Use of the Plow 3,000 BC Industrial Use of Machines Powered by Inanimate Forms of Energy 1,750 AD

Inequality has evolved in a systematic way during sociocultural evolution according to Lenski.

### Patterns of Inequality in the Modern World

During industrialization, inequality of the distribution of income has been characterized by 2 historical trends: the Kuznets Curve and the Great U-Turn.

#### 1.  The Kuznets Curve

The Kuznets Curve was named after economist Simon Kuznets (1955).  Kuznets conjectured that during industrial development in the long run, income inequality at first rises and then declines, tracing an inverted-U-shaped trajectory.  As a result, industrial societies are more equal than non-industrial societies
The inverted-U shape of the Kuznets curve is due to
• the expansion of education (producing a linear decline in inequality with economic development)
• the shift from agriculture to the secondary (manufacturing) and tertiary (services) sectors (producing an inverted-U trend of inequality because of sector dualism)
• the demographic transition (also producing an inverted-U trend of inequality, with inequality highest at point of fastest population growth)

#### 2.  The Great U-Turn in the U.S. and a Few Advanced Industrial Societies

The phrase "The Great U-Turn" was coined by Harrison & Bluestone (1988).
The term refers to the inequality upswing that took place since the early 1970s in some advanced industrial societies (especially the U.S. and the U.K.)
Why these inequality trends?
Research suggests that the inequality upswing is the result of a combination of factors including
• deindustrialization ( = decline in manufacturing employment) caused in part by globalization and international competition
• increasing reliance on technology causing increased demand (and higher returns) for education and cognitive skills
• increasing proportion of female-headed households
Additional reference: the following article from the Census Bureau looks at income inequality trends in the US from 1947 to 1998. Two salient features of the recent trend discussed in the article are
• in 1993 the Census Bureau changed data collection procedures of the Current Population Survey to raise the maximum value of reported income.  This change resulted in higher inequality figures; inequality figures before and after 1993 are therefore not comparable.
• since 1993, inequality has not changed much (it has neither increased nor decreased substantally)

#### 3. Current World Trends

Hans Rosling's Gapminder site provides graphic depictions of trends in income inequality in countries of the world.

Major trends:

• Inequality within developing countries is increasing
• Overall world inequality is decreasing because of economic development, especially of very large countries (China, India)

#### 4.  Regional Inequality Patterns in North Carolina

Race dualism (= inequality associated with the average income difference between black and white families) varies among counties of North carolina.  The following exhibits show the geographical distribution at the county level of race dualism, overall income inequality (distribution of family income), and the relationship between income inequality and dualism. It appears that regions of North Carolina are characterized by distinct patterns of inequality.

 Region Race dualism Income inequality Mountain Low High Piedmont Low to High Low to High Coastal plain High High Tidewater High High

### Discussion: Is Bill Gates Hazardous to Your Health?

How does the degree of inequality in the social environment affect individuals in that environment?  There are many issues involved here, including
• How can we distinguish an effect of inequality per se from the "absolute" effects of environmental characteristics, such as hunger or poverty?  E.g.,
• is the young man moved to break into the rich mansion because he is poor in absolute terms, or because he cannot stand the contrast between the luxurious lifestyle of the rich and his own modest circumstances?
• am I depressed because I have no money, or is my depression aggravated because I know Bill Gates has too much of it?
• It is possible that humans are so preoccupied with issues of inequality because evolution has given us a built-in "module" concerned with distributive justice, as evolutionary psychologists would argue (Trivers 1971, 1985: Chapter 15)
• Other important concepts are related to inequality but do not coincide with it, including
• poverty (measured as % below a given threshold of income)
• living standards (corresponding to some notion of average income)
• human rights (are individuals protected from torture, loss of life, loss of freedom at the hands of the powerful?)
• Is there a trade-off between inequality and economic development?

One study of the effect of income inequality on health outcomes at the county level finds a "modest independent effect [of income inequality] on the level of depressive symptoms, and on baseline and follow-up self-rated health, but no independent effect on biomedical morbidity or subsequent mortality"; these effects are substantially smaller than the effects of individual income.

### References

• Allison, Paul D.  1978.  "Measures of Inequality." American Sociological Review 43:865-80.
• Harrison, Bennett and Barry Bluestone.  1988.  The Great U-Turn: Corporate Restructuring and the Polarizing of America.  New York:  Basic Books.
• Kerbo, Harold R.  2000.  Social Stratification and Inequality.  New York: McGraw-Hill.
• Kuznets, Simon.  1955.  "Economic Growth and Income Inequality." American Economic Review 45:1-28
• Lecaillon, Jacques, Felix Paukert, Christian Morrisson, and Dimitri Germidis.  1984.  Income Distribution and Economic Development: An Analytical Survey.  Geneva, Switzerland: International Labour Office.
• Lindert, Peter H.  2000.  "Three Centuries of Inequality in Britain and America."  Pp. 167-216 in Handbook of Income Distribution, Volume 1, edited by Anthony B. Atkinson and François Bourguignon.  Amsterdam, Netherlands: Elsevier Science.
• Nielsen, François. 1994. "Income Inequality & Industrial Development: Dualism Revisited." American Sociological Review 59:654-677.
• Nielsen, François and Arthur S. Alderson. 1997. "The Kuznets Curve and the Great U-Turn: Income Inequality in U.S. Counties, 1970 to 1990." American Sociological Review 62:12-33.
• Nielsen, François and Arthur S. Alderson.  2001.  "Trends in Income Inequality in the United States."  Pp. 355-385 in Sourcebook on Labor Markets: Evolving Structures and Processes, edited by Ivar Berg and Arne L. Kalleberg.  New York: Plenum.
• Nielsen, François and Charles S. Warren. 1998. "Patterns of Income Inequality in North Carolina, 1980."  Sociological Analysis 1(3):87-112.
• Nolan, Patrick and Gerhard Lenski.  1999.  Human Societies: An Introduction to Macrosociology.  (8th edition.)  New

•      York: McGraw-Hill.
• Nygård, Fredrik and Arne Sandström.  1981.  Measuring Income Inequality.  Stockholm, Sweden: Almquist and Wiskell.
• Trivers, Robert L.  1971.  "The Evolution of Reciprocal Altruism." Quarterly Review of Biology 46:35-57.
• Trivers, Robert L.  1985.  Social Evolution.  Menlo Park, CA: Benjamin / Cummings.