Inequality Measurement

Individuals differ in countless ways. And groups are characterized by different levels of inequality in all the ways in which individuals differ. Several important examples of difference among individuals include income, wealth, power, life expectancy, and mathematical ability. There are inequalities among individuals in each of these dimensions, and different populations have different distributions of various characteristics across individuals. It is often the case that there are also inequalities among subgroups within a given population: men and women, rural and urban, black and white. It is often important to identify and measure various dimensions of inequality within a society. For the purposes of public policy, we are particularly interested in social inequalities that represent or influence differences in individuals' well-being, rights, or life prospects.

How do we measure the degree of inequalities within a POPULATION? There are several important alternative approaches, depending on whether the DISTRIBUTION of the factor is approximately NORMAL across the population. If the factor is distributed approximately normally, then the measurement of inequality is accomplished through analysis of the MEAN and STANDARD DEVIATION of the factor over the population. On this approach, we can focus on the descriptive statistics of the population with respect to the feature (income, life expectancy, weight, test scores): the shape of the distribution of scores, the mean and MEDIAN scores for the population, and the standard deviation of scores around the mean. The standard deviation of the VARIABLE across the population provides an objective measure of the degree of dispersion of the feature across the population. We can use such statistical measures to draw conclusions about inequalities across groups within a single population (“female engineers have a mean salary only 70% of that of male engineers”); conclusions about the extent of inequality in separate populations (“the variance of adult body weight in the United States is 20% of the mean, whereas the variance in France is only 12% of the mean”); and so forth.

A different approach to measurement is required for an important class of inequalities—those having to do with the distribution of resources across a population. The distribution of wealth and income, as well as other important social resources, is typically not statistically normal; instead, it is common to find distributions that are heavily SKEWED to the low end (that is, large numbers of individuals with low allocations). Here, we are explicitly interested in estimating the degree of difference in holdings across the population from bottom to top. Suppose we have a population of size N, [Page 488]and each individual i has wealth Wi, and consider the graph that results from rank ordering the population by wealth. We can now standardize the representation of the distribution by computing the percent of total wealth owned by each percent of population. And we can graph the percent of cumulative wealth against percentiles of population. The resulting graph is the Lorenz distribution of wealth for the population. Different societies will have Lorenz curves with different shapes; in general, greater wealth inequality creates a graph that extends further to the southeast. Several measures of inequalities result from the technique of organizing a population in rank order with respect to ownership of a resource. The GINI COEFFICIENT and the ratio of bottom quintile to top quintile of property ownership are common measures of inequality used in comparative economic development.

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