Quantifying inequality

Matt Bhagat-Conway

Why quantify inequality?

  • Track progress towards equity goals
  • Understand how inequality differs in different regions
  • Use models to estimate the effects of different policies on inequality

Why not quantify inequality?

  • Inequality is not necessarily a tangible thing
  • For instance, a lot of the effects of gentrification may be due to cultural changes rather than residential displacement; people no longer feeling welcome, not leaving outright (Rayle 2015)
    • This is real, but it’s not (easily) quantifiable

Measures of income inequality: the P90/P10 metric

  • The P90/P10 ratio is the ratio of the 90th percentile of income to the 10th
  • Higher values mean more inequality
  • What do you suppose the P90/P10 ratio is for the US? 5.4
  • It was 4.5 in 1990

How does the US compare to other countries?

Bar graph showing P90/P10 index for (from lowest to highest) Slovenia, Norway, Hungary, Canada, Australia, Great Britain, Latvia, the US, and Mexico.

Measures of inequality: the Lorenz curve

  • The P90/P10 ratio only looks at two points on the income distribution
  • A Lorenz curve is a plot that shows the entire income distribution
  • On the x axis it shows the percentile of income, and the y axis shows the percent of income earned by people making below that percentile of income
  • In statistical terms, it is a cumulative distribution

The Lorenz curve for wealth the US

Lorenz curve for the US, showing significant wealth inequality, with the bottom 50% holding well less than 5% of US wealth

Federal Reserve Bank of New York

Measures of income inequality: the Gini coefficient

  • The Gini coefficient is a single number based on the Lorenz curve that measures inequality
  • If income were perfectly equally distributed, the Lorenz curve would be a straight line
  • The Gini coefficient is the proportion of the area under that straight line that is above the Lorenz curve (between 0 and 1, sometimes between 0 and 100)
  • The further the Lorenz curve is from perfect equality, the higher the Gini coefficient

The Gini index in the US

The Gini index in the US, from 1963 to 2020, showing that inequality initially slightly declined, bottomed out in 1980, climbed until 1990, and has stayed relatively flat since.

How does the US compare to other countries?

GINI indices from countries around the world, with the US highlighted. The US has a higher gini coefficient than about 75% of countries.

Data: CIA World Factbook

Social mobility and the lottery effect

  • Policies to reduce income inequality often face opposition in the US
  • One reason is the “lottery effect”—lower income individuals hope to one day hit it big, and want policies to support that

Measures of social mobility

[R]ates of absolute upward income mobility in the United States have fallen sharply since 1940. . . . [u]nder the current distribution of GDP, we would need real GDP growth rates above 6% per year to return to the rates of absolute mobility seen in the 1940s. Intuitively, because a large fraction of GDP goes to a small number of high income earners today, higher GDP growth does not substantially increase the number of children who earn more than their parents.

Chetty et al. (2017)

Measures of social mobility

Plot showing declining social mobility, with 90% of Americans born in 1940 earning more than their parents, down to just over 50% in the 1980s

Percent of children earning more than their parents, by year of birth (Chetty et al. 2017)

Measures of segregation

  • The US remains highly segregated
  • Planners and sociologists have devised a number of measures of segregation
  • Formal definitions here come from Forest (2005)

Image of racial concentrations in Chicago, showing significant segregation

ESRI Demographics

Schelling’s model of spatial segregation

  • This model demonstrates how small individual preferences for neighborhood composition can lead to significant segregation
  • Developed by Thomas Schelling, best known for his work on mutually assured destruction (Schelling 1978)
  • Most user-friendly implementation: the Parable of the Polygons

Schelling’s model of spatial segregation: demonstration

Measures of segregation: the dissimilarity index

  • The dissimilarity index measures, for two groups, the proportion of either group that would have to move to create a completely unsegregated pattern
  • Ranges from 0 to 1; 0 is no segregation
  • If places were completely unsegregated, the percentage of each group in an area would be equal to the percentage of each other group
  • e.g. if a tract is 5% of the population of the area, it should have 5% of the white population and 5% percent of the black population
  • This is true even if the population sizes differ

Measures of segregation and the modifiable areal unit problem

The dissimilarity index in North Carolina, for white alone and Black alone,

  • by block: 0.64
  • by block group: 0.54
  • by tract: 0.51
  • by county: 0.33

Measures of segregation: the interaction/exposure index

  • The average proportion of people in group 2 in an area, weighted by the number in group 1
  • Put another way, what percentage of the area where a particular Black person lives is white, or vice-versa?
  • Unlike the dissimilarity index, it is asymmetrical—the percent of the area where a Black person lives that is white ≠ the person of the area where a white person lives that is Black
  • You may see this referred to as the probability that a person of one race interacts with a person of another, but that makes a lot of assumptions about social norms in the community

The interaction/exposure index in North Carolina

  • What do you think it is? (at the block level)
    • NC is 60% white, 20% black, 89% non-Hispanic, 11% Hispanic
    • For whites interacting with Blacks: 0.11
    • For Blacks interacting with whites: 0.33
    • For non-Hispanic interacting with Hispanic: 0.09
    • For Hispanic interacting with non-Hispanic: 0.72

References

Chetty, Raj, David Grusky, Maximilian Hell, Nathaniel Hendren, Robert Manduca, and Jimmy Narang. 2017. “The Fading American Dream: Trends in Absolute Income Mobility Since 1940.” Science 356 (6336): 398–406. https://doi.org/10.1126/science.aal4617.
Forest, Benjamin. 2005. Measures of Segregation and Isolation. Dartmouth College. https://www.dartmouth.edu/~segregation/IndicesofSegregation.pdf.
Rayle, Lisa. 2015. “Investigating the Connection Between Transit-Oriented Development and Displacement: Four Hypotheses.” Housing Policy Debate 25 (3): 531–48. https://doi.org/10.1080/10511482.2014.951674.
Schelling, Thomas C. 1978. Micromotives and Macrobehavior. January 1.

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This work by Matthew Bhagat-Conway is licensed under a Creative Commons Attribution 4.0 International License.