Quantifying population concentration in the US

During a recent conversation about representation and Trump’s America, I was reminded that part of the rationale for the Senate’s uniform representation (two Senators per state, regardless of population) was to protect the smaller states and to ensure rural areas were not over-run by cities.

During my ensuing Google search storm, I was left with one question lacking compelling data:

How has the concentration of the population in large cities changed since the writing of the Constitution?

The Tool: The Gini Coefficient

We know that population density increases over time (Figure 3, below) but this tells us nothing about the distribution of the population between rural and urban areas, as it is merely an average over the entire area of the country. Additionally, general population growth can wash out some of the data, so I wanted a way to quantify concentration independent of overall population growth. I turned to the Gini coefficient.

As a brief primer: the Gini coefficient is a tool used it economics to study the inequality in an income or wealth distribution. It essentially takes the Lorenz curve and turns it into a single number ranging from 0 to 1. This means that, unlike standard deviation, which can hold any value, the Gini coefficient is limited to a maximum of 1. In terms of a wealth distribution:

• A Gini coefficient of 0 represents an economy in which every person has the same share of the resources
• A Gini coefficient of 1 is an economy in which one person controls all the resources

In order to apply this to geographical population distributions, I used county-by-county population data from the US Census. County-level analysis allows us to see the relative concentration in cities without explicitly defining urban and rural areas. Here,

• A Gini coefficient of 0 represents a territory in which all counties have the exact same population
• A Gini coefficient of 1, on the other hand, represents a territory where everyone lives in one county and all the others are empty

Table 1

To build intuition, I calculated the population Gini coefficient for each state using data from the 2010 Census. We have to be very careful in comparing states, as each state’s coefficient is calculated only with the counties within that state. All we can really say is that a state with a higher coefficient has a higher concentration of its population in its most populous counties. (A hypothetical state with only one person living in the capital county and all other counties empty would have a higher Gini coefficient than New York, but that wouldn’t tell us anything about the relative sizes of the populations.)

Figure 1 gives a rough visual representation of Table 1. In general, the trend seems to be that older, geographically smaller states — such as those in the Northeast — have more uniform population distributions, while younger, larger states are more heavily concentrated in population centers, such as in the desertous Southwest. Another intuitive way to visualize population distribution is with a light pollution map (Figure 2). Perhaps obviously, the states with more uniform light distribution have more uniform population distributions.

Figure 1: Although younger, geographically larger states have consistently higher population concentrations, some states with massive population centers (New York, NY; Chicago, IL) exhibit higher concentrations than are expected for their region.

Figure 2: The 2010 DMSP light pollution data set shows the clear geographic divide between the Eastern United States and Western United States. The interactive version of this map is a lot more fun.

It is heartening to see that states with abnormally large population centers have higher Gini coefficients than the other states in their regions. In other words, we see compelling evidence that highly concentrated populations correlate with a higher Gini coefficient.

How has the US population concentration changed over time?

To address this question, I calculated the national Gini coefficient for every census since 1800. Unlike above, I included all counties in the country in the same data set and calculated one Gini coefficient for the entire nation. The results are in Figure 3.

Figure 3: Population density has generally tracked closely with population (bottom). Population concentration exhibits features not present in either.

Clearly, the population concentration metric is giving us information that the conventional population metrics miss. Some notable features are:

• Stagnating concentration during the Gilded Age (1870–1900) as (mostly empty) western territories are created
• Surging concentration due to the Great Migration (1916–1970) of black people from the rural South to Northern cities
• Stagnating concentration during “white flight” suburbanization

As for the question at hand regarding the change in population since the founding of the country, the Gini coefficient has increased from 0.43 to 0.75 despite factors such as increases in land area and fracturing of larger counties containing population centers, which should supress it some. The evidence seems to be compelling that

the population of the US is much more highly concentrated in population centers today than it was when the Constitution was written.

This also means the unequal representation in the distribution of seats in Congress is getting more unequal as time goes on. Considering the higher susceptibility to gerrymandering also in inner cities, the populations that live there are facing rising levels of structural disenfranchisement.