The Spatial GINI Coefficient

Dr. Paul C. SuttonDepartment of Geography

University of DenverPopulation Assocation of America Conference

San Francisco May 3rd, 2012

Outline• Lorenz Curve and the GINI Coefficient

as a measure of distribution of wealth

• Global gridded representations of Nighttime Satellite Imagery and Population Density as an alternative source for developing a spatially derived Lorenz Curve.

• The Human Development Index (HDI)

Data Products Used

Nighttime Lights of the WorldDMSP OLS (NGDC)

LandScan Global Grid of Population

Scatterplots of Light vs Population for Pixels in China (left) and U.S. (right)

The Spatial GINI Coefficient I10 km x 10 km

Population Grid10 km x 10 km

DMSP OLS Image0 0 0 0 0 0 0 0 0 0

0 0 1 1 2 1 2 1 4 1

1 1 3 2 3 4 4 4 3 1

1 1 4 5 5 5 10 5 5 2

1 2 5 5 10 10 10 10 10 3

1 3 5 5 10 30 50 30 10 4

2 2 5 10 10 50 100 50 10 10

15 5 5 5 10 30 50 30 10 3

4 3 5 5 10 10 10 10 10 2

0 2 5 5 5 5 10 5 5 1

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 2 0 0 0

0 0 0 0 2 2 10 1 2 0

0 0 0 0 2 50 150 50 5 0

0 0 0 0 10 150 255 150 10 2

5 0 0 0 2 50 150 50 5 0

0 0 0 0 0 5 10 5 2 0

0 0 0 0 0 0 0 0 0 0

Analysis of the population grid relative to the light grid (above)produces a table that contrasts % of Population to % of light in

any given country or area (See table below).

Light Level (DN) Pop in DN Cum % of Light Cum % of Pop0 205 0.0 25.01 10 0.1 26.22 90 1.5 37.25 55 3.7 43.910 40 7.2 48.850 120 24.8 63.4150 200 77.6 87.8255 100 100.0 100.0

Total Pop = 820 Total Light = 1137

The Spatial GINI Coefficient II(also referred to as the “Lumen GINI”)

Spatial Lorenz Curve

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative % of Population

Cu

mu

lati

ve %

of

Lig

ht

Pink Area

Yellow Area

The“Lumen GINI”

Coefficient

A ‘lumen GINI’ of 1.0implies one person liveswhere all the light is and

everyone else is in the dark.A ‘lumen GINI’ value of 0.0implies light is distributed

equally amongst all people.

63.8 % of Popwith 24.8%

of Light

The “Real” Income GINI Coefficient

Note: Research suggests the United States is on track to pass Mexico

Highly variable ‘freshness’ of Data

Due to the lack of a systematic international data collection system, the data used to calculate income Gini coefficients span nearly two decades

The Global Spatial GINI

The Lorenz curve for the global Lumen Gini Coefficient, formed by combining the data from all countries.

Lorenz curves and Lumen Gini coefficients for six countries

GINI = 0.941 GINI = 0.748 GINI = 0.981

GINI = 0.791 GINI = 0.623 GINI = 0.542

Map of national Spatial GINI Coefficients

Map of Subnational Spatial GINICoefficients

Map of Spatial GINI Coefficientsat a 0.25 degree grid

Spatial GINI vs. Income GINI

National level Lumen Gini versus Income Gini coefficients. Note the poor correlation, indicating that the two Gini’s are measuring very different phenomena.

Spatial GINI vs Per Capita Energy Consumption and

Electrification Rates

Spatial GINI vs. Human Development Index

Spatial GINI vs. Human Security Index

Spatial GINI vs. Ecological Footprint

Discussion & ConclusionsThe Spatial GINI or Lumen GINI does not measuredistribution of wealth in any manner similar to the Income GINI.

The Spatial GINI correlates strongly and significantlywith both the Human Development Index (HDI) andThe Human Security Index (HSI).

Simple, empirical measures such as the Spatial GINIas presented here present an opportunity for improvedspatially explicit characterizations of the human condition.