Studying the Tail that Wags the
Distribution:
Testing the Hypothesis of Disproportionality
Against Assumptions of Proportionate Access.
Berry, Freudenburg and Howell, 2005
The Treadmill of Production!
2nd Contradiction of Capitalism!
I=PAT!
Postmaterialism!
Ecological Modernization!
Kuznets Curve!
Testing the Competing Hypotheses:
H1: Proportionality
H2: Disproportionality
Is pollution uniform across groups of producers?
Is pollution uniform within groups of producers?
Are there just a few bad actors?
...if so, are they necessary?
Case Study: Toxic Releases
Level 1: Across major industry types
Between 2-digit SIC’s
Select largest polluter
Level 2: Within major industry
Within 2-digit SIC
Select largest polluter
Level 3: Plants within specific industry
Within 3-digit SIC
Data Sources: Toxic Release Inventory, 2000
RSEI Version 2.1
Test Statistic: Kolmogorov-Smirnov
(K-S test)
Cumulative Fraction of Toxic
Releases
Cumulative Fraction Plot
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Raw Data
Uniform
Distribution
D
1
11
21
Polluters (1:N)
31
41
Test Statistic: Kolmogorov-Smirnov
(K-S test)
Cumulative Fraction of Toxic
Releases
Cumulative Fraction Plot
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
Raw Data
Uniform
Distribution
D
0.20
0.40
0.60
Cumulative Fraction of Polluters
0.80
1.00
Across Industries
Histogram of Toxicity Across Industries
50
40
30
20
10
Std. Dev = 8.97E+10
.0
00
00
98
.0
99
00
99
00
49
99
0
99
0.
00
99
90 0
44
9
.
99
00
99
00
39
99
.0
99
00
99
00
34
99
0
99
0.
00
99
0
29
99
0
0.
99
00
99
90
24
9
.0
99
00
99
00
19
99
99
0
0.
99
00
14
97
0
99
0.
99
00
99
98
99
99
49
Mean = 2.7479E+10
N = 46.00
0
0
0.
MODELED
How important is the ‘tail’ of the distribution?
Across Industries
Cumulative Fraction of Toxic
Releases
Modeled Toxicity Across Industries
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
Raw Data
Reference
0.20
0.40
0.60
0.80
1.00
Cumulative Fraction of Polluters
K-S Test Result:
Uniform distribution? (0.000) Normal? (0.000) Log-normal (0.200)
Is the Pollution Necessary for
the Economy?
Cumulative Fraction of Toxic
Releases
Modeled Toxicity Across Industries, Normalized by % Contribution to GDP
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
Raw Data
Reference
0.20
0.40
0.60
0.80
1.00
Cumulative Fraction of Polluters
K-S Test Result:
Uniform distribution? (0.000) Normal? (0.000) Log-normal (0.028)
Is the Pollution Necessary for
Jobs?
Cumulative Fraction of Toxic
Releases
Modeled Toxicity Across Industries, Normalized by # Employees
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
Raw Data
Reference
0.20
0.40
0.60
0.80
1.00
Cumulative Fraction of Polluters
K-S Test Result:
Uniform distribution? (0.000) Normal? (0.000) Log-normal (0.058)
Across Sectors within the
Primary Metals Industry
Cumulative Fraction of Toxic
Releases
Modeled Toxicity Across SIC 33 Sectors
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
Raw Data
Reference
0.20
0.40
0.60
0.80
1.00
Cumulative Fraction of Polluters
K-S Test Result:
Uniform distribution? (0.001) Normal? (0.002) Log-normal (0.200)
Is the Pollution Necessary for
Jobs?
Cumulative Fraction of Toxic
Releases
Modeled Toxicity Across Sectors, Normalized by # Employees
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
Raw Data
Reference
0.20
0.40
0.60
0.80
1.00
Cumulative Fraction of Polluters
K-S Test Result:
Uniform distribution? (0.000) Normal? (0.000) Log-normal (0.083)
Across Plants within the Highest Polluting Sector
(Primary Smelting & Refining of Nonferrous Metals)
Cumulative Fraction of Toxic
Releases
Modeled Toxicity for Plants within SIC 333
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
Raw Data
Reference
0.20
0.40
0.60
0.80
1.00
Cumulative Fraction of Polluters
K-S Test Result:
Uniform distribution? (0.000) Normal? (0.000) Log-normal (0.031)
Across Plants within the Highest Polluting Sector
(Primary Smelting & Refining of Nonferrous Metals)
Cumulative Fraction of
Toxic Releases
Modeled Toxicity for Plants within SIC 333
Without Highest Polluter
1.0
0.8
0.6
Raw Data
0.4
Reference
0.2
0.0
0.00
0.20
0.40
0.60
0.80
1.00
Cumulative Fraction of Polluters
K-S Test Result:
Uniform distribution? (0.000) Normal? (0.000) Log-normal (0.007)
Tragedy of the Commons?
How much does each cow affect the
pasture?
Cows
Pasture
How much does each cow affect the
pasture?
Cows
10%
Pasture
10%
How much does each polluter affect
the overall level of pollution?
Polluters
Toxic Pollution
Plants within Smelting and Refining Industry
How much does each polluter affect
the overall level of pollution?
Polluters 10%
Toxic Pollution 10%
Plants within Smelting and Refining Industry
How much does each polluter affect
the overall level of pollution?
Polluters
Toxic Pollution
Plants within Smelting and Refining Industry
10%
How much does each polluter affect
the overall level of pollution?
Polluters
Toxic Pollution
Plants within Smelting and Refining Industry
10%
97.8%
How much does each polluter affect
the overall level of pollution?
Polluters
Top 10% to median
Toxic Pollution
Plants within Smelting and Refining Industry
How much does each polluter affect
the overall level of pollution?
Polluters
Top 10% to median
Toxic Pollution
Plants within Smelting and Refining Industry
97.4%
How much does each polluter affect
the overall level of pollution?
Polluters
Toxic Pollution
Top 10% to median
65%
Plants within Smelting and Refining Industry: Omitting top polluter (Rowley, UT)
Conclusions
 The hypothesis of proportionality is rejected
at all levels of analysis.
 The majority of toxic pollution does not
appear to be necessary.
 Statistical support is found for the
disproportionality hypotheses.
 These findings have far reaching
implications.
 There is more work to be done!!