Comments on the LWS Paper by Jenkins and J

1
Comments on the LWS Paper by Jenkins and Jäntti

• Frank Cowell
• January 2005

2
Objectives?

• Find a toolkit that works in theory
• New definitions new axioms?
• Address different questions?
• Find a toolkit that works in practice
• Deals with the quirks of wealth data
• Attention to estimation problems
• Foundation for a software package

3
Wealth Distribution Problems

• Negatives are Normal
• You cant assume them away
• Does inequality index work for individual
  negative values?
• What if the mean is close to zero?
• Spikes are Standard
• Outcome of economics
• Artefact of data collection
• Tails are Tiresome
• Skewness
• Sparseness

4
Wealth Distribution Solutions?

• Negatives
• Limited of indices
• Absolute rather than relative
• Spikes
• Truncation / censoring
• Mixed methodology
• Tails
• Transformations
• Patching

5
Patching

• Inadequate sample
• Sample too small?
• Contamination?
• Data just arent there?
• Could use kernel density estimation
• Could patch with a functional form
• Pareto?

6
Pareto distribution
ln n(x)
0
-1
-2
-3
-4
-5
-6
-7
0
1
2
3
4
ln x
7
Effect of Contamination

• Take two distributions such that one exactly
  Lorenz-dominates the other.
• Dagum(2,1,3)
• Dagum(2,1,2.5).
• Contaminate the first
• Take 0.25 of the largest observations
• Multiply by 10
• What happens to the L-curves?

8
Uncontaminated Dagum-I distributions
9
Contaminated Dagum-I distributions
10
Pareto regression (non-contaminated)
0
-1
LS Regression
Robust Regression
-2
-3
ln n(x)
-4
-5
-6
-7
0
1
2
3
4
ln x
11
Pareto regression (contaminated)
0
-1
LS Regression
Robust Regression
-2
-3
-4
ln n(x)
-5
-6
-7
5
0
1
2
3
4
6
7
8
ln x