The Lorenz criterion is a method for comparing income distributions, stating that one distribution is considered more equal than another if the poorest x percent of the population always has an equal or greater share of income under the first distribution.
Understanding Lorenz Dominance
The core idea behind the Lorenz criterion is to determine if one income distribution is definitively more equitable than another, without having to rely on a single aggregate measure of inequality like the Gini coefficient. Let's break this down:
- Income Distributions: We are comparing how income is distributed among a population.
- Lorenz Curve: This is the visual representation of income distribution, showing the cumulative percentage of income held by the cumulative percentage of the population.
- Dominance: Distribution L1 Lorenz dominates distribution L2 if the Lorenz curve for L1 is always above the Lorenz curve for L2 (or equal to it) at every point.
- This means that at every percentile of the population, those in distribution L1 hold at least as much income (or more) as those in the corresponding percentile of L2.
Key Components and Explanation
The reference states: "the poorest x percent of the population will always have an equal or greater share of income under L1 than under L2, regardless of what x is".
- "Poorest x Percent": This refers to any portion of the population, from the poorest 1% to the poorest 99%. The 'x' represents the size of this group.
- "Equal or Greater Share of Income": Under the Lorenz criterion, a distribution L1 is considered more equal than L2 if, for any 'x', the poorest group in L1 has at least the same share of the total income as the poorest group of the same size in L2.
- "Regardless of What x Is": This emphasizes that this condition must hold true for all values of x. For the criterion to be valid, the lower part of the income distribution of L1 must always have an equal or higher share of the overall income than the corresponding lower part of L2.
Example
Imagine two income distributions:
| Percentile of Population | Cumulative Income Share (Distribution L1) | Cumulative Income Share (Distribution L2) |
|---|---|---|
| 20% (poorest) | 5% | 3% |
| 40% | 15% | 10% |
| 60% | 30% | 25% |
| 80% | 55% | 50% |
| 100% | 100% | 100% |
In this example, distribution L1 Lorenz dominates distribution L2. At every percentile, the poorest individuals in L1 have a higher cumulative income share compared to their corresponding counterparts in L2.
How it Works in Practice
Here's a breakdown of how to practically apply the Lorenz criterion:
- Plotting: Create Lorenz curves for each distribution you want to compare. The x-axis represents the cumulative percentage of the population, and the y-axis represents the cumulative percentage of total income.
- Visual Comparison: Compare the curves visually. If one curve is always above the other, it indicates Lorenz dominance. If the curves cross, the distributions cannot be strictly ranked using the Lorenz criterion.
- Analysis: Interpret the result. If one distribution Lorenz dominates another, it's unambiguously more equal under the criterion. However, it does not imply one is "better" per se - it simply states the inequality level is lower.
Advantages of the Lorenz Criterion
- Clear Comparison: It provides a clear way to compare income distributions.
- Visual Assessment: The Lorenz curve allows for a visual comparison.
- No Single Metric: It does not rely on a single, potentially controversial, summary measure of inequality.
Limitations
- Incomparability: If Lorenz curves intersect, the distributions cannot be ranked in terms of inequality using the Lorenz criterion.
- Partial Ranking: It may not provide a complete ranking of all possible distributions.
- Sensitivity: May be sensitive to changes at different levels of the income distribution.
Conclusion
The Lorenz criterion is a key tool for understanding and comparing inequality in income distributions. It provides a visual and intuitive method for determining if one distribution has a lower level of inequality than another, based on the income share of the poorest segments of the population. However, it’s important to acknowledge its limitations, particularly in situations where Lorenz curves intersect.
