Overview
This seminar covered the challenges of measuring inequality over time, focusing on the commonly used Gini index and alternatives, and provided practical guidance for choosing and testing appropriate inequality measures for dynamic and comparative analyses.
Problems with the Gini and Relative Measures
- The Gini index is often the only available time series inequality measure in many datasets.
- Relative measures like Gini are influenced by changes in the mean (average) of the income distribution.
- This influence means Gini and similar measures can incorporate unwanted economic dynamics, distorting the analysis of inequality trends.
- Empirical results using Gini often appear unstable or insignificant in regression analyses.
Toolkit for Measuring Inequality Over Time
- Constructed a 100-year, 34-country dataset using mortality data, calculating 18 different inequality measures.
- Ran time series tests to assess which measures are suitable for dynamic analysis (e.g., trend, stationarity, mean reversion).
- Absolute inequality measures (not scaled to the mean) often perform better in dynamic and panel regression analyses.
- Some relative measures, in certain contexts or countries, may be acceptable if they pass statistical tests.
Empirical Applications & Findings
- When regressing growth on inequality, relative measures yielded unstable results; absolute measures gave more stable, non-significant effects.
- Applying vector autoregression showed that relative measures retain the effects of shocks (e.g., recessions) much longer than absolute measures.
- Converting relative measures to their "absolutized" versions (multiplying by the mean) stabilized results.
Quick Tests for Practitioners
- Two practical tests to assess suitability of an inequality measure for dynamic analysis:
- Check for temporal clustering of volatility in the measure.
- Check for non-normality in the distribution of the measure over time.
- Simple plotting over time can also reveal whether different measures tell conflicting stories.
Comparative and Cross-Country Analyses
- The recommended tests apply whether comparing trends within a country or across countries.
- Essential to check each country's measure(s) for statistical robustness before drawing comparative conclusions.
Key Terms & Definitions
- Gini Index — A relative measure of inequality based on the average difference between all pairs of incomes, divided by the mean.
- Relative Inequality Measure — Scales inequality to the mean; sensitive to changes in average income.
- Absolute Inequality Measure — Measures inequality in absolute terms, not scaled by the mean.
- Stationarity — A statistical property where a variable's shock effects fade over time; desirable for long-term analysis.
- Panel Regression — Regression analysis that uses data across entities (countries) and over time.
- Vector Autoregression (VAR) — A model capturing the effect of shocks over time in multiple time series.
Action Items / Next Steps
- Before analyzing inequality over time, plot different measures and inspect for major differences.
- Perform quick volatility clustering and normality tests on chosen inequality measures to check suitability.
- Use absolute inequality measures where possible, or test and possibly "absolutize" relative measures if needed.
- Apply the toolkit to ensure robust comparative and dynamic inequality analysis.