Measuring Inequality,An examination of the purpose and techniques of inequality measurement,inequality Function: noun 1 : the quality of being unequal or uneven: as a : lack of evenness b : social disparity c : disparity of distribution or opportunity d : the condition of being variable : changeableness 2 : an instance of being unequal,What is inequality?,From Merriam-Webster:,Our primary interest is in economic inequality. In this context, inequality measures the disparity between a percentage of population and the percentage of resources (such as income) received by that population. Inequality increases as the disparity increases.,If a single person holds all of a given resource, inequality is at a maximum. If all persons hold the same percentage of a resource, inequality is at a minimum. Inequality studies explore the levels of resource disparity and their practical and political implications.,Physical attributes distribution of natural ability is not equal Personal Preferences Relative valuation of leisure and work effort differs Social Process Pressure to work or not to work varies across particular fields or disciplines Public Policy tax, labor, education, and other policies affect the distribution of resources,Economic Inequalities can occur for several reasons:,Why measure Inequality?,Measuring changes in inequality helps determine the effectiveness of policies aimed at affecting inequality and generates the data necessary to use inequality as an explanatory variable in policy analysis.,How do we measure Inequality?,Before choosing an inequality measure, the researcher must ask two additional questions: Does the research question require the inequality metric to have particular properties (inflation resistance, comparability across groups, etc)? What metric best leverages the available data?,Choosing the best metric,Range Range Ratio The McLoone Index The Coefficient of Variation The Gini Coefficient Theils T Statistic,Some popular measures include:,Range,The range is simply the difference between the highest and lowest observations.,Number of employees,Salary,2,$1,000,000,4,6,8,12,6,$200,000,$100,000,$45,000,$24,000,$60,000,In this example, the Range = $1,000,000-$24,000,= 976,000,Range,Pros Easy to Understand Easy to Compute,Cons Ignores all but two of the observations Does not weight observations Affected by inflation Skewed by outliers,The range is simply the difference between the highest and lowest observations.,Range Ratio,The Range Ratio is computed by dividing a value at one predetermined percentile by the value at a lower predetermined percentile.,95 percentile Approx. equals 36th person,5 percentile Approx. equals 2nd person,In this example, the Range Ratio=200,000/24,000 =8.33,Note: Any two percentiles can be used in producing a Range Ratio. In some contexts, this 95/5 ratio is referred to as the Federal Range Ratio.,Number of employees,Salary,2,$1,000,000,4,6,8,12,6,$200,000,$100,000,$45,000,$24,000,$60,000,Range Ratio,Pros Easy to understand Easy to calculate Not skewed by severe outliers Not affected by inflation,Cons Ignores all but two of the observations Does not weight observations,The Range Ratio is computed by dividing a value at one predetermined percentile by the value at a lower predetermined percentile.,The McLoone Index,The McLoone Index divides the summation of all observations below the median, by the median multiplied by the number of observations below median.,Number of employees,Salary,2,1,000,000.00,4,6,8,12,6,200,000.00,100,000.00,45,000.00,24,000.00,60,000.00,Observations below median,In this example, the summation of observations below the median = 603,000, and the median = 45,000 Thus, the McLoone Index = 603,000/(45,000(19) = .7053,The McLoone Index,Pros Easy to understand Conveys comprehensive information about the bottom half,Cons Ignores values above the median Relevance depends on the meaning of the median value,The McLoone Index divides the summation of all observations below the median, by the median multiplied by the number of observations below median.,The Coefficient of Variation,The Coefficient of Variation is a distributions standard deviation divided by its mean.,Both distributions above have the same mean, 1, but the standard deviation is much smaller in the distribution on the left, resulting in a lower coefficient of variation.,The Coefficient of Variation,Pros Fairly easy to understand If data is weighted, it is immune to outliers Incorporates all data Not skewed by inflation,Cons Requires comprehensive individual level data No standard for an acceptable level of inequality,The Coefficient of Variation is a distributions standard deviation divided by its mean.,The Gini Coefficient,The Gini Coefficient has an intuitive, but possibly unfamiliar construction. To understand the Gini Coefficient, one must first understand the Lorenz Curve, which orders all observations and then plots the cumulative percentage of the populati