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| Hoover index | |
|---|---|
| Name | Hoover index |
| Other names | Robin Hood index, Schutz index |
| Type | Measure of inequality |
| Range | 0–1 (or 0–100%) |
| Developed by | Albert A. Hoover |
| Introduced | 1910s–1920s |
| Applications | Income distribution, Urban studies, Regional science |
Hoover index The Hoover index is a summary measure of spatial or income concentration and redistribution that quantifies the proportion of a population or resource that would need to be redistributed to achieve uniformity. It is used in comparative studies of income inequality, spatial segregation, and regional disparities, and often appears alongside measures like the Gini coefficient, Theil index, and Atkinson index in empirical research. Originating in early twentieth-century studies of wealth and migration, it remains a simple, intuitive metric for policymakers and researchers in fields such as demography, urban planning, and public policy.
The Hoover index is defined as half the sum of absolute deviations between observed shares and equal shares across units (areas, groups, or individuals). In discrete form for n units with population or resource shares p_i and overall shares s_i, the index H = 1/2 Σ |p_i − s_i|, where H ranges from 0 (perfect equality) to 1 (complete concentration). Calculation can be performed using data from census outputs, tax return aggregates, or administrative records from agencies such as the United States Census Bureau and national statistical offices like Office for National Statistics (United Kingdom). Computational routines are available in statistical packages used by researchers at institutions such as RAND Corporation, Brookings Institution, and university economics departments.
The measure traces to work by Albert A. Hoover and contemporaries studying wealth distribution and internal migration during the Progressive Era. Early applications appeared in analyses by analysts linked to Harvard University and University of Chicago social scientists who examined urbanization and migration patterns. Over the twentieth century the index was adopted by scholars at organizations including the International Labour Organization, League of Nations, and later by researchers at World Bank and Organisation for Economic Co-operation and Development who compared regional disparities across countries and provinces.
Several variants adapt the basic Hoover logic to continuous distributions, subgroup decomposition, or weighted populations. Related indices include the Gini coefficient used by Simon Kuznets and Corrado Gini, the Theil index associated with Henri Theil, and the Atkinson index introduced by Anthony B. Atkinson. Other connected constructs include concentration ratios used in studies by John Maynard Keynes-era statisticians and spatial segregation metrics developed in urban sociology at institutions like Columbia University and University of California, Berkeley.
Researchers apply the index to income distribution across metropolitan statistical areas, to population relocation after natural disasters studied by teams including those at Federal Emergency Management Agency and United Nations Office for Disaster Risk Reduction, and to wealth concentration in analyses by think tanks such as Economic Policy Institute and Institute for Fiscal Studies. Empirical work uses census tracts from municipalities like New York City, Los Angeles, and Chicago; national examples include provinces in India, Brazil, and South Africa. The index has been used in public finance research on tax progressivity at finance ministries and in housing studies by academics at Massachusetts Institute of Technology and University College London.
Interpreting the Hoover index is straightforward—values indicate the minimum share needing reallocation to equalize distribution—but this simplicity yields limitations. The measure is insensitive to transfers among middle ranks in ways highlighted by critics like Amartya Sen and comparisons with the Gini reveal different sensitivity to tails, a point emphasized in literature from Princeton University and Yale University. It does not capture within-unit heterogeneity or multidimensional deprivation studied by researchers at United Nations Development Programme, and can be affected by unit choice (the modifiable areal unit problem) discussed in geography research at University of California, Los Angeles.
Statistical properties of the Hoover index include sampling variability, consistency, and asymptotic behavior under large-sample assumptions. Variance estimators and confidence intervals are derived under survey designs used by agencies like the Bureau of Labor Statistics and national statistical institutes. Bootstrap methods recommended by researchers at University of Oxford and London School of Economics are common for small samples. Decomposition techniques permit between- and within-group contributions analogous to methods in studies by Econometric Society affiliates and applied econometricians.
Classic case studies include early twentieth-century analyses of county-level wealth in the United States and more recent applications to regional income disparities in China and Germany. Case studies by policy centers at European Commission and Inter-American Development Bank used the index to compare inequality across regions and to evaluate redistribution policies. Urban casework includes segregation analyses in Boston, Detroit, and Philadelphia, often paired with maps produced by municipal planning departments and academic teams at State University of New York campuses.
Category:Income inequality measures