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Mapping Inequality. A Presentation for the Committee on Spatially Integrated Social Science, Santa Barbara, November 2000. by James K. Galbraith. The University of Texas Inequality Project. http://utip.gov.utexas.edu.
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Mapping Inequality A Presentation for the Committee on Spatially Integrated Social Science, Santa Barbara, November 2000 by James K. Galbraith The University of Texas Inequality Project http://utip.gov.utexas.edu
The University of Texas Inequality Project is a small working group whose main objective has been to tap industrial and geographic data sets for evidence on levels and changes in economic inequality. Our method relies on the between-groups component of Theil’s T statistic, which permits us to compute indexes of inequality from semi-aggregated source materials. Data requirements are very simple: a population value and an income value for each of a set of consistently-measured, mutually exclusive groups. The T statistic, its components, and their evolution through time can be displayed in maps in numerous ways, each useful in illuminating different aspects of the issue of economic inequality.
1. Inequality within geographic regions The simplest concept is the measurement of inequality within geographic units over time. Calculations of TN for a region may be based on industrial groupings, from which long and dense time series of inequality may be computed. We have for instance annual measures of inequality in industrial earnings over up to 29 ISIC 2 categories calculated from the 2000 release of UNIDO’s Industrial Statistics. Because of the standardization of industrial categories, these measures can be compared across countries The map that follows shows the average value of this statistic for all available years (within the period 1963-1998), a tactic that enables us to show measurements for over 170 countries.
As the next slide shows, the expanded UTIP 2000 World Theils data set on which these maps are based has many more observations per country than the World Bank’s latest inequality data set, which has just 739 observations in all, and 10 or fewer observations for 99 of 118 countries. The Bank has 30 or more observations for only 3 countries The newest UTIP release has 10 or more observations for 109 of 151 countries, and 30 or more for 42 countries.
Dollar/Kraay data are an expanded version of Deininger and Squire, 1950-1997; UTIP are all 1963-1997
Inequality within U.S. Counties, measured across plants. We also have a new data set of pay inequalities measured across manufacturing plants within each county of the United States, at five year intervals from 1963 to 1992, for about half of all U.S. counties; this was computed for us by the U.S. Bureau of the Census. Measures of inequality across plants are not strictly comparable between counties, because the number of plants covered varies from county to county. But the change through time is comparable.
In order to show change through time effectively in maps, it is useful to consider questions of legend design and color scheme The next slides were constructed by dividing U.S. counties into quintiles of the between-plant Theil measure for 1992, and mapping data for previous periods into the 1992 quintile boundaries. Thus, the maps clearly show the evolution of inequality toward the 1992 quintiles from uniformly lower levels that pertained in the mid 1960s. For clarity, the maps shown are restricted to the Western United States.
The Scale Dark Blue: Low inequality Light blue: Below average Green: Average Yellow: Moderately high Red: Very high Scale is set to 1992 quintiles: each category has equal numbers of counties in 1992 results.
The West: 1963
2. Contribution of geographic units to inequality across units. TN is computed by summing the “contribution to inequality” of component units, where the contribution of a component with above-average income is positive, that of a component with below-average income is negative, and the contributions are weighted by population size. Where the components are geographic units, one may usefully map these contributions to the larger measure of inequality. For instance, using Local Area Personal Income Statistics, we have computed a measure of income inequality across U.S. counties for each year from 1969 to 1996. Maps that divide counties into quantile bins according to the size of their contribution to this measure of inequality in a base year, and then track the movement of counties across bins through time, clearly show the changing patterns of regional polarization in income.
We present these contributions to inequality for three years: 1969, 1982 and 1995. In the Midwest, relative incomes fell sharply between 1969 and 1982, but then recovered in some counties by 1995. Note the very uneven pattern of recovery in Michigan, for example.
In the Southwest and Far West, income inequalities across county lines rose very sharply in the 1990s. California was a middle-income state; today it is highly polarized by region. Likewise Washington state, with one rich county: the pattern of the Deep South. In the Southwest, population movements are are clearly an important factor. In the Northwest, the decline of timber is probably a key element in increasing income polarization.
3. Aggregating across regions The TN measure differs from the somewhat better-known Gini coefficient in that it can be summed: the inequality in a large region is equal to inequality within each sub-region, plus a measure of inequality computed from differences in average income across regions. Thus one may combine “inequality within countries” of (say) Europe, with the “inequality between-countries” to derive a measure of inequality for the European continent as a whole. In principle, any aggregation one might find theoretically interesting can be accomplished in this way.
The value for the U.S. on this scale is about 0.29, or roughly the height of the blue bar. Overall European pay inequality and unemployment are both higher than in the United States.
4. Integrating geographic and non-geographic data. Often grouped data on income, earnings or wages are available from (non-geographic) industrial classification schemes for national or sub-national geographic units of observation, while total income (or earnings or wages) and population are available for the geographic units themselves. So long as the underlying categories (industries, occupations, ethnic groupings, etc...) are fully nested within the geographic units (counties, states, etc...), and so long as the underlying category schemes are consistent with each other, it is legitimate to integrate the geographic and non-geographic data. In this way we have (for instance) measured inequality within provinces of China, and then aggregated these measures across provinces to achieve a detailed measure of the evolution of inequality in the country as a whole.
The simple difference of these two measures gives an indication of the pattern of change of inequality in China from 1989 to 1996. This pattern is consistent with the idea that rapid growth in the South and East has kept the rise in inequality in those regions lower than in the depressed North and West:
5. Measuring the similarity of the evolution of inequality across time and space. The existence of long and dense time series of inequality measured over the same time intervals makes possible the comparison of the paths of changing inequality across countries and through time. The Euclidean distance matrix between vectors of the rate of change of TN provides a way of assessing the degree of similarity of historical experience between every country in the data set and every other. Using the column representing these “distances from country X” as the reference case, maps can be constructed that show the degree of similarity through history between country X and all other countries. When used with economic inequality data, this esoteric but interesting technique tends to show the core-periphery character of labor market integration for most regions of the developing world, as well as the high degree of mutual integration in Europe and the OECD.
Mapping the distances... • Using the distance matrix underlying the cluster tree, we can show the relationship between countries in a series of maps. • Each of the following maps is based on a different reference column, or country, of the distance matrix. • The scale is in terms of absolute cluster distances. • A shift to yellow indicates greater distance.
Scale runs from dark blue for low distances to yellow for the highest ones The basic map and color scheme, showing absolute distance measures from the reference country, in this case the United States: NB: USSR data through 1991 only.
