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Measuring Inequality A practical workshop On theory and technique San Jose, Costa Rica August 4 -5, 2004

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Panel Session on: Mechanics to Calculate the Theil and Use of Programs and Macros

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by James K. Galbraith and Enrique Garcilazo The University of Texas Inequality Project http://utip.gov.utexas.edu Session 3

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Outline 1.Two hierarchical level grouping 2.Data Collection 3.Between Group Theil 4.Within – Group Theil 5.Programs and Macros 6.Working with Output – Analysis

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Two Level Hierarchical grouping Data typically given by geographical units and several sectors within each unit The between group component The within group component

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Collecting data Variables: –#1 Compensation earned – wages –#2 Number of people earning – employees Two sets of data –Equal number of observations for each data set –Making sure there are no zeros –Arrange data into a yearly matrix of columns and rows (columns are geographical units, rows sectors)

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Data Management Sectors = {a, b, c} Geographical units = {1, 2, 3} Check: – matching # observations between both matrixes –non zero observations

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Cleaning The Data Compare both data-bases and look for missing observations –count function in Excel –Compare # of observations in rows and columns Take out observations equal to zero If the database is time series, make sure that the number of industries included in the analysis is consistent through time

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Calculating The Between Theil The between component can be expressed by two equivalent equations: –First equation – more intuitive –Second equation – easier to calculate

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Calculating The Between Theil –Add across rows and columns

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Calculating The Between Theil

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Using natural logs instead of base 10 Interpreting the between components –Positive component means the group is above the mean –Negative component means it is below the mean Make sure the sum of all components (between Theil) is positive and inside a reasonable range Between Theil used as estimate of total Theil

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Calculating The Within Theil

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1.First: Calculate the unweighted within Theil in each group (among p individuals/groups) Calculate the Theil by sector or by region The unweighted Theil is the total Theil for the group in the second hierarchical level

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Calculating The Within Theil 2.Second - multiply the unweighted within Theil component by the income weight of each group 3.Third – take the sum of all the individual components to obtain the weighted within Theil

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Calculating The Within Theil ..

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Output For a given year obtain: –Total Theil –Between group Theil –Weighted within group Theil Interpreting the individual between Theil components The unweighted within group Theil component interpreted as the total Theil in the 2 nd hierarchical level

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Programs and Macros Excel Spreadsheet Stata program SAS options

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Type “Inequality” into Google to find us on the Web

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