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

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

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

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

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

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

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)

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

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

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

Calculating The Between Theil –Add across rows and columns

Calculating The Between Theil

 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

Calculating The Within Theil

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

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

Calculating The Within Theil ..

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

Programs and Macros  Excel Spreadsheet  Stata program  SAS options

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