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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.
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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 • Two hierarchical level grouping • Data Collection • Between Group Theil • Within – Group Theil • Programs and Macros • 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 • 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 • Second - multiply the unweighted within Theil component by the income weight of each group • Third – take the sum of all the individual components to obtain the weighted 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 2nd hierarchical level
Programs and Macros • Excel Spreadsheet • Stata program • SAS options
