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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

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


Use of Programs and Macros



James K. Galbraith and Enrique Garcilazo

The University of Texas Inequality Project

Session 3

  • Two hierarchical level grouping
  • Data Collection
  • Between Group Theil
  • Within – Group Theil
  • Programs and Macros
  • Working with Output – Analysis
two level hierarchical grouping
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
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
Data Management
  • Sectors = {a, b, c}
  • Geographical units = {1, 2, 3}
  • Check:
    • matching # observations between both matrixes
    • non zero observations
cleaning the data
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
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 theil10
Calculating The Between Theil
  • Add across rows and columns
calculating the between theil12
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 theil14
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 theil15
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
  • 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
Programs and Macros
  • Excel Spreadsheet
  • Stata program
  • SAS options