Measuring Inequality

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# Measuring Inequality - PowerPoint PPT Presentation

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