What is Distributive Analysis?

PEP - PMMA TRAINING - ADISS ABABA June 2006

DAD

A software for Distributive Analysis / Analyse Distributive

ByAbdelkrim Araar

and Jean-Yves Duclos


What is Distributive Analysis?

Distributive analysis is concerned with the distribution and redistribution of well-being, usually captured by living standards at the household level.

The distribution of living standards depends dynamically on a number of factors, such as: Average living standards at the level of the

population Living standards relative to the mean The structure of the economy and the distributional

channels of the richness. The economic policies in place (redistribution

policies) Economic shocks



Main topics linked to distribution and redistribution:

Absolute & relative poverty Absolute & relative inequality Polarisation Vertical & horizontal equity Redistribution etc..



Example of some relatively recent economic shocks in developing countries:

Economic transition from planned to market economies Application of macro adjustment programs Trade liberalisation Globalisation

These shocks can have a significant impact on the distribution of living standards at different levels (regions, countries, within households).


Positioning DAD in distributive analysis

The main features of the software can be summarized as follows:

Free! User friendly – no need for programming Estimates easily a number distributive indices and

curves that are extensively used in the literature about the distributive analysis.

Estimates accurately the sampling distribution of such indices and curves by taking into account the sampling design of household

surveys by means of analytical and numerical procedures

Provides tools for testing the robustness of comparisons Insists on the power of graphs to provide informative

pictures of the distribution of living standards


Basic descriptive tools:

Estimation of means, quantiles, variances Non parametric estimation of

density joint density non parametric regression between two

variables regression slopes

Scatter graphs Important and flexible graphical abilities


Poverty decomposition

Static decomposition: Population subgroups

FGT index - analytical approach Income components

FGT Index - Shapley approach

Dynamic decomposition: Growth and redistribution

FGT index – analytical & Shapley approaches Sectoral decomposition

FGT index – analytical & Shapley approaches Transient and chronic

FGT index – analytical approach EDE index - analytical approach

Absolute transition matrix - analytical approach


Inequality decomposition

Static decomposition: Population subgroups

S-Gini index - analytical & Shapley approaches Generalised entropy index - analytical approach

Income components S-Gini Index - analytical & Shapley approaches Coefficient of variation index – analytical approach

Dynamic decomposition: Difference: population subgroups

S-Gini index- –analytical & Shapley approaches Difference: income components

S-Gini index- –analytical & Shapley approaches Social welfare

Atkinson index – analytical approach


Simulations and policy applications

Impacts of income-component growth on Inequality, poverty and social welfare

Impact of marginal price changes on poverty, social welfare and inequality

Impact of demographic changes on poverty Impact of sectoral changes on poverty Impact of lump-sum targeting on poverty Impact of inequality-neutral targeting on

poverty


Simulations and policy applications

Gini income-component elasticity Growth elasticity of poverty Impact of marginal tax reforms on poverty and

inequality Impact of reforms to poverty alleviation

programmes, by targeting/allocation effects


Lorenz & generalized Lorenz curves Concentration & generalised concentration curves Quantile and normalised quantile curves Poverty gap & cumulative poverty gap (CPG) curves FGT curves Pro-poor curves Bi-polarisation curves Deprivation curves Consumption dominance (CD) and normalised CD

curves

Estimation of curves for descriptive and normative purposes:


Checking the robustness of poverty, social welfare, inequality and equity comparisons

Estimation of stochastic dominance curves for: poverty social welfare inequality (normalised stochastic dominance) relative poverty indirect tax reforms “Efficient” targeting reforms

Estimation of “ critical ” poverty lines for absolute and relative poverty Estimation of crossing points for Lorenz, CPG

and concentration curves


Estimating sampling distributions

Data from sample surveys usually display four important characteristics: they are stratified; they are clustered; they come with sampling weights (SW), also called

inverse probability weights; sample observations provide aggregate information

(such as household expenditures) on a number of “statistical units” (such as individuals)


Simple Random Sampling


Usual sampling procedures A country is first divided into geographical or

administrative zones and areas, called strata.

Each zone or area thus represents a strata.

The first random selection takes place within the Primary Sampling Units (denoted as PSU’s) of each stratum.

Within each stratum, a number of PSU’s are randomly selected. This random selection of PSU’s provides “clusters” of information.

PSU’s are often provinces, departments, villages, etc. Within each PSU, there may then be other levels of random selection.


Usual sampling procedures

For instance, within each province, a number of villages may be randomly selected, and within every selected village, a number of households may be randomly selected.

The final sample observations constitute the Last Sampling Units (LSU’s).

Each sample observation may then provide aggregate information (such as household expenditures) on all individuals or agents found within that LSU. These individuals or agents are not selected – information on all on them appears in the sample.

They therefore do not represent the LSUs in statistical terminology.


Sampling Design with two levels of random selection


Sampling design and statistical significance

Strata A Strata B

Highest incomes Lowest incomes PSU’s PSU’s


F ig ure 1

T h e S D o f p io rity su rve y I (1 9 9 4) o f B u rk ina

L S U s8 3 9

P S U s4 2

S tr a ta 1W e st

L S U s7 3 7

P S U s3 7

S tr a ta 2S o u th a n d W e st S o u th

L S U s1 9 6 0

P S U s9 8

S tr a ta 3N o r th C e n ter

T o ta l O b se r v a tio ns8 6 3 9

L S U s1 0 9 9

P S U s5 5

S tr a ta 4S o u th C en ter

L S U s1 2 8 8

P S U s6 6

S tr a ta 5N o r th

L S U s7 7 8

P S U s3 9

S tr a ta 6O th r e s C ities

L S U s1 9 3 8

P S U s9 7

S tr a ta 7O u a g a B o b o

E P 1 : B u r k in a (1 9 9 4)

Example:


Initialising the sampling design

From the main menu one chooses the item Edit-> Set Sample Design.

Indicate the variables to set the sample design and confirm your choice by clicking on the button OK.


Performing statistical inference

Estimating confidence intervals and p-values Estimations are included directly for:

FGT, S-Gini and Atkinson indices Can be computed via the “Confidence

interval” application in DAD Testing hypothesis

Can be performed directly for FGT, S-Gini and Atkinson indices

Can be computed via the “Confidence interval” application in DAD


DAD and DATA files

Shows two sheets to load simultaneously two data bases

Can read ASCII files safely through a data wizard Can support copy/paste to and from sheets of the

most common software (Excel, Stata,...) Offers its own ASCII format for saving data Can edit variable information and content Can add or delete observations Can generate other variables


DAD & Graphs

Flexible Graph Options For example, one can change easily the:

main title, title of axis and legends graph size template choice color, width and style of curves

Saving DAD’s graphs One can save DAD’s graphs in:

DAD Graph Format *.dgf JPEG, GIF, BMP …

One can also save curves’ coordinates in ASCII format

Editing curves’ coordinates in a new data sheet


How to learn to use DAD? The book entitled

POVERTY AND EQUITY: MEASUREMENT, POLICY AND ESTIMATION WITH DAD covers most of the measurement theory implemented in DAD. The book is also a comprehensive reference for intermediate and advanced study in distributive analysis.

DAD’s user manual provides tools for fast learning of DAD and can lead to rapid use of any of DAD’s applications.

Exercises & Technical notes were written to consolidate the learning of DAD.

Training sessions are regularly organised to teach distributive analysis and the use of DAD and other software.


DAD’s data files With DAD, micro data from household

surveys are typically required. A database used in DAD is then a matrix (a

number of columns) whose number of lines is the number of observations

DAD can load simultaneously two databases. The maximum number of variables for each

DAD file is currently 20.


DAD’s spreadsheet


The structure of a data fileI- Sampling design

Strata Specifies the name of the variable (in an integer format) that contains the Stratum identifiers.

PSU Specifies the name of the variable (in an integer format) that contains the identifiers for the Primary Sampling Units.

SAMPLING WEIGHT Specifies the name of the Sampling Weights variable.

Finite Correction Gives the Finite Population Correction variable that is needed when the number of PSU is small and sampling was one without replacement.


The structure of a data fileII- Basic distributive variables

VARIABLE OF INTEREST. This is the variable that usually captures living standards. It can be for the entire household or for individuals (e.g., per capita or per equivalent adult expenditure).

SIZE VARIABLE. This refers to the ”ethical” or physical size of the sampling observation

GROUP VARIABLE To perform computations at the group level (integer variable : ex. Rural (1) Urban (2) )


The structure of a data fileII- Basic distributive variables

GROUP NUMBER tells DAD on which value of the GROUP VARIABLE to condition the computation of some distributive statistics. The value for GROUP NUMBER should be an integer. For example, rural households might be assigned a value of 1 for some variable denoted as region.

SAMPLING WEIGHT. Sampling weights are the inverse of the sampling rate.


Importing data files into DADASCII files

After preparation of the required variables, one can export an ASCII file to be read by DAD.

To import safely the data, a wizard is used in DAD.

One can also use Copy/Paste to copy data from other software sheets (that is more risky however)

A helpful software that can be used to prepare DAF files is Stat/Transfer (though a commercial software)


Launching DAD’s applications

From the main menu one can choose the desired application; applications are organised by main themes.

After choosing the desired application, a second widows appears to indicate the number of distributions or data files that should be used.


DAD’s application for the FGT index


DAD’s window of results


DAD’s graphs (ex. Lorenz curves)


DAD’s graphs (ex. difference between Lorenz curves)


DAD’s graphs (ex. FGT curves ()


DAD’s graphs (ex. Concentration & Lorenz curves)


DAD’s graphs (ex. density curves)


DAD’s graphs (ex. Non parametric regression)

What is Distributive Analysis?

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