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PovertyAndInequalityMeasures

This generates various measures poverty and inequality from a sample dataset.

The measures are mostly taken from chs. 4-6 of the World Banks' Handbook on Poverty and Inequality.

See the test case for worked examples

Poverty:

These routines can use both 2d arrays and dataframes as inputs For the arrays, supply with integers giving the columns holding weights and incomes; for the frames, the names of the columns (as symbols).


function makepoverty(
    rawdata                       :: Array{<:Real, 2},
    line                          :: Real,
    growth                        :: Real,
    weightpos                     :: Integer = 1,
    incomepos                     :: Integer = 2,
    foster_greer_thorndyke_alphas :: AbstractArray{<:Real, 1} = DEFAULT_FGT_ALPHAS ) :: OutputDict

function makepoverty(
    rawdata,
    line                          :: Real,
    growth                        :: Real,
    weightcol                     :: Symbol,
    incomecol                     :: Symbol,
    foster_greer_thorndyke_alphas :: AbstractArray{<:Real, 1} = DEFAULT_FGT_ALPHAS,
     ) :: OutputDict

notes:

  • rawdata - each row is an observation; one col should be a weight, another is income;

positions assumed to be 1 and 2 unless weight and incomepos are supplied (or names as symbols for the frame version)

  • the dataframe version can use anything that supports the Queryverse iterable table interface;
  • line - a poverty line. This is the same for for all observations, the income measure needs to be equivalised if the line differs by family size, etc.;
  • foster_greer_thorndyke_alphas - coefficients for Foster-Greer Thorndyke poverty measures (see World Bank, ch. 4); note that FGT(0)

corresponds to the headcount measure and FGT(1) to poverty gap; count and gap are computed directly anyway but it's worth checking one against the other;

  • growth is (e.g.) 0.01 for 1% per period, and is used for 'time to exit' measure.

Output is dictionary with an entry for each measure.

Inequality

Usage is similar to makepoverty above. See chs 5 and 6 of the World Bank book, and the test case for more detail.

Version1:


function makeinequality(
    rawdata                    :: Array{<:Real, 2 },
    weightpos                  :: Integer = 1,
    incomepos                  :: Integer = 2,
    atkinson_es                :: AbstractArray{<:Real, 1} = DEFAULT_ATKINSON_ES,
    generalised_entropy_alphas :: AbstractArray{<:Real, 1} = DEFAULT_ENTROPIES ) :: OutputDict

function makeinequality(
    rawdata,
    weightcol                  :: Symbol,
    incomecol                  :: Symbol,
    atkinson_es                :: AbstractArray{<:Real, 1} = DEFAULT_ATKINSON_ES,
    generalised_entropy_alphas :: AbstractArray{<:Real, 1} = DEFAULT_ENTROPIES ) :: OutputDict

Notes:

  • rawdata a matrix with cols with weights and incomes;
  • atkinson_es inequality aversion values for the Atkinson indexes;
  • generalised_entropy_alphas vaues for Theil entropy measure;
  • weightpos - column with weights
  • incomepos - column with incomes

Return is a also a Dict of inequality measures.

There's also a method:

function adddecomposedtheil( popindic :: OutputDict, subindices :: OutputDictArray ) :: OutputDict

which takes an array of output dicts, broken down by (e.g.) Regions, Genders, etc. and produces a Theil index decomposition from them.

There's also a small binify routine which chops a dataset up into chunks of cumulative income and population suitable for drawing Lorenz Curves.

PovertyAndInequalityMeasures.add_decomposed_theil — Method

Make a wee dict with :theilbetween and :theilwithin See WB eqns 6.7/6.8. TODO

  1. there are some papers on decomposing Atkinson, but I

don't understand them ..

  1. the over time 3-part version

popindic : Inequal for the population as a whole subindices : an array of dics, one for each subgroup of interest

source
PovertyAndInequalityMeasures.binify — Function

Chop a dataset with populations and incomes into numbins groups in a form suitable for e.g. a Gini curve.

  • col1 is cumulative population,
  • 2 cumulative income/whatever,
  • 3 threshold income level.
source
PovertyAndInequalityMeasures.make_inequality — Function

Make a dictionary of inequality measures. This is mainly taken from chs 5 and 6 of the World Bank book.

  1. rawdata a matrix with cols with weights and incomes
  2. atkinson_es inequality aversion values for the Atkinson indexes
  3. generalised_entropy_alphas
  4. weightpos - column with weights
  5. incomepos - column with incomes
source
PovertyAndInequalityMeasures.make_poverty — Function

As above, but using the QueryVerse IterableTables interface rawdata - basically anything resembling a dataframe; see: [https://github.com/queryverse/IterableTables.jl] throws an exception if rawdata doesn't support iterabletable interface

source
PovertyAndInequalityMeasures.make_poverty — Function

Create a dictionary of poverty measures.

This is based on the World Bank's Poverty Handbook by Haughton and Khandker.

Arguments:

  • rawdata - an nxm array of real nunbers; each row is an observation; one col should be a weight, another is income; positions assumed to be 1 and 2 unless weight and incomepos are supplied
  • line - a poverty line, assumed same for all obs (so income is assumed to be already equivalised)
  • foster_greer_thorndyke_alphas - coefficients for FGT poverty measures; note that FGT(0) corresponds to headcount and FGT(1) to gap; count and gap are computed directly anyway but it's worth checking one against the other.
  • growth is (e.g.) 0.01 for 1% per period, and is used for 'time to exit' measure.
source
PovertyAndInequalityMeasures.make_inequalityinternal — Method

Make a dictionary of inequality measures. This is mainly taken from chs 5 and 6 of the World Bank book.

  1. rawdata a matrix with cols with weights and incomes
  2. atkinson_es inequality aversion values for the Atkinson indexes
  3. generalised_entropy_alphas
  4. weightpos - column with weights
  5. incomepos - column with incomes
source

Bibliography

Cobham Alex, and Sumner Andy. “Is Inequality All about the Tails?: The Palma Measure of Income Inequality.” Significance 11, no. 1 (February 19, 2014): 10–13. https://doi.org/10.1111/j.1740-9713.2014.00718.x.

Haughton, Jonathan, and Shahidur R. Khandker. ‘Handbook on Poverty and Inequality’. The World Bank, 27 March 2009. http://documents.worldbank.org/curated/en/488081468157174849/Handbook-on-poverty-and-inequality.

Preston, Ian. ‘Inequality and Income Gaps’. IFS Working Paper. Institute for Fiscal Studies, 5 December 2006. https://econpapers.repec.org/paper/ifsifsewp/06_2f25.htm.

Reed, Howard, and Graham Stark. ‘Tackling Child Poverty Delivery Plan - Forecasting Child Poverty in Scotland’. Scottish Government, 9 March 2018. http://www.gov.scot/Publications/2018/03/2911/0.