Dineq Manual
User Manual:
Open the PDF directly: View PDF 
.
Page Count: 23
Package ‘dineq’
February 24, 2018
Type Package
Title Decomposition of (income) inequality
Version 0.1.0
Date 2018-02-01
Author René Schulenberg
Maintainer René Schulenberg <reneschulenberg@gmail.com>
Description Decomposition of (income) inequality by population sub groups.
For a decomposition on a single variable the mean log deviation can be used.
For a decomposition on multiple variables a regression based technique can be used.
Recentered influence function regression for marginal effects of the income distribution.
Some extensions to inequality functions to handle weights and/or missings.
Depends R (>= 2.10)
Imports boot (>= 1.3-20), Hmisc (>= 4.0-3)
License GPL-3
Encoding UTF-8
LazyData true
RoxygenNote 6.0.1
NeedsCompilation no
Rtopics documented:
dineq_change_rb ...................................... 2
dineq_rb........................................... 4
gini.wtd ........................................... 5
gini_decomp ........................................ 6
mex_inc_2008........................................ 8
mex_inc_2016........................................ 9
mld.wtd ........................................... 10
mld_change......................................... 11
mld_decomp ........................................ 13
ntiles.wtd .......................................... 14
polar.wtd .......................................... 15
rif .............................................. 16
rifr.............................................. 18
rifrSE ............................................ 19
theil.wtd........................................... 21
1
2dineq_change_rb
Index 23
dineq_change_rb Decomposition of the change in inequality
Description
Decomposition of the change in (income) inequality into multiple characteristics, divided by a price
and a quantity effect.
Usage
dineq_change_rb(formula1, weights1 = NULL, data1, formula2, weights2 = NULL,
data2)
Arguments
formula1 an object of class "formula" (or one that can be coerced to that class) for the first
year/dataset: a symbolic description of the model to be fitted in the ordinary
least squares regression.
weights1 an optional vector of weights to be used in the fitting process. Should be NULL
or a numeric vector. Should be inside selected data frame in the function and
between quotation marks.
data1 a data frame containing the variables for the first year/dataset in the model.
formula2 an object of class "formula" (or one that can be coerced to that class) for the first
year/dataset: a symbolic description of the model to be fitted in the ordinary
least squares regression.
weights2 an optional vector of weights to be used in the fitting process. Should be NULL
or a numeric vector. Should be inside selected data frame in the function and
between quotation marks.
data2 a data frame containing the variables for the first year/dataset in the model.
Details
This function uses a multivariate regression-based decomposition method. Multiple characteristics
can be added to the function in order to calculate the contribution of each individual variable (in-
cluding the residual) to the change of the inequality. For instance socio-economic, demographic
and geographic characteristics (such as age, household composition, gender, region, education) of
the household or the individual can be added.
The change decomposition is divided into a price and a quantity effect for each characteristic. The
quantity effect is caused by changes in the relative size of subgroups (for instance: a higher per-
centage of elderly households). The price effect is caused by a change in the influence of the
characteristic on the dependent variable (for instance a higher income for the elderly households).
It uses a logarithmic transformation of the values of the dependent variable. Therefore it cannot
handle negative or zero values. Those are excluded from the computation in this function.
The decomposition can only be used on the variance of log income.
The main difference with the decomposition of the change of the mean log deviation is that multiple
characteristics can be analyzed at the same time. While the decomposition function only analyze
one characteristic at the same time.
The function uses two datasets for both years to compare. Pay attention that characteristics should
be the same (although can be named differently) and in the same order in the formula.
dineq_change_rb 3
Value
a list with the results of the decomposition and the parts used for the decomposition, containing the
following components:
attention optional note on the difference in the input.
variance_logincome
the values of the variance of log income of both years/datasets and difference
between both.
decomposition_inequality
the (relative) decomposition of the inequality of both years/datasets into the dif-
ferent variables. See function ’rb_decomp’.
decomposition_change_absolute
decomposition of the change in the variance of log income into the different vari-
ables and residual split into price and quantity effects. Adds up to the absolute
change in variance of log income.
decomposition_change_relative
decomposition of the change in the variance of log income into the different
variables and residual split into price and quantity effects. Adds up to 100 per-
cent.
notes number of zero or negative observations in both data sets/years. The function
uses a logarithmic transformation of x as input for the regression. Therefore
these observations are deleted from the analysis
References
Yun, M.-S. (2006) Earnings Inequality in USA, 1969–99: Comparing Inequality Using Earnings
Equations, Review of Income and Wealth, 52 (1): p. 127–144.
Fields, G. (2003) Accounting for income inequality and its change: a new method, with application
to the distribution of earnings in the United States, Research in Labor Economics, 22, p. 1–38.
Brewer M., and L. Wren-Lewis (2016) Accounting for Changes in Income Inequality: Decompo-
sition Analyses for the UK, 1978–2008. Oxford Bulletin of economics and statistics, 78 (3), p.
289-322,
See Also
dineq_rb
Examples
#Decomposition of the change in income inequality into 4 variables using the Mexican Income
#data set
data(mex_inc_2008)
inequality_change <- dineq_change_rb(formula1=income~hh_structure+education+domicile_size+age_cat,
weights1="factor",data1=mex_inc_2008, formula2=income~hh_structure+education+
domicile_size+age_cat, weights2="factor",data2=mex_inc_2016)
#selection of output: change in variance of log income decomposed in variables split into price
#and quantity effect and residual.
inequality_change["decomposition_change_absolute"]
#selection of output: relatieve change in variance of log income decomposed in variables split
#into price and quantity effect and residual. Because of negative change in variance of log
#income, the negative contributuon of education (quantity) becomes a positive number.
4dineq_rb
inequality_change["decomposition_change_relative"]
dineq_rb Regression-based decomposition of inequality
Description
Decomposition of (income) inequality into multiple characteristics. A regression-based decompo-
sition method is used.
Usage
dineq_rb(formula, weights = NULL, data)
Arguments
formula an object of class "formula" (or one that can be coerced to that class): a symbolic
description of the model to be fitted in the ordinary least squares regression.
weights an optional vector of weights to be used in the fitting process. Should be NULL
or a numeric vector. Should be inside selected data frame in the function and
between quotation marks.
data a data frame containing the variables in the model.
Details
This function uses a multivariate regression-based decomposition method. Multiple variables can
be added to the function in order to calculate the contribution of each individual variable (including
the residual) to the inequality. For instance socio-economic, demographic and geographic charac-
teristics (such as age, household composition, gender, region, education) of the household or the
individual can be added.
This decomposition can be used on a broad range of inequality measure, like Gini, Theil, mean log
deviation, Atkinson index and variance of log income.
It uses a logarithmic transformation of the values of the dependent variable. Therefore it cannot
handle negative or zero values. Those are excluded from the computation in this function.
The main difference with the decomposition of the mean log deviation or Gini coefficient is that
multiple characteristics can be analyzed at the same time. While the other decomposition functions
only analyze one characteristic at the same time.
Value
a list with the results of the decomposition, containing the following components:
inequality_measures
the values of 4 inequality measures: gini, mean log deviation, theil and variance
of log income
decomposition_inequality
the (relative) decomposition of the inequality into the different variables
regression_results
results of the ols regression which is used to make the decomposition of inequal-
ity
gini.wtd 5
note number of zero or negative observations. The function uses a logarithmic trans-
formation of x as input for the regression. Therefore these observations are
deleted from the analysis
References
Fields, G. S. (2003). ‘Accounting for income inequality and its change: a new method, with ap-
plication to the distribution of earnings in the United States’, Research in Labor Economics, 22, p.
1–38.
Brewer M., and L. Wren-Lewis (2016) Accounting for Changes in Income Inequality: Decompo-
sition Analyses for the UK, 1978–2008. Oxford Bulletin of economics and statistics, 78 (3), p.
289-322,
See Also
dineq_change_rb
Examples
#Decomposition of the income inequality into 4 variables using Mexican Income data set:
data(mex_inc_2008)
inequality_decomp <- dineq_rb(income~hh_structure+education+domicile_size+age_cat,
weights="factor", data=mex_inc_2008)
#selection of the output: decomposition of the inequality into the contribution of the
#different variables and residual (adds up to 100 percent)
inequality_decomp["decomposition_inequality"]
gini.wtd Gini coefficient
Description
Returns the (optional weighted) Gini coefficient for a vector.
Usage
gini.wtd(x, weights = NULL)
Arguments
xa numeric vector containing at least non-negative elements.
weights an optional vector of weights of x to be used in the computation of the Gini
coefficient. Should be NULL or a numeric vector.
6gini_decomp
Details
The Gini coefficient is a measure of inequality among values of a distribution. The most used single
measure for income inequality. The coefficient can theoretically range between 0 and 1, with 1 being
the highest possible inequality (for instance: 1 person in a society has all income; the others none).
But coefficients that are negative or greater than 1 are also possible because of negative values in the
distribution. Compared to other measures of inequality, the Gini coefficient is especially sensitive
for changes in the middle of the distribution.
Extension of the gini function in reldist package in order to handle missings.
Value
The value of the Gini coefficient.
Source
Handcock, M. (2016), Relative Distribution Methods. Version 1.6-6. Project home page at http://www.stat.ucla.edu/~handcock/RelDist.
References
Haughton, J. and S. Khandker. (2009) Handbook on poverty and inequality, Washington, DC:
World Bank.
Cowell F. (2000) Measurement of Inequality. In Atkinson A. and Bourguignon F. (eds.) Handbook
of Income Distribution. Amsterdam: Elsevier, p. 87-166.
Examples
#calculate Gini coefficient using Mexican Income data set
data(mex_inc_2008)
#unweighted Gini coefficient:
gini.wtd(mex_inc_2008$income)
#weighted Gini coefficient:
gini.wtd(x=mex_inc_2008$income, weights=mex_inc_2008$factor)
gini_decomp Decomposition of the Gini coefficient
Description
Decomposes the Gini coefficient into population subgroups. Distinction is made by between and
within group inequality and an overlap (interaction) term.
Usage
gini_decomp(x, z, weights = NULL)
gini_decomp 7
Arguments
xa numeric vector containing at least non-negative elements.
za factor containing the population sub groups.
weights an optional vector of weights of x to be used in the computation of the decom-
position. Should be NULL or a numeric vector.
Details
The decomposition of the Gini coefficient by between and within group inequality. In most cases
there is an overlap of the distribution of both groups. Consequence is that between and within group
inequality doesn’t add up to the total Gini coefficient. In those cases there is an overlap term. Also
referred to as interaction effect.
Within group inequality is calculated by using the Gini coefficient for each sub group. Between
group inequality by using the gini coefficient of the average of both sub groups.
Value
a list with the results of the decomposition and the parts used for the decomposition, containing the
following components:
gini_decomp a list containing the decomposition: gini_total (value of the gini coefficient of x),
gini_within (value of within-group inequality), gini_between (value of between-
group inequality) and gini_overlap (value of overlap in inequality)
gini_group a list containing gini_group (the gini coefficients of the different subgroups) and
gini_group_contribution(the contribution of the subgroups to the total within-
group inequality: adds up to gini_within)
gini_decomp a list containing the means of x: mean_total (value of the mean of x of all
subgroups combined) and mean_group (value of the mean of x of the individual
subgroups) inequality) and gini_between (value of between-group inequality)
share_groups the distribution of the subgroups z
share_income_groups
the distribution of vector x by subgroups z
number_cases a list containing the number of cases in total, by subgroup (weighted and un-
weighted): n_unweighted (total number of unweighted x), n_weighted (total
number of weighted x), n_group_unweighted (number of unweighted x by sub-
group z), n_group_unweighted (number of weighted x by subgroup z)
References
Mookherjee, D. and A. Shorrocks (1982) A decomposition analysis of the trend in UK income
inequality, Economic Journal, 92 (368), p. 886-902.
Cowell F. (2000) Measurement of Inequality. In Atkinson A. and Bourguignon F. (eds.) Handbook
of Income Distribution. Amsterdam: Elsevier, p. 87-166.
See Also
mld_decomp
8mex_inc_2008
Examples
#Decomposition of the gini coefficient by level of education using Mexican Income data set
data(mex_inc_2008)
education_decomp <- gini_decomp(x=mex_inc_2008$income,z=mex_inc_2008$education,
weights=mex_inc_2008$factor)
#complete output
education_decomp
#Selected output: decomposition into between- and within-group inequality and overlap (interaction)
education_decomp["gini_decomp"]
mex_inc_2008 Mexican income data 2008
Description
Selection of Mexican income (survey) data and household characteristic for 2008. Extracted from
ENIGH (Household Income and Expenditure Survey).
Usage
data(mex_inc_2008)
Format
A data frame containing 5000 observations and 8 variables (a selection from the original).
hh_number Household ID.
factor Population inflating weights.
income Household income.
hh_structure Household structure, factor with levels unipersonal, nuclear, ampliado, compuesto
and coresidente.
education Highest achieved education of the head of the household, factor with levels Sin in-
struccion, Preescolar, Primaria incompleta, Primaria completa, Secundaria incompleta, Se-
cundaria completa, Preparatoria incompleta, Preparatoria completa, Profesional incompleta,
Profesional completa, Posgrado.
domicile_size Population of domicile, factor with levels <2500, 2500-15000, 15000-100000, >100000.
age age (integer) of the head of the household.
age_cat age (categorical) of the head of the household , factor with levels <25, 25-34, 35-44, 45-54,
55-64, 65-74, >=75.
Details
This data set is a selecion of the original dataset of the National Institute of Statistics and Geography
in Mexico (INEGI). The original contains 29468 observations and 129 variables with information
on the income and household characteristics in Mexico. This selection is only meant to be used
as a calculation example for the functions in this package. Results will not represent the correct
information on the Mexican situation.
mex_inc_2016 9
Source
http://en.www.inegi.org.mx/proyectos/enchogares/regulares/enigh/nc/2008/default.
html, the whole data set can be obtained here.
References
INEGI (2009), ENIGH 2008 Nueva construcción. Ingresos y gastos de los hogares, Aguascalientes:
INEGI.
mex_inc_2016 Mexican income data 2016
Description
Selection of Mexican income (survey) data and household characteristic for 2016. Extracted from
ENIGH (Household Income and Expenditure Survey).
Usage
data(mex_inc_2016)
Format
A data frame containing 5000 observations and 8 variables (a selection from the original).
hh_number Household ID.
factor Population inflating weights.
income Household income.
hh_structure Household structure, factor with levels unipersonal, nuclear, ampliado, compuesto
and coresidente.
education Highest achieved education of the head of the household, factor with levels Sin in-
struccion, Preescolar, Primaria incompleta, Primaria completa, Secundaria incompleta, Se-
cundaria completa, Preparatoria incompleta, Preparatoria completa, Profesional incompleta,
Profesional completa, Posgrado.
domicile_size Population of domicile, factor with levels <2500, 2500-15000, 15000-100000, >100000.
age age (integer) of the head of the household.
age_cat age (categorical) of the head of the household , factor with levels <25, 25-34, 35-44, 45-54,
55-64, 65-74, >=75.
Details
This data set is a selecion of the original dataset of the National Institute of Statistics and Geography
in Mexico (INEGI). The original contains 70311 observations and 127 variables with information
on the income and household characteristics in Mexico. This selection is only meant to be used
as a calculation example for the functions in this package. Results will not represent the correct
information on the Mexican situation.
Source
http://en.www.inegi.org.mx/proyectos/enchogares/regulares/enigh/nc/2016/default.
html, the whole data set can be obtained here.
10 mld.wtd
References
INEGI (2017), Encuesta Nacional de Ingresos y Gastos de los Hogares 2016. ENIGH. Nueva serie.
Temas, categorías y variables, Aguascalientes: INEGI.
mld.wtd Mean log deviation
Description
Returns the (optional weighted) mean log deviation for a vector.
Usage
mld.wtd(x, weights = NULL)
Arguments
xa numeric vector containing at least non-negative elements.
weights an optional vector of weights of x to be used in the computation of the mean log
deviation. Should be NULL or a numeric vector.
Details
The mean log deviation is a measure of inequality among values of a distribution. It is a member
of the Generalized Entropy Measures. Also referred to as GE(0). A value of zero is the lowest
possible inequality. The measure does not have an upper bound for the highest inequality. It uses a
logarithmic transformation of the values of the distribution. Therefore it cannot handle negative or
zero values. Those are excluded from the computation in this function. The mean log deviation is
more sensitive for changes in the lower tail of the distribution.
Extension of the calcGEI function in IC2 package in order to handle missings.
Value
the value of the mean log deviation index.
Source
Plat, D. (2012). IC2: Inequality and Concentration Indices and Curves. R package version 1.0-1.
https://CRAN.R-project.org/package=IC2
References
Haughton, J. and S. Khandker. (2009) Handbook on poverty and inequality, Washington, DC:
World Bank.
Cowell F. (2000) Measurement of Inequality. In Atkinson A. and Bourguignon F. (eds.) Handbook
of Income Distribution. Amsterdam: Elsevier, p. 87-166.
mld_change 11
Examples
#calculate mean log deviation using Mexican Income data set
data(mex_inc_2008)
#unweighted mean log deviation:
mld.wtd(mex_inc_2008$income)
#weighted mean log deviation:
mld.wtd(x=mex_inc_2008$income, weights=mex_inc_2008$factor)
mld_change Decomposition of the change of the mean log deviation
Description
Decomposes the change of the mean log deviation between two years/data sets into population
subgroups.
Usage
mld_change(x1, z1, weights1 = NULL, x2, z2, weights2 = NULL)
Arguments
x1 a numeric vector for the first year/dataset containing at least non-negative ele-
ments.
z1 a factor for the first year/dataset containing the population subgroups.
weights1 an optional vector of weights of x for the first year/dataset to be used in the
computation of the decomposition. Should be NULL or a numeric vector.
x2 a numeric vector for the second year/dataset containing at least non-negative
elements.
z2 a factor for the second year/dataset containing the population subgroups.
weights2 an optional vector of weights of x for the second year/dataset to be used in the
computation of the decomposition. Should be NULL or a numeric vector.
Details
The change of the mean log deviation can be decomposed into three components: inequality
changes between and within groups and changes in the relative sizes of the groups. The change
of between group inequality is measures by a change in the relative income of the subgroups. The
change of within group inequality by adding up all changes in mean log deviation within the sub-
groups. And the contribution of changes in relative population size effects the change on both the
within and between group components. For the relative contributions those two are added together.
This method is introduced by Mookherjee and Shorrocks. It is an accurate approximation of the ex-
act decomposition. It uses a logarithmic transformation of the values of the distribution. Therefore
it cannot handle negative or zero values. Those are excluded from the computation in this function.
12 mld_change
Value
a list with the results of the decomposition and the parts used for the decomposition, containing the
following components:
mld_data1 the value of the mean log deviation index of x for the first year/dataset, and the
decomposition into within-group and between-group inequality
mld_data2 the value of the mean log deviation index of x for the second year/dataset, and
the decomposition into within-group and between-group inequality
mld_difference the difference between the mean log deviation and the decomposition between
the second and first year/dataset
absolute_contributions_difference
decomposition of the absolute change in inequality into: within group changes,
group size changes (split into the effect of within and between group compo-
nents) and between group changes.
relative_contributions_difference
decomposition of the change in inequality into relatieve contributions of: within
group changes, group size changes and between group changes. Adds up to 100
percent (or -100 percent for negative change)
note number of zero or negative observations in both datasets. The mean log devi-
ation uses a logarithmic transformation of x. Therefore these observations are
deleted from the analysis
References
Mookherjee, D. and A. Shorrocks (1982) A decomposition analysis of the trend in UK income
inequality, Economic Journal, 92 (368), p. 886-902.
Brewer M., and L. Wren-Lewis (2016) Accounting for Changes in Income Inequality: Decompo-
sition Analyses for the UK, 1978–2008. Oxford Bulletin of economics and statistics, 78 (3), p.
289-322,
See Also
mld_decomp
Examples
#Decomposition of the change in mean log deviation by level of eduction using
#Mexican Income data set
data(mex_inc_2008)
change_education <- mld_change(x1=mex_inc_2008$income, z1=mex_inc_2008$education,
weights1=mex_inc_2008$factor, x2=mex_inc_2016$income, z2=mex_inc_2016$education,
weights2=mex_inc_2016$factor)
#selection of the output: decomposition of the change into within- and between-group
#contribution and change in de size of groups (adds up to 100 percent)
change_education["relative_contributions_difference"]
mld_decomp 13
mld_decomp Decomposition of the mean log deviation
Description
Decomposes the mean log deviation into non overlapping population subgroups. Distinction is
made by between and within group inequality.
Usage
mld_decomp(x, z, weights = NULL)
Arguments
xa numeric vector containing at least non-negative elements.
za factor containing the population subgroups.
weights an optional vector of weights of x to be used in the computation of the decom-
position. Should be NULL or a numeric vector.
Details
The decomposition of the mean log deviation by between and within group inequality. Within
group inequality is calculated by using the mean log deviation for each sub group. Between group
inequality by the mean log deviation of the average of both sub groups.
It uses a logarithmic transformation of the values of the distribution. Therefore it cannot handle
negative or zero values. Those are excluded from the computation in this function.
Based on calcGEI function in IC2 package. Handles missings.
Value
a list with the results of the decomposition and the parts used for the decomposition, containing the
following components:
mld_decomp a list containing the decomposition: mld_total (value of the mean log devia-
tion index of x) mld_within (value of within-group inequality) and mld_between
(value of between-group inequality)
mld_group a list containing mld_group (the mean log deviations of the different subgroups)
and mld_group_contribution(the contribution of the subgroups to the total within-
group inequality: adds up to mld_within)
mld_decomp a list containing the means of x: mean_total (value of the mean of x of all
subgroups combined) and mean_group (value of the mean of x of the individual
subgroups) inequality) and mld_between (value of between-group inequality)
share_groups the distribution of the subgroups z
share_income_groups
the distribution of vector x by subgroups z
number_cases a list containing the number of cases in total, by subgroup (weighted and un-
weighted): n_unweighted (total number of unweighted x), n_weighted (total
number of weighted x), n_group_unweighted (number of unweighted x by sub-
group z), n_group_unweighted (number of weighted x by subgroup z)
14 ntiles.wtd
note number of zero or negative observations. The mean log deviation uses a loga-
rithmic transformation of x. Therefore these observations are deleted from the
analysis
Source
Plat, D. (2012). IC2: Inequality and Concentration Indices and Curves. R package version 1.0-1.
https://CRAN.R-project.org/package=IC2
References
Mookherjee, D. and A. Shorrocks (1982) A decomposition analysis of the trend in UK income
inequality, Economic Journal, 92 (368), p. 886-902.
Brewer M., and L. Wren-Lewis (2016) Accounting for Changes in Income Inequality: Decompo-
sition Analyses for the UK, 1978–2008. Oxford Bulletin of economics and statistics, 78 (3), p.
289-322,
Haughton, J. and S. Khandker. (2009) Handbook on poverty and inequality, Washington, DC:
World Bank.
See Also
mld_change gini_decomp
Examples
#Decomposition of mean log deviation by level of education using Mexican Income data set
data(mex_inc_2008)
education_decomp <- mld_decomp(x=mex_inc_2008$income,z=mex_inc_2008$education,
weights=mex_inc_2008$factor)
#complete output
education_decomp
#Selected output: decomposition into between- and within-group inequality
education_decomp["mld_decomp"]
ntiles.wtd Weighted tiles
Description
Breaks input vector into n groups. Returns the (optional weighted) tile of an individual observation
in vector x.
Usage
ntiles.wtd(x, n, weights = NULL)
polar.wtd 15
Arguments
xa numeric vector for which the quantiles are computed. Missing values are left
as missing.
nthe number of desired sub groups to break vector x into.
weights an optional vector of weights of x to be used in the computation of the tiles.
Should be NULL or a numeric vector.
Details
Breaks vector x into n sub groups. The main difference with other tile functions (for instance ntile
from dplyr) is that those functions break up vector x in exact equal size sub groups. Observations
with the same value can end up in different tiles. In this function, observations with the same value
always end up in the same tile, therefore sub groups may have different sizes. Especially when the
weights argument is used. For a weighted tile function with the same group size, see for instance
weighted_ntile from the grattan package.
When using a short-length vector (compared to the number of tiles) or with high variance weights,
output may be different than anticipated.
Value
A vector of integers corresponding to the quantiles of vector x.
Examples
#Break up the income variable in the Mexican Income data set into 10 groups (tiles)
data(mex_inc_2008)
#unweighted tiles:
q <- ntiles.wtd(x=mex_inc_2008$income, n=10)
#weighted tiles:
qw <- ntiles.wtd(x=mex_inc_2008$income, n=10, weights=mex_inc_2008$factor)
polar.wtd Polarization index
Description
Returns the (possibly weighted) polarization index for a vector. The Wolfson index of bipolarization
is used.
A bipolarized (income) distribution has fewer observations in the middle and more in lower and/or
higher part of the distribution. The regular measures of inequality (like the gini coefficient) does
not give information about the polarization of the distribution. This Polarization index computes
the level of bipolarization of the distribution. The concept is closely related to the Lorenz curve and
therefore the scalar measure is also related to the Gini coefficient. A lower number means a lower
level of polarization.
Extension of the polar.aff function in affluence-index package. Option of weighting the index is
included.
16 rif
Usage
polar.wtd(x, weights = NULL)
Arguments
xa numeric vector.
weights an optional vector of weights of x to be used in the computation of the Polariza-
tion index. Should be NULL or a numeric vector.
Value
The value of the Wolfson polarization index.
Source
Wolny-Dominiak, A. and A. Saczewska-Piotrowska (2017). affluenceIndex: Affluence Indices. R
package version 1.0. https://CRAN.R-project.org/package=affluenceIndex
References
Wolfson M. (1994) When inequalities diverge, The American Economic Review, 84, p. 353-358.
Schmidt, A. (2002) Statistical Measurement of Income Polarization. A Cross-National, Berlin 10th
International conference on panel data.
Examples
#calculate Polarization Index using Mexican Income data set
data(mex_inc_2008)
#unweighted Polarization Index:
polar.wtd(mex_inc_2008$income)
#weighted Polarization Index:
polar.wtd(x=mex_inc_2008$income, weights=mex_inc_2008$factor)
rif Recentered influence function (RIF)
Description
Returns the (optional weighted) recentered influence function of a distributional statistic.
Usage
rif(x, weights = NULL, method = "quantile", quantile = 0.5,
kernel = "gaussian")
rif 17
Arguments
xa numeric vector for which the recentered influence function is computed.
weights an optional vector of weights of x to be used in the computation of the recentered
influence function. Should be NULL or a numeric vector.
method the distribution statistic for which the recentered influence function is estimated.
Options are "quantile", "gini" and "variance". Default is "quantile".
quantile quantile to be used when method "quantile" is selected. Must be a numeric
between 0 and 1. Default is 0.5 (median). Only a single quantile can be selected.
kernel a character giving the smoothing kernel to be used in method "quantile". Op-
tions are "gaussian", "rectangular", "triangular", "epanechnikov", "biweight",
"cosine" or "optcosine". Default is "gaussian".
Details
The RIF can be used as input for a RIF regression approach. RIF regressions are mostly used to
estimate the marginal effect of covariates on distributional statistics of income or wealth.
The RIF is calculated by adding the distributional statistic (quantile, gini or variance) to the influ-
ence function. RIF is a numeric vector where each element corresponds to a particular individual’s
influence on the distributional statistic.
Value
A numeric vector of the recentered influence function of the selected distributional statistic.
References
Firpo, S., N. Fortin and T. Lemieux (2009) Unconditional quantile regressions. Econometrica,
77(3), p. 953-973.
Heckley G, U.-G. Gerdtham U-G and G. Kjellsson (2016) A general method for decomposing the
causes of socioeconomic inequality in health. Journal of Health Economics,48, p. 89–106.
Pereira, J. and A. Galego (2016) The drivers of wage inequality across Europe, a recentered in-
fluence function regression approach, 10th Annual Meeting of the Portuguese Economic Journal,
University of Evora.
See Also
rifr
Examples
data(mex_inc_2008)
#Recentered influence funtion of 20th quantile
rif_q20 <- rif(x=mex_inc_2008$income, weights=mex_inc_2008$factor, method="quantile",
quantile=0.2)
#Recentered influence funtion of the gini coefficient
rif_gini <- rif(x=mex_inc_2008$income, weights=mex_inc_2008$factor, method="gini")
18 rifr
rifr Recentered influence function regression (RIF Regression)
Description
Recentered influence function regression of a distributional statistic.
Usage
rifr(formula, data, weights = NULL, method = "quantile", quantile = 0.5,
kernel = "gaussian")
Arguments
formula an object of class "formula" (or one that can be coerced to that class): a symbolic
description of the model to be fitted in the RIF regression.
data a data frame containing the variables and weights of the model.
weights an optional vector of weights of x to be used in the computation of the recentered
influence function. Should be NULL or a numeric vector. Should be inside
selected data frame in the function and between quotation marks.
method the distribution statistic for which the recentered influence function is estimated.
Options are "quantile", "gini" and "variance". Default is "quantile".
quantile quantile to be used when method "quantile" is selected. Must be a numeric
between 0 and 1. Default is 0.5 (median). Multiple quantiles can be used.
kernel a character giving the smoothing kernel to be used in method "quantile". Op-
tions are "gaussian", "rectangular", "triangular", "epanechnikov", "biweight",
"cosine" or "optcosine". Default is "gaussian".
Details
RIF Regressions can be used to estimate the marginal effects of covariates on distributional statistics
(such as quantiles, gini and variance). It is based on the recentered influence function of a statistic.
The transformed RIF is used as the dependent variable in an ordinary least squares regression. RIF
regressions are mostly used to estimate the marginal effect of covariates on distributional statistics
of income or wealth.
Value
A list containing the results of the RIF regression.
coefficients the coefficient estimates.
SE the coefficient standard error.
tthe coefficient t-value.
pthe coefficient p-value.
adjusted_r2 the adjusted r-squares.
rifrSE 19
References
Firpo, S., N. Fortin and T. Lemieux (2009) Unconditional quantile regressions. Econometrica,
77(3), p. 953-973.
Heckley G, U.-G. Gerdtham U-G and G. Kjellsson (2016) A general method for decomposing the
causes of socioeconomic inequality in health. Journal of Health Economics,48, p. 89–106.
Pereira, J. and A. Galego (2016) The drivers of wage inequality across Europe, a recentered in-
fluence function regression approach, 10th Annual Meeting of the Portuguese Economic Journal,
University of Evora.
See Also
rif rifrSE
Examples
data(mex_inc_2008)
#Recentered influence funtion of each decile
rifr_q <- rifr(income~hh_structure+education, data=mex_inc_2008, weights="factor",
method="quantile", quantile=seq(0.1,0.9,0.1), kernel="gaussian")
#Recentered influence funtion of the gini coefficient
rifr_gini <- rifr(income~hh_structure+education, data=mex_inc_2008, weights="factor",
method="gini")
rifrSE Inference of recentered influence function regression (RIF regression)
Description
Inference of a RIF Regression using a bootstrap method.
Usage
rifrSE(formula, data, weights = NULL, method = "quantile", quantile = 0.5,
kernel = "gaussian", Nboot = 100, confidence = 0.95)
Arguments
formula an object of class "formula" (or one that can be coerced to that class): a symbolic
description of the model to be fitted in the RIF regression.
data a data frame containing the variables and weights of the model.
weights an optional vector of weights of x to be used in the computation of the recentered
influence function. Should be NULL or a numeric vector. Should be inside
selected data frame in the function and between quotation marks.
method the distribution statistic for which the recentered influence function is estimated.
Options are "quantile", "gini" and "variance". Default is "quantile".
20 rifrSE
quantile quantile to be used when method "quantile" is selected. Must be a numeric
between 0 and 1. Default is 0.5 (median). Only a single quantile can be used.
kernel a character giving the smoothing kernel to be used in method "quantile". Op-
tions are "gaussian", "rectangular", "triangular", "epanechnikov", "biweight",
"cosine" or "optcosine". Default is "gaussian".
Nboot the number of bootstrap replicates. Default is 100.
confidence significance level for estimation of the confidence interval of the fitted model.
Default is 0.95.
Details
RIF Regressions can be used to estimate the marginal effects of covariates on distributional statistics
(such as quantiles, gini and variance). It is based on the recentered influence function of a statistic.
The transformed RIF is used as the dependent variable in an ordinary least squares regression. RIF
regressions are mostly used to estimate the marginal effect of covariates on distributional statistics
of income or wealth.
The standard errors, confidence intervals and Z- and P-values are calculated by using a standard
bootstrap method (from boot package).
Value
A data frame containing the results of the RIF regression.
Coef estimated coefficients of the original (non bootstrapped) RIF regression
lower lower bound of confidence interval of estimated coefficient
upper upper bound of confidence interval of estimated coefficient
SE standard error
Z Value Z value
P Value P value
Signif Significance codes of P: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
References
Firpo, S., N. Fortin and T. Lemieux (2009) Unconditional quantile regressions. Econometrica,
77(3), p. 953-973.
Heckley G, U.-G. Gerdtham U-G and G. Kjellsson (2016) A general method for decomposing the
causes of socioeconomic inequality in health. Journal of Health Economics,48, p. 89–106.
Pereira, J. and A. Galego (2016) The drivers of wage inequality across Europe, a recentered in-
fluence function regression approach, 10th Annual Meeting of the Portuguese Economic Journal,
University of Evora.
See Also
rif rifr
theil.wtd 21
Examples
data(mex_inc_2008)
#Recentered influence funtion of 20th quantile
rifr_q <- rifrSE(income~hh_structure+education, data=mex_inc_2008, weights="factor",
method="quantile", quantile=0.2, kernel="gaussian", Nboot=100, confidence=0.95)
#Recentered influence funtion of the gini coefficient
rifr_gini <- rifrSE(income~hh_structure+education, data=mex_inc_2008, weights="factor",
method="gini", Nboot=100, confidence=0.95)
theil.wtd Theil index
Description
Returns the (optional weighted) Theil index for a vector.
Usage
theil.wtd(x, weights = NULL)
Arguments
xa numeric vector containing at least non-negative elements.
weights an optional vector of weights of x to be used in the computation of the Theil
index. Should be NULL or a numeric vector.
Details
The Theil index is a measure of inequality among values of a distribution. It is a member of the
Generalized Entropy Measures. Also referred to as GE(1). The index can have a value between 0
and ln N (the logarithm of the number of values), with 0 being the lowest possible inequality. It uses
a logarithmic transformation of the values of the distribution. Therefore it cannot handle negative
or zero values. Those are excluded from the computation in this function. The Theil Index is more
sensitive for changes in the upper tail of the distribution.
Extension of the calcGEI function in IC2 package in order to handle missings.
Value
The value of the Theil index.
Source
Plat, D. (2012). IC2: Inequality and Concentration Indices and Curves. R package version 1.0-1.
https://CRAN.R-project.org/package=IC2
22 theil.wtd
References
Haughton, J. and S. Khandker. (2009) Handbook on poverty and inequality, Washington, DC:
World Bank.
Cowell F. (2000) Measurement of Inequality. In Atkinson A. and Bourguignon F. (eds.) Handbook
of Income Distribution. Amsterdam: Elsevier, p. 87-166.
Examples
#calculate Theil Index using Mexican Income data set
data(mex_inc_2008)
#unweighted Theil Index:
theil.wtd(mex_inc_2008$income)
#weighted Theil Index:
theil.wtd(x=mex_inc_2008$income, weights=mex_inc_2008$factor)
