This note documents the method for calculating Gini Coefficients in R using 2000 Census data. Many people have use this method for computing Ginis for ZCTA’s for example. You can find these estimates for both the 50 states, as well as all US counties and additional information about Gini coefficients at https://sites.google.com/a/burkeyacademy.com/main/home/gini-coefficient

Burkey, Mark L.

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Gini Coefficients for the 2000 Census
Mark L. Burkey
North Carolina A&T State University
March 2006
Online at https://mpra.ub.uni-muenchen.de/57900/
MPRA Paper No. 57900, posted 15 August 2014 10:59 UTC
Gini Coefficients for the 2000 Census: 
Data and Methods used for calculating Gini Coefficients for Census 2000 Data in R 
by Mark L. Burkey 
Professor of Economics 
North Carolina A&T State University 
March, 2006 
 
 
Abstract: This note documents the method for calculating Gini Coefficients in R using 2000 Census 
data. Many people have use this method for computing Ginis for ZCTA’s for example. You can 
find these estimates for both the 50 states, as well as all US counties and additional information 
about Gini coefficients at https://sites.google.com/a/burkeyacademy.com/main/home/gini-
coefficients  
 
 
Here is enough information so that you can learn to computer Gini coefficients and understand how 
these were calculated.  These Ginis are from Household Income. All suggestions and corrections 
are welcome! 
 
I am using a Windows-based computer and Microsoft Excel. 
 
To compute gini coefficients with Census 2000 data: Get variables P52 and P54.  Get rid of total 
households, and total income, and total income for households less than 200,000 
 
1) Transpose data with midpoints of classes in left hand column, labeled “x” 
2) end up with 16 midpoints like so (but in a column) 
5000 12500 17500 22500 27500 32500 37500 42500 47500 55000 67500 87500 112500 137500 175000 
 
The highest midpoint is unknown since it is for all households earning above $200,000.  Leave it 
blank(the category after 175000).  Append row of total incomes for hholds making above 200000 as 
row 18 in Excel, which will become obs#17 when it is read into R 
 
3) Put the frequencies of households in counties, etc. in different groups, and label the columns 
y1, y2,… 
 
4) Read the data into R.  From Excel the easiest way is to copy all of the data to the Clipboard 
(highlight, Ctrl-C).  Then in R, type 
dataone=read.delim(“clipboard”) 
attach(dataone) 
 
5) Now, you are ready to compute gini coefficients. 
 library(ineq) 
 ineq(rep(c(x[1:15],y1[17]/y1[16]),y1[1:16]))  
Will compute the Gini coefficient for the region in column y1. 
 
6) In order to compute gini coefficients for many counties or states, you need a function to 
automatically repeat the process for y1, y2, ...  Type in the function as below: 
 
burkeyineq=function(y) ineq(rep(c(x[1:15],y[17]/y[16]),y[1:16])) #define function 
 
myginis=sapply(dataone[,2:101],burkeyineq) #apply to 100 counties in columns 2 to 101. 
uscogini=sapply(uscogin3[,2:3217],burkeyineq) #apply to 3,216 US counties 
 
Now, you can look at your Ginis by simply typing myginis at the > prompt.  You can look at a list 
of all of the objects you have created in R by simply typing ls().  If you want to transfer your Ginis 
to Excel or another program, two easy methods are: 
1) write.csv(myginis,file="ginis.csv") This will write a file to your R installation directory.  You can 
put an a: or f:\data\gini or other location in the quotes with the file name if you like. 
2) write(myginis,file="clipboard",ncolumns=1)  This will write it to your windows clipboard so you 
can paste it into Excel with control-v or edit/paste. 
7) Plot three Lorenz curves on the same graph, using observations 41,66, and 67. 
 plot(Lc(rep(c(x[1:15],y41[17]/y41[16]),y41[1:16]))) 
 lines(Lc(rep(c(x[1:15],y67[17]/y67[16]),y67[1:16])),col=2) 
 lines(Lc(rep(c(x[1:15],y66[17]/y66[16]),y66[1:16])),col=3) 
 
 
 
 
Data example below for first three counties in North Carolina: 
 
x y1 y2 y3 
5000 5231 1183 782 
12500 3113 725 389 
17500 3483 909 391 
22500 3958 930 366 
27500 3718 1195 443 
32500 3659 921 303 
37500 3223 966 314 
42500 3477 772 249 
47500 2748 814 226 
55000 5128 1540 346 
67500 5571 1521 301 
87500 4568 1009 258 
112500 1783 344 76 
137500 828 150 60 
175000 593 76 23 
 641 122 74 
 223833700 53915200 27364100 
 
 
y1, y2, for each county- you could have the county names instead if you like. 
 
See below for some more information from a handout I made. 
 
Lorenz Curves and Gini Coefficients in  
 
The ineq library in R can be used to construct Lorenz Curves and calculate Gini Coefficients. 
 
For the Gini coefficients I calculated, I used the Household Income counts from the Census 2000.  
First, I created a vector of incomes x (using the midpoint of the household income classes) and a 
vector of frequencies y1 for each county or state.  The numbers below represent the data from 
Alamance County, North Carolina: 
x y1 
5000 5231 
12500 3113 
17500 3483 
22500 3958 
27500 3718 
32500 3659 
37500 3223 
42500 3477 
47500 2748 
55000 5128 
67500 5571 
87500 4568 
112500 1783 
137500 828 
175000 593 
 641 
 223833700 
 
The last two entries in y1 are 641 families making above $200,000, and $223,833,700 was the total 
earnings for these families, for an average of $349,195 each.  We will calculate and use the income 
$349,195 and frequency 641 in the calculations, calculated on the fly since this will be different for 
each county. 
 
> library(ineq)         #load ineq library 
> plot(Lc(rep(c(x[1:15],y1[17]/y1[16]),y1[1:16])))  #plot Lorenz Curve 
> ineq(rep(c(x[1:15],y1[17]/y1[16]),y1[1:16]))   #Calculate Gini 
 
R will also calculate other inequality and dissimilarity measures, by using the function: 
 
> ineq(rep(c(x[1:15],y1[17]/y1[16]),y1[1:16]), type = “ TYPE “ ), where TYPE is one of the 
following: 
 
RS(x)      Ricci-Schutz coefficient (Pietra´s measure) 
Atkinson(x, parameter = 0.5)   Atkinson’s Measure 
Theil(x, parameter = 0)        Theil’s Entropy Index 
Kolm(x, parameter = 1)         Kolm’s Measure 
var.coeff(x, square = FALSE) Coefficient of Variation 
entropy(x, parameter = 0.5) Generalized Entropy Index 
RS is the the Ricci-Schutz coefficient (also called Pietra´s measure), Atkinson gives Atkinson´s 
measure and Kolm computes Kolm´s measure.  
If the parameter in Theil is 0 Theil´s entropy measure is computed, for every other value Theil´s 
second measure is computed.  
ineq(x, type="var") and var.coeff(x) respectively compute the coefficient of variation, while 
ineq(x,type="square.var") and var.coeff(x, square=TRUE) compute the squared coefficient 
of variation.  
entropy computes the generalized entropy, which is for parameter 1 equal to Theil´s entropy 
coefficient and for parameter 0 equal to the second measure of Theil.  
 
 
Credit goes to Achim Zeileis zeileis@ci.tuwien.ac.at, the author of the ineq function in R. 


Gini Coefficients for the 2000 Census

Munich RePEc Personal Archive

Munich Personal RePEc ArchiveGini Coefficients for the 2000 CensusBurkey, Mark L.North Carolina AT State UniversityMarch 2006Online at https://mpra.ub.uni-muenchen.de/57900/MPRA Paper No. 57900, posted 15 Aug 2014 10:59 UTCGini Coefficients for the 2000 Census: Data and Methods used for calculating Gini Coefficients for Census 2000 Data in R by Mark L. Burkey Professor of Economics North Carolina A&T State University March, 2006   Abstract: This note documents the method for calculating Gini Coefficients in R using 2000 Census data. Many people have use this method for computing Ginis for ZCTA’s for example. You can find these estimates for both the 50 states, as well as all US counties and additional information about Gini coefficients at https://sites.google.com/a/burkeyacademy.com/main/home/gini-coefficients    Here is enough information so that you can learn to computer Gini coefficients and understand how these were calculated.  These Ginis are from Household Income. All suggestions and corrections are welcome!  I am using a Windows-based computer and Microsoft Excel.  To compute gini coefficients with Census 2000 data: Get variables P52 and P54.  Get rid of total households, and total income, and total income for households less than 200,000  1) Transpose data with midpoints of classes in left hand column, labeled “x” 2) end up with 16 midpoints like so (but in a column) 5000 12500 17500 22500 27500 32500 37500 42500 47500 55000 67500 87500 112500 137500 175000  The highest midpoint is unknown since it is for all households earning above $200,000.  Leave it blank(the category after 175000).  Append row of total incomes for hholds making above 200000 as row 18 in Excel, which will become obs#17 when it is read into R  3) Put the frequencies of households in counties, etc. in different groups, and label the columns y1, y2,…  4) Read the data into R.  From Excel the easiest way is to copy all of the data to the Clipboard (highlight, Ctrl-C).  Then in R, type dataone=read.delim(“clipboard”) attach(dataone)  5) Now, you are ready to compute gini coefficients.  library(ineq)  ineq(rep(c(x[1:15],y1[17]/y1[16]),y1[1:16]))  Will compute the Gini coefficient for the region in column y1.  6) In order to compute gini coefficients for many counties or states, you need a function to automatically repeat the process for y1, y2, ...  Type in the function as below:  burkeyineq=function(y) ineq(rep(c(x[1:15],y[17]/y[16]),y[1:16])) #define function  myginis=sapply(dataone[,2:101],burkeyineq) #apply to 100 counties in columns 2 to 101. uscogini=sapply(uscogin3[,2:3217],burkeyineq) #apply to 3,216 US counties  Now, you can look at your Ginis by simply typing myginis at the > prompt.  You can look at a list of all of the objects you have created in R by simply typing ls().  If you want to transfer your Ginis to Excel or another program, two easy methods are: 1) write.csv(myginis,file="ginis.csv") This will write a file to your R installation directory.  You can put an a: or f:\data\gini or other location in the quotes with the file name if you like. 2) write(myginis,file="clipboard",ncolumns=1)  This will write it to your windows clipboard so you can paste it into Excel with control-v or edit/paste. 7) Plot three Lorenz curves on the same graph, using observations 41,66, and 67.  plot(Lc(rep(c(x[1:15],y41[17]/y41[16]),y41[1:16])))  lines(Lc(rep(c(x[1:15],y67[17]/y67[16]),y67[1:16])),col=2)  lines(Lc(rep(c(x[1:15],y66[17]/y66[16]),y66[1:16])),col=3)     Data example below for first three counties in North Carolina:  x y1 y2 y3 5000 5231 1183 782 12500 3113 725 389 17500 3483 909 391 22500 3958 930 366 27500 3718 1195 443 32500 3659 921 303 37500 3223 966 314 42500 3477 772 249 47500 2748 814 226 55000 5128 1540 346 67500 5571 1521 301 87500 4568 1009 258 112500 1783 344 76 137500 828 150 60 175000 593 76 23  641 122 74  223833700 53915200 27364100   y1, y2, for each county- you could have the county names instead if you like.  See below for some more information from a handout I made.  Lorenz Curves and Gini Coefficients in   The ineq library in R can be used to construct Lorenz Curves and calculate Gini Coefficients.  For the Gini coefficients I calculated, I used the Household Income counts from the Census 2000.  First, I created a vector of incomes x (using the midpoint of the household income classes) and a vector of frequencies y1 for each county or state.  The numbers below represent the data from Alamance County, North Carolina: x y1 5000 5231 12500 3113 17500 3483 22500 3958 27500 3718 32500 3659 37500 3223 42500 3477 47500 2748 55000 5128 67500 5571 87500 4568 112500 1783 137500 828 175000 593  641  223833700  The last two entries in y1 are 641 families making above $200,000, and $223,833,700 was the total earnings for these families, for an average of $349,195 each.  We will calculate and use the income $349,195 and frequency 641 in the calculations, calculated on the fly since this will be different for each county.  > library(ineq)         #load ineq library > plot(Lc(rep(c(x[1:15],y1[17]/y1[16]),y1[1:16])))  #plot Lorenz Curve > ineq(rep(c(x[1:15],y1[17]/y1[16]),y1[1:16]))   #Calculate Gini  R will also calculate other inequality and dissimilarity measures, by using the function:  > ineq(rep(c(x[1:15],y1[17]/y1[16]),y1[1:16]), type = “ TYPE “ ), where TYPE is one of the following:  RS(x)      Ricci-Schutz coefficient (Pietra´s measure) Atkinson(x, parameter = 0.5)   Atkinson’s Measure Theil(x, parameter = 0)        Theil’s Entropy Index Kolm(x, parameter = 1)         Kolm’s Measure var.coeff(x, square = FALSE) Coefficient of Variation entropy(x, parameter = 0.5) Generalized Entropy Index RS is the the Ricci-Schutz coefficient (also called Pietra´s measure), Atkinson gives Atkinson´s measure and Kolm computes Kolm´s measure.  If the parameter in Theil is 0 Theil´s entropy measure is computed, for every other value Theil´s second measure is computed.  ineq(x, type="var") and var.coeff(x) respectively compute the coefficient of variation, while ineq(x,type="square.var") and var.coeff(x, square=TRUE) compute the squared coefficient of variation.  entropy computes the generalized entropy, which is for parameter 1 equal to Theil´s entropy coefficient and for parameter 0 equal to the second measure of Theil.    Credit goes to Achim Zeileis zeileis@ci.tuwien.ac.at, the author of the ineq function in R. 

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Gini Coefficients for the 2000 Census

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