polarisation.EGR: Polarisation Measure from Esteban, Gradin and Ray (2007)

Description

This function computes the polarisation measure proposed in Esteban, Gradin and Ray (2007) which accounts for deviations from an n-spike representation of strata in society.

Usage

polarisation.EGR(alpha, beta, rho, y, f = NULL, dist = NULL, 
weights = NULL, pm0 = NA, lower = NULL, upper = NULL, ...)

Arguments

alpha

a scalar containing the alpha parameter from Esteban and Ray (1994) on the sensitivity to polarisation.

beta

a scalar containing the beta parameter from Esteban, Gradin and Ray (2007) on the weight assigned to the error in the n-spike representation.

rho

a dataframe with the group means in the first column and their respective population shares in the second. The groups need to be exogenously defined. Note: the two columns should be named means and shares respectively. Otherwise a warning will appear.

a vector of incomes. If f is NULL and dist is NULL, this includes all incomes of all observations in the sample, i.e. all observations comprising the aggregate distribution. If either f or dist is not NULL, then this gives the incomes where the density is evaluated.

a vector of user-defined densities of the aggregate distribution for the given incomes in y.

dist

character string with the name of the distribution used. Must be equivalent to the respective function of that distribution, e.g. norm for the normal distribution.

weights

an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector. If non-NULL, observations in y are weighted accordingly.

pm0

the point mass for zero incomes used in the gini.den function. If not specified no point mass is assumed.

lower

the lower bound of the income range considered used in the gini.den function.

upper

the upper bound of the income range considered used in the gini.den function.

...

arguments to be passed to the distribution function used, e.g. mean and sd for the normal distribution.

Value

P: the polarisation measure proposed by Esteban, Gradin and Ray (2007).
PG: the adjusted polarisation measure proposed by Gradin (2000).
alpha: the alpha parameter used.
beta: the beta parameter used.
beta: the distribution option used, i.e. whether only y, f or dist was used.

References

Esteban, J. and Ray, D. (1994): On the Measurment of Polarization, in: Econometrica, Vol. 62(4), pp. 819-851.

Esteban, J., Gradin, C. and Ray, D. (2007): Extensions of a Measure of Polarization, with an Application to the Income Distribution of five OECD Countries.

Gradin, C. (2000): Polarization by Sub-populations in Spain, 1973-91, in Review of Income and Wealth, Vol. 46(4), pp.457-474.

Examples

Run this code

## example 1
y<-rnorm(1000,5,0.5)
y<-sort(y)
m.y<-mean(y)
sd.y<-sd(y)
y1<-y[1:(length(y)/4)]
m.y1<-mean(y1)
sd.y1<-sd(y1)
y2<-y[(length(y)/4+1):length(y)]
m.y2<-mean(y2)
sd.y2<-sd(y2)
means<-c(m.y1,m.y2)
share1<- length(y1)/length(y)
share2<- length(y2)/length(y)
shares<- c(share1,share2)
rho<-data.frame(means=means,shares=shares)
alpha<-1
beta<-1
den<-density(y)
polarisation.ER(alpha,rho,comp=FALSE)
polarisation.EGR(alpha,beta,rho,y)$P
polarisation.EGR(alpha,beta,rho,y=den$x,f=den$y)$P
polarisation.EGR(alpha,beta,rho,y=seq(0,10,by=0.1),dist="norm",
mean=m.y,sd=sd.y)$P
polarisation.EGR(alpha,beta,rho,y=seq(0,10,by=0.1),dist="norm",
mean=m.y,sd=sd.y)$PG

## example 2
y1<-rnorm(100,5,1)
y2<-rnorm(100,1,0.1)
y <- c(y1,y2)
m.y1<-mean(y1)
sd.y1<-sd(y1)
m.y2<-mean(y2)
sd.y2<-sd(y2)
means<-c(m.y1,m.y2)
share1<- length(y1)/length(y)
share2<- length(y2)/length(y)
shares<- c(share1,share2)
rho<-data.frame(means=means,shares=shares)
alpha<-1
beta<-1
polarisation.EGR(alpha,beta,rho,y=seq(0,10,by=0.1),dist="norm",
                 mean=c(m.y1,m.y2),sd=c(sd.y1,sd.y2))$P