Inequality Measures
Ekaterina Prohorova
2024-05-14
#install.packages(c("readxl", "tidyverse", "ineq", "reshape2"))
library(readxl)
library(tidyverse)
library(ineq)
library(reshape2)setwd("C:/Users/user/Downloads")
decile_data <- read_excel("GCIPrawdata.xlsx", skip = 2)
head(decile_data) ## # A tibble: 6 × 14
## Country Year `Decile 1 Income` `Decile 2 Income` `Decile 3 Income`
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 Afghanistan 1980 206 350 455
## 2 Afghanistan 1981 212 361 469
## 3 Afghanistan 1982 221 377 490
## 4 Afghanistan 1983 238 405 527
## 5 Afghanistan 1984 249 424 551
## 6 Afghanistan 1985 256 435 566
## # ℹ 9 more variables: `Decile 4 Income` <dbl>, `Decile 5 Income` <dbl>,
## # `Decile 6 Income` <dbl>, `Decile 7 Income` <dbl>, `Decile 8 Income` <dbl>,
## # `Decile 9 Income` <dbl>, `Decile 10 Income` <dbl>, `Mean Income` <dbl>,
## # Population <dbl>sel_Year <- c(1980, 2014)
sel_Country <- c("Belarus", "Germany")
temp <- decile_data %>% filter(Country %in% sel_Country & Year %in% sel_Year)
temp## # A tibble: 4 × 14
## Country Year `Decile 1 Income` `Decile 2 Income` `Decile 3 Income`
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 Belarus 1980 793 1095 1332
## 2 Belarus 2014 2211 3435 4417
## 3 Germany 1980 5077 6461 7689
## 4 Germany 2014 5222 7305 9045
## # ℹ 9 more variables: `Decile 4 Income` <dbl>, `Decile 5 Income` <dbl>,
## # `Decile 6 Income` <dbl>, `Decile 7 Income` <dbl>, `Decile 8 Income` <dbl>,
## # `Decile 9 Income` <dbl>, `Decile 10 Income` <dbl>, `Mean Income` <dbl>,
## # Population <dbl>total_income <- temp[, "Mean Income"] * temp[, "Population"]
options(scipen = 999)
total_income ## Mean Income
## 1 19141355000
## 2 98213370000
## 3 764805832000
## 4 1239206436000decs_b80 <- unlist(temp[1, 3:12]) * 2
total_inc <- 20 * unlist(temp[1, "Mean Income"])
cum_inc_share_b80 <- cumsum(decs_b80) / total_inc
cum_inc_share_b80## Decile 1 Income Decile 2 Income Decile 3 Income Decile 4 Income
## 0.03994962 0.09511335 0.16221662 0.23974811
## Decile 5 Income Decile 6 Income Decile 7 Income Decile 8 Income
## 0.32730479 0.42518892 0.53471033 0.65884131
## Decile 9 Income Decile 10 Income
## 0.80468514 0.99984887decs_b14 <- unlist(temp[2, 3:12]) * 2
total_inc <- 20 * unlist(temp[2, "Mean Income"])
cum_inc_share_b14 <- cumsum(decs_b14) / total_inc
cum_inc_share_b14## Decile 1 Income Decile 2 Income Decile 3 Income Decile 4 Income
## 0.02131906 0.05444027 0.09703018 0.14941664
## Decile 5 Income Decile 6 Income Decile 7 Income Decile 8 Income
## 0.21266030 0.28859319 0.38036833 0.49400251
## Decile 9 Income Decile 10 Income
## 0.64454730 1.00000000decs_g80 <- unlist(temp[3, 3:12]) * 2
total_inc <- 20 * unlist(temp[3, "Mean Income"])
cum_inc_share_g80 <- cumsum(decs_g80) / total_inc
cum_inc_share_g80## Decile 1 Income Decile 2 Income Decile 3 Income Decile 4 Income
## 0.04093035 0.09301838 0.15500645 0.22644308
## Decile 5 Income Decile 6 Income Decile 7 Income Decile 8 Income
## 0.30750564 0.39905676 0.50299903 0.62334731
## Decile 9 Income Decile 10 Income
## 0.77026766 1.00000000decs_g14 <- unlist(temp[4, 3:12]) * 2
total_inc <- 20 * unlist(temp[4, "Mean Income"])
cum_inc_share_g14 <- cumsum(decs_g14) / total_inc
cum_inc_share_g14## Decile 1 Income Decile 2 Income Decile 3 Income Decile 4 Income
## 0.03398412 0.08152414 0.14038787 0.20963165
## Decile 5 Income Decile 6 Income Decile 7 Income Decile 8 Income
## 0.28916439 0.37970194 0.48309254 0.60342965
## Decile 9 Income Decile 10 Income
## 0.75147078 0.99998048plot(cum_inc_share_b80, type = "l", col = "blue",
lwd = 2, xlab = "Deciles", ylab = "Cumulative income share",
xlim = c(0,10), ylim = c(0,1)
)
abline(a = 0, b = 0.1, col = "black", lwd = 2)
title("Lorenz curve, Belarus, 1980")
highlight_point <- data.frame(prop = 6, y = 0.42)
points(highlight_point, col = "blue", pch = 16)
The Lorenz curve is a graphical representation of the distribution of
income or wealth in a society. It shows the cumulative proportion of
income or wealth held by the bottom x% of the population.
The point highlighted on the curve represents the situation where 60% of the population holds 42% of the income. The X-coordinate of this point is 60, which indicates that 60% of the population is at (or below) this point on the curve. The Y-coordinate of this point is 0.42, which indicates that this 60% of the population holds 42% of the income.
plot(cum_inc_share_b80, type = "l", col = "blue",
lty = 2, lwd = 2, xlab = "Deciles",
ylab = "Cumulative income share")
abline(a = 0, b = 0.1, col = "black", lwd = 2)
lines(cum_inc_share_b14, col = "green", lty = 1, lwd = 2)
lines(cum_inc_share_g80, col = "magenta", lty = 2, lwd = 2)
lines(cum_inc_share_g14, col = "orange", lty = 1, lwd = 2)
title("Lorenz curves, Belarus and Germany (1980 and 2014)")
legend("topleft", lty = 2.5:1, lwd = 2, cex = 1.2, legend =
c("Belarus, 1980", "Belarus, 2014",
"Germany, 1980", "Germany, 2014"),
col = c("blue", "green", "magenta", "orange"))
### Gini coefficient
g_b80 <- Gini(decs_b80)
g_b14 <- Gini(decs_b14)
g_g80 <- Gini(decs_g80)
g_g14 <- Gini(decs_g14)
paste("Gini coefficients")## [1] "Gini coefficients"paste("Belarus - 1980: ", round(g_b80, 2), ", 2014: ", round(g_b14, 2))## [1] "Belarus - 1980: 0.24 , 2014: 0.43"paste("Germany - 1980: ", round(g_g80, 2), ", 2014: ", round(g_g14, 2))## [1] "Germany - 1980: 0.28 , 2014: 0.31"plot(cum_inc_share_b80, type = "l", col = "blue", lty = 2,
lwd = 2, xlab = "Deciles",
ylab = "Cumulative income share")
abline(a = 0, b = 0.1, col = "black", lwd = 2)
lines(cum_inc_share_b14, col = "green", lty = 1, lwd = 2)
lines(cum_inc_share_g80, col = "magenta", lty = 2, lwd = 2)
lines(cum_inc_share_g14, col = "orange", lty = 1, lwd = 2)
title("Lorenz curves, Belarus and Germany (1980 and 2014)")
legend("topleft", lty = 2.5:1, lwd = 2, cex = 1.2, legend =
c("Belarus, 1980", "Belarus, 2014",
"Germany, 1980", "Germany, 2014"),
col = c("blue", "green", "magenta", "orange"))
text(8.4, 0.78, round(g_b80, digits = 3), col = 'blue')
text(9.4, 0.6, round(g_b14, digits = 3), col = 'green')
text(5.2, 0.37, round(g_g80, digits = 3), col = 'magenta')
text(6.4, 0.31, round(g_g14, digits = 3), col = 'orange')
Distribution of income across time, Belarus
Income inequality increased significantly from 1980 to 2014, as the Lorenz curve shifted to the right. The Gini coefficient increased from 0.24 to 0.43, indicating a widening income gap.
Distribution of income across time, Germany
Income inequality also increased slightly from 1980 to 2014, but to a lesser extent than in Belarus. The Lorenz curve shifted slightly to the right, and the Gini coefficient increased from 0.28 to 0.31.
Distribution of income across countries
1980: Belarus had a slightly more equal income distribution than Germany, as its Lorenz curve was closer to the line of perfect equality.
2014: The income distribution in Belarus became more unequal than in Germany, as the gap between the Lorenz curves widened
Similarities
Both countries experienced an increase in income inequality over time, likely due to factors such as globalization, technological change, and changes in government policies.
Differences
Belarus: The more significant increase in income inequality may be attributed to the country’s transition to a market economy and the privatization of state-owned industries. Germany: The relatively smaller increase in income inequality could be due to the country’s strong social safety net, which provides support to low-income individuals.