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Constructing a Development Index

Brendan Knapp

Environment Prep

# load packages
library(tidyverse)
library(readxl)
library(pander)
library(scales)
# set options so tables render nicely
pander::panderOptions('table.split.table', Inf)

Data

Data were retrieved from:

  • World Bank Data
    • Improved water source (% of population with access)
    • Life expectancy at birth, total (years)
    • Urban population growth (annual %)
  • UNDP Human Development Reports
    • Adult Literacy Rate (% Ages 15 and older)
    • Population with at least some secondary education (% ages 25 and older)
    • Mean years of schooling (years)
    • Inequality in education (%)
    • GNI per capita (2011 PPP$)

Read and Inspect Raw Data

We read the excel file containing our raw data and store it in a data_frame variable named combo.

combo <- read_excel("~/Development-Economics/data/combo.xlsx")

pander(combo)
Country Improved water source (% of population with access) Life expectancy at birth, total (years) Urban population % Adult Literacy Rate (% Ages 15 and older) Population with at least some secondary education (% ages 25 and older) Mean years of schooling (years) GNI per capita (2011 PPP$) Press Freedom Score (0 worst - 100 best)
Cuba 94.6 79.39 77 99.7 84.8 11.8 7280 90
Ghana 87.6 62.11 55 76.6 59.8 6.9 3472 28
India 94.1 68.05 33 72.1 48.7 6.1 5329 39
Mexico 96.1 76.7 80 94.4 57.4 8.4 16154 61
Russia 96.9 70.74 74 99.7 94.6 12 24067 81
South Africa 92.8 60.95 65 94.3 74.9 10.3 12113 33
Syria 90.1 70.16 58 86.4 38.9 5.6 2905 89
Thailand 97.8 74.86 52 96.7 43.3 7.9 14169 64

Normalize

Normalize Formula

In order to normalize our values to a 0 to 1 scale, we use the following formula:

Divide (cardinal number – minimum) by (maximum – minimum)

We create a function called normalize to achieve this result.

normalize <- function(x){
  (x - min(x)) / (max(x) - min(x))
}

Mutate

We take our normalize() function, apply it to our combo data, and store the results in a new data_frame called combo_norm. Since Country is a non-numeric column, mutate_if allows us to only apply our functions to columns where is.numeric() returns TRUE. We also rename our variables to simplify our table and drop any scale references.

combo_norm <- combo %>%
  mutate_if(is.numeric, funs(normalize)) %>%
  rename(`Press Freedom` = `Press Freedom Score (0 worst - 100 best)`,
         `Water Access` = `Improved water source (% of population with access)`,
         `Life Expectancy` = `Life expectancy at birth, total (years)`,
         `Urban Population` = `Urban population %`,
         `Adult Literacy` = `Adult Literacy Rate (% Ages 15 and older)`,
         `GNI per Capita` = `GNI per capita (2011 PPP$)`
         )

pander(combo_norm)
Country Water Access Life Expectancy Urban Population Adult Literacy Population with at least some secondary education (% ages 25 and older) Mean years of schooling (years) GNI per Capita Press Freedom
Cuba 0.6863 1 0.9362 1 0.8241 0.9688 0.2067 1
Ghana 0 0.06287 0.4681 0.163 0.3752 0.2031 0.02679 0
India 0.6373 0.3849 0 0 0.1759 0.07812 0.1145 0.1774
Mexico 0.8333 0.8541 1 0.808 0.3321 0.4375 0.6261 0.5323
Russia 0.9118 0.531 0.8723 1 1 1 1 0.8548
South Africa 0.5098 0 0.6809 0.8043 0.6463 0.7344 0.4351 0.08065
Syria 0.2451 0.4995 0.5319 0.5181 0 0 0 0.9839
Thailand 1 0.7545 0.4043 0.8913 0.07899 0.3594 0.5323 0.5806

Combine Education Variables

We decided to combine our education variables by taking their mean and assigning it to a new variable called Combined Education.

combo_norm_comb_ed <- combo_norm %>%
  group_by(Country) %>%
  mutate(`Combined Education` = mean(c(`Population with at least some secondary education (% ages 25 and older)`, `Mean years of schooling (years)`, `Adult Literacy`))) %>%
  select(-`Population with at least some secondary education (% ages 25 and older)`,
         -`Mean years of schooling (years)`,
         -`Adult Literacy`)

pander(combo_norm_comb_ed)
Country Water Access Life Expectancy Urban Population GNI per Capita Press Freedom Combined Education
Cuba 0.6863 1 0.9362 0.2067 1 0.9309
Ghana 0 0.06287 0.4681 0.02679 0 0.2471
India 0.6373 0.3849 0 0.1145 0.1774 0.08469
Mexico 0.8333 0.8541 1 0.6261 0.5323 0.5259
Russia 0.9118 0.531 0.8723 1 0.8548 1
South Africa 0.5098 0 0.6809 0.4351 0.08065 0.7283
Syria 0.2451 0.4995 0.5319 0 0.9839 0.1727
Thailand 1 0.7545 0.4043 0.5323 0.5806 0.4432

Weight

We decided on the following weighting scheme for our data: * Water: 0.30 * Education: 0.25 * GNI per Capita: 0.18 * Urban Population: 0.12 * Press Freedom: 0.09 * Life Expectancy: 0.06

We assign our weights to individual variables before using them. To ensure that we're weighting correctly, we also check that our weight sum to 1.

water_wt <- 0.30
education_wt <- 0.25
GNI_wt <- 0.18
urban_wt <- 0.12
press_freedom_wt <- 0.09
life_expect_wt <- 0.06

weights <- c(water_wt, education_wt, GNI_wt, urban_wt, press_freedom_wt, life_expect_wt)

sum(weights) == 1
## [1] TRUE

In order to weight our data, we multiply each column by the appropriate weight variable. At this point, we also round our data to 2 digits following the decimal point.

combo_weighted <- combo_norm_comb_ed %>%
  mutate(`Water Access` = `Water Access` * water_wt,
         `Life Expectancy` = `Life Expectancy` * life_expect_wt,
         `Urban Population` = `Urban Population` * urban_wt,
         `GNI per Capita` = `GNI per Capita` * GNI_wt,
         `Press Freedom` = `Press Freedom` * press_freedom_wt,
         `Combined Education` = `Combined Education` * education_wt) %>%
  mutate_if(is.numeric, funs(round(., digits = 2)))

pander(combo_weighted)
Country Water Access Life Expectancy Urban Population GNI per Capita Press Freedom Combined Education
Cuba 0.21 0.06 0.11 0.04 0.09 0.23
Ghana 0 0 0.06 0 0 0.06
India 0.19 0.02 0 0.02 0.02 0.02
Mexico 0.25 0.05 0.12 0.11 0.05 0.13
Russia 0.27 0.03 0.1 0.18 0.08 0.25
South Africa 0.15 0 0.08 0.08 0.01 0.18
Syria 0.07 0.03 0.06 0 0.09 0.04
Thailand 0.3 0.05 0.05 0.1 0.05 0.11

Score

By summing our normalized and weighted variables, we create our Score data. We also round these data to 2 digits following the decimal point.

Score <- combo_weighted %>%
  group_by(Country) %>%
  summarise(Score = sum(`Water Access`,
                        `Life Expectancy`,
                        `Urban Population`,
                        `GNI per Capita`,
                        `Press Freedom`,
                        `Combined Education`))

pander(Score)
Country Score
Cuba 0.74
Ghana 0.12
India 0.27
Mexico 0.71
Russia 0.91
South Africa 0.5
Syria 0.29
Thailand 0.66

With our Score data, we can then create our Rank data.

Score_Rank <- Score %>%
  mutate(Rank = dense_rank(desc(Score)))

pander(Score_Rank)
Country Score Rank
Cuba 0.74 2
Ghana 0.12 8
India 0.27 7
Mexico 0.71 3
Russia 0.91 1
South Africa 0.5 5
Syria 0.29 6
Thailand 0.66 4

The example format that we have seen looks like so:

To match this we need to convert our data_frame to a matrix, transpose the data, and store it in a variable that we'll call Score.

Score_Rank <- Score_Rank %>%
  as.matrix() %>%
  t()

pander(Score_Rank)
Country Cuba Ghana India Mexico Russia South Africa Syria Thailand
Score 0.74 0.12 0.27 0.71 0.91 0.50 0.29 0.66
Rank 2 8 7 3 1 5 6 4

We're then going to detach the Country row so that we can bind the Score and Rank rows to our summary table.

Score_Rank <- Score_Rank[-1, ]

pander(Score_Rank)
Score 0.74 0.12 0.27 0.71 0.91 0.50 0.29 0.66
Rank 2 8 7 3 1 5 6 4

Data Restructuring

To produce the desired table, we convert our combo_norm variable to a matrix, which we then transpose and store in a variable called combo_norm_matr_trans.

combo_norm_matr_trans <- combo_weighted %>%
  as.matrix() %>%
  t()

pander(combo_norm_matr_trans)
Country Cuba Ghana India Mexico Russia South Africa Syria Thailand
Water Access 0.21 0.00 0.19 0.25 0.27 0.15 0.07 0.30
Life Expectancy 0.06 0.00 0.02 0.05 0.03 0.00 0.03 0.05
Urban Population 0.11 0.06 0.00 0.12 0.10 0.08 0.06 0.05
GNI per Capita 0.04 0.00 0.02 0.11 0.18 0.08 0.00 0.10
Press Freedom 0.09 0.00 0.02 0.05 0.08 0.01 0.09 0.05
Combined Education 0.23 0.06 0.02 0.13 0.25 0.18 0.04 0.11

Next, we bind Score_Rank to combo_norm_matr_trans by row and store the result in a variable called combo_matrix.

combo_matrix <- rbind(combo_norm_matr_trans, Score_Rank)

Before viewing the result, we bold our Score and Rank rows and our Syria column.

emphasize.strong.rows(c(1, nrow(combo_matrix), nrow(combo_matrix) - 1))

emphasize.strong.cols(7)

Summary Table

pander(combo_matrix)
Country Cuba Ghana India Mexico Russia South Africa Syria Thailand
Water Access 0.21 0.00 0.19 0.25 0.27 0.15 0.07 0.30
Life Expectancy 0.06 0.00 0.02 0.05 0.03 0.00 0.03 0.05
Urban Population 0.11 0.06 0.00 0.12 0.10 0.08 0.06 0.05
GNI per Capita 0.04 0.00 0.02 0.11 0.18 0.08 0.00 0.10
Press Freedom 0.09 0.00 0.02 0.05 0.08 0.01 0.09 0.05
Combined Education 0.23 0.06 0.02 0.13 0.25 0.18 0.04 0.11
Score 0.74 0.12 0.27 0.71 0.91 0.50 0.29 0.66
Rank 2 8 7 3 1 5 6 4

Map

To faciliate understanding the data, we can visualize it with a map.

map_world <- map_data(map = "world")

index_countries <- Score %>%
  inner_join(map_world, by = c("Country" = "region"))

nonindex_countries <- map_world %>%
  anti_join(combo_norm, by = c("region" = "Country"))
index_map <- ggplot() +
  geom_polygon(data = index_countries,
               aes(x = long, y = lat,
                   group = group,
                   fill = Score),  size = 0.01) +
  geom_polygon(data = nonindex_countries,
               aes(x = long, y = lat, group = group),
               fill = "white",
               size = 0.1) +
  coord_map() +
  scale_fill_distiller(type = "seq",
                       palette = "RdBu",
                       breaks = pretty_breaks(n=10),
                       direction = 1) +
  coord_fixed(ratio = 1.5) +
  guides(fill = guide_legend(keywidth = 1, keyheight = 3, reverse = TRUE)) +
  ggtitle("Development Index") +
  theme(axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.ticks.x = element_blank(),
        axis.title.y = element_blank(),
        axis.text.y = element_blank(),
        axis.ticks.y = element_blank()
        )
index_map