# Empirical Project 12 Working in R

### Download the code

To download the code chunks used in this project, right-click on the download link and select ‘Save link as’. You’ll need to save the code download to your working directory, and open it in RStudio.

Don’t forget to also download the data into your working directory by following the steps in this project.

## Getting started in R

For this project you will need the following packages:

• tidyverse, to help with data manipulation
• readxl, to import an Excel spreadsheet
• knitr, to format tables
• ineq, to calculate inequality measures
• rvest, to import tables directly from websites
• zoo, to format times and dates.

If you need to install any of these packages, run the following code:

install.packages(c("tidyverse", "readxl", "knitr", "ineq", "rvest", "zoo"))


You can import the libraries now, or when they are used in the R walk-throughs below.

library(tidyverse)
library(readxl)
library(knitr)
library(ineq)
library(rvest)
library(zoo)


## Part 12.1 Inequality

One reason cited for Scheme $6,000 was to share the gains from economic growth among everyone in the society. We will be using household income data collected by the Hong Kong government to assess the potential effects of this scheme. Download the data. The first tab contains information about household incomes for certain percentiles of the population. These incomes are ‘pre-intervention’, meaning that they do not include the effects of handouts or policy interventions from the government. (If you are curious about the difference between the two tables in this tab, see the extension section ‘Nominal and real values’ at the end of Part 12.1.) 1. Using the table ‘Monthly real household income (pre-tax,$HKD)’, plot a separate line chart for each percentile, with year on the horizontal axis and income on the vertical axis. Describe any patterns you see over time.

### R walk-through 12.1 Importing a specified range of data from a spreadsheet

We start by importing the data. The data provided in the Excel spreadsheet is not in the usual format of one variable per column. Instead the first tab contains two separate tables, and we need the second table. We can therefore use the range = option of the read_excel function to specify the cells in the spreadsheet to import (note that variable headers for the years are included).

library(tidyverse)
library(knitr)
library(readxl)

income <- read_excel("Project 12 datafile.xlsx", range = "A13:I18") # Import the data, stating the cell range
names(income) <- "percentile" # Rename the first column


We can plot the change in real income over time for each of the percentile groups on a single chart as follows.

income %>%
gather(Year,real_inc,2009:2016) %>%
ggplot(.,aes(y=real_inc, x=Year, group=percentile, color=percentile)) +
geom_line(size=1) +
theme_bw() +
ylab("Monthly real household income (HKD)")


Monthly real household income over time.

Figure 12.1 Monthly real household income over time.

However, as the scale of the plot hides many of the features for each percentile group, we should create a separate chart for each percentile group. As an example, we will plot the chart for the 15th percentile.

income %>%
gather(Year,real_inc,2009:2016) %>% # Reshape the data
filter(percentile == "15th") %>% # Select only data for 15th percentile
mutate(Year = as.numeric(Year)) %>% # Set 'Year' as a numeric variable so that we can plot a line
ggplot(.,aes(y=real_inc, x=Year)) +
geom_point(size=2) +
geom_line(size=1) +
theme_bw() +
ylab("Monthly real household income for 15th percentile")


Monthly real household income for 15th percentile.

Figure 12.2 Monthly real household income for 15th percentile.

Now we will use this data to draw Lorenz curves and compare changes in the income distribution for 2011–2012. One way to do this is to make the following simplifying assumptions:

• There are 100 households in the economy (so we can think of each percentile as corresponding to one household).
• Households between the 15th and 25th percentile have the same income as the household in the 15th percentile, households between the 25th and 50th percentile have the same income as the household in the 25th percentile, and so on. (Households below the 15th percentile earn nothing.)
1. Draw Lorenz curves for 2011 and 2012 by carrying out the following:
• Create a new column for 2012 only, showing incomes following the $6,000 handout. (Remember that this amount was given to all households, including those with no income.) • Calculate the economy-wide earnings in 2011 and 2012. (Hint: Multiply the income of a given percentile by the number of households assumed to earn that amount.) • Use your answers to Question 2(b) to complete the table in Figure 12.3 below. (The second row also shows zeros in 2011 because the bottom 15% of households earned nothing.) Cumulative share of the population (%) Perfect equality line Cumulative share of income in 2011 (%) Cumulative share of income in 2012 (%) 0 0 0 0 15 15 0 25 25 50 50 75 75 85 85 100 100 100 100 Cumulative share of income, for some percentiles of the population. Figure 12.3 Cumulative share of income, for some percentiles of the population. • Draw the Lorenz curves for 2011 and 2012 in the same chart, with cumulative share of population on the horizontal axis and cumulative share of income on the vertical axis. Add the perfect equality line to your chart, and add a chart legend. ### R walk-through 12.2 Calculating cumulative income shares and plotting a Lorenz curve Questions 2(a)(c) can be completed in one stage, although there are a number of steps. Once we have selected the relevant variables, the first stage is to remove the ‘th’ suffix in the percentile values using the separate function, and convert them to numeric values. We then add an extra observation for the 0th percentile and a column representing the number of households in each percentile group (assuming 100 households in the economy). We can now apply the$6,000 handout to all percentiles in the year 2012 and calculate the economy-wide income for each percentile group. To complete Figure 12.3 we need to calculate the cumulative income for increasing percentiles. To sort the data from the lowest to highest percentile groups we use the arrange function. Next we use the cumsum function to calculate the cumulative sum of economy-wide incomes for each year.

Finally we tidy up the data to reflect Figure 12.3 by making sure that the 0th percentile has no share of the income and the 100th percentile has 100% of the cumulative income.

df.new <- income %>%
select(percentile,2011,2012) %>%             # Select the required variables
separate(percentile,"percentile","th") %>%       # Separate string from number
mutate(percentile = as.numeric(percentile)) %>%  # Change character to numeric
rbind(c(0,0,0)) %>%                              # Add observation for 0th percentile
arrange(percentile) %>%                          # Order percentile values from low to high
cbind(households = c(15,10,25,25,10,15)) %>%     # Add column for the number of households in each group
mutate(2012_handout = 2012+6000) %>%
mutate(2011_income = 2011*households, 2012_income = 2012_handout*households) %>% # Economy-wide income
mutate(2011_cum = cumsum(2011_income)/sum(2011_income)*100) %>%                    # Relative share in 2011
mutate(2012_cum = cumsum(2012_income)/sum(2012_income)*100) %>%                    # Relative share in 2012
select(percentile,households,2011_cum,2012_cum) %>%                                  # Drop interim variables
mutate(percentile=percentile+households) %>%                                             # Tidy up the table to normalize 0 and 100 percentiles
select(-households) %>%
rbind(c(0,0,0),.)

kable(df.new,format="markdown", digits=2)

| percentile| 2011_cum| 2012_cum|
|----------:|--------:|--------:|
|          0|     0.00|     0.00|
|         15|     0.00|     3.91|
|         25|     2.74|     8.44|
|         50|    15.09|    24.53|
|         75|    41.42|    50.37|
|         85|    60.50|    67.09|
|        100|   100.00|   100.00|


Using the data from Questions 2(a)(c) we can plot the Lorenz curve. Note that we use the percentile variable to draw the line of perfect equality.

df.new %>%
mutate(equality=percentile) %>%                 # Create variable for perfect equality
gather(year,cum_income,2011_cum:equality) %>% # Reshape into long format for plotting
ggplot(.,aes(y=cum_income, x=percentile, group=year, color=year)) +
geom_line(size=1) +
geom_point(size=2) +
theme_bw() +
ylab("Cumulative share of income (%)") +
xlab("Cumulative share of population (%)")


Lorenz curve (2011).

Figure 12.4 Lorenz curve (2011).

Now we will compare the Gini coefficients in 2011, 2012, and 2013 (a year after the policy came into effect).

1. Calculate the Gini coefficient by carrying out the following:
• Create a table as in Figure 12.5, and fill in the remaining values (some values for 2011 have been filled in for you). The first column should contain the numbers 1 to 100, in intervals of 1, and the remaining columns should contain the incomes earned by a household at that percentile (using the same assumption as in Question 2). To obtain accurate answers, use two decimal places instead of rounding incomes to the nearest dollar.
Percentile 2011 2012 2013
1 0.00
2 0.00
3 0.00

98 44,516.67
99 44,516.67
100 44,516.67

Incomes earned by each percentile of the population.

Figure 12.5 Incomes earned by each percentile of the population.

• Using the ineq function, calculate the Gini coefficient for each year.
• Based on the Gini coefficients from Question 3(b), what effect did the $6,000 handout appear to have on income inequality in the short run, and in the long run? Suggest some explanations for what you observe. ### R walk-through 12.3 Generating Gini coefficients #### Create table containing percentiles To create the percentiles for every percentile in our 100 household economy we need to take the income for each percentile group and expand that for every household in the respective percentile group. For example, there are 15 households in the bottom percentile group having zero income for 2011 and 2013, and$6,000 in 2012. For the 15th percentile group there are 15 households that will share income values, and so on for the other percentile groups.

To achieve this expansion we first create a new variable (households) that contains the number of households in each percentile group. Then for each group we can use the slice and rep functions together to copy the values in the 2011, 2012, and 2013 within each percentile group. The rep function takes a sequence of 1 to 6 (in other words the number of groups) and copies each number in the sequence by the corresponding value in the households variable. The result is an index containing 15 1s, 10 2s, 25 3s, and so on. The splice function then uses this index to reference each observation in the data, for example where the index value is 1 the bottom percentile group is selected, where the index value is 2 the 15th percentile group is selected, and so on.

Once the expansion is complete we order by row and generate a new sequence from 1 to 100 to represent the percentile.

df.new <- income %>%
select(2011,2012,2013) %>%
rbind(c(0,0,0)) %>%
mutate(2012 = 2012+6000) %>%              # Apply the $6,000 handout to 2012 arrange(2011) %>% # Arrange by ascending incomes in 2011 mutate(households = c(15,10,25,25,10,15)) %>% # Specify number of households in each group group_by(households) %>% slice(rep(1:n(),each=households)) %>% # Repeat values within each percentile group rowwise() %>% arrange(2011) %>% mutate(percentile = seq(1:n())) %>% # Create a sequence from 1 to 100 for percentiles select(percentile,2011,2012,2013) # We can check the first and last five percentiles to compare with Figure 12.5. head(df.new, 5)  ## # A tibble: 5 x 4 ## percentile 2011 2012 2013 ## <int> <dbl> <dbl> <dbl> ## 1 1 0 6000 0 ## 2 2 0 6000 0 ## 3 3 0 6000 0 ## 4 4 0 6000 0 ## 5 5 0 6000 0  tail(df.new, 5)  ## # A tibble: 5 x 4 ## percentile 2011 2012 2013 ## <int> <dbl> <dbl> <dbl> ## 1 96 44516. 50544. 45270. ## 2 97 44516. 50544. 45270. ## 3 98 44516. 50544. 45270. ## 4 99 44516. 50544. 45270. ## 5 100 44516. 50544. 45270.  #### Calculate Gini coefficients Using the ineq function from the ineq package, it is straightforward to obtain the Gini coefficient for each year. library(ineq) ineq(df.new$2011)

##  0.4687603

ineq(df.new$2012)  ##  0.3440174  ineq(df.new$2013)

##  0.4698187

Year Percentage increase (from previous year) Value ($) 2009 1.000 2010 2.40 1.024 2011 5.30 2012 4.10 2013 4.30 2014 4.40 2015 3.00 2016 2.40 Creating an index-based series from percentage increases. Figure 12.6 Creating an index-based series from percentage increases. • Use this table to convert nominal incomes to real incomes by dividing the nominal income by the corresponding value in the third column (for example, divide nominal incomes in 2010 by 1.024 to get the value in 2009 terms). You should get the same values as in the ‘real household income’ table. ### Extension R walk-through 12.4 Converting nominal incomes to real incomes To obtain the real income values we need to multiply the income for each percentile group by the inflation index created in Question 5(a). Note that in the code below, the inflation index is entered as a vector called inflation (with the same number of elements as the number of years in the data) and this is multiplied (element-wise) by each row of the income data using the sweep function. inflation <- c(1,1.024,1.078,1.122,1.171,1.222,1.259,1.289) # Only select columns with income data and multiply by the inflation index nom_income <- sweep(income[,-1],MARGIN=2,inflation,*) %>% cbind(percentile = c(85,75,50,25,15),.) # Reattach the percentile column kable(nom_income, format = "markdown", digits=2)  ## Part 12.2 Government popularity One possible reason why the government implemented Scheme$6,000 was to gain public approval, since there was some pressure on the government to spend the surplus on alleviating current social issues rather than reinvesting it (for example, in pension schemes). We will use a public opinion poll conducted by the University of Hong Kong to assess whether this scheme could have improved public satisfaction with the government.

1. Think about the groups who would be affected by this scheme (for example, the government or members of the public). Who would be likely to support or oppose this scheme, and why?

Download the data:

• Go to the overall performance results page on the HKU POP website, which contains half-yearly survey data on the overall performance of the government.
• Under the subheading ‘Collapsed data’, import the data contained in this table using R. (The data is not available in Excel format, so you will have to import the data manually.)

### R walk-through 12.5 Importing data directly from a website

It is quite common to use data from publicly-available websites that is presented in a table but is not available in a spreadsheet to download. Although we could copy and paste this data into a spreadsheet and then import that into R, we could instead use the rvest package to read the data in such a table directly into a dataframe. The R-bloggers site provides details on how to do this in a guide to using rvest.

library(rvest)
url <- "https://www.hkupop.hku.hk/english/popexpress/sargperf/sarg/halfyr/datatables.html"
overall <- url %>%
html() %>%
html_nodes(xpath = '//*[@id="popexpress"]/table') %>%
html_table(header = TRUE)
overall <- overall[]


Note that if the technicalities of the procedure described above are too complicated, you can still proceed by manually copying and pasting into a spreadsheet.

• R will recognize the data you have imported as text, but to make charts, the data needs to be in number format (the % signs need to be removed). Follow the steps in R walk-through 12.6 below to reformat all columns.
• Read the HKU POP survey methods page for a description of how the survey data was collected. Explain whether you think the sample is representative of the target population, and discuss some limitations of the survey method.

### R walk-through 12.6 Cleaning imported data

The names of each column from the imported data are long and contain a mixture of alphabet sets; we can rename the variables using the names property of a dataframe.

Then we use the gsub function to find and replace all instances of the ‘%’ sign in the data with an empty string, and convert all variables (except the date variable) to be numeric variables.

names(overall) <- c("Date","Total Sample",
"Sub-sample", "Positive",
"Half-half","Negative",
"DKHS","Total","Net Value")
overall <- overall %>%
mutate_all(funs(gsub("%","",.)))%>%
mutate_at(vars(-Date), funs(as.numeric))
str(overall)

## 'data.frame':    43 obs. of  9 variables:
##  $Date : chr "7-12/2018" "1-6/2018" "7-12/2017" "1-6/2017" ... ##$ Total Sample: num  3025 12092 12201 12181 12074 ...
##  $Sub-sample : num 1761 7225 8750 7380 7167 ... ##$ Positive    : num  36 35.7 39.6 28.5 24.3 25.1 24.2 27.1 27 27.6 ...
##  $Half-half : num 22.1 21.1 22.2 21.3 24.7 22.5 27.3 25.7 24.6 27.2 ... ##$ Negative    : num  40.7 42.2 35.7 49.1 49.3 51.2 47.4 45.9 47.1 43.7 ...
##  $DKHS : num 1.1 1 2.5 1.1 1.7 1.2 1 1.2 1.3 1.5 ... ##$ Total       : num  100 100 100 100 100 100 100 100 100 100 ...
##  $Net Value : num -4.7 -6.6 3.9 -20.7 -25 -26.1 -23.2 -18.8 -20 -16.1 ...  1. Assess public satisfaction with the government by carrying out the following: • Make a line chart with overall public satisfaction (net value, which is the difference between percentage of positive and negative responses) on the vertical axis, and time (Jan–June 2006 to the latest period available) on the horizontal axis. Comment on any trends in overall public satisfaction over this time period. • Go to the POP polls main data page and choose one or two other indicators that are directly related to the policy (for example, improving people’s Degree of prosperity or Degree of equality). Find a table of the data by clicking ‘Content’, then ‘Table’ (if half-yearly data is not available, choose the most similar time interval). Import the data into R, and reformat the variable of interest as in Question 2. • For each of your chosen indicators, make a separate line chart as in Question 3(a) and comment on any similarities to or differences from the chart in Question 3(a). (Since some indicators may be measured on a different scale, focus on changes over time.) • Do you think the scheme had the intended effect on government popularity? Besides the scheme, what other factors or events could explain the observed patterns? ### R walk-through 12.7 Cleaning data and setting dates For Question 3(a), Before we can plot the imported data in R, we need to format the data variable so that R understands the chronological order of the data. The imported data has the Date variable, which is a text string using ‘1-6’ to represent January to June and ‘7-12’ for July to December. This format is not useful for ordering the data. There are a number of ways that R can deal with times and dates. In this example we are going to use the yearmon function from the zoo library as this focuses on using monthly data. Although we don’t have monthly data, we can replace the ‘1-6’ text string with ‘jan-‘ and ‘7-12’ with ‘july-‘, in other words we are going to use January and July to represent the first and second half of each year respectively. Once we have the months in a format that R can understand, we use the as.yearmon function to set the Date variable to the date format (using the %b-%Y option; further details on date formats in R can be found in the Dates and Times in R page). We can use the scale_x_yearmon function when plotting the line chart to ensure that the dates on the horizontal axis are labelled correctly. library(zoo) overall %>% mutate_at(vars(Date),funs(gsub("1-6/","jan-",.))) %>% mutate_at(vars(Date),funs(gsub("7-12/","july-",.))) %>% mutate(Date = as.yearmon(Date,"%b-%Y")) %>% subset(Date >= "Jan 2006") %>% ggplot(., aes(x=Date, y=Net Value)) + geom_line(size=1) + theme_bw() + scale_x_yearmon(format="%b-%Y") + ylab("Net satisfaction")  Net public satisfaction with the government’s performance over time. Figure 12.7 Net public satisfaction with the government’s performance over time. For Question 3(b), in this example we use the variable Improving People's Livelihood. Repeating the import and cleaning processes from R walk-through 12.5 we can directly read in the relevant data. url <- "https://www.hkupop.hku.hk/english/popexpress/sargperf/live/halfyr/datatables.html" improvement <- url %>% html() %>% html_nodes(xpath = '//*[@id="popexpress"]/table') %>% html_table(header = TRUE) improvement <- improvement [] names(improvement) <- c("Date","Total Sample", "Sub-sample","Positive", "Half-half","Negative", "DKHS","Total","Net Value") improvement <- improvement %>% mutate_all(funs(gsub("%","",.)))%>% mutate_at(vars(-Date), funs(as.numeric))  For Question 3(c) repeat the steps taken for 3(a). improvement %>% mutate_at(vars(Date),funs(gsub("1-6/","jan-",.))) %>% mutate_at(vars(Date),funs(gsub("7-12/","july-",.))) %>% mutate(Date = as.yearmon(Date,"%b-%Y")) %>% subset(Date >= "Jan 2006" ) %>% ggplot(., aes(x=Date, y=Net Value)) + geom_line(size=1) + theme_bw() + scale_x_yearmon(format="%b-%Y") + ylab("Net satisfaction")  Net public satisfaction with the government’s ability to improve people’s livelihood over time. Figure 12.8 Net public satisfaction with the government’s ability to improve people’s livelihood over time. 1. In 2018, the government decided to do another cash handout. Read the article ‘Hong Kong cash handout scheme will cost government HK$330 million to administer’ and discuss how this scheme differs from the 2011 scheme. Explain whether you think this policy is an improvement over the 2011 scheme.
1. Suppose you are a policymaker in a developed country with a large budget surplus, and one of the government’s aims is to reduce income inequality. Would you recommend that the government implement a scheme similar to either the 2011 or 2018 scheme? If you recommend a cash handout, suggest some modifications that could make the scheme more effective. If not, suggest other policies that may be more effective in reducing inequality.