ARE/ECN 115A Fall 2023 Problem Set 2: Poverty, Inequality and Public Policy

Instructions:

During  this  problem  set,  you  will  use  a  panel  household-level  data  set to  evaluate changes in poverty and inequality in South Africa in the first decade after apartheid.

1.   By writing your name above and  submitting this Problem Set, you are agreeing to adhere to the Copyright statement and the Code of Academic conduct as highlighted on the course syllabus.

2.   Download this PDF file to your computer and open it using Acrobat Reader (the free version of   the software).  Trying to fill it in through your internet browser or with another software may cause some features of this document not to work.

3.   You will make extensive use of Excel in this Problem Set.  If you do not have Excel already

installed on your computer, please refer to the “Additional UC Davis Resources for Students” page on Canvas (under Modules/Syllabus & Student Resources).

4.   You can work individually or in groups of up to 3 members.  You can use the discussion board page on Canvas to find group members.

5.   Your group will turn in a single PDF of the problem set on Gradescope.  Indicate the members in

your group on both this pdf and on Gradescope at the time of submission. That is, when you

upload the assignment, you must identify all members ofyour groups; Otherwise, only the individual who uploads the assignment will receive credit.  You must also write the names and ID numbers of all your group members on this pdf. A  5 point penalty will be applied per name that is not

indicated on the pdf submission.

6.   To answer each, write your responses in the designated boxes. DO NOT change the size of the boxes.

7.   To insert the graphs:  (1) take a screenshot of the graph on Excel and save it as a .jpeg .png , or .gif   file; (2) click the Icon to insert image in the respective box on the PDF and select the file saved in the previous step. To receive full credit, ALL graphs must include a title, axes titles, and

legends when applicable.  We will randomly select groups to check their excel files; Their graphs on the PDF and the excel file should match, otherwise all points from the graphs will be set to 0.

8.   You will turn in your Excel file individually on Canvas. Note that the Excel file can be the same

among the members of the same group, but not across groups. Your individual Excel submission is worth 5 points.

9.   9. Late Problem Sets will not be accepted.

All of the data for this problem set can be found in the Problem set 2 folder in Canvas.

TheKwaZulu-Natal province  is located on the Indian Ocean coast of South Africa and is home to approximately 20% of South Africa’s population.  The KwaZulu-Natal Income Dynamics Study (KIDS) is the same data set used by Carter and May in the article “One Kind of Freedom.”  While they used the 1993 and 1998 data, another round was added in 2004. This problem set asks you to use this updated KIDS data set to explore measures of poverty and income distribution in the first 10 years of the post-apartheid period.

The excel spreadsheet KIDS Data.xls contains the KIDS data. Use the worksheet “KIDS data,” which contains columns representing monthly per-capita income (in Rand, the South African currency) for each KIDS household for the years 1993  and  2004.   These  income  figures  have  been  adjusted to the year 2000  South African price  level. The data set includes information on 560 households that provided complete information in 1993 and 2004.

1.   Poverty Measures

The national poverty line in South Africa in terms of monthly per-capita income is Z=375 Rand.1    Calculate and report in Table 1 the values of the different poverty indices for 1993 and 2004:

Report your answers using two decimal points. Exception: Report your FGT-2 using THREE decimal points.

Table 1: Poverty Indices

2.   Income Inequality: Lorenz Curve

A. Plot the Lorenz curves for household per-capita income for 1993 and 2004 in Excel. Put the two  Lorenz curves on a single graph along with line of perfect equality. Please paste your final graph into the box bellow titled “Figure 1: Lorenz Curves for 1993 & 2004.”

Figure 1: Lorenz Curves for 1993 & 2004

B. Based on your Lorenz curves in Figure 1, briefly explain what you conclude about the evolution of inequality between 1993 and 2004.

3.   Income Inequality: Gini Coefficient

A. Use the covariance formula to calculate and report in Table 2 below the Gini coefficient for per-capita    income in 1993 and 2004.2 Your Gini coefficients should be between 0 and 1. (Use two decimal spaces for display)

Table 2: Gini coefficients for per capita income: 1993 & 2004

B. Based on your Gini coefficients, briefly explain what you conclude about the evolution of inequality.

4.    Poverty Dynamics

Because it is a panel data set, the KIDS dataset permits us to explore poverty dynamics for households. Using the KIDS data,  first calculate the percentage of households that were Poor and Non-Poor in 1993.  Record your

answers in Table 4A below. Then fill in the cells ofthe Poverty Transition Matrix in Table 4B below. (In both tables, report your results in percentages with 2 decimal points. E.g., 12.25% )

Table 4A: Poverty in 1993

Table 4B: Transition Matrix for Poverty in South Africa

(Hint: Rows ofyour Transition matrix should add up to 100)

5.   POLICY 1:  A policy to reduce the Headcount Index

Assume  we  are  in  the  year   2004,  and  you  are  hired  by  the  president  of  South  Africa  to  design  a

redistribution policy to reduce the  Poverty  Headcount  Index  as  much  as  possible.    In  order  to  simplify your     calculations,  assume  that   if the  income   of  a  household   is   exactly   equal   to   the  poverty   line Z=375,  the household  is  not  poor.   In  order   to   implement  the  policy,  the  president   imposes   a  tax of  10%  on  the

income  of  all households earning 800 Rand per capita or more.

a.    How much money does the South African government collect in tax revenues in 2004? (Round

your answer to 2 decimal points)

b. In the box below, describe your redistribution policy. How would you allocate the tax revenues collected by the government to households that are poor in 2004 in order to minimize the Poverty Headcount Index in 2004?

c.    Let's now examine how your policy affects poverty dynamics between 1993 and 2004. Start by filling in Table 5A

below, which is a poverty transition matrix, using the same income values from 1993, but now using households' new

income values in 2004 after the tax and redistribution policy is implemented. In other words, income in 2004 will be

increased by any transfers that households received and decreased by any taxes that they paid. (Report  your  results to two

Table 5A: Transition Matrix After Redistribution Policy