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The Evolution of Inequality and Human Development in South Africa and the Solow Model

## Problem 1: Lorenz Curves and Gini Coefficients

Using a simulated version of the KwaZulu-Natal Income Dynamics Study (KIDS) survey, we will examine the evolution of inequality in South Africa between 1993 and 2004. (Use the data provided in the “SSI2020_PS2_template” Excel file under the worksheet titled “Q1_Lorenz and Gini_n” in the folder for problem set 2. All the numbers are reported in real values of 2000. Thus, there is no need to use any CPI conversions.)

(a) Plot the Lorenz curves for per-capita expenditures for 1993, 1998 and 2004 in Excel. Put the three Lorenz curves on a single graph. While there are multiples ways to generate the Lorenz curves, we would like you to divide your sample into ten deciles of per-capita expenditures (so that you have 10 points on the horizontal axis). Replicating and filling out the following table on Excel may help you plot the Lorenz curve for each year.

(b) Based on your Lorenz curves, briefly explain what you conclude about the evolution of inequality in South Africa.

(c) Use the covariance formula to calculate the Gini coefficient and report the Gini coefficients for 1993, 1998 and 2004.(Use three decimal spaces for display)

The Evolution of Inequality in South Africa

1993 1998 2004

Gini Coefficient

1 See Chapter 5 of Taylor and Lybbert (page 121) for instructions on calculating the Gini coefficient in Excel.

(d) Based on your Gini coefficients, briefly explain what you conclude about the evolution of inequality in South Africa.

This question asks you to empirically explore the strength of the relationship between income per capita and measurement of human development. To answer this question, use the Human Development Report Data in the second worksheet of the WQ2019_PS2_template. This file contains data from 2017 for 189 countries and comes from the United Nations Development Program country-level data sets. To calculate the indexes, use the minimum and maximum values for Gross National Income (GNI), life expectancy at birth (LE), mean years of schooling (MYSA), and expected years of schooling (EYSC) that are provided in the Excel spreadsheet.

(a) In your Excel file, calculate Human Development Index (HDI) for all countries and fill in the table below. (Use two decimal spaces for display)

(b) In your Excel file, generate the scatter plot for human development (HDI) vs. income (GNI) per capita with HDI on the vertical axis and GNI per capita on the horizontal axis (for all countries). Add a logarithmic trend-line through the data points.

(c) In a few sentences, discuss the relationship between income per capita and HDI. Do you conclude that higher income per capita leads to better performance in terms of the human development indicator? Is the relationship strong? Do you notice any outliers?

Assume that we live in an imaginary world where there are two countries: Cocoloco and Sambapati. These two countries have the same population size, population growth, depreciation rate and production function. But Cocoloco has a larger capital stock than Sambapati. Output in both countries is produced according to the following constant-returns-to-scale production function that lies at the heart of the standard Solow growth model: