Assignment: Inequality, Human Development, and Growth Models
Instructions:
All of the data for this problem set can be found in the PS2 folder in Canvas. Please fill out this Excel file and copy each of the four figures described below into the worksheet that has a title matching the figure number. We will ask you to upload one Excel file at the end of the problem set. For the open-ended questions, we recommend typing your response in this Word document and then copying your answer into the Canvas quiz.
Problem 1: Lorenz Curves and Gini Coefficients
Using theKwaZulu-Natal Income Dynamics Study (KIDS) survey, we will examine the evolution of inequality in South Africa between 1993 and 2004.(Note: the data in PS2Excel template file has been changed slightly. Don't use data in PS1!All the numbers are reported in 2000 real values - there is no need to use any CPI conversion.)
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 you have 10 points on the horizontal axis). The following table may help you plot the Lorenz curve for each year. Please copy this graph into the worksheet titled "Figure 1A" in the Excel template.
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Income Decile
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Percent of Population
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Cumulative percent of Population
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Cumulative Percent of Income 1993
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Cumulative Percent of Income 1998
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Cumulative Percent of Income 2004
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0
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0
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0.1
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10%
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0.2
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10%
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0.3
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10%
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0.4
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10%
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0.5
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10%
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0.6
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10%
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0.7
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10%
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0.8
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10%
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0.9
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10%
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1
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10%
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b) Based on your Lorenz Curves, briefly explain what you conclude about the evolution of inequality in South Africa.
c) Calculate and report the Gini coefficient for 1993, 1998 and 2004 in the table below. (Do not use the graphical method to find the GINI)
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The Evolution of Inequality in South Africa
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1993
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1998
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2004
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Gini Coefficient
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d) Based on your Gini Coefficients, briefly explain what you conclude about the evolution of inequality in South Africa.
e) Would the Gini change if we used current value Rands in each calculation? Please explain using the measuring inequality axioms, the Gini formula and the Lorenz Curve.
Problem 2: Gini and growth
Using the KwaZulu-Natal Income Dynamics Study (KIDS) survey, we will examine the evolution of inequality in South Africa between 1993 and 2004.
Create a Growth Incidence Curve (GIC) for the periods 1993-1998, and 1998-2004. For this, follow these steps:
Add up all the income in each decile for each year
Compute the growth rate for each decile. Using the annualized growth rate provided in class
Plot this information into the GIC.Please copy this graph into the Excel worksheet titled "Figure 2A" in the Excel template.
(b) What do the GICsindicate about the evolution of inequality?
(c) How do the GIC relate with the evolution of poverty that you calculated in the previous PS, in particular, how do they relate to the changes in the FGT0 and FGT2 measures. (Just use the results of FG0 and FG2 directly from PS1. No need to calculate using the new data file).
Problem 3: Human Development Index
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 PS2_Excel template. This file contains data from 2015 for 188 countries and comes from the United NationsDevelopment Programm 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. We are following instructions in the textbook, so the minimum values do not reflect the observed minimums for life expectancy, expected years of schooling, or mean years of schooling.
In your Excel file, calculate Human Development Index (HDI) for all countries and fill in the table below.
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Country
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I(LE_i) |
I(E_i) |
I(GNI_i) |
HDI |
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Germany
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Saudi Arabia
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Cuba
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Kenya
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Chad
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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. Please copy this graph into the Excel worksheet titled "Figure 3B" in the Excel template.
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?
Problem 4: Solow Model with No Technological Change
Assume that we live in an imaginary world where there are two countries: South and North. These two countries have the same population size and the same parameters, but North has a larger capital stock than South. 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:
Y(t)=10[K(t)]^0.5 [L(t)]^0.5
Assume that the savings rate is 13% (s = 0.13), the population grows at a rate of 2% per year (n = 0.02), and capital depreciates at a rate of 2% per year (d = .02).
Express the production function in per capita (y) terms (i.e., derive an expression for y as a function of k).
y = _________________
What are the steady state levels of capital per worker (kSS) and income per worker(ySS)?
k^SS = _________________
y^SS = _________________
Assume that in the initial year (t=0), the capital stock per worker in South is 100 (K(0) = 100) and the capital stock per worker in North is 400 (K(0)=400). In addition, assume that the population is 1 for both Southand North (L(0)=1).
On one graph plot the income per capita levels for the two countries over 200 years under NO exogenous technological change. Please copy this graph into the Excel worksheet titled "Figure 3C" in the Excel template.
On a separate graph, plot the income per-capita growth rates over 200 years for both countries. Please copy this graph into the Excel worksheet titled "Figure 3D" in the Excel template.
Does the model reach a steady state?
Yes
No
According to this model, when both countries have the same savings rate, does Southconverge to North?
Yes
No
Finally, suppose that a newly-elected populist leader of South wants her country to catch up with North. She is a brilliant orator and is confident that she can convince her people to consume less and save more in order to fulfill her economic catch-up mission. An expert economist informed her that she will need a savings rate of about 17 percent in order to catch up with North over a 25-year time horizon. Examine what happens in both the short- and long-term to per-capita income levels and growth rates after the savings rate increases to 0.17 in South. Assume that the savings rate remains the same in North(s = 0.13) over this time period.
In the short run, does South grow faster than North?
Yes
No
In the long run, does South grow faster than North?
Yes
No
Do South and North still converge?
Yes
No
If you were an adviser to the new populist leader of South, to what extent would you recommend that she base her policy on the Solow model? In a brief paragraph, explain your position.
Attachment:- Published.rar