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Homework 2
Economics 2000
Assigned Tuesday, October 9th, 2012
Due: Thursday, October 18th, 2012
1. GINI Coefficient for Planet Earth
Measure changes in Global Income Distribution by calculating a GINI coefficient for the
world economy. Go to World Bank World Development Indicators Databank. Choose
and then
. From
select GDP per capita, PPP (constant 2005 international $) and GDP, PPP (constant 2005
international $).
Choose 2011 and hit
to Page and Series to Column
. From
Shift Time
Sort the data according to GDP, PPP from largest to smallest (the Sort tool can be found in
Excel under Data) in descending order. Eliminate all economies with no data. Examine
the top Q=150 countries in terms of size (from the US to the Maldives). Re-sort the
data according to GDP per capita, PPP (constant 2005 international $), this time in ascending
order from poorest to richest. Treat the average person in each country as a single person.
Calculate the AVERAGE of GDP per Capita across countries. Calculate the LEVEL as
AVERAGE×Q. Index the countries q=1,…,150 where q=1 is the poorest country Congo,
Dem. Rep. and q =150 is the richest country Qatar. For country q, calculate their share
GDP per Capita q
as shareq 
. Starting at q = 1, calculate the Lorenz curve as the
LEVEL
cumulative distribution LCq = LCq-1 + shareq. In this case, share1 =0.000159, share2 =
0.000249, and share3 =0.00026, so LC1 = 0.000158, LC2 = LC1+ share2 = 0.000407 and
LC3 = LC2 + share3= 0.000664, and so on till LC150 = 1. In this case, the area under the
world’s Lorenz curve consists of 150 trapezoids of equal width. Calculate the area of the
LCq  LCq 1 1
trapezoid for country q as
 . Add the sum of the trapezoids, double, and
2
Q
subtract from 1 to calculate the GINI coefficient for the world economy.
a. Compare the inequality across countries with the inequality within Sweden, Brazil,
and China.
b. Repeat the process using data for 1990 instead of 2011. Has world income inequality
changed over time as measured by the World?
c. This measure of world income inequality treats the world as if it were made of 150
people each representing a single country. But we know that some very large
countries including China and India amongst others have grown very quickly. Discuss
how the knowledge of this fact might change how we think about the dynamics of
global income inequality?
Create a population weighted World Income Distribution GINI Coefficient for 2011.
Calculate the population of each country, Population = GDP, PPP /GDP per capita, PPP.
d. Examine the top Q=150 countries in terms of size. Re-sort the data according to
GDP per capita, PPP (constant 2005 international $), this time in ascending order from
poorest to richest.
e. Repeat the same process for 1990 and report the World Gini Coefficient.
Calculate the Lorenz Curve for each country. Calculate the World GDP,PPP as
the sum of a GDP, PPP across all q countries. Index the countries q=1,…,150 where
q=1 is the poorest country and q =150 is the richest country. For country q, calculate
GDPq
their share as shareq 
. Starting at q = 1, calculate the Lorenz curve as
World GDP
the cumulative distribution LCq = LCq-1 + shareq.
Calculate the population share Sum up the population of all Q countries in the
world. Calculate country q’s share of world population wq = Populationq/World
Population
Calculate the area of the trapezoid. In this case, the area under the world’s Lorenz
curve consists of 150 trapezoids of width depending on the share of world population.
LCq  LCq 1
 wq .
Calculate the area of the trapezoid for country q as
2
Add the sum of the areas of the trapezoids and calculate the population GINI
coefficient for the world economy, double and subtract from 1. Calculate the
population weighted GINI coefficient for the world economy.
f.
Has the world income become more evenly distributed over the last 21 years by your
calculation?
2. Your Own HDI
Get data on the UN Human Development Index for six countries: China, Egypt, Indonesia,
Pakistan, South Africa and Thailand. Go to the UN Development Program website
http://hdrstats.undp.org/en/indicators/103106.html
a. Using the HDI from 2011, rank the six economies.
Also get indicators of health I Health
http://hdrstats.undp.org/en/indicators/72206.html
j
and education I Education
j
the six economies.
http://hdrstats.undp.org/en/indicators/103706.html for each of
Create your own index of development based on consumption per capita data. From
World Development Indicators, Get data from
on Household final consumption expenditure, PPP (constant 2005 international
$ and from
on Population, total for year 2011. Define X = Consumption
per Capita as Household final consumption expenditure (constant 2005 international $)/
Population, total.
b. For country j, create the index I jX 
X j  X MIN
X MAX  X MIN
= 6,000. Rank the countries by this index.
using XMIN = 1,000 and X MAX
c. Calculate an alternative to the UD HDI I j  3 I Health
 I Education
 I jX . Rank each of
j
j
the six economies by this index.
d. Explain any differences in China’s ranking in this index with its ranking in the
United Nations Human Development Index database.
3. ICOR
Study the Incremental Capital Output Ratio in China. Go to World Development
Indicators. Link. For years 1966 to 2010, get data from
Economic Policy & Debts
National accounts Local Currency at Constant Prices on constant dollar GDP
Aggregate Indicators
GDP (Constant LCU) and
Expenditure on GDP
Gross Fixed Capital Formation (Constant LCU) .
a. For every year t from 1966 to 2010 construct lagged investment ratio,
$
GFCFt Const
1
iyt 
$ and volume growth rate.
GDPt Const
1
gtQ 
$
GDPt Const $  GDPt Const
1
.
$
GDPt Const
1
b. Construct ten year averages for iyt and g tQ for the years 1971-1980, 1981-1990,
1991-2000, and 2001-2010. Construct ICORt for each decade as the ratio of the
iy
average of ICORt  t Q .
gt