ECON 2203
Assignment #4
Assigned: March 24, 2021
Due: April 12, 2021
1. This question allows us to look at whether there has been economic convergence in the
world. To do so we will be making use of a database known as the Penn World
Tables.
To access this data go to https:
www.rug.nl/ggdc/productivity/pwt/. Click on
the blue excel button to download version 10.0 of the dataset. This dataset has infor-
mation on the GDP and population for a large number of countries.
a) We only need the following two variables:
ˆ rgdpe (Expenditure-side real GDP at chained PPPs (in mil. 2017US$))
ˆ pop (Population (in millions)).
) We are going to look at convergence from 1990 to 2019, so you can delete every
year that is not those two from your dataset.
c) You can also delete any country from your dataset whose GDP or population is
missing from either year. Additionally, remove the following four countries who
are large outliers: United Arab Emirates, Cayman Islands, Brunei, and Venezuela.
Note that in general, we must be careful when removing data points like this. We
may bias our results by doing so. However, in this case, their inclusion would
obscure the main results. In the end, you should have 177 countries.
d) Divide the real GDP by the population in both years to determine the GDP pe
capita in each country.
e) Calculate the average yearly growth rate of real GDP per capita for each country.
To do this, you need to find the rate of growth for each country that if it grew by
that percentage every year starting in 1990, it would achieve the calculated level
of GDP per capita you calculated for 2019.
As a hint, Canada’s GDP per capita in 1990 was $33, XXXXXXXXXXIn 2019 it was
$49, XXXXXXXXXXThis means that over this 29 year span Canada grew on average by
1.3717% XXXXXXXXXXeach year. Obviously some years were faster and some slower,
ut this was the average. Calculate this value for all countries.
In other words, you must find the value for g that solves the following equation
for each country:
GDP/Capita2019 = GDP/Capita1990 × (1 + g)
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f) (10 Marks) On a graph with GDP per capita in 1990 on the horizontal axis and the
average growth rate on the vertical axis, create a scatter plot for all 177 countries
in the dataset. Add a linear trendline to this graph.
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g) (10 Marks) What does this graph tell you about whether there has been conver-
gence in the world between 1990 and 2019?
h) (10 Marks) There may be a reason to suspect that convergence may be region
specific. Separate the countries by region using the list provided below. Recreate
the same graph as in part f) for each of these five regions. Important: In orde
to make your analysis easier, ensure each graph has the same range for each scale.
The horizontal axis should run from $0 to $50,000, while the vertical axis should
un from -4% to 10%.
i) (10 Marks) What do these fives graphs tell you about whether there has been
convergence in different parts of the world between 1990 and 2019?
2. Suppose Canada’s aggregate production function is given by the following:
Y = 200K
1
2N
1
2
Variables are defined as they were in class. Suppose the savings rate in Canada is 25%
(s = 0.25) and the depreciation rate is 10% (δ = XXXXXXXXXXAssume that Canada is not
cu
ently experiencing any technological change.
a) (5 Marks) Calculate the steady-state level of capital per worker and output pe
worker in Canada’s economy.
) (5 Marks) Determine the annual growth rate of output per worker in Canada.
The government wants to grow the economy by encouraging more savings. Suppose
they successfully persuade Canadians to increase the savings rate to 35% (s = 0.35).
c) (10 Marks) Graph the resulting annual growth rate of GDP per worker for the
following 100 years. What is the new steady state level of GDP per capita? Has
increased savings led to a large growth in the economy?
d) (10 Marks) Calculate the golden-rule savings rate for this economy.
e) (5 Marks) Explain what your result from part d) say about the desirability of
Canada’s increased savings policy.
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3. Suppose Canada’s aggregate production function is given by the following:
Y = K
2
3 (AN)
1
3
Variables are defined as they were in class. Suppose the savings rate in Canada is 15%
(s = 0.15), the depreciation rate is 5% (δ = 0.05), the population growth rate is 3%
(gN = 0.03), and the growth rate of technology is 2% (gA = 0.02).
a) (10 Marks) Solve for the equili
ium level of capital per effective worker ( K
AN
) and
output per effective worker ( Y
AN
). Solve for the equili
ium growth rates of the
following variables: A, N , K, Y , Y
N
, K
N
, Y
AN
, and K
AN
. Use a table to summarize
your answers.
) (10 Marks) Suppose the population growth rate slowed to 1%. Solve for the
new equili
ium level of capital per effective worker ( K
AN
) and output per effective
worker ( Y
AN
). Solve for the new equili
ium growth rates of the following variables:
A, N , K, Y , Y
N
, K
N
, Y
AN
, and K
AN
. Use a table to summarize your answers.
c) (5 Marks) Discuss whether this fall in population growth rate was a positive
change, negative change, or neutral change for the growth rate of the Canadian
economy.
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Table 1:
Africa Europe Central and South America Asia
Algeria Albania Argentina Bangladesh
Angola Austria Belize Bhutan
Benin Belarus Bolivia (Plurinational State of) Cambodia
Botswana Belgium Brazil China
Burkina Faso Bosnia and Herzegovina Chile China, Hong Kong SAR
Burundi Bulgaria Colombia China, Macao SAR
Cabo Verde Croatia Costa Rica India
Cameroon Czech Republic Ecuador Indonesia
Central African Republic Denmark El Salvador Japan
Chad Estonia Guatemala Kazakhstan
Comoros Finland Guyana Kyrgyzstan
Congo France Honduras Lao People’s DR
Côte d’Ivoire Germany Mexico Malaysia
D.R. of the Congo Greece Nicaragua Maldives
Djibouti Hungary Panama Mongolia
Egypt Iceland Paraguay Myanma
Equatorial Guinea Ireland Peru Nepal
Eswatini Italy Suriname Pakistan
Ethiopia Latvia Uruguay Philippines
Gabon Lithuania Republic of Korea
Gambia Luxembourg Middle East Singapore
Ghana Malta Armenia Sri Lanka
Guinea Montenegro Aze
aijan Taiwan
Guinea-Bissau Netherlands Bahrain Tajikistan
Kenya North Macedonia Cyprus Thailand
Lesotho Norway Georgia Turkmenistan
Liberia Poland Iran (Islamic Republic of) Uzbekistan
Madagascar Portugal Iraq Viet Nam
Malawi Republic of Moldova Israel
Mali Romania Jordan
Mauritania Russian Federation Kuwait
Mauritius Se
ia Lebanon
Morocco Slovakia Oman
Mozambique Slovenia Qata
Namibia Spain Saudi Arabia
Niger Sweden State of Palestine
Nigeria Switzerland Syrian Arab Republic
Rwanda Ukraine Turkey
Sao Tome and Principe United Kingdom Yemen
Senegal
Seychelles
Sie
a Leone
South Africa
Sudan
Togo
Tunisia
U.R. of Tanzania: Mainland
Uganda
Zambia
Zimbabwe
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