Description
In this homework you’ll explore transforming data with split/apply/combine and the plyr
package.
Gross domestic product (GDP) is a measure of the total market value of all goods and
services produced in a given country in a given year. The percentage growth rate of GDP
in year t is
100 ×
GDPt+1 − GDPt
GDPt
− 100
An important claim in economics is that the rate of GDP growth is closely related to the
level of government debt, specifically with the ratio of the government’s debt to the GDP.
The file debt.csv on the class website contains measurements of GDP growth and of the
debt-to-GDP ratio for twenty countries around the world, from the 1940s to 2010. Note
that not every country has data for the same years, and some years in the middle of the
period are missing data for some countries but not others. Throughout, use 3 significant
digits for numerical answers!! (That is, signif(mydat,3) is your friend).
debt <- read.csv(“debt.csv”, as.is = TRUE)
dim(debt)
head(debt)
1. Calculate the average GDP growth rate for each country (averaging over years). This
is a classic split/apply/combine problem, and you will use daply() to solve it.
a. Begin by writing a function, mean.growth(), that takes a data frame as its
argument and returns the mean of the ‘growth‘ column of that data frame.
b. Use daply() to apply mean.growth() to each country in debt. Don’t use something like mean(debt$growth[debt$Country==”Australia”]), except to check
your work. You should not need to use a loop to do this. (The average growth
rates for Australia and the Netherlands should be 3.72 and 3.03. Print these
values.) Report the average GDP growth rates clearly.
2. Using the same instructions as problem 1, calculate the average GDP growth rate for
each year (now averaging over countries). (The average growth rates for 1972 and
1989 should be 5.63 and 3.19, respectively. Print these values in your output.) Make
a plot of the growth rates (y-axis) versus the year (x-axis). Make sure the axes are
labeled appropriately.
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3. The function cor(x,y) calculates the correlation coefficient between two vectors x
and y.
a. Calculate the correlation coefficient between GDP growth and the debt ratio over
the whole data set (all countries, all years). Your answer should be −0.1995.
b. Compute the correlation coefficient separately for each country, and plot a histogram of these coefficients (with 10 breaks). The mean of these correlations
should be −0.1778. Do not use a loop. (Hint: consider writing a function and
then making it an argument to daply()).
c. Calculate the correlation coefficient separately for each year, and plot a histogram
of these coefficients. The mean of these correlations should be −0.1906.
d. Are there any countries or years where the correlation goes against the general
trend?
4. Fit a linear model of overall growth on the debt ratio, using lm(). Report the intercept
and slope. Make a scatter-plot of overall GDP growth (vertical) against the overall
debt ratio (horizontal). Add a line to your scatterplot showing the fitted regression
line.
5. There should be four countries with a correlation smaller than -0.5. Separately, plot
GDP growth versus debt ratio from each of these four countries and put the country names in the titles. This should be four plots. Call par(mfrow=c(2,2)) before
plotting so all four plots will appear in the same figure.
(Think about what this shows: individual relationships at the country level are sometimes concealed or ”smudged out” when data is aggregated over all groups (countries).
This conveys the importance of careful analysis at a more granular group level, when
such groupings are available!)
6. Some economists claim that high levels of government debt cause slower growth. Other
economists claim that low economic growth leads to higher levels of government debt.
The data file, as given, lets us relate this year’s debt to this year’s growth rate; to
check these claims, we need to relate current debt to future growth.
a. Create a new data frame which just contains the rows of debt for France, but
contains all those rows. It should have 54 rows and 4 columns (print the dimensions of your data frame). Note that some years are missing from the middle of
this data set.
b. Create a new column in your data frame for France, next.growth, which gives
next year’s growth if the next year is in the data frame, or NA if the next year
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is missing. (next.growth for 1971 should be (rounded) 5.886, but for 1972 it
should be NA. Print these two values.)
7. Add a next.growth column, as in the previous question, to the whole of the debt
data frame. Make sure that you do not accidentally put the first growth value for one
country as the next.growth value for another. (The next.growth for France in 2009
should be NA, not 9.167. Print this value.) Hints: Write a function to encapsulate
what you did in the previous question, and apply it using ddply().
8. Make a scatter-plot of next year’s GDP growth against this year’s debt ratio. Linearly
regress next year’s growth rate on the current year’s debt ratio, and add the line to the
plot. Report the intercept and slope to reasonable precision. How do they compare
to the regression of the current year’s growth on the current year’s debt ratio?
9. Make a scatter-plot of next year’s GDP growth against the current year’s GDP growth.
Linearly regress next year’s growth on this year’s growth, and add the line to the plot.
Report the coefficients. Can you tell, from comparing these two simple regressions
(from the current question, and the previous), whether current growth or current debt
is a better predictor of future growth?
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