MACROECONOMICS
2006
Week 2 Seminar Questions: Measurement Issues and Business Cycles
Questions for Review
1. Define a business cycle.
Fluctuations about trend in real GDP. (Figure 3.1 in the Book, Ch. 3, p. 64)
2. In a graph of the natural logarithm of an economic time series, what does the
slope of the graph represent?
An approximation of the growth rate of the series (Figure 1.2 in the book, Ch. 1, p. 6-7)
3. Why are the comovements in aggregate economic variables important?
The similarities between the fluctuation patterns of macroeconomic varibables suggest
that business cycles are more alike than different
4. What are the three features of comovement that macroeconomists are interested
in?
1) Is a series procyclical or countercyclical,
2) Does the series lead or lag real GDP,
3) Is the series more or less volatile than real GDP.
5. Describe key business cycle facts.
Tables 3.1 and 3.2 (Chapter 3, p. 84) provide a summary of business cycle facts. For a
broader analysis see Ch. 3, p. 67-84
6. Why is the index of leading economic indicators useful for forecasting GDP?
A leading variable helps us to predict the future path of the other variable. Index of
leading economic variables is a weighted average of macroeconomic variables that helps
us predicting future movements in real GDP. Turning points in the index generally
precede turning points in GDP. (Ch. 3, p. 72-73)
Problems
1.
Suppose that you are given that the government deficit is 10, interest on the
government debt is 5, taxes are 40, government expenditures are 30, consumption
expenditures are 80, net factor payments are 10, the current account surplus is -5,
and national saving is 20. Calculate the following (not necessarily in the order
given):
a.
Private disposable income
b.
Transfers from the government to the private sector
c.
Gross national product
d.
Gross domestic product
e.
The government surplus
f.
Net exports
g.
Investment expenditures
This exercise is based in Ch. 2 regarding measurement issues (p. 40-54). We have:
D=10
T=40
C= 80
CA=-5
INT=5
G=30
NFP=10
S=20
g.
Investment expenditures
S=Y+NFP-C-G=(C+I+G+NX)+NFP-C-G=I+(NX+NFP)
S=I+CA
20=I-5
I=25
e.
The government surplus
g
S = -D= -10
f.
Net exports
CA=NX+NFP
-5=NX+10
NX=-15
d.
Gross domestic product
GDP=C+I+G+NX
=80+25+30-15=120
c.
Gross national product
GNP=GDP+NFP= 120+10=130
b.
Transfers from the government to the private sector
Sg = T-TR-INT-G
-10 =40-TR-5-30
TR=15
a.
Private disposable income
Yd= Y+NFP+TR+INT-T = 120+ 10+15+5-40=110
2.
a.
Consider the following data on real GDP per capita in the United Kingdom:
Year
UK Real GDP
(1985 £Sterling)
1960
1970
1980
1990
1995
1996
1997
1998
1999
2000
2001
78983
106006
124753
163318
181168
186352
193086
198054
203495
209040
212610
Calculate the percentage growth rates in real GDP in each of the years 1995
through 2001, from the previous year.
Growth rate in 1996=
Real GDP
% change
⎞
⎛ yt
⎜⎜
− 1⎟⎟100
⎠
⎝ y t −1
1995
1996
1997
1998
1999
2000
2001
b.
181168
186352
193086
198054
203495
209040
212610
2.86%
3.61%
2.57%
2.75%
2.72%
1.71%
Now, instead of calculating the annual percentage growth rates in the years 1995 through
2001 directly, use as an approximation 100 x (ln yt – ln yt – 1) where yt is real GDP in year
t. How close this approximation comes to the actual growth rates you calculated in part
(a)?
1995
1996
1997
1998
1999
2000
2001
Real
GDP
ln Real
GDP
% Approx
181168
186352
193086
198054
203495
209040
212610
12.1072
12.1354
12.1709
12.1963
12.2234
12.2503
12.2672
2.82%
3.55%
2.54%
2.71%
2.69%
1.69%
(ln y t
− ln y t −1 )100
c. During what decade from 1960 to 2000 was growth in real GDP the highest? When
was it the lowest?
1960
1970
1980
1990
2000
Real
GDP
78983
106006
124753
163318
209040
%
change
34.21%
17.68%
30.91%
28.00%
Highest
Lowest
3. Consider the following data, which are observations on x and y over several periods
of time.
Period
1
2
3
4
5
6
7
x
100
200
200
100
50
50
100
y
500
500
1000
1000
500
250
250
a. Construct a scatter plot of y against x. Are y and x positively correlated,
negatively correlated, or uncorrelated? Explain your answer.
1200
1000
800
600
400
200
0
0
50
100
150
200
250
X
Correlation coefficient=0.46. Hence, there is a weak positive correlation between x
and y.
b. Now, construct a time series of y and x. Is y a leading, lagging, or coincident
variable with respect to x? Explain your answer.
250
1200
200
1000
800
150
600
100
400
50
200
0
0
1
2
3
4
x
5
6
7
y
y is a lagging variable with respect to x
c. Do x and y exhibit persistence? Explain.
Percentage Deviation from the Trend in X
40.00%
20.00%
0.00%
-20.00%
1
2
3
4
5
6
7
-40.00%
-60.00%
-80.00%
Perentage Deviation from the Trend in Y
40.00%
20.00%
0.00%
-20.00%
1
2
3
4
5
6
7
-40.00%
-60.00%
-80.00%
Yes. Persistence is the tendency of a time series to stay above (below) trend when it has
been above (below) trend during recent past.