International Economics
ECON-UA XXXXXXXXXX
Homework 3
Due Date: 3:00pm Wednesday 7 August 2019
Question 1: Exercises with the IS–LM Model
For each of the following situations, use the IS-LM-FX model to illustrate the effects of the
shock and the policy response. Assume the government responds by using monetary policy to
stabilize output, and assume the exchange rate is floating. For each case, state the effect of the
shock on the following variables: Y, i, E,C, I and TB.
1.a) Foreign output decreases.
1.b) Investors expect a depreciation of the home cu
ency.
1.c) The money supply increases.
1.d) Government spending increases.
Question 2: the IS-LM model during the recession
Consider the IS-LM model in the open economy. The purpose of this question will be to explore
the effects of the XXXXXXXXXXrecession and the policy responses to it within our model.
The backbone of the IS-LM model is the demand equation, which is given by:
D � C � I �G� TB
� c
�
Y � T
�
� Ipiq �G� TB
�
EP �
P
, Y � T , Y � � T
�
(1)
Throughout question 1, suppose that the functional form for the consumption function is:
C � cpY � T q � α� µpY � T q, (2)
where α is an intercept, and µ is the slope of the consumption function.
2.a) What is the name for the slope of the consumption function, µ? What is the name for the
parameter 1 � µ?
2.b) During the recession of XXXXXXXXXX, the price of houses fell dramatically, which reduced
household assets, driving many households to increase their rate of saving. We can model this
as a temporary increase in the parameter 1 � µ, or a decrease in the parameter µ. Draw the
1
consumption function in Equation (2) before and after the change in µ. (I.e. draw consumption
for high µ1 and then for low µ2 on the same graph).
2.c) Draw the demand function in Equation (1) before and after the change in µ. (Hint: You
can assume that µ � µH � µF and that the change in µ affects both components equally).
2.d) Draw two graphs, side-by-side: 1) the IS-LM curves and the associated equili
ium, 2) the
foreign exchange market and the associated equili
ium. Now draw a second IS curve after the
change in µ. What happens to the equili
ium output, interest rate, and spot exchange rate
after the change in µ?
2.e) Suppose the home country maintains a floating exchange rate and free capital mobility.
How could economic policy makers use fiscal policy to increase output during this recession?
On a new graph: 1) show the effect of the change in µ on equili
ium, 2) show the effect of
implementing the fiscal policy measure you discussed. Be sure to show all effects on the interest
ate, output, and the exchange rate.
2.f) Suppose the recession caused output to fall by $100 billion dollars. If policy makers were
to use fiscal policy to return output to its pre-recession level, would they need to increase
government spending by more or less than $100 billion? Provide an explanation for your answer.
2.g) Suppose the home country maintains a floating exchange rate and free capital mobility.
How could economic policy makers use monetary policy to increase output during this reces-
sion? On a new graph: 1) show the effect of the change in µ on equili
ium, 2) show the effect
of implementing the monetary policy measure you discussed. Be sure to show all effects on the
interest rate, output, and the exchange rate.
2.h) A liquidity trap occurs when the amount of money demanded is very unresponsive to
interest rates. The situation in the money market along with the associated LM curve is plotted
elow. Using the Money Market, IS-LM, and foreign exchange market figures, draw the effect
of using monetary policy during a liquidity trap. Be sure to show all the effects on the interest
ate, output, and the exchange rate. During a liquidity trap, is monetary policy effective at
eversing the effects of the recession?
M{P
i MS
pM{P q�
MDi
�
(a) US Money Market
Y
i
IS
LM
i�
Y �
(b) IS-LM
nyu
2
Question 3: changes in demand during the recession
In this question, we will look at what happens to the components of demand and income, during
a recession. We will focus on the United Kingdom during the XXXXXXXXXXrecession, since this
was a large shock for the the UK economy. We are interested in observing the relationship
etween the components of demand, the real exchange rate, and domestic interest rates.
3.a) Produce a figure with four subplots. The subplots will show:
• Real GDP and the following components of real GDP: consumption, investment, govern-
ment spending (Quarterly data)
• The components of (real) net exports: export volumes and import volumes (Quarterly
data)
• The (nominal)) UK-US exchange rate (Quarterly data)
• The Bank of England (nominal) Policy Rate (Quarterly data)
For all the first three graphs:
• Plot the percentage deviation from XXXXXXXXXX: i.e. plot ỹt �
yttu�ytt�Jan,2008u
ytt�Jan,2008u
.
• For the interest rate, plot the percentage point deviation from XXXXXXXXXX: i.e. plot
̃t � rttu � rtt�Jan,2008u.
Finally, we will plot recession shading for the UK recession from January 1st 2008 until June
30th 2009 (See the hint at the end of the homework for how to do this).
Every data series should be at quarterly frequency for the period January 1st 2003 to
December 31st 2012 (i.e. 10 years of data starting in XXXXXXXXXXThe following hints will help
you find the co
ect series on the FRED website1:
• Go to the FRED page “A Millennium of Macroeconomics Data for the UK” (https:
fred.stlouisfed.org/categories/33839)
• For GDP components, search in the section “National Accounts”
• For Interest rate and exchange rate variables, search in the section “Financial Markets”
• Search for the variables named:
– Search for “Real Gross Domestic Product at Market Prices”
– Search for “Real Consumption Expenditures”
– Search for “Real Investment Expenditures”
– Search for “Real Government Consumption of Goods and Services”
– Search for “Trade Volumes: Export Volumes”
– Search for “Trade Volumes: Import Volumes”
– Search for “U.S. / U.K. Foreign Exchange Rate”
– Search for “Bank of England Policy Rate”
1https:
fred.stlouisfed.org
3
https:
fred.stlouisfed.org/categories/33839
https:
fred.stlouisfed.org/categories/33839
https:
fred.stlouisfed.org
Note that the exchange rate you download from FRED should be interpreted as foreign cu
ency
per UK pound. This means that an increase in the exchange rate in the data is the same as an
appreciation of the UK pound. If you like, you can invert the exchange rate so that it matches
the format we have discussed in class (although you do not need to do this).
3.b) Consider the path of GDP components during the recession. How did overall GDP, con-
sumption, investment, and government spending respond during the recession? Relative to
it’s trajectory prior to the recession, do you think government spending increases or decreases
during the recession?
3.c) Which component of the trade balance falls by more during the recession? Overall, does
the UK trade balance increase or decrease during the recession?
3.d) In your plots for 3.a), you plotted the nominal interest rate and the nominal exchange rate.
Suppose UK inflation had been relatively high during this period. Relative to the nominal rates
you plotted, what does a high rate of UK inflation imply about the paths of the real interest
ate and the real exchange rate? (Hint: use the definition of the real exchange rate to explain
your answer).
3.e) Consider the model of demand in an open economy. What effect does a decrease in the
UK interest rate have on demand? What effect does an depreciation of the UK pound have
on demand? Be sure to explain which variables are affected by these changes (i.e. how do the
interest rate and exchange rate pass through other variables into demand).
3.f) Are the changes you observe in the data consistent with the model discussed in 3.e)? Why
or why not?
3.g) The UK maintains a floating exchange rate and free capital mobility. Describe two policies
that UK policy makers could use during the recession to increase output. What effect would
the two policies you described have on the variables you plotted in 3.a)? Are these effects what
you actually observe in the data you plotted? (Hint: consider your answer to 3.b))
3.h) One major goal of economic policy is to stabilize economic activity during recessions.
According to the data you plotted in 3.a), did the policies enacted perfectly stabilize economic
activity? If not, do you think policy makers could have done more to help stabilize the economy?
(Hint 1: consider the role of the ”zero lower bound” for monetary policy).
Python tips
Normalizing variables
It is often useful to normalize variables to 1 at a particular date (called the “index date”). We
can then use this index date to compute the percentage deviation from the index date. This
helps us see how the variable moves relative to the index date. In Python we need to do this
in two steps. First, suppose our data structure is called UKdata. Let’s normalize to the date
XXXXXXXXXXFirst, we run:
UKdata2008Q1 = UKdata[UKdata.index==' XXXXXXXXXX']
Then our new variable UKdata2008Q1 contains all of the variables inside our original UKdata,
ut only at the date XXXXXXXXXXNow we want to compute the percentage change from this
4
date. As noted above, mathematically we are computing ỹt � yt�yt�Jan,2008yt�Jan,2008 . Suppose we want
to find the value for GDP, and we have named the variable 'Y', which can be accessed in the
original data with UKdata['Y']. We can then get the percentage deviation in Python via:
UKdata['Y'] = (UKdata['Y'] - UKdata2008Q1['Y'][0])/UKdata2008Q1['Y'][0]*100
The components of this code are: UKdata['Y'] accesses the original value of GDP at all dates;
UKdata2008Q1['Y'][0] accesses the value of GDP at the index date (note, the [0] on the end
of the code just makes sure we are accessing the data, not all the other information associated
with the variable); multiplying by 100 just gives us the percentage change.
Recession shading
In this homework exercise, we will plot recessions “manually” (i.e. by giving specific recession
dates to the code). First, we set the start and end dates of the recession:
ecstart = dt.datetime(2008, 1, 1)
ecend = dt.datetime(2009, 6, 30)
Then, when we want to plot a recession, simply include the following two lines:
ylim = plt.ylim()
plt.fill_between([recstart, recend], y1=ylim[0], y2=ylim[1], alpha=0.75, color=’lightblue’)
The first line finds the bottom and top of the y-axis for the cu
ent figure. The second line
plots recession shading during the start and end dates of the recession that we specified in the
previous two lines.
Plotting a grid
It