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

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

Answered Same DayAug 07, 2021

International Economics

ECON-UA 238-002

Homework 3

Due Date: 3:00pm Wednesday 7 August 2019

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 2008-2009 recession 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 T B

c Y

Ipiq

T B

EP

, Y

, Y

(1)

T

G

T

T

P

Throughout question 1, suppose that the functional form for the consumption function is:

(2)

C cpY T q α µpY T q,

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 2008-2009, 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

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 rate, 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 below. 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 rate, output, and the exchange rate. During a liquidity trap, is monetary...

ECON-UA 238-002

Homework 3

Due Date: 3:00pm Wednesday 7 August 2019

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 2008-2009 recession 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 T B

c Y

Ipiq

T B

EP

, Y

, Y

(1)

T

G

T

T

P

Throughout question 1, suppose that the functional form for the consumption function is:

(2)

C cpY T q α µpY T q,

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 2008-2009, 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

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 rate, 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 below. 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 rate, output, and the exchange rate. During a liquidity trap, is monetary...

SOLUTION.PDF## Answer To This Question Is Available To Download

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