Consumption Smoothing
Basic Framework
Consider a two-period small open economy (SOE) model,
with exogenous world interest rate r
Let the discount factor be = 1
1+ .
Household receives endowments/incomes Y1 & Y2 in periods
1 & 2.
Its (lifetime utility) maximisation problem is:
maxU = u(C1) + u(C2) w:r :t: C1 & C2 (1)
subject to following present value budget constraint:
C1 +
C2
1 + r
= Y1 +
Y2
1 + r
(2)
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Dublin Institute of Technology
M.Sc. International Macroeconomics Assignment, Term I
October 2015
Submission Due: 14:30, 17th November 2015
IMPORTANT: Late submissions will NOT be accepted. Answers should be
typed. Please use Times New Roman, font size 12, and 1.5 spacing.
Question 1: Balance of Payments & International Investment Position
The ratio of the net international investment position to GDP evolves according to the
dynamic equation:
???! = ??! – ??!!! = ????????! +
??!
! – ??!
1 + ??!
??!!! +
??!
! – ??!
!
1 + ??!
??!!! + ??!
In the questions that follow, assume ??! = 0.
a) State algebraically the condition under which a country can run a trade deficit yet
experience an improvement in its net foreign asset position. Explain the different factors that
might generate this configuration.
b) Suppose the trade deficit is -0.05 and the inherited net foreign asset position from the end
of period ?? – 1 is -0.20. The output growth rate is +0.03, the gross stock of foreign assets
(as a fraction of GDP) at the end of period ?? – 1 is 1.20, the return on liabilities is +0.02 and
the return on assets is +0.05. What is ??!? Interpret.
c) Consider the same conditions as in b) except that the country in question is now a creditor,
with ??!!! = +0.20. What is ??!? Interpret.
d) Suppose ??!
! = ??!
! = 0.04, ?? = 0.02, and ??!!! = -0.50. What value of the trade balance is
required in order to stabilise the net foreign asset position at ??! = -0.50?
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e) Now suppose that ??!
! = ??!
! = 0.01, ?? = 0.02, and ??!!! = -0.50. What value of the trade
balance is required in order to stabilise the net foreign asset position at ??! = -0.50?
Comment on the differences between the answers to parts d) and e).
f) Download Lane and Milesi-Ferretti’s updated External Wealth of Nations II dataset from
http://www.philiplane.org/EWN.html. What were the NFA-CA (net foreign assets-current
account) configurations for China, USA, Ireland and Malta in the year 2010 (e.g. country X
had positive NFA and positive CA in year 2010. Note that NFA is a stock variable reported at
the end of the year, while CA is a flow variable). Comment on any two of these
configurations. Using your knowledge about Ireland, what impact is net factor income from
abroad (NFIA) having on its current account position? Explain.
g) Write an essay (max. 1200 words) examining the trend in global external imbalances over
the past 15 years. A significant part of your essay should be devoted to analysing the external
adjustment phase during the global crisis.
Question 2: Consumption Smoothing in the Two-Period Model
Consider the two-period small open economy model, where preferences are given by:
?? =
??!
!!!
1 – ??
+ ??
??!
!!!
1 – ??
where ?? ? 1. The representative consumer receives endowments ??! and ??! in periods 1 and 2
respectively and can borrow and lend at the exogenously-given world interest rate ??. For the
a) What is the optimal relation between ??! and ??! in this environment?
b) Suppose that ?? 1 + ?? = 1 . If ??! = 90 and ??! = 40 , what is the optimal level of
consumption in period 1? What is the value of the current account in period 1? (Note: your
answers will be in terms of ??.)
c) Under what condition will ??! exceed ??!?
d) What is the role played by the intertemporal elasticity of substitution, !
!, in determining the
relation between ??! and ??!?
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Question 3: Fiscal Policy and the Current Account
Consider the two-period small open economy model, where preferences are given by:
?? =
??!
!!!
1 – ??
+
1
1 + ??
??!
!!!
1 – ??
The representative consumer receives endowments ??! = ??! = ?? in periods 1 and 2
respectively and can borrow and lend at the exogenously-given world interest rate ?? = ??,
where ?? is the rate of time preference (or discount rate). Government consumption equals ??!
and ??! in periods 1 and 2 respectively. In answering the questions that follow, please ensure
that explanations are provided (i.e. intuition).
a) Suppose that ??! = ??! = ??! . What is the optimal relation between ??! and ??! in this
environment? What is the value of the current account in period 1?
b) Now suppose that there is a shift in planned government consumption such that ??! = ??! =
??! < ??!. How do consumption and the current account respond to this shift in government
consumption?
c) Now suppose that ??! = ??! and ??! = ??! (with ??! < ??! as in b)). How do consumption and
the current account respond to this shift in government consumption?
Question 4: Savings and Investment in the Global Two-Country Model
Consider a world composed of two countries that are initially identical. The Home and
Foreign production functions are
?? = ????(??) and ??* = ??*??(??*)
a) Using a graphical analysis, show the qualitative response of the Home and Foreign current
accounts and the world interest rate to an anticipated increase in the value of ?? (??* is
b) Suppose rather that there is an anticipated global productivity boom, with the values of ??
and ??* increasing by the same amounts. Again, using a graphical analysis, show the
qualitative responses of Home and Foreign current accounts and the world interest rate in this
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c) In contrast to being anticipated in the future, let’s now assume that a Home productivity
rise is observed today (no change in Foreign’s productivity). Examine the responses in Home
and Foreign current accounts and the world interest rate (use graphs).
d) Imagine that Home is now more impatient, represented by a higher rate of time preference
?? (no change in Foreign’s impatience). Examine the responses in Home and Foreign current
accounts and the world interest rate (use graphs).
e) Using a graphical analysis, first explain the impact of an outward shift in the foreign
country’s saving schedule (that is, it wants to save more at any given interest rate). Next,
explain the impact of an inward shift in the foreign country’s investment schedule (that is, it
wants to invest less at any given interest rate). Which scenario better captures the impact of
emerging Asia on the world economy since the late 1990s? Discuss.