Download Dynamics of current account – Permanent income hypothesis

JEM111 International Macroeconomics – Homework Solution
Seminar 2 and 3: Dynamics of current account – Permanent income
hypothesis & OLG model
Important note: This is only one of possible solutions. If your answers/ solution were
different, I focused on the argumentation. I will bring corrected HWs next seminar so you
can see them. If you have any question, please contact me on [email protected].
Q1) Infinite-horizon model of a small open economy (1 p.)
a) In the last seminar you discussed the two-period model. Although it provides an important
lesson, it suffers from some limitations. What are the limits of the model?
- Both, individuals and economy (incl. government) live only for 2 periods (in reality,
individuals optimize over more periods)
- One single tradable good, only non-durable (=no investment)
- 2-period model lead to very uneven results regarding the equilibrium real interest rate,
very high debt levels or unusual level of savings (e.g. negative).
- We cannot work with limits on growing foreign debt
- etc.
b) Is it realistic to consider infinitely lived individuals? Why (not)?
- Y/N answer possible, depends on argumentation
- N – mortality
- Y – thinking in terms of the whole family / descendants; parents care about their
descendants, who, in turn, care about theirs (“an economy with finite-lived individuals
may behave just like one peopled by immortals (Obstfeld and Rogoff, pp 58)”)
c) We focus on the case of a small open economy. What does this assumption mean (in terms
of the world interest rate)? Is it realistic? Why (not)?
Obstfeld and Rogoff, pp 58:
- For a SOE, the interest rate is the same as the world interest rate, as the economy is too
small to influence world interest rate; SOE takes world interest rate as exogenous =
realistic.
- Problematic assumption if
o country’s GDP were perpetually to grow faster than world GDP  country would
become large,
o country is high saver with even-growing net foreign assets.
Q2) Dynamics of the current account (1.5 p.)
a) Consider a small open economy with infinitely lived representative agents maximizing 𝑈 =
𝑠−𝑡
∑∞
𝑢(𝐶𝑡 ) with 𝛽 = 1/(1 + 𝑟 ∗ ). Each period the economic agent receives an
𝑠=𝑡 𝛽
endowment income 𝑌𝑡 = 200 and can borrow / lend without limits at 3% world interest
rate. Show graphically the consumption plan (of individuals and aggregate), current account
and trade balance dynamics for (i) 𝛽 = 0.9, (ii) 𝛽 = 1/1.03 and (iii) 𝛽 = 0.99. Which of these
cases leads to realistic outcomes of the model? Why?
(i) 𝛽 = 0.9
1200
400
1000
200
0
800
Y
600
C
-200
TB
CA
-400
400
-600
200
-800
0
-1000
1
11
21
31
41
51
61
71
81
91
1
11
21
31
41
period
51
61
71
81
91
period
(ii) 𝛽 = 1/1.03
250
1
0,9
200
0,8
0,7
150
0,6
Y
C
100
TB
0,5
CA
0,4
0,3
50
0,2
0,1
0
0
1
11
21
31
41
51
61
71
81
91
1
11
21
31
41
period
51
61
71
81
91
period
(iii) 𝛽 = 0.99
500
14000
0
1
11
21
31
41
51
61
71
81
12000
91
-500
10000
-1000
Y
-1500
C
8000
TB
CA
6000
-2000
4000
-2500
-3000
2000
-3500
0
1
period
11
21
31
41
51
61
71
81
91
period
(see the simulation file from the lecture)
(i) and (iii) lead to unrealistic outcomes - infinite, zero or negative consumption
b) Discuss briefly the idea behind permanent income hypothesis.
Economic agents divide consumption equally among their whole life-time. They have no time
preferences in consumption. They spend money at such level which is consistent with their
expectations about future income.
Q3) OLG model (1.5 p.)
a) Is the equilibrium in OLG model Pareto-efficient? Explain.
No, there is a problem of dynamic inconsistency. The economy exists forever; there is an
infinite number of agents and also the total value of resources is infinite. Social planner
(central planner, government) can make the current old generation better off through
transfers from each young generation (intergeneration transfer scheme).
b) What is meant by the term “twin deficits”? Name some countries and some period of time in
which this phenomenon was observed.
CA deficit caused by government deficit, both deficits appear at the same time, e.g. US –
1980s, Germany – 1990s.