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What is the role played by the intertemporal elasticity
Course:- Macroeconomics
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Question 1: Balance of Payments & International Investment Position

The ratio of the net international investment position to GDP evolves according to the dynamic equation:

Δbt = bt - bt-1 = bgstt + (rtL - gt)/(1 + gt)bt-1 + rtA-rtL/(1+gt)at-1 + ∈t

In the questions that follow, assume ∈t = 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 t - 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 t - 1 is 1.20, the return on liabilities is +0.02 and the return on assets is +0.05. What is bt? Interpret.

c) Consider the same conditions as in b) except that the country in question is now a creditor, with bt-1 = +0.20. What is bt? Interpret.

d) Suppose rtA = rtL = 0.04, g = 0.02, and bt-1 = -0.50. What value of the trade balance is required in order to stabilise the net foreign asset position at bt = -0.50?

e) Now suppose that rtA = rtL = 0.01, g = 0.02, and bt-1 = -0.50. What value of the trade balance is required in order to stabilise the net foreign asset position at bt = -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. 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 20 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:

U = C11-ρ/(1-ρ) + β C21-ρ/(1-ρ)

where ρ ≠ 1. The representative consumer receives endowments Y1 and Y2 in periods 1 and 2 respectively and can borrow and lend at the exogenously-given world interest rate r. For the questions that follow, please explain your answers.

a) What is the optimal relation between C1 and C2 in this environment?

b) Suppose that β(1 + r) = 1. If Y1 = 90 and Y2 = 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 r.)

c) Under what condition will C2 exceed C1?

d) What is the role played by the intertemporal elasticity of substitution, 1/ρ, in determining the relation between C1 and C2?

Question 3: Fiscal Policy and the Current Account

Consider the two-period small open economy model, where preferences are given by:

U = C11-ρ/(1-ρ) + 1/(1 + δ).C21-ρ)/1-ρ

The representative consumer receives endowments Y1 = Y2 = Y in periods 1 and 2 respectively and can borrow and lend at the exogenously-given world interest rate r = δ, where δ is the rate of time preference (or discount rate). Government consumption equals G1 and G2 in periods 1 and 2 respectively. In answering the questions that follow, please ensure that explanations are provided (i.e. intuition).

a) Suppose that G1 = G2 = G‾0. What is the optimal relation between C1 and C2 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 G1 = G2 = G1 < G0‾. How do consumption and the current account respond to this shift in government consumption?

c) Now suppose that G1 = G0‾ and G2 = G1‾ (with G1‾ < G0‾ 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

Y = AF(K) and Y* = A*F(K*)

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 A(A* is unchanged). Explain the intuition for your answer.

b) Suppose rather that there is an anticipated global productivity boom, with the values of A and A* 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 case. Explain the intuition for your answer.

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 δ (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.

Question 5: Real Exchange Rates & the Balassa-Samuelson Model

a) Identify the key assumptions of the Balassa-Samuelson model discussed in lectures. Briefly outline the hypothesis it posits.

b) How could one augment the Balassa-Samuelson model such that the demand side also plays a role? In this case, explain three other factors that could potentially influence the real exchange rate in the long run.

c) Consider production functions across traded (T) and nontraded (N) sectors in home (h) and foreign (f) that are given by Yi,T = Ai,TLi,T and Yi,N = Ai,NLi,N where i ∈ {h, f}, Y is output, A is productivity, and L is labor. Pi,T and Pi,N denote output prices, while wi,T and wi,N denote wages.

Given this information, answer the following.

i) For each country, obtain an expression for the relative price of nontradables.

ii) Noting that the real exchange rate is defined as Q = SPf/ph, where Ph = Pαh,T P1-αh,N and Pf = Pαf,T P1-αf,N are aggregate prices, S is the nominal exchange rate, and Ph,T = Pf,T, examine the implications of the configuration Ah,T < Af,T and Ah,N = Af,N for Q(relative to Q = 1)

Explain what happens when α = 1?




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