Exercise 4 Consider an economic environment where there are only two economies, a domestic and a foreign, and where assets are perfect substitutes. Assume that the accumulation of net foreign assets by the domestic economy follows the dynamics given by the following equation in differences:

Bt11 5 ð1 1 rÞBt 1 TBðqt; ztÞ

where Bt represents the NIIP in period t, r represents the real domestic exchange rate, TB()

is a function that measures the trade balance of the domestic economy, qt represents the real exchange rate, in terms of units of foreign economy goods necessary to acquire one unit of domestic economic good, and zt is a variable that synthesizes all other factors that influence the trade deficit, such as preferences for domestic and foreign goods, among others.

Assume that the trade balance function is given by TBðqt; ztÞ 5 θqt 1 zt, that the domestic interest rate is equal to the foreign rate, that is, r 5 r
, both constant, and that goods prices are constant. In this economic environment, the uncovered interest rate parity is given by:

ð1 1 rÞ 5 ð1 1 r
Þ St Et½St11

a. Based on the hypotheses presented in the problem, what could you say regarding the evolution of the real exchange rate over time? Explain your answer.

b. Solving the equation in differences from the NIIP forward, and imposing a condition that the net debt does not grow at a rate superior to the interest rate (the transversality condition), obtain the value of the real exchange rate. Present an economic interpretation for your answer.

c. Based on your answer to the previous item, find an expression that determines the evolution of Bt 2 Bt21. Present an economic interpretation for your answer.

Chapter 8 • Portfolio Diversification and Capital Flows 225

d. Now consider that a permanent and unexpected shock occurs in zt. What would be the impact of this shock on the real exchange rate and on the net external debt for the domestic economy? Present an economic explanation for the shock, for the exchange rate evolution and the NIIP.

e. Could the results obtained in the previous item be used to explain the current-account dynamics for the American economy up to 2007? Explain your answer. What is the role of perfect substitutability among assets on the explicatory power of this model in light of the behavior of the empirical data?