Solucionario Examen Eco Internacional

International Macroeconomics A
Spring 2010 - Prof. Ph. Bacchetta

Makeup Exam - Solutions

1. (10) What is the impact of an increase in the rate of time preference on the current account? benchmark case: (1 + r) = 1 ) C1 = C2 = C " ) : ‡ consumption path at < 1=(1 + r)

increase in the rate of time preference:

In this alternative scenario the consumer becomes more impatient and desires toconsume more immediately: C1 > C2 . In an SOE the agent can lend and borrow, therefore he can satisfy his impatience by borrowing C1 Y1 in the …rst period and repaying (1 + r)(C1 Y1 ) in the second period. Thus, he will run a current account de…cit in the …rst period and match it by a current surplus in the second period in order to satisfy intertemporal feasibility. 2. (10) Switzerland has experienceda dramatic reduction in its current account surplus in 2008. What explains this reduction? The current account is de…ned by the following accounting relationship: CAt = N Xt + N F It + T rt Considering the Swiss current account statistics, it appears that foreign trade has slightly increased between 2007 and 2008 while services have remained roughly stable over that same time frame. Labor incomeas well as current transfers have not been subject to remarkable ‡ uctuations. The main driver of the reduction in the current account surplus has been the sharp reversal in investment income (from +21:47% to 24:5%). 3. (10) What is the consumption co-movement puzzle? Basic setup: two countries, uncertainty and complete markets

# )

C1 + C1

= Y1 + Y1 Y2 (a)W Y2 (b)W

C2 (a) + C2 (a) = Y2 (a) + Y2(a) C2 (b) + C2 (b) = Y2 (b) + Y2 (b) Consider the case where ln(C) ) U 0 (C) = 1=C

(1 + r) 6= 1 and assume a speci…c utility function: U (C) =

Solving for optimal consumption in state a we obtain C2 (a) = (a) (1 + r) C1 : p(a) 1

The same result holds for Foreign, thus C2 (a) + C2 (a) = (a) (1 + r) (C1 + C1 ): p(a)

By substituting into the equilibrium equation we get Y2 (a)W = This implies C(a) Y2 (a)W C2 (a) = 2 = ; C1 C1 Y1W meaning that the per capita consumption growth rate should be perfectly correlated across countries if markets are complete. More generally, with …nancial globalization and risksharing consumption co-movements should be higher than output co-movements. However, empirical evidence shows the exact opposite: corr(y; y w ) > corr(c; cw ). The two most advocatedexplanations to the consumption co-movement puzzle are the following: …rst, markets are far from being complete, and second, there exists a “home-bias puzzle" for equities. 4. (10) Greece is on the brink of bankruptcy and there is some probability it will default on its sovereign debt. There is actually a probability p of a 20% haircut on the debt. There is a spread of 2000 basis points on thisdebt, while the risk-free corresponding interest rate is 5%. Compute p. (Remarks: i) the solution can be found without calculator; ii) the numbers used in this question are …ctitious) haircut (1 z) = 20% rf = 20% (a) (1 + r) W Y1 p(a)

spread on debt rs rf = 5%

) compute the probability of default p 1 + rf = (1 = [1 p)(1 + rs + pz(1 + rs ) p(1 z)](1 + rs )

Manipulating this expression, we …nallyobtain p = = = 1 1 z 1 1 + rf 1 + rs 1:05 1:25

1 1 0:20 4 5

5. (25) Consider the benchmark two-period model with consumption only. Assume that there is uncertainty on future output so that ( Y1 + with probability 1/2 Y2 = Y1 with probability 1/2 2

Also assume that

= 1=(1 + r) and that the utility function is ln C1 + E1 [C2 ]

a) (15) What is the impact of " on the current account in this case?C1 ;C2

max

ln C1 + E1 [C2 ] B1 C1 ) C1 ) + (1 + r)(Y1

subject to

C1 = Y1
H C2 L C2

= Y1 + + (1 + r)(Y1 = Y1

Set up the Lagrangian replacing E1 [C2 ]: L = ln C1 + f0:5[Y1 + + (1 + r)(Y1 The …rst order condition w.r.t. C1 reads 1 = [0:5(1 + r) + 0:5(1 + r)] C1 , C1 = 1 Plugging this result in the current account identity, we obtain CA1 = B1 = Y1 = Y1 C1 1: C1 )] + 0:5[Y1 + (1 + r)(Y1 C1 )]g...