Control 3 2017 - 02

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Controle 3 - Answers
Caio Machado
Instituto de Econoḿıa
Pontificia Universidad Católica de Chile
Macroeconomia II, 2017
The uncovered interest rate parity condition means that interest rates are
equal across countries.
FALSE. The uncovered interest rate parity (in its approximated linear form)
says that
it = i∗ −
E et+1 −Et
Et
Thus, if agents expect an appreciation or depreciation of domestic currency,
the interest rates may be different across countries.
According to the Mundell-Fleming model, a fiscal expansion, all other
factors equal, tends to increase net exports.
FALSE.
• i does not change, so the exchange rate does not change.
• Higher output leads to higher imports, worsening the trade balance.
Graphically, ZZ shifts up.
DD
ZZ ′
ZZ
0
NX
Y
Y
NX
Z
A
A′
A
A′
45o
If financial investors expect the dollar to depreciate against the yen over the
coming year, one-year interest rates will be higher in the United States than
in Japan.
TRUE. Using the uncovered interest rate parity
it = i∗t −
E et+1 −Et
Et
Thus, if E
e
t+1−Et
Et < 0, the US interest rate will be the Japanese interest rate
plus a positive number, and therefore is higher than the Japan interest rate.
The J-Curve predicts that a real depreciation leads initially to an
improvement and then to a deterioration of the trade balance.
FALSE. It is the exact opposite.
According to the Mundell-Fleming model, an increase in domestic demand
leads to an increase in domestic output and an improvement of the trade
balance.
FALSE. For the same reason that an increase in G leads to a worsening of
the trade balance.
Consider an open economy characterized by the following equations:
C = c0 + c1 (Y −T )
I = d0 + d1Y
IM = m1Y
X = x1Y ∗
where, C denotes consumption, Y denotes the domestic income, I denotes
investment, IM and X are the quantity of imports and exports, respectively.
The parameters m1 and x1 are the propensities to import and export.
Assume that the real exchange rate is fixed at a value of 1 and treat foreign
income, Y ∗, as fixed. Also assume that taxes, T , are fixed and that
government purchases, G , are exogenous (i.e., decided by the government).
1. Write the equilibrium condition in the market for domestic goods and
solve for Y .
Y = c0 + c1 (Y −T ) + d0 + d1Y + G + x1Y ∗ −m1Y
Y = 11 − c1 −d1 + m1
[c0 − c1T + x1Y ∗ + d0 + G ]
2. What is the government spending multiplier? (Assume that
0 < m1 < c1 + d1 < 1)
The government spending multiplier is
1
1 − c1 −d1 + m1
3. What is the change in net exports when government purchases increase
by one unit?
Let NX = X − IM = x1Y ∗ −m1Y (remember that the real exchange rate is
one). The, since output increases in 11−c1−d1+m1 when government
spending increases in one unit, the change in NX is
∆NX = −m1︸ ︷︷ ︸
dNX/dY
 11 − c1 −d1 + m1︸ ︷︷ ︸
dY /dG

4. Suppose the government decides to close the economy, not allowing
trade with the rest of the world (i.e., IM = X = 0). Find the government
spending multiplier. Is it larger or smaller than the multiplier you found in
item 2? Explain, in words, why the two multipliers are different.
The equilibrium condition becomes
Y = c0 + c1 (Y −T ) + d0 + d1Y
And therefore
Y = 11 − c1 −d1
[c0 − c1T + d0 + G ]
And thus the multiplier is 11−c1−d1 . Since m0 > 0, it is larger than the
multiplier in item 2. The reason is that in the open economy part of the
increase in demand caused by the increase in G (and the subsequent
increases in income) do not become demand for domestic goods, but
demand for foreign goods.
1. Using the uncovered interest rate parity, briefly explain why under a fixed
exchange regime the central bank loses control over monetary policy.
The interest parity says that:
it = i∗t −
E et+1 −Et
Et
But under a fixed exchange regime, E et+1 = Et = E . Thus, the exchange
rate parity becomes it = i∗t meaning that the central bank cannot choose
the interest rate.
2. Suppose a country operates under a fixed exchange rate regime and has
perfect capital mobility. At date t, the central bank spends 100 units of
local currency buying domestic bonds in an open market operation.
Suppose that between dates t + 1 and t financial investors had time to fully
react to the open market operation.
(a) Is the monetary base at t + 1 larger, equal or smaller than the monetary
base at date t?
(b) Did the central bank balance sheet change between dates t + 1 and t?
If yes, how did it change?
(a) The monetary base is the same. When the central spends $100 buying
bonds, it initially increases the monetary base lowering domestic interest
rates (i < i∗). Noticing the low domestic interest rates, investors start to
exchange domestic currency for foreign currency to invest abroad. This
forces the central bank to sell its reserves, decreasing the monetary base
back again. He keeps selling reserves until the change in interest rate is
totally offset, which happens when the monetary base return to its previous
level. Since all this adjustment is quick and happens between t and t + 1,
the monetary base does not change between those dates.
(b) It changed. Now the central bank has less reserves and more bonds.