**14.02 Quiz 2 Solutions**

- TRUE

Under perfect capital mobility, the
interest parity condition must hold: i = i* + (E(e)-E)/E. Each of the variables on the right hand side
is fixed or exogenous under fixed exchange rates, so the domestic interest rate
is determined and the government is not free to choose it. Full credit *may* be given for arguing that, under a credible fixed exchange rate
regime, the expected exchange rate is equal to the exchange rate so that the
interest parity condition implies that the domestic interest rate is equal to
the foreign interest rate. (You should
have made the assumption of credible fixed exchange rates explicit if you made
this argument.) Finally, it is not
correct to assume that the country is the ‘lead country’ and hence it can set
its interest rate and everyone else has to follow. This is because, first, one should not make unwarranted
assumptions outside the model, and second, there does not have to be a ‘lead
country’ (this might make sense if you’re considering the US in an exchange
rate system with several Caribbean islands, but not if it’s a group of
similarly sized economies).

- TRUE

The domestic demand for goods is C + I + G,
the demand for domestic goods is C + I + G + NX. If NX = 0, or the trade deficit is zero, these are equal.

- FALSE

If the US dollar is expected to depreciate,
then E^{e}>E. So the
interest parity condition, i = i* + (E^{e}-E)/E, then implies that
i>i*. One could also argue that
foreign investors in US bonds must be compensated for the loss they will make
on the currency side of their transactions with a higher nominal interest rate.

- FALSE

This question is actually trickier than many
realized. A recession in a foreign
country is a fall in Y*. This results
in a drop in exports for the domestic economy, which lowers domestic income,
Y. But lower domestic income means
lower purchases of imports. The total
effect on net exports is *not* ambiguous, however. If the import effect outweighed the export
effect, then NX would rise, but this would imply that Y also rises (and that
the only change in the model is the fall in Y*), contradicting the assumption
that Y fell causing Q to fall. Thus the
fall in Y* causes a decrease in both Y and NX.

- TRUE

A depreciation of the currency is consistent
with a fall in the interest rate (the arbitrage equation is downward
sloping). A monetary expansion would
cause a decrease in i, but it would also have the effect of increasing Y (as we
move along the IS curve). Similarly, a
fiscal contraction would cause a decrease in i, but only with a decrease in
Y. A combination of these two policies,
however, can lower the interest rate, depreciating the currency, without
changing Y.

- TRUE

This question is about *overshooting*,
which is covered in the appendix to chapter 21. The increase in the interest rate generated by a contractionary
monetary policy will attract investment to the domestic economy. This causes an appreciation of the currency,
i.e. a decrease in the exchange rate.
But this only tells you the direction of the effect on the exchange
rate, not the magnitude of the effect. Arguing that if the exchange rate is
higher for longer, more investment will be attracted, so the effect is bigger
is not acceptable. Rather, the
magnitude of the effect is determined by the arbitrage equation: the expected
depreciation of the currency *in each year
of the contraction* must be equal to the difference in domestic and foreign
interest rates. So the current
appreciation is equal to the number of years the monetary expansion is expected
to last times the difference in interest rates. (To see this from the arbitrage equation, consider that if the exchange rate is expected to return to
its long-run level at time t+2, and the currency is going to depreciate by, say,
2% from t+1 to t+2, then you expect the exchange rate to be 2% lower at time
t+1 than the long-run level, i.e. E^{e}(t+1) changes. But then for the currency to depreciate 2%
from t to t+1, the exchange rate must now be (approximately) 4% lower at time t
than its long-run level.) A longer
contraction will thus result in a greater current appreciation. See the text for the graphs and additional
explanation.

Additionally, please note that a contraction
is a sudden event: the money supply is moved from one level to another
quickly. The duration is the amount of
time before the money supply is returned to its pre-contraction level, not the
amount of time it takes to get to the lower level.

- FALSE

A depreciation will cause an immediate decrease in net exports. The Marshall-Lerner condition says that a depreciation will cause net exports to rise, but this is only after both prices (the exchange rate) and quantities (X and Q) have adjusted. In the very short run, quantities are fixed so the rise in the exchange rate causes net exports to fall before they rise since NX = X(E) - EQ(E).

** **

*(3 points)*LM: 295=Y-50*i; this is an upward-sloping line in the Y-i space. The interpretation of this equation is that it represents equilibrium in the money market. There are no differences r/e the closed economy; equilibrium is driven by liquidity need for transactions. Since you only need domestic currency for liquidity, openness should not (significantly) affect the money market.

*(4 points)*Goods market equilibrium is Y=C+I+G+NX, where demand is equal to supply of goods. The difference between the closed and open economy is that you have to add net exports, which introduces the real exchange rate and foreign output as other variables that influence demand. Net exports are increasing in output, which decreases the feedback (multiplier) effect.

Note: “solving” this model for the closed economy (with the same numbers) gives a “negative” multiplier; doing this alone is not a complete answer to the question of the difference between the closed and open systems.

*(5 points)*A complete answer to this question must begin with stating the returns on domestic bond investment, (1 + i), and foreign bond investment, (1/E_{t})(1 + i*)(E_{t+1 }). Answers should equate the two, get the precise formula; then state the convenient (approximate) form: i = i* + (E^{e}_{t+1 }- E_{t })/E_{t}. The graph is a downward-sloping curve in the i-E space.

*(5 points)*The IS curve combines the goods market and interest parity relations: Y=0.8*Y+92-20*i-30/E=0.8*Y+92-20*i-30-30*i=30*i^{*}=0.8*Y+65-50*i, so Y=325-250*i. The graph is downward sloping in the Y-i space. The interpretation is that the equation shows output for a given interest rate, consistent with both interest parity and goods market equilibrium. Higher interest rates depress investment, and appreciate the currency and thus depress net exports. Both effects generate a decrease in demand, which then gets multiplied and translates into smaller output. The distinctions between open and closed are the different multiplier (smaller in the open economy) and a second interest rate channel (through the exchange rate and net exports.)

Note: if you answered with an IS curve that did not include E substituted in (i.e. holding E constant), and used this expression, you may also receive full credit. You must in this case, however, explicitly worry about “second order shifts” of the IS curve in the next exercises (G changing so IS moves, but then E changes which moves IS again, so that net effect is either larger because the IS moves in the same direction, or may be smaller, etc.)

*(12 points)*With a fiscal expansion, higher G means increased demand for any level of the interest rate, so the IS shifts out. This means higher output, higher interest rates (because the money supply is fixed, so interest rates must increase to make people happy with their existing cash holdings but more income), thus an appreciation (higher interest rates here, so the country must have a depreciation by tomorrow – this implies an appreciation today). The effect on investment is ambiguous, since higher output increases I but higher interest rates decrease I. For net exports, higher Y decreases NX, higher i (via lower E) also has a negative effect, so NX goes down.

For a monetary expansion, higher M implies lower interest rates for any level of output. The LM curve shifts out. Lower interest rates boost I and NX (moving along the IS curve), so we have higher Y, lower i and thus higher E (depreciation) eventually. Investment is higher, NX is unclear (Y effect vs. E effect).

*(7 points)*The government can accomplish this goal with a policy mix of fiscal contraction and monetary expansion. In this case, the LM shifts out and the IS shifts in, keeping Y fixed. This increases E, so the only effect on NX is due to higher E: NX increases.

*(6 points)*In our model, the government has M, G and T as policy tools. However, G and T have the same effect on everything (but C), so it is as if in fact we have only two instruments. To achieve three targets, this is not, in general, enough. In reality (and this can be incorporated into the model), you can influence net exports through export subsidies, import tariffs, etc. – any third policy tool that has a direct effect on NX would do.

* *

**QUESTION 3**

*(10 points)*With a fiscal expansion: G goes up, so the IS must shift out (there is higher demand for any fixed i). To maintain i=i^{*}, the country must have an increase in M as well (by the Central Bank (CB), or by investors selling foreign currency to the CB and getting domestic currency in return). This results in the LM shifting out, keeping i fixed. So output goes up, i is unchanged, but NX must have gone down.

*(10 points)*With a devaluation, for any level of i, NX is higher, so demand and hence output are higher. This means that the IS shifts out. Again, this shift in the IS comes with a shift in LM. This movement in the LM might come from an open market operation (changing B) or automatically (by changing R, foreign currency reserves). Y is higher, i is the same, and NX should also be higher: the E effect dominates the Y effect. (Precise argument for bonus points: using the ZZ and DD lines, one can show that NX must go up because DD is flatter than the 45^{o}line.)

*(10 points)*If there is a speculative attack, i>i^{*}follows from the interest parity condition. This means that the CB must raise interest rates – i.e., contract M. Again, this may be achieved either by a contractionary open market operation (changing B, not R) or automatically (decreasing R). Here the CB has more motivation to use the open market operations since it does not want to let reserves fall dramatically. This drop in M would imply a movement along the IS curve, higher interest rates, and lower output (via depressed investment). If, for this (or any other) reason, the CB is not ready to increase i fully (not selling enough bonds), then investors would buy the CB’s foreign currency reserves, and pay with domestic currency in return. This gradual process would continue until either expectations are cooled down (the crisis is over, with lower reserves but i back to i^{*}), or the country has a devaluation, either because reserves actually run out or the government abandons its fixed E.