14.02 Quiz 2 Solutions
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).
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.
If the US dollar is expected to depreciate, then Ee>E. So the interest parity condition, i = i* + (Ee-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.
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.
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.
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. Ee(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.
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).
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.
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.)
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).