Exchange rate overshooting
a. Suppose there is a permanent 10% increase in M in a closed economy. What is the effect on the price level in the medium run? (Hint: If you need a refresher, review the analysis in Chapter 7.) In a closed economy, we said that money was neutral because in the medium run, a change in the money stock affected only the price level. A change in the money stock did not affect any real variables. A change in the money stock is also neutral in an open economy with flexible exchange rates. In the medium run, a change in the money stock will not affect the real exchange rate, although it will affect the price level and the nominal exchange rate.
b. Consider an open economy with a flexible exchange rate. Write the expression for the real exchange rate. Suppose there is a 10% increase in the money stock and assume that it has the same effect on the price level in the medium run that you found in part (a). If the real exchange rate and the foreign price level are unchanged in the medium run, what must happen to the nominal exchange rate in the medium run?
c. Suppose it takes n years to reach the medium run (and everyone knows this). Given your answer to part (b), what happens to Ee t+n (the expected exchange rate for n periods from now) after a 10% increase in the money stock?
d. Consider equation (21.5). Assume that the foreign interest rate is unchanged for the next n periods. Also assume, for the moment, that the domestic interest rate is unchanged for the next n periods. Given your answer to part (c), what happens to the exchange rate today (at time t) when there is a 10% increase in the money stock?
e. Now assume that after the increase in the money stock, the domestic interest rate decreases between time t and time t + n. Again assume that the foreign interest rate is unchanged. As compared to your answer to part (d), what happens to the exchange rate today (at time t)? Does the exchange rate move more in the short run than in the medium run?
The answer to part (e) is yes. In this case, the short-run depreciation is greater than the medium-run depreciation. This phenomenon is called overshooting and may help to explain why the exchange rate is so variable.
