Question

Describe the consequences of a permanent decrease in the US Money Supply for the nominal exchange rate and for the US interest rate, in the short run as well as over time and in the long run. Draw time path plots for real money balances in the US, the nominal exchange rate, and the interest rate. Explain how your results relate to the idea of “exchange rate overshooting,” in no more than one paragraph.

Answer 1

We assume flexible exchange rates and perfect capital mobility to depict consequences of decrease in the money supply.

• Suppose, Fed decreases the US Money supply permanently. Now in short run, prices are sticky so goods market will adjust slowly and prices won't change immediately. However, financial market will adjust quickly. The LM Curve will shift left to LM' and at point e' interest rate rises. This is also called liquidity effect.

• The decease in MS induces a current appreciation of the US$, so the nominal exchange rate decreases.
• Given the interest rate parity and rise in interest rate, there shall be decrease in Ee and future depreciation of the exchange rate.
• In order to generate an expected depreciation, the currency over-appreciates (i.e. overshoots) in short-run vs. it's long-run level.
• The currency appreciation, together with ΔP = 0 in the short-run, implies that q falls, and IS shifts to the left to IS'
• The shifts in IS and LM shift aggregate demand, which equals short-run aggregate supply. There is an decrease in output produced at point e1.
• Deficit in the aggregate demand reduces the prices in the US economy. Consequently, the decreased price level increases real money supply so the LM shifts back to its initial equilibrium. The interest rate falls to its initial position, and as this happens the domestic currency depreciates.
• The decreased prices, together with the currency depreciation, improves the U.S. economy's competitive advantage in the goods market (so the change in q is a sum of change in E and P), and IS shifts back to its initial level at point e.
• After so many adjustments, we finally reach the initial real equilibirum (Point e) with reduced prices and appreciated nominal exchange rate.

We can show above adjustment with time path which are similar to Exchange overshooting model.

• Suppose, Fed decreases the US Money supply by 10% from $100 billion to $90 billion and keeps it at this level permanently.
• As per above, the U.S. interest rate will rise immediately - say from 10% to 11% at time t0.
• Now, as per interest rate parity the interest rates in US are higher than the Rest of the world interest rate. Consequently, investors will increase demand for the US dollar to purchase US bonds. The immediate impact would be appreciation or decrease in the exchange rate. We assume dollar immediately appreciate by more than the 10 percent - say from $1 to $0.84 in the short run, so that in the long run it reaches long-run equilibirum of $0.90 by slow depreciation.
• The above happened due to the uncovered interest parity condition which is explained by equation or . The UIP says that interest differential between two countries will always be equal the expected change in the exchange rate between two currencies.
• We can see that dollar appreciated more in the short run i.e. by 16%. However, it depreciate by 6% in the long run to remove excess appreciation at time t0. This is also necessary to hold PPP theory

This explanation is similar to the Dornbusch exchange rate overshooting model as we can clearly see that exchange rate overshoots due to the price expectations. Though prices were sticky and couldnot adjust quickly in the short run, their expectations changed quickly. Thus, explaining volatility in the exchange rates.