Understanding the Impact of Interest Rates and Income on Exchange Rates - Prof. Harvey E. , Assignments of Economics

Download Understanding the Impact of Interest Rates and Income on Exchange Rates - Prof. Harvey E. and more Assignments Economics in PDF only on Docsity! Spring 2004 Harvey Lapan Econ 455 Answers - Problem Set 5 (extra credit) 1. The Current Account Balance measures the difference between exports and imports (including goods and services, net investment income and unilateral transfers). A deficit signifies that imports exceed exports and means that there is net foreign borrowing by domestic residents; a surplus indicates net foreign lending. As an identity: X-M = Y-(C+I+G) = + (T-G) - I pS where symbols were defined in class. In particular, a balance of trade surplus (deficit) indicates that domestic saving (the sum of private saving ( ) and government saving (T-G)) exceeds (is less than) investment. pS a) A Current Account deficit is neither bad nor good, per se. As noted above, a deficit implies low current savings or high current investment, and hence borrowing. What it does mean is that Net Foreign Indebtedness will increase, and this debt will (probably) have to be repaid in the future. However, sometimes it makes sense to borrow against future income - for example, a poor country that knows its oil revenue will increase in the future due to current exploration or, by analogy, a college student who knows her (his) income will increase in future years. Furthermore, if the current borrowing is used to increase investment and if this investment has a higher return than the interest rate on the borrowing, then both current and future consumption could be increased. Thus, the issue is not whether there is a deficit, but whether the funds are being "wisely" spent. b) A US Current Account deficit occurs, as an identity, when US absorption (C+I+G) is high relative to income, or savings ( +T-G) is low relative to investment. Policies that would help reduce the deficit include policies that would increase income or lower spending; (or increase saving or reduce investment). However, that does not mean these policies are good simply because of to their effect on the current account. For example, if income can be increased (there is unemployment), that should be done regardless of the Current Account deficit. And these policies interact - e.g., a policy that reduces investment (an investment tax) may also reduce income. pS c) It is true that Congress has passed laws which would impose tariffs on goods from countries that run large current account surpluses with the US; these laws would come in force if the US deficit exceeded a certain threshold. The question is: what would such tariffs accomplish? They certainly would reduce imports but - from the Current Account identity - the deficit can only decrease if the tariffs lead to reduced US spending or higher income. If there were large unemployment, then possibly the tariffs would redirect spending to domestic goods and increase employment and income (assuming foreigners do not retaliate). However, if the country is near full employment, then the only way the tariff can reduce the deficit is if it reduces domestic spending. There is little reason to expect it to accomplish that. The above discussion is with respect to across the board tariffs. Raising tariffs on one country is likely to be even less effective in decreasing the overall deficit as imports will just come from other foreign suppliers. Thus, the increased tariff on imports from Japan could reduce our deficit with Japan but would almost surely increase our deficit with other countries and have little impact on the overall deficit. 2. The following Table lists some (current) exchange rates. Answer all questions as if there were no arbitrage costs. Currency Exchange Rate (as US$ per foreign currency, except for Japan) Canada (dollar) $.749/Can$ Euro 180-day forward rate $1.193/Euro $1.181/Euro British Pound $1.818/£ Japanese Yen 180-day forward rate 106.9¥/$ 105.8¥/$ a) The spot rate of the Yen in terms of the British pound can be determined as follows: determine how many yen per US dollar, how many US $ per British pound and multiply: From the table: (106.9¥/$)x($1.81/£)= 193.49¥/£ b) The semi-annual US interest rate is 1.5%; since the forward rate of the Euro is below the spot rates, you will require a higher interest rate on Euro assets to be willing to hold them. From the formula in class: ( )( )us uk f s sR R E E E= + − → ( ).015 .012 1.193 .01uk ukR R= + − = − → or (semi-annual interest rate). The forward rate on the yen is at a premium compared to the spot rate (i.e., the yen increases in value) so Japanese interest rates should be lower than US rates. Thus: .015 .01 .025ukR = + = 2.5%ukR = ( )( )$/¥ $/¥ $/¥ 100 1.03f s sE E E− ⋅ ≅ , so: . 1.50 1.03 0.47%JR = − = c) Suppose your research department forecasts that, in 180 days, the spot price of the Euro will $1.25. On the basis of this information, you buy 1 million Euro forward. i. If your research department is correct, you will make $.069 per Euro, or $69,000 from this speculative purchase. ii. If enough people have the same beliefs (or your forward purchases of the euro are large enough), this will cause the forward rate of the Euro to appreciate. As a result of this appreciation in the forward rate, through covered interest arbitrage people will wish to buy Euros spot, or will increase investment in Euro interest bearing assets (decrease holdings of $ interest-bearing assets). Consequently, one of the following must happen: US interest rates increase, Euro interest rates decrease, and/or the spot Euro appreciates. Further, movements in either interest rate (as indicated) will cause the spot Euro to appreciate (unless the European Central Bank (ECB) increases the money supply). Hence, speculation (beliefs) on forward rates will affect spot rates. 3. Use the covered interest arbitrage relationship to explain how the following are likely to affect the spot $/Euro rate. In answering, explain your reasoning (and, in particular, what variables you are holding fixed): 2 part (c), we know that, ceteris paribus, higher European income levels will increase the demand for Euros and thus cause the Euro to appreciate (dollar to depreciate) in 2005. Hence, if people believe this forecast for 2005, they will expect the $ to depreciate in 2005 - meaning the current forward rate of the $ will depreciate. Through covered interest arbitrage, this will make US securities look less attractive (compared to foreign securities), meaning U.S. interest rates will rise or the spot rate of the $ will depreciate (both will happen: the increase in US interest rates causes the spot depreciation). Thus, in this case higher U.S. interest rates are associated will a weaker (depreciating) dollar. On the other hand, for example, a temporary decrease in the U.S. money supply will cause higher interest rates and a (temporary) appreciation of the dollar. Thus, you cannot say that higher interest rates lead to an appreciation (or depreciation) of the dollar because interest rates, like exchange rates, are endogenous - determined by supply and demand. You have to explain why interest rates change in order to predict how the exchange rate will change (note the difference in the two examples cited). Also note that the current exchange rate depends on current income and money supplies, and current forecasts of future income levels and money supplies. 5. Using the aggregate demand-aggregate supply model of Chapter 16: a) Show how a permanent increase in the money supply affects the exchange rate and income levels in the short run and in the long run. The key here is identifying what variables can change, and what are fixed, in each “time period”. By assumption, in the short run prices are fixed, but real income levels can change; in the long run, prices may adjust, but real income will equal its full employment level (and thus is not affected by policy). Working backward, in the long run prices and the exchange rate will “increase” (depreciate) in proportion to the money supply increase, but income levels and interest rates will not change. Thus, for the long run: P E M P E M ∆ ∆ ∆⎛ ⎞ ⎛ ⎞ ⎛= =⎜ ⎟ ⎜ ⎟ ⎜ ⎝ ⎠ ⎝ ⎠ ⎝ ⎞ ⎟ ⎠ In the short run, prices are fixed; thus, interest rates must change (decrease) to absorb the additional money supply. In addition, the forward exchange rate depreciates; thus, the spot exchange rate must depreciate, and by more than in the long run (because of the temporary decrease in the interest rate due to the price rigidity). The lower interest rate (in the short run) and depreciation of the currency (implying a short run depreciation of the real exchange rate) increases the demand for domestic goods, implying that the money supply increase temporarily increases income. 5 Y E A A Y* Y* D D A’ A’ K D* D* L A* A* M In the figure above, K represents the original equilibrium, and Y* represents the equilibrium (full employment) level of income. Given prices, the money expansion shifts the money market curve (AA) out to (A’A’), reflecting the short run depreciation of the currency. Given prices, this depreciation makes domestic goods relatively cheaper, and leads to higher income in the short run. The point L marks the short run impact of the monetary expansion. Over time, prices of goods increase; this shifts the A’A’ curve downward, to A*A* (since higher prices reduce real money balances) and shifts the aggregate demand curve DD upward to D*D* as, given the exchange rate, higher prices reduce demand for domestic goods (through the current account). Thus, in adjusting to the long run equilibrium, the exchange rate appreciates and income declines (relative to the short run effect); the long run equilibrium is at M. The dotted line from L to M shows this adjustment, and reflects the “overshooting” phenomenon discussed in Chapter 14. b) Show how a temporary increase in government spending affects the exchange rate and income level in the short run. What is the short run effect of a permanent increase in government spending? Why? Again, the distinction between short run and long run depends on whether prices (or income) are held fixed, whereas the distinction between temporary and permanent depends on whether the forward exchange rate changes (which is crucial in determining how the spot rate and interest rates change). With a temporary increase, the forward exchange rate does not change. The increased fiscal spending increases demand and hence leads to an appreciation of the real exchange rate; since prices are fixed, this must come about due to a spot appreciation of the nominal exchange rate (E). In the money market, the spot appreciation, coupled with an unchanged future exchange rate, means domestic interest rates rise (as they must so that money demand accommodates the increased income levels). This is all shown in the diagram below; the AA curve does not shift (since prices, money supply and the forward exchange rate are all fixed), while the DD curve 6 shifts down due to the fiscal expansion; the equilibrium temporarily moves from L to M . The temporary policy leads to a (temporary) increase in income and appreciation of the exchange rate. Y E A A D D D’ D’ L M Finally, a permanent increase in fiscal policy will cause a permanent increase in the real exchange rate. In the long run, real income will be unchanged (by the assumption of full employment) and the nominal interest rate will be unchanged (since, in the long run, spot and forward exchange rates will be equal). But, from money market equilibrium, this implies that the long run domestic price level will not change from its current level (otherwise real money balances would change, which would be inconsistent with money market equilibrium). Thus, the long run impact of the permanent fiscal expansion is to lead to an appreciation of the nominal (and real) exchange rate, but no change in the price level or in income levels. But since price levels do not change, the short run and long run impacts are identical! Permanent fiscal policy has no impact on equilibrium income, even in the short run. This result can be represented in a diagram like that above; the only difference is, since the forward rate appreciates, the AA curve shifts down (to A’A’). And since the short run and long run are the same, the new equilibrium income must be the same as the old equilibrium. Hence, in the diagram, the equilibrium jumps immediately from L to N. 7