International economics 6th edition phần 8 pdf

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International economics 6th edition phần 8 pdf

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very little ability to manage its own monetary affairs. Although they were not followed precisely, 2 the formal system is based on two rules: 1 National currencies are to be backed rigidly by gold; that is, the stock of base money is determined solely by the stock of gold held by the government or the central bank. The central bank therefore has no monetary policy discretion; it must create a money supply that is based on its holdings of gold. 2 Gold is to be the only foreign exchange reserve asset; that is, payments deficits cause a parallel loss of gold, and vice versa. These two rules mean that the domestic money supply is determined by the balance of payments (and by the gold-mining industry). A payments surplus causes an inflow of gold and a parallel increase in the stock of base money. A deficit causes gold to flow out, and the money supply must fall proportionally. This is analogous to the monetarist world described in the previous chapter, except that sterilization cannot occur. The money supply must be allowed to fall when a country has a payments deficit and to rise in the case of a surplus. These changes in the money supply produce payments adjustment through three linkages. In the case of a payments deficit, the resulting decline in the money supply: 1 raises domestic interest rates, which attracts capital inflows, thereby improving the capital account of the balance of payments; 2 puts downward pressure on the price level, thereby improving price competitiveness. Exports should rise and imports fall, improving the current account; 3 puts downward pressure on economic activity and on real incomes. Imports should fall by the marginal propensity to import times the decline in domestic incomes. A reduction in the money supply is recessionary and discourages imports, thereby improving the current account. The first two of these linkages are not particularly difficult or painful; the third, however, is unpleasant or worse for deficit countries. To the extent that wages and prices are down- ward rigid or sticky in the short run, which appears to be the case in modern industrialized economies, the second linkage becomes largely inoperative, necessitating greater reliance on the third. This payments adjustment mechanism means that countries with payments deficits are likely to be forced into recessions and then be unable to use an expansionary monetary policy to escape such downturns. For surplus countries, the same three linkages operate in the opposite direction. Interest rates fall, worsening the capital account, and prices rise, a condition that hurts the trade account. Output and incomes rise, thereby increasing imports. If the economy is fully employed, however, output and real incomes cannot rise. Thus inflation can become serious as the money supply rises without the central bank being able to control it. This system means that the central bank has no policy discretion in the management of the money supply. The recessionary implications for deficit countries, and the prospects for inflation in the case of a surplus, suggest why this system was abandoned. In the late 1970s and early 1980s a few “gold bugs” argued for a return to this approach, but this discussion has now largely ended. The pre-1914 gold standard has the additional disadvantage of being subject to shocks from the gold-mining industry. When major ore discoveries are made, the government or central bank is required to purchase gold and issue new money, resulting in inflation. Spain 16 – Adjustment with fixed rates 353 experienced disastrous inflation in the sixteenth century when its conquest of Latin America produced huge inflows of gold. Dollarization or Euroization The specie flow mechanism may seem to be an historic relic, but is remains quite relevant today, and may become more so in the near future. A number of small countries have always lacked their own currencies and have instead used the currency of another country, and there is a modest trend toward more countries adopting this approach. Panama and Liberia have always used the US dollar, and a number of small island countries in the South Pacific use Australian or New Zealand money. Kosovo and Montenegro are now largely or entirely “euroized,” in that almost all circulating currency is euros, and most bank accounts, loans, and other transactions are denominated in euros. Ecuador recently abandoned its national currency and is now dollarized, and El Salvador is in transition to that circumstance. A balance of payments deficit in such a country means that there is more money flowing out of the country than is flowing in, and there is no central bank to sterilize the outflows and restore the previous money supply level. A payments deficit reduces the money supply in the amount of the deficit, producing the specie flow adjustment process with the same three linkages discussed earlier. A payments deficit increases the money supply by the amount of the surplus, producing the same adjustment process in the opposite direction. 3 Dollarization or euroization requires that the country start out with sufficient foreign exchange reserves to buy back from the public all outstanding base money. Foreign exchange reserves are turned into cash which is transported (with considerable security efforts) into the country and the local currency is simply bought back from the populace. Banks accounts and loans are denominated in dollars or euros, with reserves against deposits also being held in dollars. In adopting this approach, the country gives up the profit or seignoriage that comes from running a central bank and must live with the monetary policy adopted by the country whose currency it uses. Monetary policy in Kosovo is determined by the Governing Council of the European Central bank, and the policy prevailing in Ecuador is settled by the Federal Open Market Committee of the Federal Reserve System. Seignoriage for the two countries goes to the ECB and the Federal Reserve System. One major disadvantage in the use of a foreign money, or with the operation of a currency board which is discussed below, is the lack of an apparent lender of last resort for commercial banks. One of the original and important functions of a central bank is to provide prompt loans to solvent commercial banks that are experiencing liquidity problems. The San Francisco Federal Reserve Bank cannot be expected to lend to banks in Quito, and banks in Kosovo are unlikely to find an accommodating loan officer at the European Central Bank in Frankfurt. Countries that dollarize or euroize must set up separate financial institutions to make such loans, and arranging adequate funding for such entities may be difficult. One might wonder why a country would even consider giving up its own currency for the dollar or the euro. Often countries that do so have had a very poor history of economic and monetary policy management, and adopting a foreign money is a means of gaining credi- bility. Ecuador is a prime example of this circumstance; before it dollarized, its currency was held in very low regard by its citizens, and its economy was in crisis. Dollarization, although painful, calmed the economy and allowed a recovery to begin. When a country has a long and firmly established history of mismanaging monetary policy, maybe it should give up the effort and let someone else provide a policy for it. Argentina would then appear to be an obvious candidate for dollarization, but its recent debt crisis drained its 354 International economics foreign exchange reserves so thoroughly that it may lack sufficient dollars to undertake the effort. Currency boards Currency boards, which have recently drawn increased attention among policy makers and economists, create another situation in which balance-of-payments adjustment occurs through the specie flow mechanism. A currency board resembles a central bank with one very large difference: it is forbidden from purchasing assets other than foreign exchange reserves. It is prohibited by law from lending to the government or purchasing other domestic assets. This means that changes in foreign exchange reserves cannot be sterilized through purchases or sales of government debt. A loss of foreign exchange reserves, resulting from a balance-of-payments deficit, must create a parallel reduction in the stock of base money. If the reserve ratio is unchanged, which is supposed to be the case, a proportionate reduction in the money supply must occur. The money supply is regulated by changes in foreign exchange reserves that result from payments imbalances, and adjustment occurs through the specie flow mechanism. In the past currency boards were maintained primarily by small countries with historic ties to the United Kingdom, such as the members of the United Arab Emirates, or by British dependencies. During the 1990s currency boards have been adopted in some high-inflation developing countries, such as Argentina, and in transition economies, such as Estonia and Bulgaria. In the latter two cases, such arrangements were very successful in bringing down what had been high rates of inflation. Although a currency board would appear primarily to be a restraint on monetary policy, in practice it represents a more severe constraint on fiscal policy, because such a replacement for a central bank makes it impossible for the government to force the central bank to monetize its budget deficits. As was noted in the previous chapter, central banks in many developing and transition economies have little or no policy independence, but instead must create money to finance government deficits. In some underdeveloped countries, as was also noted earlier, the government actually orders the central bank to print paper money in the amount of its projected budget shortfall, which has typically meant large increases in the money supply and rapid inflation. A currency board is intended to absolutely end such behavior. A currency board is a means of gaining credibility for a central bank and a currency which have had little in the past, because of high inflation driven by the monetization of govern- ment budget deficits. If the public understands that domestic money is backed by foreign exchange reserves rather than by domestic government debt, people will become willing to use and hold the local currency, reversing the common use of dollars or euros as a local currency. Currency boards work best in small open economies where modest changes in the money supply will produce relatively prompt payments adjustment and where the foreign exchange requirements for financing such an enterprise are not prohibitive. In the case of Bulgaria, for example, the IMF strongly encouraged the creation of such a board and lent the foreign exchange which allowed it to begin operations. When such an arrangement was suggested for Indonesia, however, the IMF opposed such a decision because massive amounts of foreign exchange would have been required to finance its operations, and because the Indonesian economy is large and not very open, meaning that the specie flow mechanism would have been particularly painful. Suggestions that a currency board be adopted in Russia are likely 16 – Adjustment with fixed rates 355 to fail for the same reasons: the economy is too large and insufficiently open, and the financial requirements of such a board would be excessive. Currency boards may be set up, however, in more of the small countries which emerged from the USSR if it becomes clear that fiscal and monetary discipline cannot be realized through any other means. The Estonian and Bulgarian currency boards have reportedly operated thus far in a traditional manner with fixed commercial bank reserve ratios, which result in domestic money supplies which rise and fall proportionately with changes in foreign exchange reserves, thereby producing the classic specie flow adjustment process. Perhaps because they followed the rules closely, these currency boards have been successful. Argentina’s, however, collapsed in early 2002. The Argentinian board was reportedly somewhat more “creative” in finding ways to escape the intended constraints of the specie flow mechanism. Changes in reserve ratios for domestic commercial banks were sometimes used to offset changes in foreign exchange reserves, thereby allowing the money supply to remain unchanged despite balance of payments deficits or surpluses. As this and other means of evading the rules came to be understood by investors, confidence in Argentina’s currency board deteriorated. More importantly, the expected constraints on government budget deficits never materialized, and various levels of government (particularly the provinces) borrowed enormous amounts of money, with many of the loans denominated in dollars. As it became apparent that these loans could not be repaid, and that both fiscal and monetary policy were unsound, confidence collapsed and massive capital outflows quickly drained foreign exchange reserves. The fixed parity of the peso to the dollar had to be abandoned for a float which produced a massive depreciation. This created a broader finan- cial and political crisis, which remains unresolved at the time of this writing. If a currency board is to be successful, its rules must be followed fully, and it must produce constraints on fiscal deficits as well as on money supply expansion. Neither occurred in Argentina. 4 This same specie flow mechanism forces the balance of payments of a state or region within a country toward adjustment. We usually do not think of the balance of payments of Massachusetts, but there is one, and it must be adjusted when it is out of equilibrium. A deficit in the Massachusetts balance of payments means that residents of the state are making more payments to nonresidents than they are receiving from them. The stock of dollars held by Massachusetts residents must fall by the amount of that deficit. As checks are cleared against Massachusetts banks and in favor of out-of-state banks, the stock of member bank reserves in the local banking system declines, requiring a reduction of lending activity. A payments deficit reduces the money supply of a state, and imposes the same adjustment process as was described above for a country on the gold standard. The implications of this mechanism are often quite severe. When a state or region suffers a major export loss, the resulting declines in output and incomes are not limited to the export industry. The resulting payments deficit drains money out of the local economy and banking system, deepening the resulting economic downturn. Eventually, local wages and other costs of doing business decline sufficiently to attract new businesses, and a recovery begins. The migration of unemployed people out of the state reduces both purchases of imports and the demand for local housing, which lowers real estate prices, making the state more attractive for incoming businesses. A sharp decline in the textile and shoe industries in Massachusetts during the 1950s caused such an adjustment process, and the state economy did not fully recover for many years. Declining expenditures on national defense and weak markets for the state’s computer industry produced a similar process in Massachusetts during the early 1990s. The recent collapse of the dot com sector of the US economy means that the San Francisco area is now in the same unpleasant situation. 356 International economics 16 – Adjustment with fixed rates 357 Box 16.1 The IS/LM/BP graph as a route to understanding balance-of- payments adjustment A graphical technique that is widely used in domestic macroeconomics can be readily extended to an open economy framework. It allows a somewhat more rigorous, if still oversimplified, analysis of the effects of various policies designed to produce payments adjustment. For students who have had an intermediate macroeconomics course, the purely domestic portion of what follows will probably not be new, and even part of the international extension may be familiar. For those who have not been introduced to these graphs, an introduction follows. The IS/LM graph The domestic economy is modeled as a real sector and a market for money. The real sector is in equilibrium when I i = S, that is, when intended investment equals savings, which is the standard definition of equilibrium in a simple Keynesian model. The market for money is in equilibrium when MD = MS, that is, when the demand for money equals the supply. If both the market for goods and the market for money are in equilibrium, then Walras’s law implies that the market for bonds must also be in equilibrium. Thus to analyze equilibrium in the entire economy, we need consider only two markets, goods and money. Returning to the real sector, which is to be represented by the IS line, we find that savings is a positive function of domestic income (Y) through the marginal propensity to save. Intended investment (I i ) is a negative function of the interest rate (r), so: + S = F(Y) and – I i = F(r) The situation in which S = I i can then be represented as shown in Figure 16.1. Along IS, intended investment equals savings; therefore GNP is at its equilibrium level. To the left of IS intended investment is greater than savings, so GNP tends to rise. Interest rates are too low (which increases investment) or incomes are too low (which represses saving), resulting in the excess of intended investment over savings. The opposite situation holds to the right of IS. The economy automatically moves toward IS when it is out of equilibrium through changes in output up to the level of full employ- ment, beyond which there is inflation which raises nominal GNP. A movement from point A to point B illustrates the offsetting impacts of an increase in Y and a decline in the interest rate. Starting from equilibrium at point A, an increase in output and incomes causes an increase in savings, making it exceed previously intended levels of investment. If interest rates fell by ∆r, however, intended investment would rise to the new level of savings and the economy would be at point B. 358 International economics The slope of IS reflects the relationship between the size of the marginal propensity to save and the impact of changes of the interest rate on intended investment levels. If the marginal propensity to save was high or if intended investment was insensitive to changes in the interest rate, IS would be steep because a large change in interest rates would be required to offset the effect of a small change in incomes. A flatter IS would imply the opposite situation: that investment is highly sensitive to interest rates and/or that the marginal propensity to save is low, so that a large change in incomes would be required to offset the effect of a small change in the interest rate. Since this graph has only two dimensions, the effects of only two variables (Y and r) on the savings/investment relationship can be shown. If any other relevant factor shifts, the IS line moves. A more expansionary fiscal policy, for example, would shift it to the right, as would an increase in export sales caused by an economic expansion abroad. Either event would increase the level of GNP that was consistent with a given level of the interest rate, because domestic savings would have to rise relative to private domestic investment to make room for the larger government budget deficit or the stronger current account. With a government sector and with international trade, the savings investment identity becomes: I = S + (T – G) + (M – X) It should be remembered that in this identity I is actual investment, including unintended changes in inventories. This identity must be true, but intended investment equals the sum of the items on the right-hand side of the equation only when the economy is at equilibrium, that is, when intended investment equals actual investment, because there are no unintended changes in inventories. The market for money is in equilibrium when MD = MS, where the money supply is determined by the central bank. The demand for money is a positive function of income (the transactions demand for money, stressed by monetarists) and a negative r Y d r d Y A B S I S > I i I i > S Figure 16.1 Equilibrium in the savings/investment relationship. Intended investment equals savings along the IS line because as interest rates decline, investment rises, and as output and incomes increase, savings rise. The slope of IS reflects the relative sensitivity of intended investment to interest rates and of savings to increases in output and incomes. 16 – Adjustment with fixed rates 359 function of the interest rate under the assumption that money does not pay interest and that therefore the interest rate is the opportunity cost of holding money rather than bonds. This can be shown as +– MD = F (Y, r) MS = MS, meaning that the money supply is determined outside the model, i.e. by the central bank. MD = MS in equilibrium With a given money supply, which has been determined by the central bank, equilibrium exists in the market for money along the LM line shown in Figure 16.2. Starting from point A, an increase in the interest rate reduces the amount of money people want to hold, creating an excess supply of money. An increase in incomes of ∆Y would raise the transactions demand for money sufficiently to return the market to equilibrium with the pre-existing money supply. The slope of LM reflects the relative sensitivity of the demand for money to changes in incomes and in interest rates. A monetarist would believe that the role of income is far stronger and that the line is therefore very steep. A Keynesian would argue for a stronger role for the interest rate and would therefore believe that the line was flatter, particularly at low interest rates. Since only the level of national income and the interest rate are shown on the two axes, any other factors that affect the market for money cause the LM line to shift. An increase in the money supply, for example, would cause it to shift to the right, whereas a decision of people to hold more money at every level of GNP (a reduction in the velocity of money) would cause LM to shift to the left. r Y d r d y A B M L MS > MD MD > MS Figure 16.2 Equilibrium in the market for money. With a constant money supply, the market for money clears along LM. The demand for money is positively related to the level of output and negatively related to the interest rate, which is the opportunity cost of holding money. If the money supply were increased, LM would shift to the right. The slope of LM reflects the relative sensitivity of the demand for money to changes in output and in the interest rate. 360 International economics If the two lines derived above are put on the same graph, it is possible to see where the economy is in equilibrium and how it reacts to policy changes (see Figure 16.3). At the equilibrium levels of Y and r, the real economy is at rest, because intended investment equals savings, and the market for money is in equilibrium, because the demand for money equals the supply. If a more expansionary fiscal policy were adopted, the situation shown in Figure 16.4 would hold. A more expansionary budget causes GNP to rise because a higher level of income is required to produce enough additional private saving to offset the decrease in government saving (G – T). It also produces a higher interest rate owing to the effect of the higher level of incomes on the I r Y M S L r e y e Figure 16.3 Equilibrium in the real and monetary sectors. In a closed economy equilibrium is reached where IS crosses LM because only at that level of output and of interest rates is intended investment equal to savings and the demand for money equal to the supply of money. There is no other situation in which both conditions hold. I r Y M S L r e Y e I′ S′ Y e ′ r e ′ ∆ r ∆ Y Figure 16.4 Impacts of fiscal expansion. An expansionary fiscal policy shifts IS to the right, producing a higher level of output and higher interest rates. 16 – Adjustment with fixed rates 361 transactions demand for money. If the LM line were steeper, the expansionary effect on Y would be smaller. If the LM were vertical, as some monetarists would suggest, there would be no effect on Y; the expansionary fiscal policy is entirely crowded out through its effects on interest rates. The central bank’s decision to increase the money supply would have the effects illustrated in Figure 16.5. The expansion of the money supply causes the interest rate to fall, which increases intended investment. At the resulting higher level of output, savings rise to the new level of investment and the economy is again at equilibrium. Balance-of-payments equilibrium, as an additional line If the balance of payments is added to this macroeconomy and if payments equilibrium is a goal or policy constraint, a new line is needed. If the balance of payments is viewed in the oversimplified form: – CA = F(Y) and + KA = F(r) with equilibrium where CA + KA =0 then the balance of payments is in equilibrium along the line shown in Figure 16.6. It would be in surplus to the left of BP and in deficit to the right of that line. ∆ r ∆ Y I r Y M L r e Y e S M′ L′ Y e ′ r e ′ Figure 16.5 Impacts of an expansion of the money supply. An increase in the money supply shifts LM to the right, producing a higher level of output and lower interest rates. 362 International economics The slope of the BP line represents the relationship between the impact of the interest rate on the capital account and the impact of domestic incomes on imports. If the marginal propensity to import is very high or if international capital flows are unresponsive to changes in local interest rates, BP is steep. If, instead, capital markets are closely integrated, so large amounts of capital flow in response to small interest-rate differentials, and/or if the marginal propensity to import is low, BP becomes much flatter. It is worth noting that the capital account is positively related to the level of domestic interest rates rather than to recent changes in yields. A flow-adjustment model of the capital account, rather than a stock-adjustment approach, is implicit in the BP line. It would not be possible to define the IS and LM lines, and therefore to combine the three functions, if changes in interest rates were on the vertical axis of this graph, as would be implied by a stock-adjustment or portfolio balance approach. Since only the effect of interest rates and domestic income on the balance of payments can be shown directly on the graph, any other factor that shifts the payments situation causes BP to shift. An increase in foreign incomes, for example, that caused an increase in the demand for domestically produced exports would cause BP to shift to the right. A devaluation of the local currency, which strengthened the current account, would have the same effect. If a devaluation was expected in the near-term future, BP would shift up because of speculative capital outflows. If, for example, a devaluation of 10 percent was expected in about 12 months, short-term interest rates would have to rise by enough to offset the expected devaluation, to compensate people for holding assets denominated in the currency that was going to be devalued. If such interest-rate increases do not occur, a large payments deficit will result from the withdrawal of speculative funds from the country. r Y B P d Y d r BOP > 0 BOP < 0 Figure 16.6 Equilibrium in the balance of payments. The balance of payments is in equilibrium along BP, in deficit to the right, and in surplus to the left. Higher interest rates attract capital, while higher levels of output and income increase imports, so increases in interest rates and output offset each other. The slope of BP reflects the relative sensitivity of the balance of payments to an increase in incomes and an increase in interest rates. [...]... Amsterdam: Elsevier, 1995, pp 186 5–911 • Solomon, R., The International Monetary System 1945–1976: An Insider’s View, New York: Harper and Row, 1977 376 International economics Notes 1 David Hume, “On the Balance of Trade,” originally written in 1752, published in D Hume, Essays: Moral, Political, and Literary (London: Longmans Green, 189 8), reprinted in R Cooper, ed., International Finance: Selected... Activity, no 1, 1 984 , pp 1–64 For a more recent survey of this subject, see T Persson and G Tabellini, “Double-Edged Incentives: Institutions and Policy Coordination,” in G Grossman and K Rogoff, eds, Handbook of International Economics, Vol III (Amsterdam: Elsevier, 1995), ch 38 See also M Feldstein, “Thinking about International Economic Coordination,” Journal of Economic Perspectives, Spring 1 988 , pp 3–13... pound sterling would rise, for example, from $1 .80 to $1. 98, thereby causing US prices of British goods to increase proportionally A British car with a price of £10,000 would have previously cost $ 18, 000; now it will cost $19 ,80 0, which it is hoped will discourage US buyers of such vehicles, who will instead shift to domestic models 380 International economics The US price increase would be smaller... which should encourage domestic firms to make greater efforts to sell abroad 382 International economics Returning to the above numerical example, we find that if a product carries an unchanging British price of £100, the $1 .80 exchange rate means a US price of $ 180 , and the 10 percent devaluation to $1. 98 means a US price of $1 98, which both earns US firms more revenue for the same volumes of exports and... Approach,” Journal of Political Economy, 19 68, pp 89 3–920 See also K Hamada, “A Strategic Analysis of Monetary Interdependence,” Journal of Political Economy, 1976, pp 677–700 Suggestions as to why policy coordination is likely to fail can be found in K Rogoff, International Economic Coordination May Be Counterproductive,” Journal of International Economics, February 1 985 , pp 199–217 For econometric work... Press, 1951 • Mundell, R., International Economics, New York: Macmillan, 19 68 • Oudiz, G and J Sachs, “Macroeconomic Policy Coordination among Industrialized Countries,” Brookings Papers on Economic Activity, no 1, 1 984 , pp 1–64 • Person, T and L Svensson, “The Operation and Collapse of Fixed Exchange Rate Regimes,” in G Grossman and K Rogoff, eds, Handbook of International Economics, Vol III, Amsterdam:... P Kenen, “Macroeconomic Theory and Policy: How the Closed Economy Was Opened,” in R Jones and P Kenen, eds, Handbook of International Economics, Vol II (Amsterdam: NorthHolland, 1 985 ), pp 625– 78 The history of international economic policy in this era is covered in R Solomon, The International Monetary System: 1945–1976: An Insider’s View (New York: Harper and Row, 1977), chs 2–13 6 James Meade, The... Policy (Amsterdam: North-Holland, 1952), chs 4 and 5 For a review of the impact on international economics of the Mundell–Fleming approach, see J Frenkel and M Mussa, “The Mundell–Fleming Model a Quarter Century Later,” IMF Staff Papers, December 1 987 , pp 567–620 9 R Mundell, International Economics (New York: Macmillan, 19 68) , p 235 10 See J Niehans, “Monetary and Fiscal Policies in Open Economies under... produce, no matter how miserable the standard of living implied by that level of income 388 International economics The requirements of the absorption condition can also be seen in the relationship between the trade balance and the savings/investment gap, which was discussed in Chapter 12 Returning to page 286 , you will find: I + (X – M) = Sp + (T – G) which can be reorganized into: (X – M) = Sp +... further reading • Argy, V., International Macroeconomics: Theory and Policy, New York: Routledge, 1994 • Eichengreen, B., The Gold Standard in Theory and History, 2nd edn, New York: Routledge, 1997 • Frenkel, J and M Mussa, “The Mundell–Fleming Model a Quarter Century Later,” IMF Staff Papers, December 1 987 , pp 567–620 • Hume, D., “On the Balance of Trade [1752],” in R Cooper, ed., International Finance: . investment would rise to the new level of savings and the economy would be at point B. 3 58 International economics The slope of IS reflects the relationship between the size of the marginal propensity to. the payments surplus will also lead to recovery from the domestic recession. In case 2, the same 3 68 International economics situation holds, but the policies are to shift in the opposite direction. Tighter. students who have had an intermediate macroeconomics course, the purely domestic portion of what follows will probably not be new, and even part of the international extension may be familiar.

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  • Open economy macroeconomics with fixed exchange rates

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