Loyola University College of Business Administration

International Economics Economics B305

Instructor: Dr. Barnett Semester: Fall, 2010 Class meetings: Mondays & Wednesdays, 8:00 a.m.-9:15 a.m. Room: 112 Miller Hall Office hours: Mondays and Wednesdays, 1:00 p.m.- 2:00 p.m., Tuesdays, 8:00 a.m. – 10:00 a.m., and by appointment Office: 319 Miller Hall Phone nos.: Office: 864-7950; Home: 737-9498 E-mail: wbarnett@loyno.edu Course Prerequisites: Economics B201 and junior standing. Only those students who have completed at least 56 credit hours may enroll in 300 or 400 level business courses. Catalog description: This course considers exchange rate systems; adjustments in international disequilibrium situations; relationships among rates of exchange, inflation, interest, and unemployment; and, domestic and international economic policies. It also considers various theories of competitive advantage in international trade, the nature and effects of commercial policies, and international economic integration. (3 hours.) Course purpose: The purpose of this course is to expose the student to the basic ideas of international economics. Because of the breadth of the field, we will cover a wide variety of topics rather than a few in depth. Each student should develop the ability to read the relevant portions of the Wall Street Journal and similar publications, and put the events of the day in perspective, as they relate to businesses and the decisions entrepreneurs and managers must make. Course Learning Objectives Students completing this course successfully will be able to: 1) explain the international payments accounts and the relationships among the various accounts; 2) explain the differences among various exchange rate regimes; 3) explain the parity conditions and the relationships among them; 4) explain the concept of real exchange rates and their relationship to the terms of trade; 5) explain the determination of spot and futures (forward) exchange rates; 6) explain various approaches to the causes of, and adjustments to, international macroeconomic disequilibrium; 7) explain the effects of exchange rate policies, and of domestic monetary and fiscal policies on the foreign sector; 8) explain the fixed v. floating exchange rate controversy; 9) explain various concepts of the terms of trade; 10) explain various theories concerning the bases of comparative advantage; 11) explain the nature and effects of factor mobility; 12) explain the effects of various commercial policies; 13) explain the free trade v. protectionist (“fair trade”) controversy; 14) explain the nature and effects of various types of economic integration. This is a lecture/discussion class. Students are encouraged to ask questions.

Text: Husted, Steven, and Melvin, Michael. International Economics, 8th ed. Reading, MA.: Addison-Wesley Educational Publishers, 2004. In addition to the text you will provided a set of handouts: H1 - Barnett, W. The International Payments Accounts (Balance of Payments Accounts) and the National Income and Product Accounts H2 - Barnett, W. Hedging and Speculating with Futures Exchange Rate Contracts, H3 - Barnett, W. International Monetary Parity Conditions H4 - Barnett, W., and J. S. Wood. Depreciation, The J-Curve, and the Balance of Trade Deficit, unpub. manu., 1987. H5 - Barnett, W. The Current Account Balance, Financial Account Balance, and Fluctuating Exchange Rates Absent Government Intervention in the Foreign Exchange Market H6 – Barnett, W. Gold Export and Import Points Grading: There will be three examinations, weighted 30%, 30%, and 40%; the 40% weight will be assigned on an individual basis to that exam with the highest grade. I reserve the right to adjust your final grade upward or downward by 1/2 of a letter grade based upon your classroom performance. The grading scale is: A>89≥A->86≥B+>82≥B>79≥B->76≥C+>72≥C>69≥C->66≥D+>62≥D>59≥F. Communications: All Loyola email correspondence will be directed to students’ Loyola email address only. You are responsible for any communications addressed to your Loyola email account. Attendance: You will be held responsible for all lecture material and class discussions as well as all of the reading assignments. Therefore, although there is no formal attendance requirement, you are strongly urged to attend all class meetings. Academic Integrity Statement:

I consider honesty and integrity to be of the utmost importance and presume that my students do also, and thus that each and every one of you is a person of integrity. Therefore, I have one simple rule: you are to do your own work. I will not tolerate academic dishonesty in any way, shape, or form. The penalty in my class for cheating, no matter how minor the infraction might appear to be, is an F for the course. If you have any doubt whatsoever as to whether a particular course of action or inaction would constitute academic dishonesty, you should consult me immediately.

Disabilities: A student with a disability that qualifies for accommodations should contact Sarah Mead Smith, Director of Disability Services at 865-2990 (Academic Resource Center, Room 405, Monroe Hall). A student wishing to receive test accommodations (e.g., extended test time) should provide the instructor with an official Accommodation Form from Disability Services in advance of the scheduled test date.

All dates except that of the final exam are approximate. Dates

(# of classes) Material Reading

T=text H=handout Introduction Aug. 31 (1) The Distinctiveness, and the Nature and Causes of the Importance of

International Economic Intercourse T Ch. 1

Part I The International Accounts, Exchange Rates, Adjustment to

Disequilibrium, and International Monetary Systems

Sept. 2-14 (3) The International Payments Accounts and Their Relationship to the NIPA T Ch. 11-12 H1

Sept. 16-30 (5) Exchange Rates and Exchange Rate Systems: Various Exchange Rate Regimes: Gold (and other commodity) standards; fiat standards - fixed, adjustable peg, floating, and dirty (managed) floats; and, exchange controls (multiple rates); futures/forward rates; purchasing power parity, real exchange rates, and the terms-of-trade; the Fisher Effect, the International Fisher Effect, interest rate parity (covered arbitrage margin), unbiased futures/forward rates; real exchange rates; demand for, and supply of, foreign exchange, both spot and futures/forward: traders, investors, hedgers, arbitrageurs, speculators, and exchange rate determination.

T Ch. 13-16, 19 H2, H3, & H6

Oct. 5-14 (4) Adjustment to/Suppression of Disequilibrium: The nature and causes of international macroeconomic disturbances, domestic and international adjustments associated therewith, and domestic and international policies for coping therewith; overvalued and undervalued currencies, appreciations(reevaluations)/ depreciations(devaluations); BOP imbalances (imbalances in the overall balance/autonomous account); imbalances in the sub-accounts – Current Account/”Balance of Trade” deficits and Capital Account imbalances and saving; and exchange controls.

T Ch. 17-18, & 20-21 H4 & H5

Oct. 21-26 (2) International Monetary Systems: Historical Experiences T Ch. 19 Oct. 28 (1) First Exam Part II

Trade Theory & Commercial Policy

Trade Theory (6) Nov. 2 (1) The Gains from Trade T Ch. 2 Nov. 4-11 (3) Comparative Advantage and Its Sources: factor endowments & the

H-O model; the Linder, product cycle, and Porter models; transactions-costs, imperfect competition, intra-industry trade, technology, factor mobility, and multinational enterprise

T Ch. 3-5

Commercial Policy Nov. 16-30 (4)

The Effects of Tariffs and Non-tariff Barriers to Trade, and Free Trade and Protectionism and “Modern Trade Policy”

T Ch. 6-8

Dec. 2-9 (3) Economic Integration: multilateral trade agreements, free trade areas, customs unions, common markets, economic union(s), monetary union(s), political union(s) - trade creation & diversion, and optimal currency areas. (EU & EMU, WTO/GATT, NAFTA, Mercosur, etc ).

T Ch. 9-10

Dec. 14 Final Exam (9:00 a.m. – 11:00 a.m.)

H1: Balance of Payments Accounts (International Payments Accounts) for the U.S. in $ and

National Income and Product Accounts Account Receipts (+) of $

from: Payments (-) of $ for: Balance in $

Current Account Merchandise Exports of Tangible Goods Imports of Tangible Goods Merchandise Balance Services Exports of Intangible

Services Imports of Intangible Services Services Balance

Unilateral Transfers Private & Governmental Unilateral Transfers from ROW to U.S.

Private & Governmental Unilateral Transfers from U.S. to ROW

Unilateral Transfers Balance

Investment Income

Receipts of Investment Income from ROW

Payments of Investment Income to ROW

Investment Income Balance

Employment Income Receipts of Employment Income from ROW

Payments of Employee Income to ROW

Employment Income Bal.

Sum of these 5 accounts Sum of these 5 accounts Current Account Balance. Financial Account Long-term Financial Exports of Long- term

Financial & Real Assets Imports of Long- term Financial & Real Assets

Long-term Financial Balance

Short-term Financial. Exports of Short-term Financial Assets

Imports of Short-term Financial Assets

Short-term Financial Balance

Sum of these 2 accounts Sum of these 2 accounts Financial Account Balance

Balancing entry made either to receipts, $X or payments to payments, $Z, as necessary to balance the total payments and receipts

Statistical Discrepancy1, was Net Errors & Omissions

$X $Z

Statistical Discrepancy

Sum of the above 7 accounts

+ Stat. Disc. (if applicable) Sum of the above 7 accounts + Stat. Disc. (if applicable)

Official Settlements Balance.

OFFICIAL RESERVES Monetary Gold Sales of Monetary Gold to

ROW Purchases of Monetary Gold from ROW

Foreign Monies Sales of Foreign Monies to ROW

Purchases of Foreign Monies from ROW

Other Reserve Assets Sales of Other Reserve Assets from ROW

Purchases of Other Reserve Assets from ROW

Sum of these 3 accounts Sum of these 3 accounts Bal. of Official Reserve Trans. TOTAL RECEIPTS AND PAYMENTS2

The sum of ALL receipts; i.e., all 10 accounts above +Stat. Disc. (if applicable)

The sum of ALL payments i.e., all 10 accounts above +Stat. Disc. (if applicable)

= 0 TOTAL RECEIPTS AND PAYMENTS MUST BALANCE

1 Standard practice is to include the Statistical Discrepancy item in the Financial Account, though I am unaware of any good reason to do so. It would seem to be equally valid to include it in the Current Account. Therefore, I separate it out completely. 2 There is one more account, the Capital Account. Because the transactions recorded in it are both relatively rare, and minor in value, and of such a nature that they could, in my opinion, be as easily included in the Current Account as in the Financial. Therefore, I do not separate out these transactions.

National Income and Products Accounts

GDP is a measure of the production of goods (and the employment necessary to such production) to

satisfy our wants; therefore, it is only concerned with currently produced goods.3 Specifically, a country’s gross domestic product (GDP) is the monetary value4 of “all” final goods and services5 produced in a certain period of time, using resources located within the borders of that country. The dollar ($) value of GDP may be taken as we find it, or we may adjust it to eliminate the effects of any changes in the value of the $ itself; i. e., to correct for inflation or deflation.6 Unadjusted values are referred to as “nominal” or “current dollar” values; e. g., nominal GDP or current dollar GDP. Adjusted values are referred to as “real” or “constant dollar” values; e. g. real GDP or constant dollar GDP. We shall be concerned primarily with real values.

We shall consider two approaches to GDP: the flow of expenditures approach and the uses of income

approach. The Flow of Expenditures

This approach arrives at GDP by adding together the expenditures made in purchasing currently produced goods by the different sectors involved in the economy: households, businesses, governments, and foreigners. Expenditures on preexisting goods only transfer their ownership from one person to another; they do not involve the creation of new goods, with attendant employment, to satisfy our wants.7Let: C = consumption expenditures – private expenditures on consumer goods by households resident in the U.S., IGPD = gross private domestic investment; gross expenditures on capital goods by businesses resident in the U.S., GPUR = governmental purchases; expenditures on goods by all levels of domestic governments, EX = exports; expenditures by non-residents of the U.S. on goods produced in the U.S., IM = imports; expenditures by U. S. residents on goods produced outside of the U.S.,

3 “Currently produced goods” should be understood to refer to goods produced during the relevant time period, usually a year or a quarter of a year. 4 In the USA this is the dollar value; hereinafter we shall use dollar values, but we should remember that other countries measure their GDPs in terms of their own currency or monetary units. 5 Hereinafter, the word “goods” should be taken to refer to “goods and services,” unless explicitly noted otherwise. 6 Of course, GDP is not the only variable we adjust for changes in the value of the $; rather adjustments are made for all variables whose value is affected by such changes. 7 To the extent that there are transactions costs incurred in purchasing preexisting goods, such costs involve the production of current services, and therefore are included in GDP. Transactions costs are those involved in searching for desirable exchanges, negotiating exchanges, and enforcing ones rights in such cases.

XNET = net exports; exports minus imports, XNET = EX - IM, E = total expenditures, and E = GDP. Then: E = C + IGPD + GPUR + EX - IM8 E = C + IGPD + GPUR + XNET

8 Because C, IGPD, and GPUR include expenditures on imported goods as well as on domestically produced goods, in order to not count the imports as part of U.S. GDP it is necessary to subtract them out of the right-hand side of the equation.

The Uses of Income

Income arises from production of goods; it is the payments to the people whose resources, including their own labor, were used to produce the goods. If there were no production there would be no income. This approach arrives at GDP by adding together the uses to which people put their incomes received from the current production of goods. Income is used for consumption expenditures, saving, and the payment of taxes. Let: C = consumption expenditures - expenditures on consumer goods by households resident in the U.S., SPRI = private saving; saving by households and businesses out of current income, T = total taxes; taxes paid to all levels of government, GTRAN = transfer payments; expenditures by all levels of government for which no currently produced goods are received,9 TNET = net taxes; total taxes less transfer payments, TNET = T - GTRAN, Y = total income, and Y = GDP. Then: Y + GTRAN

= C + SPRI + T10 Y = C + SPRI + T - GTRAN Y = C + SPRI + TNET Governmental Budgetary Relationships Let: GPUR = governmental purchases; expenditures on goods by all levels of domestic governments, GTRAN = transfer payments; expenditures by all levels of government for which no currently produced goods are received, G = total governmental expenditures by all levels of government, G = GPUR + GTRAN T = total taxes; taxes paid to all levels of government, TNET = net taxes; total taxes less transfer payments, TNET = T - GTRAN, and SGOV = governmental saving; governmental saving is the difference between total tax revenues and total governmental expenditures at all levels of government. 9 The two major components of transfer payments are payments for “entitlements” and for interest on the national debt. 10 Because the amount of money available to be used for consumption expenditures, private saving, and tax payments includes transfer payments received from all levels of government as well as income (from production), in order to correctly account for the uses of income it is necessary to add them to the left-hand side of the equation.

Then: SGOV = T - G SGOV = T - (GPUR + GTRAN) SGOV = T - GTRAN - GPUR SGOV = (T - GTRAN) - GPUR SGOV = TNET - GPUR The International Sector When a country’s exports exceed its imports, its receipts from foreign countries exceed its payments to them. That is, it earns a surplus of foreign monies. Such a situation is referred to as a surplus in the “current account.”11 The only thing that a country can do with such a surplus of foreign monies is to invest it in the foreign countries. Thus, if the U.S.’s exports exceed its imports the U.S. has a current account surplus, and, necessarily, the only thing the U.S can do with this surplus of foreign monies is invest it in foreign countries. This is referred to as positive net foreign investment for the U.S. (or a capital outflow from the U.S. to foreign countries).

When a country’s imports exceed its exports its payments to foreign countries exceed its receipts from them. That is, the foreign countries have a surplus of that countries money. Such a situation is referred to as a deficit in the “current account.”12 The only thing that the foreign countries can do with such a surplus of the relevant country’s money is to invest it in that country. Thus, if the U.S.’s imports exceed its exports, the U.S. has a current account deficit, and foreign countries have a surplus of U. S. dollars. The only thing the foreign countries can do with their surplus of U.S. dollars is invest it in the U.S. This is referred to as negative net foreign investment for the U.S. (or a capital inflow into the U.S. from foreign countries.). Let: NFI = net foreign investment, EX = exports; expenditures by non-residents of the U.S. on goods produced in the U.S., IM = imports; expenditures by U. S. residents on goods produced outside of the U.S., XNET = net exports; exports minus imports, XNET = EX - IM, and XNET = NFI. Then, if, for the U.S., XNET > 0, then NFI > 0, then the U.S. has positive net foreign investment, or if, for the U.S., XNET < 0, then NFI < 0, then the U.S. has negative net foreign investment. Saving and Investment 11 Since a country may have a current account surplus with one country and a current account deficit with another country, in order to properly account for international economic activity the such surpluses and deficits must be netted. 12 Since a country may have a current account surplus with one country and a current account deficit with another country, in order to properly account for international economic activity the such surpluses and deficits must be netted.

Total saving is the sum of private saving and governmental saving. Total investment is the sum of gross private domestic investment and net foreign investment. Let: SPRI = private saving, SGOV = governmental saving, STOT = total saving; total saving is the sum of private saving and governmental saving, STOT = SPRI + SGOV IGPD = gross private domestic investment, NFI = net foreign investment, and ITOT = total investment; total investment is the its sum of gross private domestic investment and net foreign investment. ITOT = IGPD + NFI Expenditures = Income and Saving = Investment Every dollar of expenditures on currently produced goods becomes a dollar of income for the owners of these sources used to produce the goods. Therefore expenditures must be equal to income. E = Y C + IGPD + GPUR + XNET = C + SPRI + TNET IGPD + GPUR + XNET = SPRI + TNET IGPD + XNET = SPRI + TNET - GPUR IGPD + XNET = SPRI + SGOV IGPD + XNET = STOT IGPD + NFI= STOT ITOT = STOT XNET = STOT - IGPD NFI = STOT - IGPD SUMMARY in SYMBOLS E = C + IGPD + GPUR + EX - IM EX - IM = XNET E = C + IGPD + GPUR + XNET Y + Tran

= C + SPRI + T Y = C + SPRI + T - GTRAN T - GTRAN = TNET Y = C + SPRI + TNET E = Y C + IGPD + GPUR + XNET = C + SPRI + TNET IGPD + GPUR + XNET = SPRI + TNET

IGPD + XNET = SPRI + TNET - GPUR TNET = T - GTRAN IGPD + XNET = SPRI + T - GTRAN - GPUR GPUR + GTRAN = G IGPD + XNET = SPRI + T - G T - G = SGOV IGPD + XNET = SPRI + SGOV SPRI + SGOV = STOT IGPD + XNET = STOT STOT - IGPD = XNET XNET = NFI STOT - IGPD = NFI STOT = IGPD + NFI

IGPD + NFI = ITOT STOT = ITOT

H2: HEDGING AND SPECULATING WITH FUTURES EXCHANGE RATE CONTRACTS

William Barnett II September 7, 1993

NOTATION ρS : today's spot exchange rate (in $/£) ρE : today's expectation as to what the spot exchange rate (in $/£) will be six months from today ρF : today's futures exchange rate (in $/£) for six months from today; e.g., ρF = $2/£1 means that today I can enter into a contract to buy or sell a specific quantity of £ (sell or buy a specific quantity of $) at the rate of $2/£1 with the actual exchange of $ for £ (£ for $) taking place in six months; i.e., we agree on the price (exchange rate) and quantity (volume of currency) today, but the actual exchange does not take place today; rather, it is set to take place six months from today. pUS : today's expected inflation rate of the $ over the next six months pUK: today's expected inflation rate of the £ over the next six months I. The Relationship Between ρS and ρE This relationship is considered on pages 325-330 of the textbook: Root, Franklin R., International Trade and Investment, 7th ed. (Southwestern, 1994.) It can be expressed as in Eq.1: 1. ρE = ((1+ pUS) / (1+ pUK)) * ρS 2. dρE

/ dρS = (1+ pUS) / (1+ pUK) Thus changes in ρS will be reflected in changes in ρE. II. The Relationship Between ρF and ρE Any systematic divergence between ρF and ρE creates (expected) profit opportunities for speculators. Thus, ρF "should be" an unbiased estimator of ρE. That is expected changes in the spot exchange rate should be reflected in the premium (discount) of the futures exchange rate over (under) the spot exchange rate. 3. ρF = ρE

Example

If ρE = $1.99/£1 and ρF = $2.00/£1, then speculators could sell £ futures at the rate of $2.00/£1 (agree today to deliver £ six months from today at the rate of $2/£1), expecting to be able to acquire the £ at the rate of $1.99/£1 in the spot market six months from today, and thereby earn a profit of $0.01 for each £1 that is sold in the futures market today. The sale of £ futures would tend to decrease the price of the £ futures (decrease ρF) and the increase in the volume of £ expected to be purchased in the spot market six months from now would tend to increase the expected spot rate (ρE) resulting in their convergence. Put another way, (still assuming that ρE = $1.99/£1 and ρF = $2.00/£1, speculators could buy $ futures at the rate of $2.00/£1 (agree today to take delivery of $ six months from today at the rate of $2/£1), expecting to be able to dispose of the $ at the rate of $1.99/£1 in the spot market six months from today, and thereby earn a profit of approximately £0.005 for each $1 that is bought in the futures market today. The purchase of $ futures would tend to decrease the price of the £ futures (decrease ρF) and the increase in the volume of $ expected to be sold in the spot market six months from now would tend to increase the expected spot rate (increase ρE) resulting in their convergence. Alternatively, if ρE = $2.01/£1 and ρF = $2.00/£1, then speculators could buy £ futures at the rate of $2.00/£1 (agree today to take delivery of £ six months from today at the rate of $2/£1), expecting to be able to dispose of the £ at the rate of $2.01/£1 in the spot market six months from today, and thereby earn a profit of $0.01 for each £1 that is bought in the futures market today. The purchase of £ futures would tend to increase the price of the £ futures (increase ρF) and the increase in the volume of £ expected to be sold in the spot market six months from now would tend to decrease the expected spot rate (decrease ρE) resulting in their convergence. Put another way, (still assuming that ρE = $2.01/£1 and ρF = $2.00/£1), speculators could sell $ futures at the rate of $2.00/£1 (agree today to deliver $ six months from today at the rate of $2/£1), expecting to be able to acquire the $ at the rate of $2.01/£1 in the spot market six months from today, and thereby earn a profit of £0.005 for each $1 that is sold in the futures market today. The sale of $ futures would tend to increase the price of the £ futures (increase ρF) and the increase in the volume of $ expected to be purchased in the spot market six months from now would tend to decrease the expected spot rate (decrease ρE) resulting in their convergence. Thus as noted above, the presence of speculators causes the ρE and ρF to converge; absent transactions and/or transportation costs the convergence is absolute: ρF = ρE

III. Hedging A. Receipts of Pounds Consider someone (A) who expects to receive £1,000,000 in six months. Neither does A want the £, nor does A wish to speculate on the spot exchange rate. Currently, ρS = $1.98/£1 and the ρF = $2.00/£1 for the contract for six months from now. And, since ρF = ρE, ρE = $2.00/£1. A must make a choice: either hedge or speculate on the spot exchange rate.

1. Speculation and the Receipt of £ A can choose to do nothing until the £1,000,000 are received six months from now, at which time the £1,000,000 can be sold at the then current spot exchange rate, which is expected to be $2.00/£1. Thus today A expects to receive $2,000,000 for the £1,000,000 six months from today. If, however, six months from now the spot exchange rate is not $2.00/£1 as A expects today, but rather is, say, $2.01/£1, the £1,000,000 can be sold at that time for $2,010,000; or, if the spot rate has decreased to, say, $1.99/£1 the £1,000,000 can be sold at that time for $1,990,000. That is, even though A expects to receive $2,000,000 six months from now for the £1,000,000 he expects to have at that time, he realizes that his expectations as to what the spot exchange rate will be six months from today may prove to be incorrect and, therefore, he may receive more or less depending on the actual course of the spot exchange rate over the six month interval. Thus A, by doing nothing until the £1,000,000 are received, is, in effect, speculating on the exchange rate for a period of six months. 2. Hedging and the Receipt of £ Alternatively, A can sell six-month contracts totaling £1,000,000 on the futures market for $2,000,000. This would require A to deliver £1,000,000 in six months and receive, at that time $2,000,000. A reasons as follows: 1) If, over the next six months, ρE increases, say to $2.01/£1, then ρF will also increase to $2.01/£1. At that time A can buy back the same £1,000,000 contracts he had previously sold for $2,010,000, thus incurring a loss of $10,000 on the sale and subsequent repurchase of £ on the futures market. However, he expects that he would then be able to sell the £1,000,000 at the expected spot exchange rate (which would then be $2.01/£1) for $2,010,000. After subtracting his $10,000 loss on the futures transactions, A would net $2,000,000 for the £1,000,000. 2) If, over the next six months, ρE decreases, say to $1.99/£1, then ρF will also decrease to $1.99/£1. At that time A can buy back the same £1,000,000 contracts he had previously sold for $1,990,000, thus realizing a gain of $10,000 on the sale and subsequent repurchase of £ on the futures market. However, he expects that he would then be able to sell the £1,000,000 at the expected spot exchange rate (which would then be $1.99/£1) for $1,990,000. After adding his $10,000 gain on the futures transactions, A would net $2,000,000 for the £1,000,000. Note that whether the ρF increases or decreases, A has locked in a price of $2.00/£1 for the £1,000,000 he expects to have in six months. B. Payment of Pounds Consider someone (A) who expects to have to pay £1,000,000 in six months. Neither does A have the £, nor does A wish to speculate on the spot exchange rate. Currently, ρS = $1.98/£1 and the ρF = $2.00/£1 for the contract for six months from now. And, since ρF = ρE, ρE = $2.00/£1. A must make a choice: either hedge or speculate on the spot exchange rate. 1. Speculation and the Payment of £ A can choose to do nothing until the £1,000,000 must be paid six months from now, at which time the £1,000,000 can be purchased at the then current spot exchange rate, which is expected to be $2.00/£1. Thus today A expects to pay $2,000,000 for the £1,000,000 six months

from today. If, however, six months from now the spot exchange rate is not $2.00/£1 as A expects today, but rather is, say, $2.01/£1, the £1,000,000 can be purchased at that time for $2,010,000; or, if the spot rate has decreased to, say, $1.99/£1 the £1,000,000 can be purchased at that time for $1,990,000. That is, even though A expects to pay $2,000,000 six months from now for the £1,000,000 he must have at that time, he realizes that his expectations as to what the spot exchange rate will be six months from today may prove to be incorrect and, therefore, he may pay more or less depending on the actual course of the spot exchange rate over the six month interval. Thus A, by doing nothing until the £1,000,000 must be paid, is, in effect, speculating on the exchange rate for a period of six months. 2. Hedging and the Payment of £ Alternatively, A can buy six-month contracts totaling £1,000,000 on the futures market for $2,000,000. This would require A to take delivery of £1,000,000 in six months and deliver, at that time $2,000,000. A reasons as follows: 1) If, over the next six months, ρE increases, say to $2.01/£1, then ρF will also increase to $2.01/£1. At that time A can sell back the same £1,000,000 previously purchased contracts for $2,010,000, thus realizing a gain of $10,000 on the purchase and subsequent resale of £ on the futures market. However, he expects that he would then be able to buy the £1,000,000 at the expected spot exchange rate (which would then be $2.01/£1) for $2,010,000. After subtracting his $10,000 gain on the futures transactions, A would pay a net $2,000,000 for the £1,000,000. 2) If, over the next six months, ρE decreases, say to $1.99/£1, then ρF will also decrease to $1.99/£1. At that time A can sell back the same £1,000,000 previously purchased contracts for $1,990,000, thus incurring a loss of $10,000 on the purchase and subsequent resale of £ on the futures market. However, he expects that he would then be able to buy the £1,000,000 at the expected spot exchange rate (which would then be $1.99/£1) for $1,990,000. After adding his $10,000 loss on the futures transactions, A would pay a net $2,000,000 for the £1,000,000. Note that whether the ρF increases or decreases, A has locked in a price of $2.00/£1 for the £1,000,000 he expects to need in six months.

IV. Speculation Speculation occurs when someone's (A's) expectation as to what the spot rate of exchange will be in, say six months, differs from the "market's" expectation as to what the spot exchange rate will be at that time, the market's expectation being expressed in the futures exchange rate for six-month contracts, and A is willing to "bet" that he is right and the market wrong. Example ρME : the market's expectation as to what the spot exchange rate (in $/£) will be six months from today ρF : today's futures exchange rate (in $/£) for six months from today ρAE : A speculator's (A's) expectation as to what the spot exchange rate will be six months from today

1) If A's expectation as to what the spot exchange rate will be in six months is lower than the market's expectation, then A thinks that he can realize a financial gain by selling £ futures today and buying £ spot six months from today. Thus if ρME = $2.00/£1, and thus ρF = $2.00/£1, also, and ρAE = $1.98/£1, then today A sells six-month contracts totaling, say £1,000,000 at ρF = $2.00/£1 for $2,000,000, expecting to be able to buy the £1,000,00 (at $1.98/£1) for $1,980,000, for an expected gain of $20,000. If A is right and six months from now the spot rate is $1.98/£1, A will realize the $20,000 gain. If, however, A is wrong and instead of being lower, the spot exchange rate is in fact higher than the market expected, say $2.02/£1, then A will have to pay $2,020,000 for the £1,000,000, in which case A will realize a $20,000 loss. And, if the market's expectation was correct, then A will pay $2,000,000 for the £1,000,000, realizing neither a gain nor a loss, save for transactions costs. 2) If A's expectation as to what the spot exchange rate will be in six months is higher than the markets expectation, then A thinks that he can realize a financial gain by buying £ futures today and selling £ spot six months from today. Thus if ρME = $2.00/£1, and thus ρF = $2.00/£1, also, and ρAE = $2.02/£1, then today A buys six-month contracts totaling, say £1,000,000 at ρF = $2.00/£1 for $2,000,000, expecting to be able to sell the £1,000,00 (at $2.02/£1) for $2,020,000, for an expected gain of $20,000. If A is right and six months from now the spot rate is $2.02/£1, A will realize the $20,000 gain. If, however, A is wrong and instead of being higher, the spot exchange rate is in fact lower than the market expected, say $1.98/£1, then A will receive $1,980,000 for the £1,000,000, in which case A will realize a $20,000 loss. And, if the market's expectation was correct, then A will receive $2,000,000 for the £1,000,000, realizing neither a gain nor a loss, save for transaction costs.

H3: International Monetary Parity Conditions: Relationships among Inflation Rates, Interest Rates, and Exchange Rates

and Analysis of Real Exchange Rates and the Terms of Trade, and Effective Exchange Rates

William Barnett II

Revised: October, 2000

International Monetary Parity Conditions Notation: ∴ : therefore ≈ : is approximately (equal to) ≠ : is not equal to $ : United States (ρS ) dollar(s) £ : United Kingdom (UK) pound(s) X : a specific representative bundle of goods. $P0 : today's $ price of X $P1 : today's expectation as to the $ price of X in one year £P0 : today's £ price of X £P1 : today's expectation as to the £ price of X in one year ρS : today's spot exchange rate between $ and £ in terms of $ per £ ($/£); i. e., , the number of $ it takes to buy one £ today ρE : today's expectation as to the spot exchange rate (in $/£) one year hence ρF : today's futures exchange rate (in $/£) for one year hence; e.g., ρF = $2.00/£1 means that today I can enter into a contract to buy or sell a specific quantity of £ (sell or buy a specific quantity of $) at the rate of $2.00/£1 with the actual exchange taking place one year hence; i. e., we agree on the price (exchange rate) and quantity (volume of currency) today, but the actual exchange of currencies does take place today; rather, it is set to take place one year from today. pUS : today's expected inflation rate of the $ over the next year pUK : today's expected inflation rate of the £ over the next year iUS : today's nominal interest rate of "risk-free" loans of $ maturing in one year iUK : today's nominal interest rate on "risk-free" loans of £ maturing in one year rUK : today's expected real interest rate on "risk-free" loans of $ maturing in one year rUK : today's expected real interest rate on "risk-free" loans of £ maturing in one year

Assumptions Throughout I assume that transactions and transportation costs, and non-market barriers to exchange, including taxes, do not exist. 1. pUS = ($P1 -

$P0) / $P0

2. pUS = ($P1 / $P0) - 1

3. 1 + pUS = ($P1 / $P0)

4. $P1 = $P0 * (1+ pUS)

5. pUK = (£P1 - £P0 ) / £P0

6. pUK = (£P1 / £P0 ) - 1

7. 1 + pUK = £P1 / £P0 8. £P1 =

£P0 * (1 + pUK) The following assumed data will be used in all of the examples in this handout. 9. $P0 = $2,000 / X 10. £P0 = £1,000 / X 11. pUS = 7% = 0.07 12. pUK = 5% = 0.05 13. rUS = 3% = 0.03 14. rUK = 3% = 0.03 Substituting into the RHS of Eqs.4 and 8 yields: 15. $P1 = $2000 / X * (1+.07) 16. $P1 = $2140 / X 17. £P1 = £1000 / X * (1+.05) 18. £P1 = £1050 / X.

Analysis

1. The Law of One Price (LOOP) and Arbitrage In the absence of transactions and transportation costs, and non-market barriers to trade a good must trade for the same price in all markets (i. e., one and the same price must prevail in all markets), for if more than one price exists, then a "guaranteed" profit can be made by buying in the market in which a lower price exists and selling in the market where a higher price exists (a practice called arbitrage). As demand increases in the market with the lower price, the price in that market will, sooner or later, rise, and as supply increases in the market with the higher price, the price in that market will, sooner or later, fall. Since arbitrage will continue as long as the prices in the two markets are different, sooner or later the prices in the two markets must converge. This principle, that in the absence of transactions and transportation costs and non-market barriers to exchange a good must trade for the same price in all markets, is called the law of one price (LOOP). Notes: 1) to the extent that transactions and transportation costs, or non-

market barriers to trade exist, the prices may not completely converge, rather they will converge to the limits set by these costs and barriers; 2) the speed with which prices adjust varies greatly depending upon the particular good and markets being considered. 2. Purchasing Power Parity (PPP) In international economics and finance, PPP is the name given to the analysis of the LOOP as it applies to situations involving different monies or currencies. We will be concerned with three variations of PPP: 1) absolute purchasing power parity PPP-A; 2) relative purchasing power parity, PPP-R; and, 3) futures purchasing power parity PPP-F. 2.A. Absolute Purchasing Power Parity (PPP-A) The first variant of PPP, PPP-A, is concerned with the exchange value of one money in terms of another money at a point in time. PPP-A maintains that at a point in time a given amount of a particular money ought be able to purchase the same amount of goods in different markets, specifically markets using a different money. Thus, a given amount of $ ought be able to buy the same amount of goods whether the goods are bought directly with the $, or whether the $ are first exchanged for £, and then the £ are used to buy the goods; and, a given amount of £ ought be able to buy the same amount of goods whether the goods are bought directly with the £, or whether the £ are first exchanged for $, and then the $ are used to buy the goods. If the LOOP holds for the two monies, then PPP-A holds, and: 19. $P0 = ρS * £P0 20. ρS = $P0 / £P0 Example of PPP-A:

Substituting into the RHS of Eq.20 yields: 21. ρS = ($2,000 / X) / (£1,000 / X) 22. ρS = $2/£1 Only if £1,000 can be exchanged for $2,000 will the value of the £ be the same whether it is spent directly on goods or first exchanged for $, which $ are then spent on goods; and, only if $2,000 can be exchanged for £1,000 will the value of the $ be the same whether it is spent directly on goods or first exchanged for £, which £ are then spent on goods. Thus, only if the spot exchange rate is $2/£1 will PPP-A hold. At any spot exchange rate other than $2/£1, a given amount of money will have different values depending upon whether it is spent directly or indirectly on goods.

That is, with the same price data, if ρS = $2.02/£1 instead of $2.00/£1, then: £1,000 will buy one X, but it will also buy $2,020, which $2,020 will buy 1.01 X; i. e., a £ will buy 1% more X if it is first exchanged for $ than if it is spent directly X. Likewise, if with the same price data, ρS = $2.02/£1 instead of $2.00/£1, then $2,000 will buy one X, but it will only buy ≈ £990.10, which £990.10 will buy ≈ 0.99 X; i. e., , a $ will buy 1% less X if it is first exchanged for £

than if it is spent directly on X. (In such a case the $ is said to be undervalued relative to the £, and the £, overvalued relative to the $. As PPP-A not hold, an opportunity for arbitrage exists. In this case arbitrage would work as follows: 1) an arbitrageur with, say, £1,000,000 would sell them at the rate of $2.02/ £1 for $2,020,000; 2) the $2,020,000 would be used to buy, at a price of $2,000 per X, 1,010 X; 3) the 1,010 X would be sold, at a price of £1,000 per X, for £1,010,000; or, a profit of £10,000 (a 1%. profit on the original £1,000,000). Note that this series of exchanges began with the arbitrageur selling his £ and buying $; this would tend to decrease the value of the £ and increase the value of the $. This series of transactions would continue until the value of the $ (£) was increased (decreased) from $2.02/£1 to $2/£1. 2. B. Relative Purchasing Power Parity (PPP-R) The second variant of PPP, PPP-R, is concerned with changes (or the absence of change) in the exchange value of one money in terms of another money over a period of time. PPP-R maintains that differences between the expected inflation rates of two monies should be reflected in the premium (discount) of the expected spot exchange rate over (under) the current spot exchange rate, and that changes in the differences between the expected inflation rates should be reflected in changes in the premium (discount) of the expected spot exchange rate over (under) the current spot exchange rate, and vice versa. If PPP-A holds today and is expected to continue to hold a year from now, then PPP-R holds, then: 23. PPP-A @ t =0 ⇔ ρS = $P0 / £P0 24. PPP-A @ t =1 ⇔ ρE = $P1 / £P1

25. (ρE - ρS) / ρS = (pUS - pUK) / (1 + pUK) (For the derivation of this result, see the Mathematical Appendix.) That is, if PPP-R holds, then, in terms of $/£, the expected percentage change in the spot exchange rate [ (ρE - ρS) / ρS ] must be equal to the difference between the expected inflation rates of the $ and £, taken as a percentage with respect to the expected inflation rate of the £ [ (pUS - pUK) / (1 + pUK) ]. (In terms of £/$, the expected percentage change in the spot exchange rate must be equal to the difference between the expected inflation rates of the £ and $, taken as a percentage with respect to the expected inflation rate of the $.) Eq. 25 is an exact formulation of PPP-R. PPP-R can be approximated by: 26. (ρE - ρS) / ρS ≈ pUS - pUK

We can interpret this formulation as follows: if PPP-R holds, then, in terms of $/£, the expected percentage change in the spot exchange rate [ (ρE - ρS) / ρS ]may be approximated by the difference between the expected inflation rates of the $ and £ [ pUS - pUK ]. (In terms of £/$, the expected percentage change in the spot exchange rate may be approximated by the difference

between the expected inflation rates of the £ and $.) These approximations are not always good ones. For more on the accuracy of these approximations see Appendix 1. Example of the exact version of PPP-R: Evaluating the RHS of Eq.25 yields: 27. (pUS - pUK) / (1 + pUK) = (.07-.05)/1.05 28. (pUS - pUK) / (1 + pUK) = 0.0190476 = 1.90476% Thus if PPP-R holds, because taken as a percentage with respect to the expected inflation rate of the £, the 7% expected inflation of the $ is 1.90476% greater than the 5% expected inflation of the £, then the $ must be expected to lose, 1.90476% more of its value than the £ is expected to lose of its value. Therefore, in terms of $/£, the $ must be expected to lose 1.90476% of its nominal value against the £, and thus the expected spot rate must be 1.90476% greater than the current spot rate. Substituting into the LHS and RHS of Eq.25 yields: 29. (ρE - ($2/£1)) / ($2/£1) = 0.0190476 30. ρE = (0.0190476 * ($2/£1)) + ($2/£1) 31. ρE = $2.0380952/£1 That is, for PPP-R to hold, the spot exchange rate must rise from $2.00/£1 to $2.0380952/£1, which is a 1.90476% increase, or, which is the same, the $ must lose 1.90476% of its nominal value against the £. Example of the approximation of PPP-R: Evaluating the RHS of Eq. 26 yields: 32. pUS - pUK= (.07-.05) = .02 Substituting into the LHS and RHS of Eq.22 yields: 33. (ρE - ($2/£1))/$2/£1 ≈ .02 34. ρE ≈ (0.02 * $2/£1)+($2/£1) 35. ρE ≈ $2.04/£1 That is, for PPP-R to hold, the spot rate must rise from $2.00/£1 to ≈ $2.04/£1, which is a 2% increase. Although the approximate value, $2.04/£1, is quite close to the exact value, $2.0380952/£1 (it is only off by approximately 0.095%) because of the huge volumes of currencies traded in foreign exchange markets, these small percentage differences can add up to very large absolute amounts. For more on the accuracy of this approximation, see Appendix 1. 2.C. Unbiased Futures Exchange Rates (UFR)

UFR is concerned with the futures exchange rate and the expected spot exchange rate. UFR maintains that expected changes in the spot exchange rate should be reflected in the premium (discount) of the futures exchange rate over (under) the spot exchange rate. If UFR holds, then any divergence between the futures exchange rate and the expected spot rate sets up a "speculative" profit opportunity. This opportunity may also be conceived of as a potential for intertemporal arbitrage. 36. PPP-R + intertemporal arbitrage ⇔ ρF = ρE 37. (ρF - ρS

/ ρS = (ρE - ρS) / ρS

That is, the futures exchange rate is considered to be an unbiased estimator of the expected spot rate. That is, if UFR holds, then, in terms of $/£ and taken as a percentage with respect to the spot exchange rate, the premium (discount) on the futures exchange rate over (under) the spot exchange rate [ (ρF - ρS

/ ρS ] must be equal to the expected percentage increase (decrease) of the spot exchange rate [ (ρE - ρS) / ρS ]. (In terms of £/$ and taken as a percentage with respect to the spot exchange rate, the premium (discount) on the futures exchange rate over (under) the spot exchange rate must be equal to the expected percentage increase (decrease) of the spot exchange rate.) Eqs.36 and 37 are exact formulations of UFR. Example of intertemporal arbitrage: If ρE = $1.99/£1 and ρF = $2.00/£1, then speculators could sell £ futures for $2.00/£1 (agree today to deliver £ one year from today for $2/£1), expecting to be able to acquire the £ for $1.99/£ in the spot market one year from today, and thereby earn a profit of $0.01 for each £1 that is sold future today. 2.D. Futures Purchasing Power Parity (PPP-F) The third variant of PPP, PPP-F, is concerned with the premium or discount of the exchange value of one money in terms of another money in the futures market (the futures exchange rate) over or under the exchange value in the spot market (spot exchange rate). PPP-F maintains that differences between the expected inflation rates of two monies should be reflected in the premium (discount) of the futures exchange rate over (under) the spot exchange rate, and that changes in the differences between the expected inflation rates should be reflected in changes in the premium (discount) of the futures exchange rate over (under) the spot exchange rate, and vice versa. 38. PPP-A ⇔ ρS = $P0 /

£P0

39. PPP-R & UFR ⇔ ρF = $P1 / £P1

40. (ρF - ρS) / ρS = (pUS - pUK) / (1 + pUK) (For the derivation of this result, see the Mathematical Appendix.) That is, if PPP-F holds, then, in terms of $/£ and taken as a percentage with respect to the spot exchange rate, the premium (discount) of the futures exchange rate over (under) the spot exchange rate [ (ρF - ρS) / ρS ] must be equal to the difference between the expected inflation

rates of the $ and £, taken as a percentage with respect to the expected inflation rate of the £ [ (pUS - pUK) / (1 + pUK) ]. (In terms of £/$ and taken as a percentage with respect to the spot exchange rate, the premium (discount) on the futures exchange rate over (under) the spot exchange rate must be equal to the difference between the expected inflation rate of the £ and $, taken as a percentage with respect to the expected inflation rate of the $.) Eq.40 is an exact formulation of PPP-F. PPP-F can be approximated by: 41. (ρF - ρS) / ρS ≈ pUS - pUK We can interpret this formulation as follows: if PPP-F holds, then, in terms of $/£ and taken as a with respect to the spot exchange rate, the premium (discount) of the futures exchange rate, over (under) the spot exchange rate [ (ρF - ρS) / ρS ], may be approximated by the difference between the expected inflation rates of the $ and £ [ pUS - pUK ]. (In terms of £/$ and taken as a percentage with respect to the spot exchange rate, the premium (discount) of the futures exchange rate, over (under) the spot exchange rate, may be approximated by the difference between the expected inflation rates of the £ and $.) These approximations are not always good ones. For more on the accuracy of these approximations see Appendix 2. Example of the exact version of PPP-F: Evaluating the RHS of Eq.40 yields: 42. (pUS - pUK) /(1 + pUK) = (.07-.05) / 1.05 = 0.0190476 That is, because taken as a percentage with respect to the expected inflation rate of the £, the 7% expected inflation of the $ is 1.90476% greater than the 5% expected inflation of the £, if PPP-F holds, then the $ must be expected to lose, 1.90476% more of its value than the £ is expected to lose of its value. Therefore, in terms of $/£, the $ must be expected to lose 1.90476% of its nominal value against the £, and thus the futures exchange rate must be at a 1.90476% premium to the spot rate. Substituting into the LHS and RHS of Eq.40 yields: 43. (ρF - ($2/£1)) / ($2/£1) = 0.0190476 44. ρF = (0.0190476 * ($2/£1)) + ($2/£1) 45. ρF = $2.0380952 / £1 That is, if PPP-F holds, then futures contracts must trade at $2.0380952/£1 which is a 1.90476% premium over the $2/£1 spot rate, or, which is the same, we expect the $ to lose 1.90476% of its nominal value against the £. Example of the approximation of PPP-F: Evaluating the RHS of Eq.42 yields: 46. pUS - pUK = (.07 - .05) = .02 Substituting into the LHS and RHS of Eq.41 yields:

47. (ρF - ($2/£1)) / ($2/£1) ≈ .02 48. ρF ≈ (0.02 * ($2/£1)) + ($2/£1) 49. ρF ≈ $2.04/£1 That is, if PPP-F holds, then the futures exchange rate must be ≈ $2.04/£1, which is a 2% premium over the spot rate of $2/£1. Although the approximate value, $2.04/£1, is quite close to the exact value, $2.0380952/£1 (it is only off by approximately 0.095%) because of the huge volumes of currencies traded in futures foreign exchange futures markets, these small percentage differences can add up to very large absolute amounts. For more on the accuracy of this approximation, see Appendix 2. 3. The Fisher Effect (FE) The FE is concerned with the relationship between the nominal interest rate on loans of a particular money and the expected inflation rate of the same money. The FE maintains that the nominal interest rate on loans of money should reflect the expected inflation rate for the same money. The FE refers to the fact that the greater is expected inflation, the higher are the interest rates that lenders demand and borrowers are willing to pay. Because inflation allows borrowers to repay creditors with money whose value is less than what it was when lent, creditors demand, and borrowers are willing to pay, an interest premium to (attempt to) offset the expected reduced value of the repaid money. That is, what is important to both lenders and borrowers is the expected real interest rate on loans; i. e., , the nominal interest rate adjusted for the (expected) effects of expected inflation. In order for the interest premium to be expected to exactly offset the expected loss due to expected inflation the following relationships, in terms of $ and in terms of £, must hold: 50. 1 + iUS = (1+ rUS) * ( 1+ pUS) 51. 1 + iUS = 1+ rUS + pUS + ( rUS * pUS) 52. rUS = (iUS - pUS) / (1 + pUS) 53. 1 + iUK = (1 + rUK) * (1 + pUK) 54. 1 + iUK = 1 + rUK + pUK + (rUK * pUK) 55. rUK = (iUK - pUK) / (1 + pUK) (For derivations, see the Mathematical Appendix.) That is, if the FE holds, then the expected real interest rate on loans of $ [rUS] must be equal to the difference between the nominal interest rate on loans of $ and the expected inflation rate of the $, taken as a percentage with respect to the expected inflation rate of the $ [(iUS - pUS) / (1 + pUS)]. (The expected real interest rate on loans of £ [rUS] must be equal to the difference between the nominal interest rate on loans of £ and the expected inflation rate of the £, taken as a percentage with respect to the expected inflation rate of the £[ (iUK - pUK) / (1 + pUK) ]. Eqs. 50 - 55 are exact formulations of the FE. The FE, in $ terms, can be approximated by: 56. iUS ≈ rUS + pUS 57. rUS ≈ iUS - pUS

The FE, in £ terms, can be approximated by: 58. iUK ≈ rUK + pUK 59. rUK ≈ iUK - pUK We can interpret these formulations as follows: if the FE holds, then the expected real interest rate on loans of $ [rUS]may be approximated by the difference between the nominal interest rate on loans of $ and the expected inflation rate of the $ [iUS - pUS]. (The expected real interest rate on loans of £ [rUK] may be approximated by the difference between the nominal interest rate on loans of £ and the expected inflation rate of the £ [iUK - pUK]. These approximations are not always good ones. For more on the accuracy of this approximation, see Appendix 3.

Example of the exact formulations of the FE: Substituting into the RHS of Eqs. 50 and 53 yields: 60. 1+ iUS = 1.03 * 1.07 = 1.1021 61. iUS = 10.21% 62. 1+ iUK = 1.03 * 1.05 = 1.0815 63. iUK = 8.15% That is, if the FE holds, then the nominal interest rates on loans of $ and £ are 10.21% and 8.15%, respectively.

Example of approximations of the FE: Substituting into the RHS of Eqs. 56 and 58 yields: 64. iUS ≈ .03+.07 = .10 65. iUS ≈ 10% 66. iUK ≈ .03+.05 = .08 67. iUK ≈ 8%

That is, if the FE holds, then the nominal interest rates on loans of $ and £ should be approximately 10% and 8%, respectively. 3.A. The Fisher Effect and the LOOP (FE + LOOP) The FE & LOOP is concerned with the relationship between the difference between the nominal interest rates on loans of different monies and the difference between the expected inflation rates of the same monies. The FE + LOOP maintains that the difference in the nominal interest rates on loans of different monies should reflect the difference in the expected inflation rates for the same monies.

If the FE + LOOP hold, and if the expected inflation rate of one money is higher than the expected inflation rate of another money, then the nominal interest rate on loans of the money with the higher expected inflation rate must also be higher than the nominal interest rate on loans of the other money, in order that the greater expected loss due to higher expected inflation be expected to be offset by a greater gain from higher nominal interest. Since the expected real interest rate on loans is a measure of the price of credit, the LOOP requires that the expected real interest rate on loans of $ be equal to the expected real interest rate on loans of £. 68. LOOP ⇔ rUS = rUK 69. LOOP + FE ⇔ (1+ iUS) / (1 + pUS) = (1 + iUK) / (1 + pUK) 70. (iUS - iUK) / (1+ iUK) = (pUS - pUK) / (1 + pUK) That is, if the FE + LOOP hold, then, in terms of $/£ and taken as a percentage with respect to the nominal interest rate on loans of £, the difference between the nominal interest rate on loans of $ and the nominal interest rate on loans of £ [(iUS – iUK) / (1+ iUK)] must be equal to the difference between the expected inflation rate of the $ and the expected inflation rate of the £, taken as a percentage with respect to the expected inflation rate of the £ [(pUS - pUK) / (1 + pUK)]. (In terms of £/$ and taken as a percentage with respect to the nominal interest rate on loans of $, the difference between the nominal interest rate on loans of £ and the nominal interest rate on loans of S must be equal to the difference between the expected inflation rate of the £ and the expected inflation rate of the $, taken as a percentage with respect to the expected inflation rate of the $. Eqs. 69-70 are exact formulations of the FE + LOOP. The FE + LOOP can be approximated by: 71. (iUS - pUS) ≈ (iUK - pUK) 72. (iUS - iUK) ≈ (pUS - pUK) We can interpret this formulation as follows: if the FE + LOOP hold, then the difference between the nominal interest rate on loans of $ and the nominal interest rate on loans of £ [ (iUS - iUK) ] may be approximated by the difference between the expected inflation rate of the $ and the expected inflation rate of the £ [(pUS - pUK)]. (The difference between the nominal interest rate on loans of £ and the nominal interest rate on loans of $ may be approximated by the difference between the expected inflation rate of the £ and the expected inflation rate of the $. Example of an exact version of the FE + LOOP: Evaluating the LHS & RHS of Eq.70 yields: 73. (iUS - iUK) / (1+ iUK) =

(.03 + .07+(.03 * .07)) - (.03 + .05 + (.03 * .05)) / (1+ (.03 + .05 + (.03 *.05)) 74. (iUS - iUK) / (1+ iUK) = (.1021 - .0815) / 1.0815 = .0190476 75. (pUS - pUK) / (1+ pUK) = (.07 - .05) / 1.05 = .0190476 That is, if the FE + LOOP hold, then the nominal interest rate on loans of $ (10.21%) taken as a percentage with respect to the nominal interest rate on loans of £ (8.15%), is greater

than the nominal interest rate on loans of £ by 1.90476%, which is the same as the amount by which the expected inflation of the $ (7%) is greater than the expected inflation of the £ (5%), when taken as a percentage with respect to the expected inflation of the £. Example of the approximation of the FE + LOOP: Evaluating the LHS of Eq.72 yields: 76. iUS - iUK ≈ .1021 - .0815 = .0206 = 2.06%

That is, if the FE + LOOP hold, then we can approximate the difference in expected rates of inflation of the $ and the £ by the difference between the nominal interests rate on loans of $ and the nominal interest rate on loans of £; that is, by 2.06%.

Alternatively, substituting into the RHS of Eq.72 yields: 77. pUS - pUK ≈ (.07-.05) = .02 = 2%

That is, if the FE + LOOP hold, then we can approximate the difference between the nominal interests rate on loans of $ and the nominal interest rate on loans of £ by the difference in expected rates of inflation of the $ and the £; that is, by 2 %. 4. The International Fisher Effect (IFE) The IFE is concerned with the relationship between expected changes in the spot exchange rate between different monies and differences in the nominal interest rates on loans of those monies. The IFE maintains that differences, and changes in the differences, in nominal interest rates denominated in different monies should be reflected in the premium (discount), and changes in the premium (discount), of the expected future spot exchange rate over (under) the current spot exchange rate, and vice versa. 78. PPP-R ⇔ (ρE

- ρS) / ρS = (pUS - pUK) / (1+ pUK)

79. FE + LOOP ⇔ (iUS - iUK) / (1+ iUK) = (pUS - pUK) / (1+ pUK) 80. (ρE - ρS) / ρS = (iUS - iUK) / (1+ iUK) (For the derivation, see the Mathematical Appendix.) If the IFE holds, then, in terms of $/£, the expected percentage change in the spot exchange rate must be equal to the difference between the nominal interest rates on loans of $ and £, taken as a percentage with respect to the nominal interest rate on loans of £. (In terms of £/$, the expected percentage change in the spot exchange rate must be equal to the difference between the nominal interest rates on loans of £ and $, taken as a percentage with respect to the nominal interest rate on loans of $. Eq. 80 is an exact formulation of the IFE. The IFE can be approximated by: 81. (ρE - ρS) / ρS = (iUS - iUK)

We can interpret this formulation as follows: if the IFE holds, then, in terms of $/£, the expected percentage change in the spot exchange rate may be approximated by the difference between the nominal interest rates on loans of $ and £. (The expected percentage change in the spot exchange rate, in terms of £/$, may be approximated by the difference between the nominal interest rates on loans of £ and $.) This approximation is not always a good one. For more on this matter see Appendix 5. Example of the exact version of the IFE: Evaluating the RHS of EQ.80 yields: 82. (iUS - iUK) / (1+ iUK) = (.1025 - .0815) / (1+ .0815) = .0190476 Substituting into the LHS and RHS of Eq.85 yields: 83. (ρE - ($2/£1)) / ($2/£1) = .0190476 84. ρE = (.0190476 * ($2/£1)) + ($2/£1) = $2.0380952 That is, if the IFE holds, then the spot exchange rate is expected to rise to $2.0380952/£1, which is a 1.90476% increase, or which is the same, we expect the $ to lose 1.90476% of its nominal value against the £. Example of the approximation of the IFE: Evaluating the RHS of EQ.81. yields: 85. (iUS - iUK) = (.1021 - .0815) = .0206 Substituting into the LHS and RHS of Eq.86 yields: 86. (ρE - ($2/£)) /($2/£1) ≈ .0206 87. ρE ≈ (.0206 * ($2/£1)) + ($2/£1) = $2.0412/£1 That is, if the IFE holds, then the spot rate must be expected to rise from $2/£1 to approximately $2.0412/£1. 5. Interest Rate Parity (IRP) or Covered Arbitrage Margin (CAM) IRP is concerned with the relationship between nominal interest rates denominated in different monies and the premium (discount) of the futures exchange rate over (under) the spot exchange rate. IRP maintains that differences, and changes in the differences, in nominal interest rates denominated in different monies should be reflected in the premium (discount), and changes in the premium (discount), of the futures exchange rate over (under) the spot exchange rate, and vice versa. 88. PPP-R ⇔ (ρF - ρS) / ρS = (pUS - pUK) / (1+ pUK) 89. FE + LOOP ⇔ (iUS - iUK) / (1+ iUK) = (pUS - pUK) / (1+ pUK) 90. (ρF - ρS) / ρS = (iUS - iUK) / (1+ iUK)

That is, if IRP holds, then, in terms of $/£ and taken as a percentage with respect to the spot exchange rate, the premium (discount) on the futures exchange rate over (under) the spot exchange rate must be equal to the difference between the nominal interest rates on loans of $ and £, taken as a percentage with respect to the nominal interest rate on loans of £. (In terms of £/$ and taken as a percentage with respect to the spot exchange rate, the premium (discount) on the futures exchange rate over (under) the spot exchange rate must be equal to the difference between the nominal interest rates on loans of £ and $, taken as a percentage with respect to the nominal interest rate on loans of $. Eq. 90 is an exact formulation of the IRP. The IRP can be approximated by: 91. (ρF - ρS) / ρS ≈ (iUS - iUK) We can interpret this formulation as follows: if IRP holds, then, in terms of $/£ and taken as percentage with respect to the spot exchange rate, the premium (discount) on the futures exchange rate, over (under) the spot exchange rate, may be approximated by the difference between the nominal interest rates on loans of $ and £. (In terms of £/$ and taken as percentage with respect to the spot exchange rate, the premium (discount) on the futures exchange rate, over (under) the spot exchange rate, may be approximated by the difference between the nominal interest rates on loans of £ and $. Example of the exact version of the IRP: Evaluating the RHS of EQ.90 yields: 92. (iUS - iUK) / (1+ iUK)= (.1021 - .0815) / (1+ .0815) = .0190476 Substituting into the LHS and RHS side of Eq.90 yields: 93. (ρF - ($2/£1)) / ($2/£1) = (.1021 - .0815) / (1+ .0815) = .0190476 94. ρF = (.0190476 * ($2/£1)) + ($2/£1) = $2.0380952/£1 That is, if IRP holds, then futures contracts must trade at $2.0380952/£1 which is a 1.90476% premium over the $2/£1 spot rate, or, which is the same, we expect the $ to lose 1.90476% of its nominal value against the £. Example of the approximation of the IRP: Evaluating the RHS of EQ.91 yields: 95. (iUS – iUK) = (.1021 - .0815) ) = .0206 Substituting into the LHS and RHS of Eq.915 yields: 96. (ρF - ($2/£1)) / ($2/£1) ≈ .0206 97. ρF ≈ (.0206 * ($2/£1)) + ($2/£1) = $2.0412/£1

That is, if IRP holds, then futures contracts must trade at approximately $2.0412/£1, which is a 2.06% premium over the spot rate.

The Terms of Trade and the Real Exchange Rate 1. The Terms of Trade (TOT) Although there are several different measures referred to as terms of trade (TOT), usually when the term “terms of trade” is used without a modifier it refers to the “commodity, or net barter, TOT.” It is this concept, the commodity, or net barter, TOT, that is considered here. The TOT measures the purchasing power of a country’s goods. Specifically, it measures the quantity of imports of foreign goods that can be acquired in exchange for a unit of exports of domestic goods. We define the TOT as the weighted (by quantity) average price of a country’s exports divided by the weighted (by quantity) average price of the country’s imports. Thus, the TOT is also a measure of a country’s competitiveness. An increase (decrease) in the TOT occurs when the weighted average price of its exports goes up (down) relative to the weighted average price of its imports; that is, the TOT increase (decrease) when the prices of the things it sells go up (down) relative to the prices of the things it buys. Therefore, an increase (decrease) in a country’s TOT can be seen as a decline (improvement) in its competitiveness because the goods it sells are becoming relatively more (less) to costly and the goods it buys are becoming relatively less (more) costly. It should go without saying, that if country A’s TOT with country B improve (decline), country B’s TOT with country A decline (improve).

Notation: EX : one unit of a specific, representative bundle of goods exported to the U.K. IM : one unit of a specific, representative bundle of goods imported from the U.K. $PEX = the $ price (in index form) of EX £PIM = the £ price (in index form) of IM Σ ((EXi / EX) * $Pi) = weighted (by quantity) average $ price of U.S. exports to the U.K. (in the form of an index of prices of U.S. exports) IMh = quantity of U.S. imports of good h from the U.K.

IM = Σ IMh = quantity of U.S. imports of all goods from the U.K. IMh / IM) = the fraction imports of good h of are of the total quantity of imports of all goods £Ph = the £ price of good h ρS * £Ph = the $ price of good h Σ ((IMh / IM) * £Ph)) = weighted (by quantity) average £ price of U.S. imports from the U.K. Σ ((IMh / IM) * (ρS * £Ph)) = weighted (by quantity) average $ price of U.S. imports from the U.K. (in the form of an index of prices of U. S. imports) 98. TOT = Σ ((EXi / EX) * $Pi) / Σ ((IMh / IM) * (ρS * £Ph))

Since EXi / EX is a fraction, (EXi / EX) * $Pi is in terms of $ per unit of good i ($/i) and Σ ((EXi / EX) * $Pi) is in terms of $ per unit of U.S. exports ($/x). Similarly, since IMh / IM is a fraction, IMh / IM) * £Ph is in terms of £ per unit of good h (£/h) and Σ ((EXi / EX) * $Pi) is in terms of £ per unit of U.S. imports (£/m). And, Σ ((IMh / IM) * (ρS * £Ph)) is in terms of $ per unit of U.S. imports ($/m). Thus, the TOT are measured in terms of ($/x) / ($/m) = m / x; that is, the TOT are measured in terms of quantity of imports that can be purchased per unit of exports. 2. The Real Exchange Rate (RER)

The relationships among inflation rates, interest rates, and exchange rates analyzed in this paper are parity conditions that would hold if markets functioned perfectly. That is, for the parity conditions to hold, among other things, the LOOP must function perfectly. Thus, in the real world of imperfect markets, these parity conditions do not hold. In fact, actual divergences from the parity conditions can be quite large in the short run; however, they do come quite close in the long run. If the parity conditions always held, then the real (inflation adjusted) purchasing power of each currency relative to every other currency would not change. The existence in actuality of deviations from the parity conditions gives rise to attempts to measure changes in the real (inflation adjusted) purchasing power of various currencies relative to other currencies. One concept used to make such measurements is the RER. There are two basic approaches to the concept of the RER. One is related to the TOT and the other to PPP-R. The former approach is unrelated to the parity conditions and, although important in its own right, will be given short shrift in this handout. The other latter approach is directly related to the parity conditions and will be treated in some depth.

A. TOT Approach to the RER The TOT approach to the RER treats the RER as price of foreign goods in terms of

domestic goods, that is units of exports per unit of imports; i. e., in units of x/m.

99. RER = ρRt = Σ ((IMh / IM) * (ρS * £Ph)) / Σ ((EXi / EX) * $Pi)

Thus, this approach to the RER, measures the RER as the reciprocal of the TOT, and vice versa. If the TOT increase (decrease) the RER decreases (increases). A decrease (increase) in the RER means that, adjusted for inflation, the U.S. has to pay relatively fewer (more) $ for its imports, and the U.K. has to pay relatively more (fewer) £ for U.S. exports and, thus, adjusted for inflation, the value of the $ has gone up (down); i. e., , there has been real appreciation (depreciation) of the $ - the RER of the $ has appreciated (depreciated). And the U.S. has become relatively less (more) competitive. Of course, if the RER of country A’s currency relative to country B’s currency appreciates (depreciates) then the RER of country B’s currency relative to country A’s currency depreciates (appreciates).

B. PPP-R Approach to the RER The PPP-R approach treats the RER as the inflation adjusted nominal exchange rate. The

RER at time t is the actual nominal exchange rate (NER) at that time adjusted for differences, if any, between the inflation rates of the different monies between time t and some prior time, 0. It is used to measure changes, if any, in the relative real (inflation adjusted) values of different currencies over time. This RER analysis maintains that if changes in the NER between two currencies perfectly offset any differences in inflation rates between the currencies, then the RER remains constant. (Of course, if changes in the NER between two currencies perfectly offset any differences in inflation rates, then PPP-R holds.) Thus, if PPP-R holds between two currencies over a period of time, the real exchange rate between the two currencies is the same at the beginning and end of the relevant time period, and vice versa.

However, if PPP-R does not hold, then the real exchange rate has changed, and vice

versa. Thus, if a country's money has more (less) value at the real exchange rate at time t than it had at the actual spot exchange rate at time 0, or, which is the same, if a country's money has more (less) value at the actual spot exchange rate at time t than it would have at the PPP-R exchange rate at time t, then the real value of it's money has appreciated (depreciated) relative to the other country's money. Thus, if the RER of the $ in terms of the £ appreciates (depreciates), it means that, adjusted for inflation the $ has gone up (down) in value relative to the £; i. e., adjusted for inflation it takes fewer (more) $ to buy a £ and more (fewer) £ to buy a $. Since, the U.S. requires (directly or indirectly) £ to buy U.K. goods and the U.K. requires (directly or indirectly) $ to buy U.S. goods, a real appreciation (depreciation) of the $ can be seen as a decline (improvement) in the U.S.’s competitiveness. Again, we see that the RER can be used to measure changes in a country's competitive position. There are those who think that real depreciations of a country's money may be desirable for a country with a persistent deficit in its balance of trade.

Note: Unlike actual spot and futures exchange rates which exist in reality, real exchange rates have to be constructed from actual spot exchange rates and inflation rate data.

Notation: $P0 : the $ price of one X at time 0 £P0 : the £ price of one X at time 0 $Pt : the $ price of one X at time t £Pt : the £ price of one X at time t ρS

0 : the spot exchange rate at time 0, some time in the past and prior to t ρA

t : the actual spot exchange rate at time t; t may be today or some earlier time, but it may not be in the future ρR

t : the real exchange rate at time t ρP

t : the PPP-R exchange rate at time t; this is the exchange rate that would exist (or would have existed) at time t if PPP-R had held over the relevant time period pUS : the actual inflation rate of the $ between time 0 and time t pUK : the actual inflation rate of the £ between time 0 and time t 100. ρR

t = ((1+ pUK) / (1+ pUS)) * ρAt

That is, in terms of $/£, the RER at time t is equal to the actual spot exchange rate at time t adjusted for inflation since time 0. This is done by multiplying the actual spot, at time t, by the relative rates of inflation rates for the period from time 0 to time t of the £ and the $. In terms of £/$, the RER at time t is equal to the actual spot exchange rate at time t multiplied by the ratio of one plus the inflation rate of the $ to one plus the inflation rate of the £, both inflation rates for the period from time 0 to time t. 101. PPP-R ⇔ ρP

t = ((1+ pUS) / (1+ pUK)) * ρS0

102. ρS0 = (1+ pUK) / (1 + pUS)) * ρP

t 103. ρR

t / ρS0 = ρA

t / ρPt

If PPP-R holds, then: 104. PPP-R ⇔ ρA

t = ρPt

105. ρRt / ρS

0 = 1 106. ρR

t = ρS0

That is, if PPP-R held over the period from time 0 to time t, then the RER at time t must be equal to what the actual spot exchange rate was equal to at time 0. That is, adjusted for inflation the relative values (purchasing power) of the two currencies is (was) the same at time t as it was at time 0. However, if PPP-R does not hold, then: 107. ρA

t ≠ ρPt

108. ρRt / ρS

0 ≠ 1 109. ρR

t ≠ ρS0

That is, if PPP-R did not hold over the period from time 0 to time t, then the RER at time t can not be equal to what the actual spot exchange rate was equal to at time 0 or, what is the same, adjusted for inflation the relative values (purchasing power) of the two currencies is (was) the same at time t as it was at time 0.

Example of the RER assuming PPP-R holds: This example uses the same assumed data as the examples supra, except that the inflation rates are taken to refer to the period from 0 to t, rather than from 0 to 1. 110. $P0 = $2,000 / X 111. £Pt = £1,000 / X

112. ($2,000 / X) = ρS0 * (£1,000 / X)

113. ρS0 = $2/£1

114. $Pt / X = (1.07) * $2,000 = $2,140 / X 115. £Pt / X = (1.05) * £1,000 = £1,050 / X

116. PPP-R ⇔ ($2,140 / X) = ρPt * (£1,050 / X)

117. ρPt = $2.0380952/£1

118. PPP-R ⇔ ρAt = ρP

t 119. ρA

t = $2.0380952/£1 120. ρR

t = ((1.05) / (1.07) * $2.0380952/£1 = $2/£1 121. ρR

t = ρS0 = $2/£1

Thus if PPP-R held over the period from 0 to t, the real exchange rate at time t would be the same as the spot exchange rate at time 0, $2/£1. That is, if the actual spot exchange rate at time 0 was $2/£1, and the inflation rates of the $ and £ over the period from 0 to t were 7% and 5%, respectively, for PPP-R to have held over that period then the actual spot exchange rate at time t must be $2.0380952/£1; that is the $ must have depreciated in nominal terms by $0.0380952/£1 or 1.90476%; that is, it takes $0.0380952 more to buy £1 at time t than it took to buy £1 at time o. However, in real terms (adjusted for differences in inflation) neither did the $ depreciate (nor did the £ appreciate). Rather, there relative values (purchasing power) did not change; it remained constant. Example of RER, assuming that PPP-R does not hold: 122. ρP

t = $2.0380952 / £1

123. ρAt ≠ ρP

t 124. ρA

t ≠ $2.0380952 / £1 Consider the situation if the actual exchange rate had risen to $2.04 at time t: 125. ρA

t = $2.04/£1 100. ρR

t = ((1+ pUK) / (1+ pUS)) * ρAt

126. ρRt = ((1.05) / (1.07)) * ($2.04 / £1)

127. ρRt = ($2.00186916 / £1)

128. $2,140 / ($2.04 / £1) = £1,049.02 129. £1,050 * ($2.04 / £1) = $2142 The RER at time t is $2.00186916 / £1 compared to $2 / £1 at time 0. Thus, adjusted for inflation it takes $0.00186916 more to buy £1 at time t than at time 0. At the actual exchange rate ($2.04 / £1), instead of the PPP-R exchange rate ($2.0380952 / £1) the $2,140 required to buy one X at time t will only buy £1,049.02, which less than the £1050 required to buy one X at time t; and, the £1,050 required to buy one X at time t will buy $2,142, which is more than the $2140 required to buy one X at time t. Thus, the $ has lost real value (depreciated) relative to the £; or which is the same, the £ has gained real value (appreciated) relative to the $.

3. Effective Exchange Rates

So far we have been considering the NER and the RER in terms of the exchange rate between two currencies. Effective exchange rates are calculated in terms of one currency relative to a group of other currencies. Usually the group is limited to those of the major trading partners of the country whose NER and/or RER is under consideration.

Notation ρi

S0 : the spot exchange rate at time 0 between the $ and currency i

ρiS

t : the spot exchange rate at time t between the $ and currency i ρi

Ft : the futures exchange rate for time t at time 0 between the $ and currency i

ρ0ENER

: the effective NER at time 0 ρt

ENER : the effective NER at time t

ρtERER

: the effective RER at time t ρt

EFER : the effective futures exchange rate at time t wi = the weight assigned to currency i; it is approximately equal to country i's share in the foreign trade of the country whose NER and/or RER is under consideration pi : the inflation rate of currency i from time 0 to time t pROW : weighted average inflation rate of the rest of the world from time 0 to time t 130. ρ0

ENER = Σ (wi * ρi

S0)

131. ρtENER

= Σ (wi * ρiS

t) 132. ρt

EFER = Σ (wi * ρiF

t) 133. pROW = Σ (wi * pi) 134. ρt

ERER = (1+ pROW) / (1+ pUS)) * ρt

ENER

A. Modified RER analysis: from retrospective to prospective One result of the prior analysis of the RER was the following ratio: 135. ρR

t /ρS0 = ρA

t /ρPt

If we take time 0 to be today, time t to be some time in the future, and the inflation rates to refer to expected inflation rates between time 0 and time t; and, if, based on UFR, we substitute the futures rate for time t, in place of the actual spot rate exchange rate at time t in the above ratio, then: 136. ρP

t / ρS0 = ρF

t /ρPt

137. ρRt = (ρF

t * ρS0) / ρP

t 138. ρR

t = (ρFt * ρS

0) / (((1+ pUS) / (1+ pUK)) * ρS0)

139. ρRt = ((1+ pUK) / (1 + pUS)) * ρF

t

Thus, we can estimate the future real exchange rates for those for those monies for which futures rates exist. Such rates usually only exist for relatively short periods into the future and for major countries’ monies. Nevertheless, such estimates provide some information, and may be useful for spotting trends. It would also be possible to estimate the effective real exchange over short periods into the future, using the following formula: 140. ρt

EFER = Σ (pi * ρiF

t) 141. ρt

ERER = (1+ pROW) / (1+ pUS)) * ρt

ENER 142. ρP

t = (1+ pROW) / (1+ pUS)) * ρtEFER

MATHEMATICAL APPENDIX

Derivation of PPP-R 143. PPP-A ⇔ ρS = $P0 /

£P0 144. PPP-R ⇔ ρE = $P1 /

£P1

145. ρE/ρS = ($P1 / £P1) / ($P0 /

£P0) 146. ρE/ ρS = ($P1 /

$P0 ) / (£P1 / £P0 )

147. ρE/ ρS = (1+ pUS) / (1+ pUK) 148. (ρE/ ρS) -1 = ((1+ pUS) / (1+ pUK)) -1 149. (ρE/ ρS) - (ρS/ ρS) = ((1+ pUS) / (1+ pUK)) – ((1+ pUK) / (1+ pUK)) 150. (ρE - ρS) / ρS = ((1+ pUS) - (1+ pUK)) / (1+ pUK) 151. (ρE - ρS) / ρS = (pUS - pUK) / (1 + pUK)

Derivation of PPP-F 152. PPP-A ⇔ ρS = $P0 /

£P0 153. PPP-R ⇔ ρE = $P1 /

£P1

154. UFR ⇔ ρF = ρE 155. ρF = $P1 /

£P1 156. ρF/ ρS = ($P1 /

£P1) / ($P0 / £P0 )

157. ρF/ρS = ($P1 / $P0) / (£P1 /

£P0 ) 158. ρF/ρS = (1+ pUS) / (1+ pUK) 159. (ρF /ρS ) - 1 = ((1+ pUS) / (1+ pUK)) - 1 160. (ρF /ρS ) - (ρS /ρS ) = (1+ pUS) / (1+ pUK) - (1+ pUK) / (1+ pUK) 161. (ρF - ρS) /ρS ) = ((1+ pUS) - (1+ pUK)) / (1+ pUK) 162. (ρF -ρS) /ρS = (pUS - pUK) / (1 + pUK)

Derivation of the Fisher Effect This derivation assumes a the period of the loan is one year.

Notation $L0 : the principal amount (L) of a loan of $ $L1′: the amount one would have to receive on a loan of $L0 in order merely to maintain the real value of the principal $L1 : the total receipts of principal and interest on a loan of $L0

163. $L0′ = (1+ pUS) * $L0 164. $L1 = (1+ iUS) * $L0 165. $L1 = (1+ rUS * $L0′ 166. $L1 = (1+ rUS * ((1 + pUS) * $L0) 167. 1+ iUS = (1+ rUS) * ((1+ pUS) 168. 1+ rUS = (1+ iUS) /(1+ pUS) 169. rUS = (1+ iUS) / (1+ pUS) - 1 170. rUS = (1+ iUS) / (1+ pUS) - ((1+ pUS) / (1+ pUS) 171. rUS = ((1+ iUS) - (1+ pUS)) / (1+ pUS) 172. rUS = (iUS - pUS) / (1 + pUS) 173. ∴ PUS = 0 ⇔ iUS = rUS 174. PUS ≠ 0 ⇔ iUS = rUS + pUS + (rUS * pUS) ⇔ rUS = (iUS - pUS) / (1 + pUS)

Derivation of the IFE 175. FE ⇔ 1+ rUS = (1+ iUS) / (1+ pUS) 176. FE ⇔ 1+ rUK = (1+ i) / (1+ pUK) 177. LOOP ⇔ 1+ rUS = 1+ rUK 178. (1+iUS) / (1+ pUS) = (1+ iUK) / (1+ pUK) 179. (1+ iUS) / (1+ iUK) = (1+ pUS) / (1+ pUK) 180. ((1+iUS) / (1+iUK)) – 1 = ((1+ pUS) / (1+ pUK)) -1 181. ((1+ iUS) / (1+ iUK)) - ((1+ iUK) / (1+ iUK)) = ((1+ pUS) / (1+ pUK)) - ((1+ pUK) / (1+ pUK)) 182. ((1+ iUS) - (1+ iUK)) / (1+ iUK) = ((1+ p US) - (1+ pUK) ) / (1+ pUK) 183. (iUS - iUK) / (1+ iUK) = (pUS - pUK) / (1+ pUK)

APPENDIX 1

Accuracy of the Approximation of PPP-R 184. approximation = (ρE - ρS) / ρS ≈ pUS - pUK 185. exact formulation = (ρE - ρS) / ρS = (pUS - pUK) / (1 + pUK)

That is, if PPP-R holds, then the ratio of the approximation of the expected percentage change in the spot exchange rate to the exact percentage change in the spot exchange rate is: 186. (pUS - pUK) / ((pUS - pUK) / (1 + pUK)) = (1+ pUK) That is, if PPP-R holds, then the greater is the expected inflation of the £, the less accurate is the approximation. Note: This applies only when the exchange rate is in terms of $/£. If the exchange rate is in terms of £/$, then the ratio of the approximation of the expected percentage change in the spot exchange rate to the exact percentage change in the spot exchange rate is: 187. (pUK - pUS) / ((pUS - pUK) / (1 + pUK)) = (1+pUS) That is, if PPP-R holds, then the greater is the expected inflation of the $, the less accurate is the approximation. Note: This applies only when the exchange rate is in terms of £/$.

APPENDIX 2

Accuracy of the Approximation of PPP-F 188. approximation = (ρF - ρS) / ρS ≈ pUS - pUK 189. exact formulation = (ρF - ρS) / ρS = (pUS - pUK) / (1+ pUK) That is, if PPP-F holds, then the ratio of the approximation of the premium (discount) of the futures exchange rate over (under) the spot exchange rate, taken as a percentage with respect to the spot exchange rate, to the exact premium (discount) of the futures exchange rate over (under) the spot exchange rate, taken as a percentage with respect to the spot exchange rate is: 190. (pUS - pUK) / ((pUS - pUK) / (1+ pUK)) = 1+ pUK That is, if PPP-F holds, then the greater is the expected inflation of the £, the less accurate is the approximation. Note: This applies only when the exchange rate is in terms of $/£. If the exchange rate is in terms of £/$, then the ratio of the approximation of the premium (discount) of the futures exchange rate over (under) the spot exchange rate, taken as a percentage with respect to the spot exchange rate to the exact premium (discount) of the futures exchange rate over (under) the spot exchange rate, taken as a percentage with respect to the spot exchange rate is: 191. (pUK - pUS) / ((pUS - pUK) / (1+ pUK)) = 1+ pUS

That is, if PPP-F holds, then the greater is the expected inflation of the $, the less accurate is the approximation. Note: This applies only when the exchange rate is in terms of £/$.

APPENDIX 3

Accuracy of the Approximation of the FE 192. approximation = rUS ≈ iUS - pUS 193. exact formulation = rUS = (iUS - pUS) / (1+ pUS) That is, if the FE holds, then the ratio of the approximation of the expected real interest rate to the exact expected real interest rate is: 194. (iUS - pUS) / ((iUS - pUS) / (1+ pUS)) = 1+ pUS That is, if the FE holds, then the greater is the expected inflation of the $, the less accurate is the approximation. Note: This applies only to loans of $. The approximation of the FE for the £ is: 195. approximation = rUK ≈ iUK - pUK 196. exact formulation rUK = (iUK - pUK) / (1+ pUK) That is, if the FE holds, then the ratio of the approximation of the expected real interest rate to the exact expected real interest rate is: 197. (iUK -pUK) / (iUK - pUK) / (1+ pUK)) = 1+ pUK That is, if the FE holds, then the greater is the expected inflation of the £, the less accurate is the approximation. Note: This applies only to loans of £.

APPENDIX 5 Accuracy of the Approximation of the IFE

198. approximation = (ρE - ρ) / ρS ≈ iUS - iUK 199. exact formulation = (ρE - ρS) / ρS = (iUS - iUK) / (1+ iUK) That is, if the IFE holds, then the ratio of the approximation of the expected percentage change in the spot exchange rate to the exact percentage change in the spot exchange rate is: 200. (iUS - iUK) / ((iUS - iUK) / (1+ iUK)) = 1+ iUK That is, if the IFE holds, then the greater is the nominal interest rate on loans of £, the less accurate is the approximation. Note: This applies only when the exchange rate is in terms of $/£. If the exchange rate is in terms of £/$, then the ratio of the approximation of the expected percentage change in the spot exchange rate to the exact percentage change in the spot exchange rate is: 201. (iUK - iUS) / ((iUK - iUS) / (1+ iUS)) = 1+ iUS That is, if the IFE holds, then the greater is the nominal interest rate on loans of $, the less accurate is the approximation. Note: This applies only when the exchange rate is in terms of £/$.

APPENDIX 6 Accuracy of the Approximation of IRP (CAM) 202. approximation = (ρF - ρS) / ρS ≈ iUS - iUK 203. exact formulation = (ρF - ρS) / ρS = (iUS - iUK) / (1+ iUK) That is, if IRP holds, then the ratio of the approximation of the premium (discount) of the futures exchange rate over (under) the spot exchange rate, taken as a percentage with respect to the spot exchange rate to the exact premium (discount) of the futures exchange rate over (under) the spot exchange rate, taken as a percentage with respect to the spot exchange rate is: 204. (iUS - iUK) / ((iUS - iUK) / (1+ iUK)) = 1+ iUK That is, if IRP holds, then the greater is the nominal interest rate on loans of £, the less accurate is the approximation. Note: This applies only when the exchange rate is in terms of $/£. If the exchange rate is in terms of £/$, then the ratio of the approximation of the premium (discount) of the futures exchange rate over (under) the spot exchange rate, taken as a percentage with respect to the spot exchange rate to the exact premium (discount) of the futures exchange rate over (under) the spot exchange rate, taken as a percentage with respect to the spot exchange rate is: 205. ((iUK - iUS) / (iUK - iUS)) * (1+ iUS) = 1+ iUS That is, if IRP holds, then the greater is the nominal interest rate on loans of $, the less accurate is the approximation. Note: This applies only when the exchange rate is in terms of £/$.

H4: THE CURRENT ACCOUNT BALANCE, FINANCIAL ACCOUNT BALANCE, AND FLUCTUATING EXCHANGE RATES, ABSENT GOVERNMENT

INTERVENTION IN THE FOREIGN EXCHANGE MARKET

William Barnett II May 24, 2001

Notation: US = United States of America $ = US dollar(s) RoW = the Rest of the World FC = Foreign currencies CA = the US's current account balance FA = the US's financial account balance BOP = the US's balance of payments ↑ = increases or increasing ↓ = decreases or decreasing APP = appreciation or appreciating DEP = depreciation or depreciating G&S = goods and services; refers to those consumer and capital goods and services counted in the CA R&FA = those real assets and long and short term financial assets counted in the FA $↑ = an appreciation of the $; i.e., an increase in the value of the $ relative to an appropriately weighted basket of FC. (a ↓ in the # of $ it takes to buy an appropriately weighted basket of FC) $↓= a DEP of the $; i.e., a decrease in the value of the $ relative to an appropriately weighted basket of FC. (an ↑ in the # of $ it takes to buy an appropriately weighted basket of FC) POINTS TO REMEMBER 1. If a country’s currency is overvalued at the current exchange rate, there will be: 1) a surplus of that currency on the foreign exchange markets; and, 2) a deficit in that country’s BOP. The result, in a system of fluctuating exchange rates, will be a depreciation of that currency. Therefore, if the US has a deficit in its BOP with the RoW (which implies an exactly equal surplus in the RoW's BOP with the US), the appropriately weighted average exchange rate of the $ will depreciate until the imbalance (deficit) is eliminated. 2. If a country’s currency is undervalued at the current exchange rate, there will be: 1) a shortage of that currency on the foreign exchange markets; and, 2) a surplus in that country’s BOP. The result, in a system of fluctuating exchange rates, will be an appreciation of that currency. Therefore, if the US has a surplus in its BOP with the RoW (which implies an exactly equal deficit in the RoW's BOP with the US), the appropriately weighted average exchange rate of the $ will appreciate until the imbalance (deficit) is eliminated. 3. Because such appreciations/depreciations occur very rapidly: US BOP = RoW BOP = 0

4. Since the CA + FA = BOP, and BOP = 0, then CA = − FA. Therefore, a deficit in the US's CA (which implies an exactly equal surplus in the RoW's CA) implies an exactly equal surplus in the US's FA (which implies an exactly equal deficit in the RoW's FA). Further, a surplus in the US's CA (which implies an exactly equal deficit in the RoW's CA) implies an exactly equal deficit in the US's FA (which implies an exactly equal surplus in the RoW's FA). Therefore: US CA deficit = US FA surplus = RoW CA surpluS = RoW FA deficit and US CA surplus = US FA deficit = RoW CA deficit = RoW FA surplus. Also: US CA deficit ↑ = US FA surplus ↑ = RoW CA surplus ↑ = RoW FA deficit ↑ US CA surplus ↓ = US FA deficit ↓ = RoW CA deficit ↓ = RoW FA surplus ↓ and US CA deficit ↓ = US FA surplus ↓ = RoW CA surplus ↓ = RoW FA deficit ↓ US CA surplus ↑ = US FA deficit ↑ = RoW CA deficit ↑ = RoW FA surplus ↑ ======================================================================== Consider the possibilities. I. The US has a deficit in the CA and the deficit is ↑ while $↓. Of course, if the US CA deficit is ↑ then, of necessity, the surplus in the US FA, the RoW CA surplus, and the RoW FA deficit are all also ↑. (Analytically, this situation is no different from one in which the US has a CA surplus and the surplus is ↓ while $↓. Of course, if the US CA surplus is ↓ then, of necessity, the US FA deficit, the RoW CA deficit, and the RoW FA surplus are all also ↓. Call this situation I-A.) There are two possible causes of situation I or I-A. Since both situations involve $↓, the causes must involve either an ↑ in US demand for FC (which implies an ↑ in US supply of $) or a ↓ in RoW demand for $ (which implies a ↓ in RoW supply of FC). The two possible causes of I or IA are: 1. An ↑ in US demand for RoW G&S. Because of desire of the US to ↑ purchases of RoW G&S the US demand for FC (US supply of $) would ↑, causing $↓. The ↑ purchases by the US of RoW G&S would cause the US CA deficit (situation I) to ↑ or the US CA surplus (situation I-A) to ↓, with concomitant effects on the US FA, RoW CA, and RoW FA. 2. A ↓ in RoW demand for US G&S. Because of the desire of the RoW to ↓ purchases of US G&S the RoW demand for $ (RoW supply of FC) ↓, causing $↓. The ↓ purchases by the RoW of US G&S would cause the US CA deficit (situation I) to ↑ or the US CA surplus (situation I-A) to ↓, with concomitant effects on the US FA, RoW CA, and RoW FA.

II. The US has a CA deficit and the deficit is ↓ while $↓. Of course, if the US CA deficit is ↓ then, of necessity, the US FA surplus, the RoW CA surplus, and the RoW FA deficit are all also ↓. (Analytically, this situation is no different from one in which the US has a CA surplus and the surplus is ↑ while $↓. Of course, if the US CA surplus is ↑ then, of necessity, the US FA deficit, the RoW CA deficit, and the RoW FA surplus are all also ↑. Call this situation II-A.) There are two possible causes of situation II or II-A. Since both situations involve $↓, the causes must involve either an ↑ in US demand for FC (which implies an ↑ in US supply of $) or a ↓ in RoW demand for $ (which implies a ↓ in RoW supply of FC). The two possible causes are: 1. An ↑ in US demand for RoW R&FA. Because of desire of the US to ↑ purchases of RoW R&FA the US demand for FC (US supply of $) would ↑, causing $↓. The ↑ purchases by the US of RoW RFA would cause the US FA surplus (situation II) to ↓ or the US FA deficit (situation II-A) to ↑, with concomitant effects on the US FA, RoW CA, and RoW FA. 2. A ↓in RoW demand for US R&FA. Because of the desire of the RoW to ↓ purchases of US R&FA the RoW demand for $ (RoW supply of FC) ↓, causing $↓. The ↓ purchases by the RoW of US R&FA would cause the US FA surplus (situation II) to ↓ or the US FA deficit (situation II-A) to ↑, with concomitant effects on the US FA, RoW CA, and RoW FA. III. The US has a CA deficit and the deficit is ↑ while $↑. Of course, if the US CA deficit is ↑ then, of necessity, the US FA surplus, the RoW CA surplus, and the RoW FA deficit are all also ↑. (Analytically, this situation is no different from one in which the US has a CA surplus and the surplus is ↓ while $↑. Of course, if the US CA surplus is ↓ then, of necessity, the US FA ↓, the RoW CA deficit, and the RoW FA surplus are all also ↓. Call this situation III-A.) There are two possible causes of situation III or III-A. Since both situations involve $↑, the causes must involve either a ↓ in US demand for FC (which implies a ↓ in US supply of $) or an ↑ in RoW demand for $ (which implies an ↑ in RoW supply of FC) The two possible causes are: 1. A ↓ in US demand for RoW RFA. Because of desire of the US to ↓ purchases of RoW R&FA the US demand for FC (US supply of $) would ↓, causing $↑. The ↓ purchases by the US of RoW R&FA would cause the US FA surplus (situation III) to ↑ or the US FA deficit (situation III-A) to ↓, with concomitant effects on the US FA, RoW CA, and RoW FA. 2. An ↑ in RoW demand for US R&FA. Because of the desire of the RoW to ↑ purchases of US R&FA the RoW demand for $ (RoW supply of FC) ↑, causing $↑. The ↑ purchases by the RoW of US R&FA would cause the US FA surplus (situation III) to ↑ or the US FA deficit (situation III-A) to ↓, with concomitant effects on the US FA, RoW CA, and RoW FA.

IV. The US has a CA deficit and the deficit is ↓ while $↑. Of course, if the US CA deficit is ↓ then, of necessity, the US FA surplus, the RoW CA surplus, and the RoW FA deficit are all also ↓. (Analytically, this situation is no different from one in which the US has a CA surplus and the surplus is ↑ while $↑. Of course, if the US CA surplus is ↑ then, of necessity, the US FA ↓, the RoW CA ↓, and the RoW FA surplus are all also ↑. Call this situation IV-A.) There are two possible causes of situation IV and IV-A. Since both situations involve $↑, the causes must involve either a ↓ in US demand for FC (which implies a ↓ in US supply of $) or an INC in RoW demand for $ (which implies an ↑ in RoW supply of FC). The two possible causes are: 1. A ↓ in US demand for RoW G&S. Because of desire of the US to ↓ purchases of RoW G&S the US demand for FC (US supply of $) would ↓, causing $↑. The ↓ purchases by the US of RoW G&S would cause the US CA deficit (situation IV) to ↓ or the US CA SURPLUS (situation IV-A) to ↑, with concomitant effects on the US FA, RoW CA, and RoW FA. 2. An↑in RoW demand for US G&S. Because of the desire of the RoW to ↑ purchases of US G&S the RoW demand for $ (RoW supply of FC) ↑, causing $↑. The ↑ purchases by the RoW of US G&S would cause the US CA deficit (situation IV) to ↓ or the US CA SURPLUS (situation IV-A) to ↑, with concomitant effects on the US FA, RoW CA, and RoW FA. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

1C. An ↑ in US supply of R&FA to RoW. Because of the desire of the US to ↑ sales of US R&FA the US demand for FC (US supply of $) INC, causing $-DEP. The INC sales by the US of FA RFA would cause the US FA SURPLUS (situation 1) to INC or the US FA DEFICIT (situation 1A) to DEC, with concomitant effects on the US CA, RoW CA, and RoW FA. 1D. A DEC in RoW SUPPLY of FA RFA to US. Because of the desire of the RoW to DEC sales of RoW FA RFA the RoW DEMAND FOR $ (SUPPLY of FC) DEC, causing $-DEP. The DEC sales by the RoW of FA RFA would cause the US FA SURPLUS (situation 1) to INC or the US FA DEFICIT (situation 1A) to DEC, with concomitant effects on the US CA, RoW CA, and RoW FA.

2C. An INC in US SUPPLY of CA G&S to RoW. Because of the desire of the US to INC sales of US CA G&S the US DEMAND for FC (SUPPLY of $) INC, causing $-DEP. The INC sales by the US of CA G&S would cause the US CA DEFICIT (situation 2) to DEC or the US CA SURPLUS (situation 2A) to INC, with concomitant effects on the US CA, RoW CA, and RoW FA.

2D. A DEC in RoW SUPPLY of CA G&S to US. Because of the desire of the RoW to DEC sales of RoW CA G&S the RoW DEMAND FOR $ (SUPPLY of FC) DEC, causing $-DEP. The DEC sales by the RoW of CA G&S would cause the US CA DEFICIT (situation 2) to DEC or the US CA SURPLUS (situation 2A) to INC, with concomitant effects on the US CA, RoW CA, and RoW FA.

3C. A DEC in US SUPPLY of CA G&S to RoW. Because of the desire of the US to DEC sales of US CA G&S the US DEMAND for FC (SUPPLY of $) DEC, causing $-APP. The DEC sales by the US of CA G&S would cause the US CA DEFICIT (situation 3) to INC or the US CA SURPLUS (situation 3A) to DEC, with concomitant effects on the US CA, RoW CA, and RoW FA. 3D. An INC in RoW SUPPLY of CA G&S to US. Because of the desire of the RoW to INC sales of RoW CA G&S the RoW DEMAND FOR $ (SUPPLY of FC) INC, causing $-APP. The INC sales by the RoW of CA G&S would cause the US CA DEFICIT (situation 3) to INC or the US CA SUF (situation 3A) to DEC, with concomitant effects on the US CA, RoW CA, and RoW FA.

4C. A DEC in US SUPPLY of FA RFA to RoW. Because of the desire of the US to DEC sales of US FA RFA the US DEMAND for FC (SUPPLY of $) DEC, causing $-APP. The DEC sales by the US of FA RFA would cause the US FA SURPLUS (situation 4) to DEC or the US FA DEFICIT (situation 4A) to INC, with concomitant effects on the US CA, RoW CA, and RoW FA. 4D. An INC in RoW SUPPLY of FA RFA to US. Because of the desire of the RoW to INC sales of RoW FA RFA the RoW DEMAND FOR $ (SUPPLY of FC) INC, causing $-APP. The INC sales by the RoW of FA RFA would cause the US FA SURPLUS (situation 4) to DEC or the US FA DEFICIT (situation 4A) to INC, with concomitant effects on the US CA, RoW CA, and RoW FA.

1

Notes

1. The terms "debtor nation" and "creditor nation" are highly unsatisfactory for several reasons. First, only people, individually or in groups, can be debtors or creditors. Second, the people of every nation, taken as a whole, always both hold claims against foreigners and have claims held against them by foreigners. Therefore aggregate net claims are what determines a nation's debtor or creditor status. But this datum has limited usefulness to decision-makers in international financial markets. In fact, it is highly unlikely that any individual nation will end up with a zero balance in the BOT over any reasonably short period of time. Thus, all nations exhibit deficits or surpluses. And except for rare, fleeting moments are either net debtors or net creditors. Further, in and of itself, it is not a cause for concern for a debtor whether it is running deficits or surpluses. Third, from the point of view of decision makers, the citizenship or residency of those people against whom they hold claims or who hold claims against them is of virtually no importance. In fact, many, if not most, debtors and creditors do not know who their creditors and debtors, respectively, are. What is important to existing creditors is that they receive what they are due, timely, and to existing debtors, that they pay what they owe, timely. And, for prospective borrowers and lenders, what is important are the terms and conditions of the prospective loans, and the risks involved. Fourth, it is not at all clear what meaning ought be attached to the terms "foreign" and "foreigner" in this context. And yet this is a crucial matter, for if a nation is a debtor or creditor this must mean that on net the rest of the world holds claims against it or it holds claims against them, respectively. That is either they owe foreigners or foreigners owe them. But who are these foreigners and what constitutes foreign debt? Should a U.S. T-bill owned by a citizen of some other nation, resident in the U.S.A. be considered foreign debt? Does the answer hinge on whether the individual is permanently or only temporarily residing in the U.S.A.? Should a U.S. T-bill owned by a citizen of the U.S.A., resident in some other nation be considered foreign debt? Does the answer hinge on whether the individual is permanently or only temporarily residing in the other nation? Does it matter, in any case, whether the actual physical evidence of the claim is located in the U.S.A. or some other nation? And what of securities sold by a corporation chartered in the U.S.A., of whose stockholders some are resident citizens of the U.S.A., some non-resident citizens, some resident non-citizens, and some non-resident non-citizens? Does it make any difference where the securities were issued, or where they were and are subsequently traded, or in what currency they are denominated? Further, since it is exports and imports of goods and services which create, respectively, claims against foreigners and foreigners' claims against a nation, the terms "exports" and "imports" implying, as they do, physical movement between nations, also are unsatisfactory.

Thus to speak of the U.S.A.'s trade deficit and the U.S.A. as a debtor nation, as a matter of concern, is to exhibit a certain degree of nationalism. It should make no difference to the debtor or creditor in any loan transaction whether the other party is a fellow national or a "foreigner," ceteris paribus, unless the debtor intends to try to use that difference as a means, in one way or another, to take advantage of the creditor, in a way inconsistent with the original intent of the loan contract; i.e., unless the debtor hopes to use that difference as a basis to induce governmental intervention to the creditor's detriment. Neither is debt qua debt, nor are deficits qua deficits, cause for concern. Rather, what is important are two other matters: 1) the nature of the activities for which the debt was incurred to finance; and, 2) the type of activity which the deficit is making possible. At least one, and possibly one additional, type of activity is fit grist for the mill of deficit/debt relationships. These are, respectively: 1) investment in capital goods; and, 2) purchases of durable consumer goods. Running a BOT deficit and incurring debt in order to increase the capability to produce is acceptable because such activity is engaged in only if it is expected that the debt, both principal and interest, can be repaid from the proceeds of the additional output produced with the additional capital goods. Some would say that it also is acceptable to finance durable consumer goods via deficit/debt as a method by which to coordinate intertemporally the benefits and costs of such goods. There is, however, general agreement that for one type of activity, except in the most dire emergencies, deficit/debt relationships are absolutely inappropriate. This is the financing of purchases of consumer goods for periods in excess of their economic lives; i.e., living beyond one's means, current and future. This latter case inevitably leads to the need to reduce living standards in the future, or to borrow ever more in the future - with, inescapably, one of two results, when lenders will no longer support such borrowing: a lowering of living standards or a repudiation of the debt in part or sum. (It makes no difference if such repudiation is disguised as moratoria of payments of principal or interest, or renegotiated terms more favorable to the debtor, extracted under threat of formal bankruptcy or repudiation.) Thus, throughout this paper when we speak of a nation we mean the citizens thereof, thusly: The deficit/debt situation is of serious concern because it has been a sine qua non for the U.S.A. (meaning the citizens thereof) to live beyond its (their) means. 1. The generalized Marshall-Lerner conditions for a decrease in a U.S. BOT deficit with another country, as a result of a depreciation of the $ against the other country's money are: d$BOT/dR = ($EX / ρS) * ((($IM /

$EX) * (Elas:EXUK) * (1+ Elas:IMUS) / (Elas:IMUS - Elas:EXUK)) - ((Elas:IMUK) * (1+ Elas:EXUS) / (Elas:EXUS - Elas:IMUK))) > 0 Where: UK : the United Kingdom; the other country d$BOT : the change in the US BOT with the UK in terms of $ ρS : the spot exchange rate in terms of $/£

$EX : the value in $ of US exports $IM : the value in $ of US imports Elas:EXUS : the elasticity of US supply of exports Elas:IMUS : the elasticity of US demand for imports Elas:EXUK : the elasticity of UK supply of exports Elas:IMUK : the elasticity of UK demand for imports The US's elasticities of demand and supply are with respect to changes in $ prices and the UK's elasticities of demand and supply are with respect to changes in £ prices.. The usual conclusion is that the relevant elasticities are such that depreciations are stabilizing; i.e., depreciations reduce BOT deficits of the depreciating nations, at least for industrialized nations. 1. The term "net capital flows" does not refer to international movements of real capital goods, but rather to increases or decreases in net foreign claims against a nation's real assets. A nation is said to have a "net capital outflow" (net foreign disinvestment) or "net capital inflow" (net foreign investment), as the net foreign claims against its assets increase or decrease, respectively. 1. One simple, but frequently encountered, problem in BOT analysis is a failure to distinguish between values and volumes. Thus, when a depreciation in the value of a nation's currency causes the volume of its exports to rise and that of its imports to decline, conversion of these new volumes into values at the new exchange rate and prices, is frequently neglected. The analysis is then conducted, implicitly, in volume, not value, terms. But, of course, it is value, not volume, that is relevant for BOT analysis. 1. Typical of the nonsense written on this subject is the following: "The distinction between traded and nontraded goods is especially important for small trading communities. Local prices of nontraded goods are determined by local conditions affecting demand and supply. Local prices of traded goods (whether exportables or importables) are determined for this country by conditions in the rest of the world. Through policy changes, the home country can affect prices of nontraded goods, but it cannot affect prices of traded goods.(Note 14) In any case, a country produces all its nontraded goods as well as whatever exportables are suggested by comparative advantage and importables that prove competitive with world prices augmented by the relative transportation costs." (Note 14) "This distinction is important in such questions as the effect of exchange-rate changes for a small country." - Richard E. Caves and Ronald W. Jones, World Trade and Payments, pg. 122, 2 ed., 1977, Little, Brown and Company 1. Richard E. Caves and Ronald W. Jones, World Trade and Payments, pp. 332-333, 2 ed., 1977, Little, Brown and Co.

1. Another way of phrasing the issue is: "Why is the U.S.A. selling assets, i.e., capital goods and claims against future goods, in order to import consumer goods?" 1. Let: BOT : the U.S. balance of trade with the United Kingdom (UK) ROW : the rest of the world $ : US dollar £ : UK's money $PX: the $ prices of the USA's BOT type goods $PA: the $ prices of the USA's non-BOT type goods £PM : the £ prices of the UK's BOT type goods £PA: the £ prices of the UK's non-BOT type goods ρS : the spot exchange rate in terms of $/£ S : the ratio of the $ prices of the USA's BOT type goods to the $ prices of the UK's BOT type goods T : the ratio of the $ prices of the USA's non-BOT type goods to the $ prices of the UK's non-BOT type goods R : the ratio of 1) the ratio of the $ prices of the USA's BOT type goods to the $ prices of the USA's non-BOT type goods; to, 2) the ratio of the $ prices of the UK's BOT type goods to the $ prices of the UK's non-BOT type goods Then: R = ($PX /

$PA) / ((£PM * ρS)/( £PA * ρS)) = ($PX / (£PM * ρS)) / ($PA / (£PA * ρS)) S = $PX /( £PM * ρS) T = $PA / (£PA * ρS) Thus: P = S / T If: BOT = f(R); with dBOT / R < 0 Given: R = g(ρS); with dR/dρS = 0 Then: dBOT/dρS = [dBOT/dR] * [dR/dρS] But : dR/dρS = 0 Thus: dBOT/dρS = 0 Note that in any case the exchange rate, dρS, cancels out in the Eq. for R. Compare with the standard formulation: If: BOT = h(S); with dh(S) < 0 Given: S = j(dρS); with: dS / dρS = - $PX / (£PM * (ρS)2) < 0 Thus: dBOT / dρS = (dBOT / dS) * (dS / dR)

But: dS/dR < 0 Thus: dBOT/dR < 0

That is, the error in the standard theory is the omission of the ratio of the prices of non-BOT type goods of the ROW to those of the US. This omission is fatal to the standard theory. 1. Real per unit labor cost is defined as total monetary labor cost per man-hour, relative to product prices, and adjusted for productivity; i.e., (W / P) / (Q / L) = (W * L) / (P * Q) where W = total monetary labor cost per man-hour, P = price of output, Q = real output and L = man-hours of labor. It is measured as the fraction of a unit of output which the employer must relinquish in order to acquire labor. 1. BOT deficits are not considered to be problems if, and, when they are incurred to finance economically sound investments. BOP deficits, however, always are considered to be problems; but whether they are problems of the deficit nation(s), or of the surplus nation(s) (of which there must be at least one if there is a deficit nation), or of both, is not clear. Although BOP deficits usually are considered to be problems of the deficit nation(s), we think that they are problems of the surplus nation(s) which, however, usually are caused by the deficit nation(s).

H6: Gold Export and Import Points When the U.S. mint stood ready to buy gold from, or sell gold to, anyone who wished at the price of $35 per (troy) ounce and the Royal mint stood ready to buy gold from, or sell gold to, anyone who wished at the price of £14.58⅓ per (troy) ounce, the mint parity ratio was $35/oz ÷ £14.58 ⅓/oz = $2.40/£1. If the transaction expenses, including brokerage fees, transportation fees, insurance fees, and foregone interest, of buying gold in one country and selling it in the other were, say, 1%, then the gold export point for the U.S would have been $2.424/£1 and the gold import point would have been $2.3762376…+/£1. Then if the actual exchange rate between the $ and £ went above $2,424/£1, it would have been profitable to buy gold, say 30,000 oz, from the U.S. mint for $1,050,000 @ $35/oz and export the gold to the UK, and sell the 30,000 oz to the Royal mint for £437,500 @ £14.58⅓/oz. The £437,500 could then have been exchanged for $1,060,500+ (i.e., more than $1,060,500). That is, at exactly $2.424/£1 there would be no profit as the $10,500 gain ($1,060,500 − $1050,000) would have been just sufficient to cover the transactions expenses (0.01×$1,050,000). There would be a $437.50 profit, after all expenses, for each for one-tenth of a penny the exchange rate was above $2.424/£1. Alternatively, if the actual exchange rate between the $ and £ went below $2,3762376…/£1, it would have been profitable to buy gold, say 30,000 oz, from the Royal. mint for £437,500 @ £14.58⅓ oz and export the gold to the U.S., and sell the 30,000 oz to the U.S. mint for $1,050,000 @ $35/oz. The $1,050,000 could then have been exchanged for £441,875+ (i.e., more than £441,875). That is, at exactly $2.3762376…/£1 there would be no profit as the £4,375 gain (£441,875 − £437,500) would have been just sufficient to cover the transactions expenses (0.01×£437,500). There would be approximately £186 profit, after all expenses, for each for one-tenth of a penny the exchange rate was below $2.3762376…/£1.