Open-Economy Macroeconomics: Key Concepts and Formulas (12-1 to 12-5)

12-1 The International Flows of Goods and Capital

• Open economy interacts with other economies in two main ways: by trading goods and services in world product markets, and by trading capital assets (stocks and bonds) in world financial markets.
• Two key international flows:
  • Flow of goods and services: exports and imports. Net exports (NX) measures the trade balance of a country.
  • Flow of capital: net capital outflow (NCO) measures the purchase of foreign assets by domestic residents minus the purchase of domestic assets by foreigners.
• Key definitions:
  • Exports: domestically produced goods/services sold abroad.
  • Imports: foreign-produced goods/services sold domestically.
  • Net exports (NX): NX = ext{Value of country’s exports} - ext{Value of country’s imports}
  • If NX > 0, country runs a trade surplus; if NX < 0, trade deficit; NX = 0 means balanced trade.
• Important identity for open economies: net exports and net capital outflow are two sides of the same coin; they are linked by the accounting identity NX = NCO. This is an identity that must hold because every international transaction involves an exchange of one type of asset for a good or service.
• Why factors that affect NX matter: tastes for domestic vs foreign goods, prices at home/abroad, exchange rates, incomes, transport costs, and government trade policies all influence exports, imports, and NX.

12-1a The Flow of Goods: Exports, Imports, and Net Exports

• Exports are goods/services produced domestically and sold abroad; imports are foreign goods/services purchased domestically.
• Examples:
  • Bombardier sells subway trains to Paris → Canada exports; France imports.
  • Volvo car sells to Canada → Canada imports; Sweden exports.
• Net exports (NX) measure whether a country is a net seller or buyer in world markets for goods/services; NX is also called the trade balance.
• Classification of NX:
  • Positive NX: trade surplus (exports > imports).
  • Negative NX: trade deficit (exports < imports).
  • Zero NX: balanced trade (exports = imports).
• Factors that influence NX (and thus NX’s value): tastes, relative prices, exchange rates, incomes, transportation costs, and government trade policies.

12-1b The Flow of Financial Resources: Net Capital Outflow

• In addition to trading goods/services, residents participate in world financial markets by trading financial assets (stocks, bonds).
• Net Capital Outflow (NCO) is the purchase of foreign assets by domestic residents minus the purchase of domestic assets by foreigners:
  • NCO = ext{Purchase of foreign assets by domestic residents} - ext{Purchase of domestic assets by foreigners}
• NCO can be positive (capital flows out) or negative (capital flows in).
• Examples:
  • A Canadian buying Mexican government bonds → increases NCO (capital outflow for Canada).
  • A Japanese resident buying Canadian government bonds → decreases Canada’s NCO (capital inflow).
  • Direct investment (e.g., opening a subsidiary abroad) vs portfolio investment (buying stocks/bonds).
• Relationship to NX: NX is the trade balance in goods/services; NCO is the balance of financial assets cross-border. Both flows must balance in an economy on a global basis, which leads to the key identity NX = NCO.

12-1c The Equality of Net Exports and Net Capital Outflow

• NX and NCO are equal for an economy as a whole (NX = NCO): every international transaction affects one side of the identity by the same amount as the other.
• Example: Bombardier sells subway trains to Japan. Canada records an export (NX rises). At the same time, Canada acquires yen as payment, which is a foreign asset; this increases NCO.
• The equality holds because transactions are exchanges: a sale of goods for foreign currency/assets links NX and NCO by the same value.
• Implications for trade balances:
  • If a country runs a trade surplus (NX > 0), it is also experiencing a net outflow of capital (NCO > 0): capital leaves the country to acquire foreign assets.
  • If a country runs a trade deficit (NX < 0), it is financing the deficit by attracting foreign investment (NCO < 0).
• FYI: Current account balance is defined as
  • ext{Current account balance} = NX + ext{Net inflow of dividends and interest payments}
  • Dividends/interest are part of the current account; in many basic analyses they are often ignored, but they are included in the broader accounting for accuracy.

12-1d Saving, Investment, and Their Relationship to the International Flows

• The economy’s GDP identity (with NX) is:
  • Y = C + I + G + NX
• National saving (S) is income not spent on current consumption and government purchases:
  • S = Y - C - G
• By rearranging the GDP identity and using saving, investment, and NX, we obtain:
  • S = I + NX
  • Since NX = NCO, this can also be written as S = I + NCO
• Interpretation: a nation’s saving can be used either to finance domestic investment (I) or to purchase foreign assets (NCO).
• Closed-economy special case: NCO = 0 → S = I
  ight) saving must equal domestic investment.
• Open-economy interpretation with a saving example (capital allocation): savings may fund domestic investment or foreign investment through financial markets (e.g., mutual funds investing domestically or abroad).
• Table 12.1 (summary of three outcomes for an open economy):
  • Trade Deficit: Exports < Imports (NX < 0) → Y < C + I + G → S < I → NCO < 0.
  • Balanced Trade: Exports = Imports (NX = 0) → Y = C + I + G → S = I → NCO = 0.
  • Trade Surplus: Exports > Imports (NX > 0) → Y > C + I + G → S > I → NCO > 0.

12-1e Summing Up

• Three key relationships in an open economy:
  • NX > 0 (trade surplus) implies NCO > 0 (capital outward flow) and S > I.
  • NX = 0 (balanced trade) implies NCO = 0 and S = I.
  • NX < 0 (trade deficit) implies NCO < 0 (capital inflow) and S < I.
• Saving, investment, and international capital flows are tightly linked through the identities NX = NCO and S = I + NCO.
• These identities form the basis for analyzing how policy, saving behavior, and global financial conditions affect a country’s trade balance and capital flows.

12-2 The Prices for International Transactions: Real and Nominal Exchange Rates

• In addition to quantities (NX and NCO), economists study the prices at which international transactions occur: nominal and real exchange rates.
• Nominal exchange rate is the rate at which you can trade one currency for another; e.g., 80 yen per dollar.
• Expressions and conventions:
  • If the rate is 80 yen per dollar, 1 dollar = 80 yen; equivalently, 1/80 dollar per yen.
  • In this text, the nominal exchange rate is expressed as units of foreign currency per Canadian dollar (e.g., 80 yen per CAD).
  • Appreciation vs depreciation: if the dollar buys more foreign currency, the dollar appreciates; if it buys less, the dollar depreciates.
• Exchange-rate indices: to summarize movements across many currencies, economists use an index; the Bank of Canada’s Canadian-dollar effective exchange-rate index (CERI) includes six currencies (USD, EUR, JPY, GBP, CNY, MXN) with weights based on trade shares; about 80% of Canada’s trade is with the United States, so CAD/USD movements dominate the index.

12-2b Real Exchange Rates

• Real exchange rate (RER) measures how many goods and services in one country you can trade for goods/services in another country. It is the price-adjusted measure of the exchange rate.
• Definition (as given):
  • ext{Real exchange rate} = rac{e imes P}{P^*}
  • Here, e is the nominal (foreign currency per domestic currency) exchange rate, P is the domestic price level, and P^* is the foreign price level.
• Example logic: if a bushel of Canadian wheat costs 200 and a bushel of Russian wheat costs 1600 rubles, and the nominal rate is 4 rubles per dollar, then the price in rubles of Canadian wheat is 200 imes 4 = 800 rubles; the real exchange rate shows whether Canadian wheat is cheaper or more expensive relative to Russian wheat.
• Implication: lower real exchange rate (depreciated real value) means Canadian goods are cheaper relative to foreign goods, boosting NX; higher real exchange rate means Canadian goods are more expensive, reducing NX.
• The real exchange rate is tied to price levels and the nominal rate; changes in the money supply affect price levels and thus influence the nominal and real exchange rates.

12-3 A First Theory of Exchange-Rate Determination: Purchasing-Power Parity (PPP)

• PPP is a long-run theory asserting that a unit of currency should buy the same quantity of goods in every country (law of one price extended across borders).
• 12-3a The Basic Logic of PPP
  • Law of one price: identical goods should sell for the same price in different locations; arbitrage eliminates price differentials.
  • If a good costs more in one country, arbitrage would move demand toward the cheaper market, eliminating the price difference.
  • Extending to currencies: PPP implies a currency should have the same purchasing power across countries; thus the nominal exchange rate should reflect relative price levels.
  • PPP relation (derived): the nominal exchange rate equals the ratio of foreign to domestic price levels, i.e.,
  • e = rac{P^*}{P}
  • Equivalently, the condition that the real exchange rate remains at unity under PPP: 1 = rac{e imes P}{P^*}.
• 12-3b Implications of PPP
  • If price levels rise faster in Canada than in the foreign country, the Canadian dollar should depreciate to restore PPP; conversely, lower relative inflation leads to appreciation.
  • In the long run, the real exchange rate should hover around the PPP level; large long-run movements in nominal exchange rates typically reflect changes in price levels (inflation) rather than short-run mispricing.
• 12-3c Limitations of PPP
  • PPP is a useful first approximation but not exact:
  • Non-tradable goods (e.g., haircuts) cannot be arbitraged away easily, so price differences persist.
  • Even tradable goods may not be perfect substitutes across countries due to consumer preferences, quality differences, brand loyalties, etc.
  • PPP can explain long-run trends (e.g., depreciation of CAD vs DM in the past) but not exact short-run movements.
• Case study: The Hamburger Standard (Big Mac Index)
  • The Economist uses Big Mac prices to compare PPP across countries. Example data from 2018:
  • Canada: price ≈ 6.55 CAD; US: price ≈ 5.28 USD; predicted rate ≈ 1.24 CAD/USD; actual ≈ 1.25 CAD/USD.
  • South Korea: price ≈ 833.3 won; predicted ≈ 1,069.3 won/USD; actual ≈ 1,069.3 won/USD (close).
  • Japan: price ≈ 380 yen; predicted ≈ 72.0 yen/USD; actual ≈ 110.7 yen/USD (far from PPP).
  • Sweden, Mexico, Euro area, Britain data also shown; predictions and actuals usually in the same ballpark, but not exact.
  • Conclusion: PPP provides a reasonable first approximation but is not a precise predictor of exchange rates; market arbitrage in practice can be imperfect.

12-4 Interest Rate Determination in a Small Open Economy with Perfect Capital Mobility

• The following framework describes Canada as a small open economy with perfect capital mobility in world financial markets.
• 12-4a A Small Open Economy
  • A small open economy has negligible impact on world prices and world interest rates; its own actions do not affect global financial conditions.
• 12-4b Perfect Capital Mobility
  • With perfect capital mobility, the domestic real interest rate must equal the world real interest rate: r = r^w
  • Intuition: if domestic rates differ from world rates, rational savers/investors would arbitrage away the difference by shifting funds across borders until the rates equalize.
  • Example logic:
  • If r^w = 8 ext{%} and r = 5 ext{%}, savers would shift to foreign assets paying 8%, forcing domestic borrowers to raise the domestic rate to attract funds, bid up to 8%.
  • Conversely, if r^w = 5 ext{%} and r = 8 ext{%}, borrowers would borrow from abroad, bringing the domestic rate down toward 5%
• 12-4c Limitations to Interest Rate Parity
  • Two key reasons why real interest rate parity may not hold exactly:
  • Default risk: the possibility of debt default is higher in some countries; lenders demand a risk premium, causing after-tax and pre-tax returns to diverge; even after arbitrage, differences may persist.
  • Tax treatment differences: different tax regimes mean after-tax returns may be equalized across countries even if pre-tax returns differ; thus arbitrage operates on after-tax returns, not pre-tax rates.
  • Empirical evidence: over 1984–2017, Canadian and U.S. real interest rates moved together, with a small average gap (Canada about 3.5%, U.S. about 2.8%); the gap narrowed since 1996 (about 0.3 percentage points on average).
  • Conclusion: while real interest rate parity is not exact due to default risk and taxation, it remains a persuasive framework suggesting that Canadian real interest rates tend to move with world rates.

12-5 Conclusion

• The chapter develops key concepts for open economies:
  • NX = NCO: net exports equal net capital outflow.
  • S = I + NCO: national saving equals domestic investment plus net capital outflow.
  • Real and nominal exchange rates; PPP as a theory for exchange-rate determination and its limitations.
  • Interest rate parity in a small open economy with perfect capital mobility: domestic real rates tend to align with world rates, subject to risk and tax considerations.
• These building blocks set the stage for modeling how trade balances and exchange rates respond to policy and external shocks in the next chapter.

Quick Quizzes and Case Highlights

• Quick Quiz (12-1): Define net exports and net capital outflow. Explain how they are related.
  • NX = Exports − Imports; NCO = Purchase of foreign assets by domestic residents − Purchase of domestic assets by foreigners; NX = NCO (identity).
• Quick Quiz (12-2): Define nominal exchange rate and real exchange rate, and explain how they are related.
  • Nominal: e.g., units of foreign currency per CAD; Real: ext{Real exchange rate} = rac{e imes P}{P^*}; PPP implies long-run relationship between price levels and exchange rates.
• Quick Quiz (12-4): Over the past 20 years, Brazil has higher inflation than Japan. What has happened to the number of Brazilian reais you can buy with a Japanese yen? (PPP intuition: higher inflation in Brazil relative to Japan tends to depreciate the real relative to the yen; fewer reais per yen.)

Illustrative Equations (recap)

• Net exports: NX = ext{Exports} - ext{Imports}
• Net capital outflow: NCO = ext{Purchase of foreign assets by domestic residents} - ext{Purchase of domestic assets by foreigners}
• Equality identity: NX = NCO
• GDP identity with NX: Y = C + I + G + NX
• Saving identity with NCO: S = I + NCO
• Current account balance: ext{Current account balance} = NX + ext{Net inflow of dividends and interest payments}
• Real exchange rate: ext{Real exchange rate} = rac{e imes P}{P^*}
• PPP nominal rate relation: e = rac{P^*}{P} ext{ (under PPP)}
• PPP condition in real terms: 1 = rac{e imes P}{P^*}
• Interest rate parity (conceptual): domestic real rate tends toward world real rate, i.e., r
  ightarrow r^w
• In a small open economy with perfect capital mobility: r = r^w