Exchange Rates and International Finance

International Finance and Short-Run Macroeconomics

• International trade of goods and services exceeds $20\%$ of Gross Domestic Product (GDP) in most countries globally.
• Exchange rate dynamics connect national economies through international trade, capital flows, and price adjustments across short-run and long-run horizons.

Historical International Monetary Systems

• The Gold Standard System:

  • Individual national currencies were directly tied and pegged to a fixed weight of gold.
  • Maintained fixed exchange rates through gold convertibility.

• The Bretton Woods System:

  • A gold-exchange standard established post-World War II.
  • The United States dollar ($US\text{ dollar}$ or \) was pegged directly to gold at a fixed price per ounce.
  • All other world currencies were subsequently pegged to the U.S. dollar.

• Modern Floating Exchange Rate System:

  • Modern exchange rates are primarily determined by market forces of supply and demand in foreign exchange markets.
  • Monetary policies are uncoordinated across individual sovereign central banks.

Nominal Exchange Rates in the Long Run

• Definition of Nominal Exchange Rate ($E$):

  • The rate at which one currency trades for another.
  • Expressed as the price of domestic currency relative to foreign currency (or foreign currency units per domestic currency unit).
  • Example: An exchange rate where $1\,\text{USD} = 16\,\text{ZAR}$.

• Currency Depreciation:

  • Defined as a decline in the value or price of the domestic currency relative to a foreign currency.
  • Represented by a decline in the exchange rate measure relative to foreign purchasing power.
  • Example: Moving from $1\,\text{USD} = 16\,\text{ZAR}$ to $1\,\text{USD} = 17\,\text{ZAR}$ indicates a depreciation of the South African Rand (ZAR).

• Currency Appreciation:

  • Defined as an increase in the value or price of the domestic currency relative to a foreign currency.
  • Represented by an increase in the exchange rate measure relative to foreign purchasing power.
  • Example: Moving from $1\,\text{USD} = 16\,\text{ZAR}$ to $1\,\text{USD} = 15\,\text{ZAR}$ indicates an appreciation of the South African Rand (ZAR).

The Law of One Price and Exchange Rate Determination

• Law of One Price (LOOP):
  • States that in the long run, identical goods must sell for the exact same price in all countries when converted to a common currency.
  • Example: A BMW 3 Series model should carry the same effective price worldwide.
  • Formal condition:

$EP = P^w$

• Where:

  • $E$ is the nominal exchange rate (foreign currency units per domestic currency unit).

  • $P$ is the domestic price of the good.

  • $P^w$ is the world/foreign price of the good.

  • Arbitrage Mechanism:

• If prices differ across countries ($EP \neq P^w$), arbitrage opportunities exist, prompting market participants to buy low in one market and sell high in another until price convergence occurs.

  • Frictions Preventing Exact Long-Run Parity:

• Differential tax structures and rates.

• Import tariffs and non-tariff trade barriers.

• Divergent local production costs.

• Transportation and logistics costs.

  • Long-Run Exchange Rate Determination via Quantity Theory of Money:

• The Quantity Theory of Money pins down long-run national price levels ($\bar{P}$ and $\bar{P}^w$).

• The Law of One Price pins down the long-run nominal exchange rate ($\bar{E}$):

$\bar{E} = \frac{\bar{P}^w}{\bar{P}}$

• Consequently, the long-run exchange rate is determined by the relative supply of money between two economies (i.e., the ratio of paper currency units stamped "rand" relative to those stamped "dollar").
• Inflation Implications:
  • If a domestic currency depreciates over time, domestic inflation must exceed foreign inflation.
  • High relative domestic inflation drives structural currency depreciation.

The Big Mac Index

• Concept:

  • Developed by The Economist to measure Purchase Power Parity (PPP) by comparing the price of a McDonald's Big Mac across various countries using the U.S. dollar price as a benchmark.
  • Based on the premise that a Big Mac represents a uniform basket of local inputs and should cost the same globally.

• Empirical Data (January 2023):

• Failure Modes of the Big Mac Index:
  • Undervaluation / Overvaluation: Currency distortions make prices appear artificially low in undervalued currency nations (e.g., South Africa at $2.34\,\text{USD}$) or high in overvalued currency nations (e.g., Norway at $6.26\,\text{USD}$).
  • Nontradable Inputs: Big Macs incorporate nontradable inputs such as local commercial real estate rent and local labor costs, which are significantly lower in developing countries like China and India.
  • Trade Barriers: Local taxes, tariffs, and distribution costs cause systematic deviations from LOOP.
  • General Rule: The Law of One Price holds strictly only for easily tradable, standardized commodities.

The Real Exchange Rate (RER)

• Definition:

  • The nominal exchange rate adjusted for relative aggregate price levels between economies.
  • Measures the price of domestic goods relative to foreign goods (i.e., the units of foreign goods required to purchase a single unit of the equivalent domestic good).

• Mathematical Formulation:

$\text{real exchange rate} \equiv \frac{EP}{P^w}$

• Dimensional Unit Analysis:

$\frac{EP}{P^w} = E\left(\frac{\text{foreign currency}}{\text{domestic currency}}\right) \times P\left(\frac{\text{domestic currency}}{\text{domestic good}}\right) \times \frac{1}{P^w}\left(\frac{\text{foreign good}}{\text{foreign currency}}\right) = \frac{\text{foreign good}}{\text{domestic good}}$

• Long-Run Real Exchange Rate Value:
  • Under the assumption that the Law of One Price holds in the long run ($\bar{E}\bar{P} = \bar{P}^w$), the long-run real exchange rate ($R\bar{E}R$) equals 1:

$R\bar{E}R = \frac{\bar{E}\bar{P}}{\bar{P}^w} = 1$

• Distinction Between Nominal and Real Exchange Rates:
  • Nominal exchange rate ($E$): Price at which national currencies exchange.
  • Real exchange rate (RER): Price at which physical goods and services exchange.

Exchange Rates in the Short Run

• Foreign Exchange Market Scale:

  • Trading volume in global foreign exchange (FX) markets averages approximately $5\text{ trillion dollars}$ per day, driven by international trade and cross-border financial transactions.

• Short-Run Market Mechanics:

  • Currency Supply: Controlled and determined by central banks.
  • Currency Demand: Generated by international trade flows and global financial investment transactions.
  • Equilibrium Nominal Exchange Rate ($E$): Pinned down continuously in global trading markets.

• Interest Rate Transmission Mechanism:

  • Holding world interest rates constant, movements in the domestic nominal interest rate ($i$) cause the nominal exchange rate ($E$) to move in the same direction:

$\uparrow i^{\text{US}} \Rightarrow \uparrow E \quad \text{and} \quad \downarrow i^{\text{US}} \Rightarrow \downarrow E$

• Federal Reserve Rate Hike Example:

  • When the Federal Reserve increases U.S. nominal interest rates ($i^{\text{US}}$), returns on U.S. financial assets (bonds) rise relative to foreign assets.
  • Global investors demand U.S. dollars to buy higher-yielding U.S. bonds.
  • Demand for dollars increases, causing the dollar nominal exchange rate to appreciate ($\uparrow E$).

• South African Reserve Bank (SARB) Rate Hike Example:

  • An increase in SARB interest rates to curb domestic inflation attracts international investors seeking higher returns on Rand-denominated interest-linked bonds.

  • Foreigners purchase Rands, driving up Rand demand and resulting in currency appreciation.

  • Sticky Inflation and Short-Run RER Fluctuations:

• Aggregate price levels ($P$ and $P^w$) are sticky in the short run and adjust slowly.

• Unanticipated short-run changes in nominal exchange rates ($E$) translate directly into movements in the real exchange rate ($\frac{EP}{P^w}$):

$\uparrow E \Rightarrow \uparrow \frac{EP}{P^w}$

• In the short run, RER deviates from 1, and the Law of One Price fails due to price stickiness, nonzero transportation costs, and transaction delays.

Summary: Long-Run vs. Short-Run Determination

Fixed Exchange Rate Regimes

• Definition:

  • Institutional arrangements where a central bank pegs (ties) its domestic exchange rate to a specific fixed level relative to another currency or basket of currencies over a given period.

• Operational Mechanics and Constraints:

  • To successfully defend a fixed exchange rate, a central bank must expand or contract its domestic money supply in exact proportion to changes in the anchor country's money supply.
  • Central banks surrender domestic monetary policy sovereignty when maintaining a fixed peg.

• Rationale and Risks:

  • Applied to prevent wild exchange rate volatility and anchor inflation expectations.
  • Risks: Hyperinflation and financial instability often arise when fiscal deficits force central banks to print money, breaking the fixed exchange rate peg.

The Open Economy Short-Run Model and the Enriched IS Curve

• Exchange Rates and Net Exports:

  • Trade balance / Net Exports ($NX = \text{Exports} - \text{Imports}$) depends on short-run variations in the Real Exchange Rate (RER).
  • When RER is high (domestic goods are expensive relative to foreign goods):
  • Exports ($EX$) fall because domestic products are uncompetitive abroad.
  • Imports ($IM$) rise because foreign products are cheap domestically.
  • Net exports ($NX$) decline.
  • Conversely, when domestic currency depreciates (low RER):
  • Exports increase (benefiting domestic exporters).
  • Imports decline (foreign goods become costlier).

• Short-Run Net Exports Equation:

  • Integrates the medium-run trade balance ($\bar{a}_{nx}$) and business cycle real interest rate differentials:

$\frac{NX_t}{\bar{Y}_t} = \bar{a}_{nx} - \bar{b}_{nx}(R_t - \bar{R}^w)$

• Where:

  • $\frac{NX_t}{\bar{Y}_t}$ is net exports as a share of potential output.

  • $\bar{a}_{nx}$ is the baseline long-run trade balance parameter.

  • $\bar{b}_{nx}$ measures the sensitivity of net exports to real interest rate differentials.

  • $R_t$ is the domestic real interest rate.

  • $\bar{R}^w$ is the world real interest rate.

  • Transmission Chain of Domestic Monetary Tightening:

$\uparrow i \Rightarrow \uparrow R \text{ and } \uparrow E \Rightarrow \uparrow \frac{EP}{P^w} \Rightarrow \downarrow \frac{EX}{\bar{Y}} \text{ and } \uparrow \frac{IM}{\bar{Y}} \Rightarrow \downarrow \frac{NX}{\bar{Y}}$

• Rewriting Net Exports with Marginal Product of Capital (MPK):
  • Expressing the equation relative to the domestic natural rate of interest ($\bar{r}$, equal to world MPK):

$\frac{NX_t}{\bar{Y}_t} = \bar{a}_{nx} - \bar{b}_{nx}(R_t - \bar{r}) + \bar{b}_{nx}(\bar{R}^w - \bar{r})$

• National Income Accounting and Open Economy Savings:
  • In an open economy, national savings ($S$) finances domestic investment ($I$) and net foreign investment ($NX$):

$S = I + NX$

• Derivation of the Enriched Open Economy IS Curve:
  • Short-run output deviation equation:

$\tilde{Y}_t = \bar{a} - \bar{b}(R_t - \bar{r})$

• Where aggregate demand parameter $\bar{a}$ and sensitivity parameter $\bar{b}$ are redefined for the open economy:

\bar{a} \equiv \bar{a}_c + \bar{a}_i + \t\bar{a}_g + \bar{a}_{nx} - 1 + \bar{b}_{nx}(\bar{R}^w - \bar{r})

$\bar{b} \equiv \bar{b}_i + \bar{b}_{nx}$

• Key Properties of the Enriched IS Curve:
  • Flatter Slope: Because $\bar{b} = \bar{b}_i + \bar{b}_{nx}$, short-run output is more sensitive to changes in domestic real interest rates in an open economy compared to a closed economy. Interest rate changes affect both domestic investment ($\bar{b}_i$) and net exports ($\bar{b}_{nx}$).
  • Foreign Shocks: Changes in foreign real interest rates ($\bar{R}^w$) act as aggregate demand shocks, shifting $\bar{a}$.
  • In long-run equilibrium, $\bar{R}^w = \bar{r}$ and short-run output deviation $\tilde{Y}_t = 0$

Macroeconomic Policy Analysis and External Shocks

• Event #1: Domestic Monetary Policy Tightening:
  • Central bank increases nominal interest rate ($i$\uparrow).
  • Due to sticky inflation, domestic real interest rate rises ($R$\uparrow).
  • Investment Effect: $R > \bar{r}$ causes firms to reduce investment demand.
  • Exchange Rate Effect: Capital inflows appreciate currency ($E$\uparrow), increasing RER ($\frac{EP}{P^w}$\uparrow). Domestic goods become more expensive relative to foreign goods, driving exports down and imports up ($NX$\downarrow).
  • Total Effect: Output falls along the flatter IS curve (movement from point A to point B).

• Event #2: Foreign Interest Rate Increase (e.g., ECB Rate Hike):
  • European Central Bank raises euro area interest rates ($\bar{R}^w$\uparrow).
  • Global investors shift capital toward euro-denominated assets, increasing demand for euros relative to dollars.
  • Euro appreciates; dollar nominal exchange rate ($E$) depreciates.
  • U.S. Real Exchange Rate ($\frac{EP}{P^w}$) depreciates.
  • Price of U.S. goods falls relative to foreign goods, increasing U.S. net exports ($NX$\uparrow).
  • Aggregate demand parameter $\bar{a}$ increases, shifting the Aggregate Demand ($AD$) curve outward to $AD_1$
  • Short-Run Adjustment Path: Economy moves from point A to point B (higher short-run output and inflation). Over time, price adjustments shift Aggregate Supply ($AS$) upward to $AS_8$, moving output through point C and eventually back toward baseline equilibrium point D.

• International Transmission Mechanism:
  • Demonstrates how monetary policy choices in one region (e.g., Eurozone) transmit across international borders to affect real output and inflation in other sovereign economies (e.g., United States).

Historical Perspective on Exchange Rate Regimes

• Historical data of the U.K. Pound to U.S. Dollar exchange rate highlights three distinct eras:

  • Gold Standard Period (1800–1914/1930s): High rate stability centered around ~$0.20\text{ pounds per dollar}$.
  • Bretton Woods Era (1944–1973): Fixed exchange rates pegged around ~$0.35\text{ pounds per dollar}$.
  • Floating Rate Era (1973–Present): Substantial exchange rate volatility and secular drift ($0.40\text{ to } 0.80\text{ pounds per dollar}$).---

• Long-Run Relevance of Exchange Rates:

  • Nominal exchange rates have minimal structural impact on economic performance in the long run.
  • While empirical positive correlations exist between exchange rate strength and macroeconomic performance, causation flows from economic health to currency strength (i.e., sound macroeconomic policies yield low inflation and strong currencies, rather than vice versa).

The Policy Trilemma in Open Economies

• Three Primary Goals of the International Monetary System:

  1. Stable Exchange Rates: Facilitates international trade planning and eliminates currency risk.
  2. Monetary Policy Autonomy: Allows domestic central banks to adjust interest rates to stabilize domestic output and inflation shocks.
  3. Free Flows of International Finance: Optimizes global capital allocation across international borders.

• The Trilemma Constraint:

  • A country can choose at most two of these three objectives simultaneously; achieving all three concurrently is mathematically and operationally impossible.

• Three Structural Policy Regimes:

  1. Option 1: Floating Exchange Rates (Bottom Edge)
  • Chooses: Monetary Policy Autonomy + Free Financial Flows.
  • Gives Up: Exchange Rate Stability.
  • Example: The United States and major developed nations. Exchange rate fluctuates freely based on global monetary shifts.
  1. Option 2: Exchange Rate Peg / Currency Board / Monetary Union (Right Side)
  • Chooses: Exchange Rate Stability + Free Financial Flows.
  • Gives Up: Domestic Monetary Policy Autonomy.
  • Example: Argentina (1991–2001 currency board matching pesos to dollars). Requires total backing with central bank foreign exchange reserves ($USD$ or gold). If foreign exchange reserves run out, a speculative currency crisis occurs.
  1. Option 3: Capital Controls (Left Side)
  • Chooses: Exchange Rate Stability + Monetary Policy Autonomy.
  • Gives Up: Free Flows of International Finance.
  • Example: China (1996–2005). Imposed strict restrictions on capital movement and foreign exchange conversion to peg the yuan while controlling domestic interest rates.