Open Economy Macroeconomics: Policy, Exchange Rates, and the Trade Balance

Learning Objectives

By the end of this lecture, students should be able to:

• Explain how openness affects both goods and financial markets.

• Distinguish between nominal and real exchange rates and interpret their movements.

• Understand the Uncovered Interest Parity (UIP) condition and its implications.

• Analyse how the real exchange rate affects net exports and aggregate demand.

• Derive and interpret the open economy multiplier.

• Evaluate the effects of fiscal policy on output and the trade balance.

• Assess how a real depreciation affects net exports and output.

• Explain the Marshall–Lerner condition and the J-curve dynamics.

Motivation and Key Macroeconomic Questions

Open economies are defined by trade and financial linkages. Key characteristics include:

• Domestic Demand: In an open economy, domestic demand involves foreign components (exports).

• Capital Flows: These link interest rates and exchange rates across borders.

• Competitiveness: Changes in relative competitiveness affect both output and the trade balance.

Theoretical Questions Raised:

• Why is fiscal policy less powerful in an open economy compared to a closed one?

• Do currency depreciations always lead to an improvement in the trade balance?

• How do exchange rates serve as the link between financial markets and goods markets?

Real-World UK Context:

• Analysis of why UK inflation rose sharply after 2021.

• Reasons for the Bank of England's aggressive interest rate increases.

• The causes behind the pound's depreciation and subsequent recovery.

• The impact of policy decisions on trade, exchange rates, and output.

Dimensions of Openness

Openness manifests in three primary markets:

• Openness in Goods Markets: The ability of consumers and firms to choose between domestic and foreign goods.     * Even in free-market economies, trade may be restricted by tariffs (taxes on imports) and quotas (quantity restrictions).

• Openness in Financial Markets: The ability of investors to choose between domestic and foreign assets.     * Historically, many nations utilized capital controls to limit foreign asset holdings by residents or domestic asset holdings by foreigners.

• Openness in Factor Markets: The ability of firms to decide where to locate production and the ability of workers to choose where to work.     * Example: The NAFTA (1993) agreement facilitated the relocation of production across the United States, Canada, and Mexico.

Exchange Rates and Goods Market Openness

Definitions and Terminology

• Nominal Exchange Rate ($E$): The price of the domestic currency expressed in terms of foreign currency.

• Real Exchange Rate ($\epsilon$): The price of domestic goods relative to the price of foreign goods.

Exchange Rate Movements

• Appreciation (Nominal): An increase in $E$; the domestic currency becomes stronger.

• Depreciation (Nominal): A decrease in $E$; the domestic currency becomes weaker.

• Fixed Exchange Rate System: A regime where countries maintain a constant exchange rate.     * Revaluation: A policy-driven increase in the exchange rate under a fixed system.     * Devaluation: A policy-driven decrease in the exchange rate under a fixed system.

Mathematical Formulation of the Real Exchange Rate

The real exchange rate ($\epsilon$) measures competitiveness and is defined as:

$\epsilon = \frac{E \times P}{P^*}$

Where:

• $E$ = Nominal exchange rate.

• $P$ = Domestic price level.

• $P^*$ = Foreign price level.

Interpretations:

• Higher $\epsilon$: Domestic goods are more expensive relative to foreign goods, leading to lower competitiveness.

• Lower $\epsilon$: Domestic goods are cheaper relative to foreign goods, leading to higher competitiveness.

• Real Appreciation: An increase in $\epsilon$ (domestic goods become relatively more expensive).

• Real Depreciation: A decrease in $\epsilon$ (domestic goods become relatively cheaper).

Practical Example: Real Exchange Rate and the iPhone 16

To compute the relative price (transcribing the real exchange rate essentially as the price of foreign goods relative to domestic goods in a common currency):

• Product: iPhone 16 (128GB).

• UK Price ($P$): \text{#699}.

• Germany Price ($P^*$): $\text{‑949}$.

• Exchange Rate: \text{‑1} = \text{#0.865}.

Step 1: Convert foreign price to domestic currency \text{‑949} \times 0.865 \approx \text{#821}

Step 2: Compute the real exchange rate (relative price) \epsilon = \frac{\text{#821}}{\text{#699}} \approx 1.18

Interpretation: The iPhone is approximately $18\%$ more expensive in Germany than in the UK. This indicates UK goods are relatively cheaper and more competitive in this instance.

Historical Context: UK-US Exchange Rates (1970s–Early 1980s)

During this period, there was a strong divergence between nominal and real exchange rates in the UK:

• Real Exchange Rate: Rose sharply, making UK goods more expensive.

• Nominal Exchange Rate: Went down, meaning the pound was depreciating.

• Result: Despite a weaker pound, UK competitiveness worsened because UK inflation was higher than US inflation. This demonstrates that a nominal depreciation does not guarantee improved competitiveness.

Financial Markets and Asset Returns

Investors choose between domestic and foreign bonds based on interest rates and expected exchange rate movements.

• Return on UK bond (in \text{#}): $1 + i$

• Return on US bond (converted to \text{#}): Depends on the US interest rate ($i^*$) and the expected exchange rate ($E^e_{t+1}$).

Uncovered Interest Parity (UIP)

The arbitrage condition is expressed as: $(1 + i_t) = (1 + i^*<em>t) \frac{E_t}{E^e</em>{t+1}}$

The Linear Approximation: $i_t \approx i^*<em>t - \frac{E^e</em>{t+1} - E_t}{E_t}$

Economic Intuition:

• The domestic interest rate equals the foreign interest rate minus the expected appreciation of the domestic currency.

• If the UK interest rate is higher than the US interest rate (i > i^*), investors must expect the pound to depreciate (E^e_{t+1} < E_t) to offset the higher yield.

Financial Integration:

• UK and US short-term interest rates move closely together over time, reflecting high capital mobility.

• Interest rate differentials are not persistent; when they arise, they are typically associated with expected exchange rate movements. Arbitrage keeps rates aligned.

Demand for Goods in an Open Economy

The Open Economy IS Curve

The demand for domestic goods ($Z$) is defined as: $Z = C + I + G - \frac{IM}{\epsilon} + X$

Components and Mechanisms:

• Domestic Demand: $C(Y-T) + I(Y, r) + G$.

• Imports ($IM$): $IM = IM(Y, \epsilon)$. Higher income ($Y$) leads to more imports.

• Exports ($X$): $X = X(Y^<em>, \epsilon)$. Higher foreign income ($Y^</em>$) leads to more exports.

• Real Exchange Rate ($\epsilon$) Impact:     * Higher $\epsilon$ (Real Appreciation) $\rightarrow$ Lower exports ($X \downarrow$) and higher imports ($IM \uparrow$).     * $\epsilon$ directly affects the demand for domestic goods by altering competitiveness.

Equilibrium and the Multiplier

• Equilibrium Condition: $Y = Z$.

• ZZ Line: Represents demand. In an open economy, the ZZ line is flatter than in a closed economy because a portion of demand "leaks" into imports.

• Trade Balance: In equilibrium, the trade balance can be a deficit or surplus. An increase in output ($Y$) causes imports to rise, which worsens the trade deficit.

Multiplier Derivation and Numerical Example

Behavioral Equations

• $C = c_0 + c_1(Y - T)$

• $I = d_0 + d_1Y$

• $IM = m_1Y$

• $X = xY^*$

Deriving the Open Economy Multiplier

Substitute components into the equilibrium condition: $Y = c_0 + c_1(Y - T) + d_0 + d_1Y + G + xY^* - m_1Y$

Group terms involving $Y$: $Y(1 - c_1 - d_1 + m_1) = c_0 - c_1T + d_0 + G + xY^*$

Let Autonomous Demand ($A$) = $c_0 - c_1T + d_0 + G + xY^*$

Equilibrium Output ($Y$): $Y = [\frac{1}{1 - c_1 - d_1 + m_1}] \times A$

Numerical Comparison (Closed vs. Open)

Assumptions:

• $c_1 + d_1 = 0.6$

• $m_1 = 0.2$

• $\Delta G = 100$

Closed Economy Multiplier: $\text{Multiplier} = \frac{1}{1 - (c_1 + d_1)} = \frac{1}{1 - 0.6} = 2.5$ $\Delta Y = 2.5 \times 100 = 250$

Open Economy Multiplier: $\text{Multiplier} = \frac{1}{1 - 0.6 + 0.2} = \frac{1}{0.6} \approx 1.667$ $\Delta Y = 1.667 \times 100 = 166.7$

Effect on Trade Balance ($\Delta TB$): $\Delta TB = \Delta X - \Delta IM = 0 - m_1\Delta Y$ $\Delta TB = -0.2 \times 166.7 = -33.34$

Conclusion: Fiscal expansion boosts output but worsens the trade balance. The multiplier is smaller in an open economy due to import leakage.

Effects of Demand Shocks

Increase in Domestic Demand ($G \uparrow$)

• Shifts $ZZ$ upward.

• Output ($Y$) rises.

• Imports increase, causing the trade balance to move toward a deficit.

• The effect on output is smaller than in a closed economy.

Increase in Foreign Demand ($Y^* \uparrow$)

• Raises exports ($X$).

• Shifts $ZZ$ upward.

• Output ($Y$) rises.

• Net exports increase, and the trade balance improves.

• The effect on output is stronger than domestic demand because there is no initial leakage through imports.

Real-World Evidence and Cases

• UK Current Account: The UK has run mostly current account deficits since 1987.

• Ireland: Ireland maintains a large trade surplus, but this is largely driven by multinational accounting practices rather than domestic production.

• USA (Early 2020s): Expansive fiscal policies (e.g., the CARES Act) to mitigate COVID-19 increased output but, combined with supply chain issues, led to a record-high trade deficit through a surge in imports.

• Indonesia (1997-1998): The rupiah plummeted from $2,500\,IDR/USD$ to over $11,000\,IDR/USD$. Initially, the trade balance worsened due to inelastic short-term demand and existing contracts. Over time, the lower value enhanced export competitiveness and reduced imports, gradually improving the balance.

Depreciation and the Marshall–Lerner Condition

A real depreciation ($\epsilon \downarrow$) has two opposing effects on net exports ($NX$):

1. Quantity Effect (Positive): Exports ($X$) increase, and Imports ($IM$) decrease as domestic goods become cheaper.

2. Price Effect (Negative): Imports become more expensive in terms of domestic currency.

The Marshall–Lerner Condition: A depreciation improves the trade balance only if the sum of the price elasticities of exports and imports is greater than 1: |\epsilon_x| + |\epsilon_m| > 1

The J-Curve

This describes the dynamic response of the trade balance over time after a depreciation:

• Short Run: Quantities adjust slowly. The price effect dominates, and the trade balance worsens.

• Medium Run: Quantities adjust; exports increase while imports decrease. The trade balance improves.

• Intuition: An initial deterioration followed by a gradual improvement.

Main Takeaways

• Aggregate demand in an open economy includes net exports ($NX$).

• The real exchange rate ($\epsilon$) is the central variable for competitiveness.

• Fiscal expansions increase output but generally worsen the trade balance.

• The open economy multiplier is smaller than the closed economy multiplier due to import leakage.

• A currency depreciation does not automatically improve net exports; improvement depends on the Marshall–Lerner condition.

• The J-curve explains why trade balances may initially worsen before improving following a depreciation.

Mandatory Reading

• Primary Textbook: Blanchard, Olivier (2025). Macroeconomics, Pearson. 8th or 9th Editions, Chapters 17-19.

• Additional Reading: Mankiw, Gregory (2016). Macroeconomics, MacMillan Learning. 9th Edition, Chapters 6 and 13.