International Trade in Goods and Assets: Two-Period Real Intertemporal Small Open Economy Models

International Trade in Goods and Assets

Overview of Chapter 15 Topics

This chapter explores the macroeconomic analysis of international trade in goods and assets using two-period real intertemporal small open economy (SOE) models. It covers credit market imperfections, sovereign default, production and investment, and the effects of global shocks such as changes in interest rates, government spending, and productivity. The Ukraine War is discussed as a real-world application.

• Two-period SOE models: Endowment and production/investment versions

• Credit market imperfections and sovereign default

• Current account dynamics and macroeconomic shocks

• Application to global events (e.g., Ukraine War)

Models

A Real Intertemporal Small Open Economy Model (Endowment)

This model analyzes a small open economy over two periods (current and future), focusing on consumption and government spending, with exogenous incomes and world real interest rates.

• Two periods: Current and future

• Representative consumer with exogenous incomes

• World real interest rate is exogenous (SOE is a price-taker)

• Current account surplus equals national savings (no investment in this version)

A Real Intertemporal Small Open Economy Model (Production and Investment)

This extension includes endogenous production and investment, allowing analysis of output, consumption, investment, and government spending, with the world real interest rate remaining exogenous.

• Aggregate supply and demand curves intersect at the world real interest rate

• Current account adjusts to ensure equilibrium

Budget Constraints

Consumer’s Lifetime Budget Constraint

The consumer chooses consumption in both periods subject to their lifetime resources.

• Equation:

$C + \frac{C'}{1+r} = Y - T + \frac{Y' - T'}{1+r}$

$S_p = Y - T - C$

• Private saving is current income minus taxes and consumption

Government’s Lifetime Budget Constraint

The government’s intertemporal budget constraint reflects spending and tax revenues over both periods.

• Equation:

$G + \frac{G'}{1+r} = T + \frac{T'}{1+r}$

$S_g = T - G$

• Government saving is taxes minus government spending

Nation’s Lifetime Budget Constraint

The national budget constraint combines private and government constraints, linking them to the current account.

• Equation:

$C + G + \frac{C' + G'}{1+r} = Y + \frac{Y'}{1+r}$

• Current account surplus: $CA = S - I = S_p + S_g - I = (Y - T - C) + (T - G)$

• Current and future period constraints:

$C + G + CA = Y$

$C' + G' = (1 + r)CA + Y'$

Current Account Dynamics

Implications for the Current Account Surplus

Changes in the world real interest rate, output, or taxes affect the current account through income and substitution effects.

• CA > 0 (lender): Increase in $r$ has ambiguous effects due to opposing income and substitution effects.

• CA < 0 (borrower): Increase in $r$ increases CA surplus (reduces deficit); both effects work in the same direction.

• Analyze effects on $C + G$ and CA for changes in $Y$ or $T$.

Credit Market Imperfections and Default

Sovereign Debt and Limited Commitment

Credit market frictions can lead to sovereign default, where nations may fail to honor debt obligations.

• Recent defaults: Belarus, Lebanon, Ghana, Sri Lanka, Zambia (2023)

• Limited commitment: Nations may be denied access to credit markets after default and suffer future penalties

• Constraint: $B' \leq v$ (future debt cannot exceed penalty threshold)

Budget Constraints for the Nation

• Debt stock ($B$): At beginning of current period

• Debt stock ($B'$): At end of current period/beginning of future period

• Current account: $CA = B - \frac{B'}{1+r}$

• Current period constraint: $C + G + CA = Y$

• Future period constraint: $C' + G' = Y' - B'$

• Present-value constraint: $C + G + \frac{C' + G'}{1+r} = Y + \frac{Y'}{1+r} - B$

Default Decision

Default occurs when the nation’s debt exceeds its ability to pay, considering penalties and access to future credit.

• Default condition:

$Y > Y - B + \frac{v}{1+r}$

$B > \frac{v}{1+r} \implies B(1+r) > v$

• Likelihood of default increases with high debt, high interest rates, and low penalties

Case Study: Greece and Sovereign Default

Greece’s experience illustrates how high debt and rising interest rates increase default risk.

• Low interest rates after joining Euro area

• 2008 crisis increased perceived default risk and borrowing costs

Open Economy Macroeconomics: Production and Investment

Closed vs. Open Economy

Closed economies must exhaust output among domestic uses; open economies can borrow/lend internationally.

• Closed economy: $Y = C + I + G$ (domestic absorption)

• Open economy: $Y = C + I + G + CA$ (domestic absorption plus current account)

• Current account surplus: $CA = S - I = NX + NFI$ (assuming $NFI = 0$)

Capital Account (KA) and Current Account (CA)

The capital account records asset transactions; the balance of payments includes both CA and KA.

• Capital inflow: Foreigners purchase domestic assets

• Capital outflow: Domestic residents purchase foreign assets

• Balance of payments: $BP = CA + KA = 0$

• Example: Canadian tourist spends €100 in Paris (CA outflow, KA inflow)

Macroeconomic Shocks in the SOE Model

Four Examples of Shocks

• Increase in world real interest rate

• Increase in government spending

• Increase in current total factor productivity

• Increase in future total factor productivity

Effects of an Increase in the World Real Interest Rate

Higher world real interest rates affect domestic absorption, output, and the current account.

• Consumers substitute future for current consumption

• Firms reduce investment as cost of capital rises

• Output supplied increases; CA increases; KA falls (capital outflow)

Effects of an Increase in Government Spending

Government spending shifts output demand and supply curves, affecting equilibrium output and the current account.

• Output demand curve shifts right

• Output supply curve shifts slightly right (small effect)

• CA falls; KA rises (capital inflow)

Effects of an Increase in Total Factor Productivity

Productivity shocks shift output supply and demand, affecting output, the current account, and capital flows.

• Current productivity: Output supply and demand shift right; CA increases; KA decreases

• Future productivity: Output demand shifts right; CA falls; KA rises (capital inflow)

Application: The Ukraine War

Global and SOE Effects

The Ukraine War is analyzed using the real intertemporal closed economy model and SOE model.

• War increases global government spending ($G$)

• War destroys physical capital ($K$)

• War reduces total factor productivity ($z$)

• Global output supply curve shifts left; excess demand raises world real interest rate ($r^*$)

• For SOEs, higher $r^*$ increases output and net exports, but reduces domestic investment and may affect consumption

Key Terms and Definitions

• Small Open Economy (SOE): An economy that takes world prices and interest rates as given.

• Current Account (CA): Measures net exports of goods/services and net income from abroad.

• Capital Account (KA): Records transactions in financial assets.

• Intertemporal Budget Constraint: Links current and future consumption/spending to lifetime resources.

• Default: Failure to meet debt obligations.

• Limited Commitment: Restriction on borrowing to prevent default.

Summary Table: Budget Constraints

Constraint	Equation	Description
Consumer	$C + \frac{C'}{1+r} = Y - T + \frac{Y' - T'}{1+r}$	Lifetime budget for private consumption
Government	$G + \frac{G'}{1+r} = T + \frac{T'}{1+r}$	Lifetime budget for government spending
Nation	$C + G + \frac{C' + G'}{1+r} = Y + \frac{Y'}{1+r}$	Combined national budget constraint
Current Account	$CA = S - I = (Y - T - C) + (T - G)$	National savings minus investment
Debt/Default	$B' \leq v$	Limited commitment constraint

Example Application

• Canadian tourist in Paris: Spending €100 is a CA outflow (import of service), matched by a KA inflow (France holds claim on Canadian asset).

• Greece’s sovereign default risk: High debt and interest rates post-2008 increased default probability.

Additional info: The notes expand on the brief points in the slides, providing definitions, equations, and context for the models and macroeconomic shocks discussed in Chapter 15.