Chapters 13 through 16 developed macroeconomic theory for a closed economy — one that neither trades nor borrows internationally. This chapter opens the economy. Goods, services, and capital now flow across borders, and exchange rates become a central macroeconomic variable. The stakes are high: exchange rate crises have destroyed decades of growth in months, and the architecture of international monetary cooperation shapes the policy space of every country on Earth.
We begin with the accounting framework (the balance of payments), move to exchange rate determination (PPP, UIP, Dornbusch overshooting), build a workhorse two-country model (Obstfeld-Rogoff Redux), and then tackle the great policy questions: When should countries share a currency? How should they coordinate monetary policy? When do sovereigns default on their debts? And why does capital flow “uphill” from poor countries to rich ones?
By the end of this chapter, you will be able to:
Prerequisites: Chapters 8 (Mundell-Fleming basics), 13 (dynamic optimization), 14 (DSGE methods), 15 (Calvo pricing, NK model), 16 (Barro-Gordon, FTPL, intertemporal GBC).
Every international transaction is recorded in the balance of payments (BOP) — a double-entry ledger that tracks a country’s economic exchanges with the rest of the world. Before we build models, we must master this accounting framework, because it imposes ironclad constraints on what any open economy can do.
Current account. The sum of the trade balance (exports minus imports of goods and services), net primary income (returns on foreign assets minus payments to foreign liabilities), and net secondary income (transfers). In compact form:
where $X_t$ is exports, $M_t$ is imports, $r$ is the return on net foreign assets, $NFA_{t-1}$ is the net foreign asset position at the end of the previous period, and $NTR_t$ is net secondary income (transfers). The trade balance $X_t - M_t$ captures current flows; the net factor income term $r \cdot NFA_{t-1}$ captures income on the accumulated stock of international assets and liabilities; and $NTR_t$ captures remittances, aid, and other unilateral transfers.
Balance of payments identity. The fundamental accounting identity:
where $KA_t$ is the capital (financial) account balance, defined with sign convention such that capital inflows are positive. This is not a behavioral equation — it is an accounting identity that holds by construction. A current account deficit must be financed by a capital account surplus.
The idea that trade imbalances are self-correcting traces to the eighteenth-century price-specie-flow doctrine — the mercantilist trade-surplus obsession and Adam Smith's demolition of it. See the intellectual lineage in the history of economic thought (C-Ch.2, Mercantilism & physiocracy).
Construct the BOP for a country and verify the identity $CA + KA = 0$.
Consider a small open economy with the following annual data (billions of dollars): Goods exports: 250; Goods imports: 310; Service exports: 80; Service imports: 60; Net primary income: -15; Net secondary income: -5; FDI inflows: 30; Portfolio inflows: 45; Other investment inflows: 25; Change in official reserves: -40 (reserve accumulation).
Step 1: Trade balance in goods: \$150 - 310 = -60$.
Step 2: Trade balance in services: \$10 - 60 = +20$.
Step 3: Current account: $CA = (-60) + 20 + (-15) + (-5) = -60$.
Step 4: Capital (financial) account: $KA = 30 + 45 + 25 + (-40) = +60$.
Step 5: Verify: $CA + KA = -60 + 60 = 0$. ✔ The identity holds.
Interpretation: This country runs a current account deficit of \$60B — it consumes and invests more than it produces. The deficit is financed by net capital inflows of \$60B (FDI, portfolio flows, bank lending), partially offset by reserve accumulation of \$40B.
The exchange rate — the price of one currency in terms of another — is perhaps the most important price in an open economy. This section builds from long-run benchmarks (PPP) through short-run arbitrage (UIP) to the Dornbusch overshooting model, which explains why exchange rates are more volatile than fundamentals.
If a basket of goods costs 100 yuan in China and 15 dollars in the U.S., PPP predicts $E = 100/15 \approx 6.67$ yuan per dollar.
where $e_t = \ln E_t$ is the log nominal exchange rate and $\pi_t, \pi_t^*$ are domestic and foreign inflation rates. Relative PPP performs better than absolute PPP empirically — the correlation between inflation differentials and exchange rate changes is strong over horizons of 5 years or more.
If the domestic interest rate exceeds the foreign rate by 2%, UIP predicts the domestic currency will depreciate by 2%. Empirically, UIP fails dramatically at short horizons — high-interest-rate currencies tend to appreciate, creating excess returns for carry traders (the “forward premium puzzle”).
The magnitude of the overshoot is $\Delta e_{impact} = \Delta m + \frac{\Delta m}{\delta \cdot \lambda}$, where $\lambda$ is the interest semi-elasticity of money demand and $\delta$ is the speed of price adjustment. Slower price adjustment (small $\delta$) produces larger overshooting. (This formula uses the approximation $|\mu| \approx \delta \cdot \lambda$, where $\mu$ is the stable eigenvalue of the system $\mu^2 + \delta\mu - \delta/\lambda = 0$. The approximation is valid when $\delta$ is small relative to $1/\lambda$.)
Why it matters: Monetary expansion makes the currency jump past its new long-run value on impact, then crawl back. The exchange rate moves first and most because prices can't — it absorbs the entire short-run shock alone. Drag the slider on Figure 17.1 to watch the jump-then-converge: bigger shocks and stickier prices make the overshoot larger.
The apparatus above assumes floating exchange rates — but that regime is historically recent. The post-1944 order fixed rates by design (the Bretton Woods architecture, with the structural strain Triffin foresaw), and the move to floating dates from its 1971 collapse and the Plaza–Louvre coordination that followed.
The figures who built this apparatus — Mundell, Dornbusch, Obstfeld and Rogoff — belong to the postwar synthesis and counter-revolution era. Place them on the intellectual-genealogy timeline.
Given a 10% permanent money supply increase, compute the instantaneous exchange rate jump, the long-run exchange rate, and trace the adjustment path.
Initial steady state: $e_0 = p_0 = 0$ (logs normalized). Money supply increases by $\Delta m = 0.10$ (10%). Parameters: $\delta = 0.3$, $\lambda = 2$.
Step 1: Long-run exchange rate: $e_{LR} = e_0 + \Delta m = 0.10$. Prices also rise: $p_{LR} = 0.10$.
Step 2: Impact exchange rate: $\Delta e_{impact} = 0.10 + \frac{0.10}{0.3 \times 2} = 0.10 + 0.167 = 0.267$. The exchange rate jumps to 0.267 — a 26.7% depreciation, far exceeding the long-run 10%.
Step 3: After the initial jump, the exchange rate appreciates gradually from 0.267 toward 0.10, while prices rise from 0 toward 0.10.
Step 4: On impact, the interest rate falls. Over time, rising prices reduce real balances, pushing the interest rate back to the world level.
Key insight: The exchange rate overshoots because it bears the entire burden of short-run adjustment when prices cannot move.
Figure 17.1. Dornbusch overshooting phase diagram. The $\dot{p}=0$ and $\dot{e}=0$ loci intersect at the steady state. A money supply increase shifts both loci; the exchange rate jumps to the saddle path and converges gradually. Drag the slider to change the shock size.
Peter Schiff told Joe Rogan's audience that Bitcoin has no intrinsic value and will end like every bubble before it. Michael Saylor fired back: "Bitcoin is the apex property of the human race." The clash reframes the "what is money?" debate that monetary theory has wrestled with for centuries. After learning Dornbusch overshooting, where exchange rate volatility emerges from sticky prices meeting instant asset-market clearing, you can see why Bitcoin's price swings are structural: fixed supply meeting speculative demand produces exactly this pattern.
IntermediateThe Dornbusch model is insightful but ad hoc — it lacks microfoundations. Obstfeld and Rogoff (1995) built the Redux model, a two-country New Keynesian framework with monopolistic competition, nominal rigidities, and explicit welfare analysis.
When the Home currency depreciates, Home goods become cheaper relative to Foreign goods ($\hat{\tau}$ rises), and demand shifts toward Home goods. The elasticity of substitution $\theta$ governs the strength of this switching.
Two symmetric countries; Home monetary expansion. Compute the terms-of-trade change, relative consumption shift, and welfare effect.
Symmetric countries ($\gamma = 0.75$), elasticity $\theta = 2$, Home monetary expansion $\Delta m_H = 5\%$, Foreign unchanged.
Step 1: Terms-of-trade change: $\hat{\tau} = \frac{0.05}{1 + (0.5)(1)} = 0.033$ (3.3% deterioration for Home).
Step 2: Expenditure switching: $\hat{C}_H - \hat{C}_F = 2 \times 0.033 = 0.067$ (6.7% relative demand shift).
Step 3: Home output rises ~6.7%. Home welfare gain ~4.2% (output gain minus terms-of-trade loss).
Step 4: Foreign output falls ~1.7%, but Foreign enjoys a terms-of-trade improvement. Net Foreign welfare is ambiguous.
Key insight: The Redux model shows monetary policy in open economies involves a tradeoff between output stimulus and terms-of-trade deterioration. High openness (low $\gamma$) makes the beggar-thyself effect more likely.
Figure 17.2. PPP vs actual exchange rates. Countries above the 45-degree line have undervalued currencies; below, overvalued. The Balassa-Samuelson pattern is visible: low-income countries systematically above the line. Toggle between decades.
Figure 17.3. Two-country Redux model. Home and foreign monetary shocks interact through expenditure switching. Symmetric shocks cancel; asymmetric shocks create winners and losers. Home bias modulates spillover magnitude. Drag sliders to explore.
When should countries abandon their own currencies in favor of a shared one? Robert Mundell’s (1961) theory of optimal currency areas (OCA) provides the analytical framework.
The formal tradeoff: Benefits $B = \phi \cdot \tau$ (trade share times transaction cost savings). Costs $C = \alpha \cdot \sigma^2_{asymmetric} / \mu$ (shock asymmetry divided by alternative adjustment mechanisms). A monetary union is optimal when $B > C$.
Frankel and Rose (1998) argued that OCA criteria are endogenous: joining a monetary union increases bilateral trade and may synchronize business cycles. Countries that do not satisfy criteria ex ante may satisfy them ex post.
Evaluate whether a hypothetical country pair satisfies Mundell’s criteria.
Consider Alphaland and Betaland. Scores (0–10): Labor mobility: 3 (different languages, restrictive policies). Fiscal transfers: 2 (no supranational authority). Trade openness: 8 (35% bilateral trade). Shock symmetry: 5 (diversified but different structures). Financial integration: 7 (cross-listed banks, free capital flows). Assessment: High trade and financial integration favor union, but low labor mobility and absent fiscal transfers mean asymmetric shocks cannot be easily absorbed — similar to the Eurozone periphery.
Figure 17.4. OCA criteria radar chart. Higher scores on all axes = stronger case for monetary union. The threshold ring (score 6) represents minimum viable OCA. US States dominate; Eurozone Periphery shows clear weakness on shock symmetry and fiscal transfers. Select regions to compare.
When one country’s monetary policy spills over to others through the exchange rate, uncoordinated policy becomes a strategic game. Each country faces an incentive to expand, but when all expand simultaneously, exchange rate effects cancel and only inflation remains.
Why it matters: Each country ignores the spillover its own depreciation imposes on its neighbors, so everyone expands at once — and the exchange-rate effects cancel, leaving only higher inflation. Both lose relative to coordinated restraint. Drag the spillover slider on Figure 17.7 to watch the Nash-versus-cooperative gap widen as spillovers grow.
Sustaining cooperation requires institutions: the IMF, the G7/G20, the Plaza and Louvre Accords, and central bank swap lines. In a repeated game, cooperation can be sustained by trigger strategies.
Set up a 2×2 monetary policy game, compute payoffs, identify the Nash equilibrium, and show the cooperative improvement.
Two symmetric countries choose Expand (E) or Tighten (T). Payoffs (loss values, lower is better): (E,E)=(3,3), (E,T)=(1,5), (T,E)=(5,1), (T,T)=(2,2). Expand is a dominant strategy for both. Nash: (E,E) with loss 3. Cooperative: (T,T) with loss 2. Surplus = 1 per country.
Key insight: International monetary policy is a prisoner’s dilemma. Each country rationally pursues competitive depreciation, but the collective outcome is worse than coordinated restraint.
Figure 17.7. Policy coordination game. The 2×2 payoff matrix shows each country’s loss from Expand vs Tighten. Nash equilibrium (red) is Pareto-inferior to the cooperative outcome (green). Higher spillovers widen the gap. Drag the spillover slider.
Sovereign debt differs fundamentally from private debt: there is no international bankruptcy court. Sovereign repayment is ultimately voluntary — a country repays because the costs of default exceed the costs of repayment.
Why it matters: A sovereign repays only when the cost of being shut out of credit markets exceeds the burden of paying the debt. Default is a choice, not an accident — which is why willingness, not just ability, drives the math. Drag the sliders on Figure 17.5 to see when the debt path stabilizes versus when it explodes.
Given initial debt/GDP = 90%, primary surplus = 1%, growth = 2%, interest rate = 4%, compute the debt trajectory and stabilizing surplus.
Step 1: Interest-growth differential: $r - g = 4\% - 2\% = 2\%$.
Step 2: Stabilizing surplus: $s^* = (r - g) \cdot d_0 = 0.02 \times 0.90 = 1.8\%$ of GDP.
Step 3: Actual surplus (1%) is below $s^*$ (1.8%). Debt will rise over time.
Step 4: Trajectory: Year 1: 90.8%, Year 5: 94.2%, Year 10: 98.8%, Year 20: 109.4%, Year 30: 122.5%.
Step 5: To stabilize at 90%, need $s^* = 1.8\%$. To reduce to 60% over 20 years: ~$s = 3.0\%$.
Key insight: If creditors demand higher rates (risk premium feedback), the stabilizing surplus jumps — creating a “debt trap” dynamic.
Figure 17.5. Sovereign debt sustainability. The trajectory depends on the interest-growth differential ($r - g$) and the primary surplus. When $r > g$ and the surplus is insufficient, debt explodes. When $r < g$, debt stabilizes even with small deficits. Drag sliders to explore.
Standard theory predicts that capital should flow from rich countries (abundant capital, low marginal product) to poor countries (scarce capital, high returns). The data tell a different story.
Lucas calculated that if $Y = AK^\alpha L^{1-\alpha}$, the ratio of marginal products between India and the US should be ~58:1. Yet capital was not flooding into India.
Why it matters: Standard theory says capital should flood from rich countries to poor ones, where it is scarce and returns are high. It doesn't — that is Lucas's puzzle. Differences in productivity, sovereign risk, and financial frictions block the flow. Open the GDP map below to see the cross-country picture the puzzle is about.
The post-2008 consensus has shifted toward accepting some role for capital flow management measures (CFMs). The IMF’s Institutional View (2012, revised 2022) acknowledges that CFMs can be appropriate as a temporary measure when capital inflows are surging.
When those imbalances unwound, the sudden-stop dynamics above played out at global scale: see the 2008 collapse and the Eurozone crisis that followed in economic history.
Figure 17.6. Sudden stop simulator. A capital flow reversal forces instant current account adjustment. The exchange rate regime determines whether the pain falls on the exchange rate (flexible) or on output (fixed). Adjust the reversal magnitude and regime.
Kaelani faces its most severe crisis yet. After the commodity shock (Ch 14) and the ZLB episode (Ch 15), foreign investors abruptly withdraw capital. Portfolio flows reverse from +6% of GDP to -4% in one quarter — a classic sudden stop.
The BOP crisis. Kaelani’s current account deficit of 8% of GDP is suddenly unfinanceable. The BOP identity forces instant adjustment: the current account must swing by 10 percentage points. Exports cannot increase overnight, so adjustment falls on imports.
Exchange rate response. Under Kaelani’s managed float, the currency depreciates 25%. This triggers expenditure switching but also worsens debt: 40% of sovereign debt is dollar-denominated (original sin). Effective debt/GDP jumps from 85% to 95%.
Debt sustainability. With $d = 95\%$, $r = 6\%$, $g = 1\%$: $s^* = (0.06 - 0.01) \times 0.95 = 4.75\%$ of GDP. Current surplus: only 1%. The gap is enormous.
Resolution. Kaelani accepts a modified IMF program: moderate fiscal consolidation ($s = 3\%$), debt reprofile (maturity extension, not haircut), and temporary capital flow management. The crisis stabilizes but leaves scars: output 5% below trend, debt takes a decade to return to pre-crisis levels.
The Kaelani crisis demonstrates every concept: BOP accounting, expenditure switching, original sin, debt sustainability dynamics, sovereign default risk, and the limitations of international policy coordination for small economies.
Asian Financial Crisis (1997–98) and European Sovereign Debt Crisis (2010–12): two crises bracketing the open-economy policy spectrum.
Asia: Thailand’s baht peg collapsed in July 1997. Capital inflows of +10% of GDP reversed to outflows of -10% in months. The crisis exposed the impossible trinity: Thailand tried to maintain a fixed exchange rate, open capital account, and independent monetary policy simultaneously. IMF programs prescribed austerity and high rates — controversial for a capital account crisis. Malaysia imposed capital controls and recovered at a similar pace, challenging Washington Consensus orthodoxy. Original sin amplified the crisis as 40–80% currency depreciations exploded dollar-denominated corporate debt.
Europe: Greece, Ireland, Portugal, Spain, and Italy faced sovereign debt crises within a monetary union. Without their own currencies, they could not depreciate to restore competitiveness — the OCA criteria failure in action. Greece’s debt sustainability arithmetic was stark: $s^* = (0.07 - (-0.04)) \times 1.30 = 14.3\%$ of GDP — impossibly large. The ECB’s “whatever it takes” (Draghi, 2012) eliminated the multiple-equilibrium problem, but the underlying structural issue — monetary union without fiscal union — remains.
| Label | Equation | Description |
|---|---|---|
| Eq. 17.1 | $CA_t = X_t - M_t + r \cdot NFA_{t-1} + NTR_t$ | Current account |
| Eq. 17.2 | $CA_t + KA_t = 0$ | BOP identity |
| Eq. 17.3 | $E = P / P^*$ | Absolute PPP |
| Eq. 17.4 | $\Delta e_t = \pi_t - \pi_t^*$ | Relative PPP |
| Eq. 17.5 | $E_t[e_{t+1}] - e_t = i_t - i_t^*$ | Uncovered interest parity |
| Eq. 17.6 | $q_t = e_t + p_t^* - p_t$ | Real exchange rate |
| Eq. 17.7 | $\dot{e} = \theta(\bar{e} - e)$ | Dornbusch exchange rate dynamics |
| Eq. 17.8 | $\dot{p} = \delta(e - p + p^*)$ | Dornbusch price adjustment |
| Eq. 17.9 | $C = [\gamma^{1/\theta} C_H^{(\theta-1)/\theta} + (1-\gamma)^{1/\theta} C_F^{(\theta-1)/\theta}]^{\theta/(\theta-1)}$ | CES consumption aggregator |
| Eq. 17.10 | $\hat{C}_H - \hat{C}_F = \theta \cdot \hat{\tau}$ | Expenditure switching |
| Eq. 17.11 | $L_i = (\pi_i - \bar{\pi})^2 + \alpha(y_i - \bar{y})^2 + \beta(e_i)^2$ | Policy loss function |
| Eq. 17.12 | $L^{Nash} > L^{Coop}$ | Coordination gains |
| Eq. 17.13 | $V^{Repay}(b) \geq V^{Default}$ | Eaton-Gersovitz repayment condition |
| Eq. 17.14 | $\Delta d_t = (r_t - g_t) d_{t-1} - s_t$ | Debt sustainability dynamics |
| Eq. 17.15 | $i_t = i_t^{rf} + \rho(d_t, s_t, g_t)$ | Sovereign risk premium |
| Eq. 17.16 | $f'(k) = r + \delta$ | Neoclassical capital allocation |
Coming in Part VI: theory meets the real world. Institutions, behavior, and development.
Mundell (1961, 1963); Fleming (1962); Dornbusch (1976); Obstfeld & Rogoff (1995, 1996); Eaton & Gersovitz (1981); Lucas (1990); Calvo (1998); Balassa (1964); Samuelson (1964); Frankel & Rose (1998); Reinhart & Rogoff (2009).