Level: Upper-level Undergraduate / Master’s Introductory
Duration: ~45–50 minutes
[SLIDE 1: Title & Overview]
- Title: Thirlwall’s Law and BoP-Constrained Growth
- Subtitle: Why Demand, Foreign Exchange, and Trade Elasticities Limit Long-Run Growth
- Agenda:
- Origins & Neoclassical vs. Post-Keynesian Growth Paradigms
- The Theoretical Framework & Mathematical Derivation
- Empirical Evidence & Real-World Examples
- Policy Implications & Structural Principles
- Criticisms, Limitations, and Modern Extensions
1. Introduction & Origins: A Paradigm Shift
[Lecturer Speaking]
Good morning/afternoon, everyone. Today, we are exploring one of the cornerstone models of Post-Keynesian open-economy macroeconomics: Thirlwall’s Law, first articulated by British economist A.P. Thirlwall in his seminal 1979 paper, “The Weight of International Trade Theory for Development Economics” (published in the Journal of Post Keynesian Economics).
To appreciate Thirlwall’s insight, we must first contrast it with orthodox growth theory.
Standard supply-side models—such as the Solow-Swan neoclassical model or Endogenous Growth Theory—posit that long-run growth is dictated entirely by factor accumulation (capital, labor) and total factor productivity ($A$). In these models, a country grows as fast as its supply capacity allows. Demand simply adjusts to supply via flexible relative prices and exchange rates.
Supply-Side (Neoclassical): Inputs & Tech (Supply) ──> Long-Run Growth
Demand-Side (Thirlwall): Export Demand & Foreign Exchange Constraint ──> Long-Run Growth
Thirlwall turned this on its head by extending Keynes’s principle of effective demand to an open economy context over the long run. He posed a fundamental question: What happens if an economy attempts to grow faster than its balance of payments allows?
If a country grows rapidly, its imports rise. If exports do not grow at a rate sufficient to pay for those imports, the country incurs a persistent current account deficit. While foreign borrowing can bridge this gap in the short run, it is unsustainable in the long run. Eventually, the nation faces a foreign exchange constraint, forcing domestic policy to slow the economy down (e.g., through monetary tightening or fiscal austerity) long before it hits its supply-side potential.
Thus, Thirlwall’s Law asserts that long-run economic growth is ultimately constrained by the balance of payments, driven by external demand and income elasticities of trade.
2. Theoretical Framework & Mathematical Derivation
[SLIDE 2: Model Setup]
- Key Assumptions:
- Long-run equilibrium on the trade balance (or current account balance).
- Constant real exchange rates in the long run ($\Delta P / P \approx \Delta P^* / P^*$).
- Export demand is a function of world income; import demand is a function of domestic income.
[Lecturer Speaking]
Let’s formalize the model. We begin with the basic long-run trade balance condition:
$$P_t X_t = P_t^* E_t M_t$$
Where:
- $X_t$ = export volume
- $M_t$ = import volume
- $P_t$ = domestic price level
- $P_t^*$ = foreign price level
- $E_t$ = nominal exchange rate (units of domestic currency per unit of foreign currency)
Taking natural logarithms and differentiating with respect to time gives us the growth rate equation of trade balance:
$$p + x = p^* + e + m$$
Where lowercase letters represent percentage growth rates ($x = \frac{dX/dt}{X}$, etc.).
Next, we specify multiplicative constant elasticity demand functions for exports and imports:
Export Demand Function
$$X = A \left(\frac{P}{P^* \cdot E}\right)^{\eta} Y^{*\varepsilon}$$
Where $\eta < 0$ is the price elasticity of demand for exports, $Y^*$ is foreign (world) income, and $\varepsilon > 0$ is the foreign income elasticity of demand for exports.
In growth rates:
$$x = \eta (p – p^* – e) + \varepsilon y^*$$
Import Demand Function
$$M = B \left(\frac{P^* \cdot E}{P}\right)^{\psi} Y^{\pi}$$
Where $\psi < 0$ is the price elasticity of demand for imports, $Y$ is domestic income, and $\pi > 0$ is the domestic income elasticity of demand for imports.
In growth rates:
$$m = \psi (p^* + e – p) + \pi y$$
[SLIDE 3: Deriving the Law]
- Substitute $x$ and $m$ into the differentiated balance-of-payments equilibrium equation.
- Solve for domestic income growth rate ($y$).
[Lecturer Speaking]
Now, substitute the export ($x$) and import ($m$) growth equations back into our trade balance growth condition ($p + x = p^* + e + m$):
$$p + \left[\eta (p – p^* – e) + \varepsilon y^*\right] = p^* + e + \left[\psi (p^* + e – p) + \pi y\right]$$
Rearranging terms to isolate relative price growth $(p – p^* – e)$ and domestic income growth ($y$):
$$(1 + \eta + \psi)(p – p^* – e) + \varepsilon y^* = \pi y$$
Solving for domestic income growth, denoted as $y_b$ (the balance-of-payments-constrained growth rate):
$$y_b = \frac{(1 + \eta + \psi)(p – p^* – e) + \varepsilon y^*}{\pi}$$
[SLIDE 4: The Core Equation]
- Key Assumption: Relative prices/real exchange rates are relatively stable over the long run, or price elasticities are low ($\eta + \psi \approx -1$).
- Thirlwall’s Law (Basic Form):$$y_b = \frac{\varepsilon y^*}{\pi} = \frac{x}{\pi}$$
[Lecturer Speaking]
This brings us to Thirlwall’s key empirical observation: over the long run, real exchange rates display relative stability (Purchasing Power Parity tends to hold roughly, or terms of trade do not show continuous trend appreciation/depreciation sufficient to correct structural deficits). Furthermore, price elasticities of demand in international trade are often low in aggregate (the Marshall-Lerner condition may hold, but price effects are dwarfed by income effects).
When relative price changes in international trade approximate zero over the long run ($(p – p^* – e) \approx 0$), the equation simplifies dramatically:
$$y_b = \frac{\varepsilon y^*}{\pi}$$
Because total export growth $x$ is equal to $\varepsilon y^*$ (under constant relative prices), we can rewrite this as:
$$y_b = \frac{x}{\pi}$$
Thirlwall’s Law in Plain Words: A country’s long-run growth rate ($y_b$) equals its export volume growth rate ($x$) divided by its income elasticity of demand for imports ($\pi$). Alternatively, it is the product of world growth ($y^*$) and the ratio of income elasticities ($\varepsilon / \pi$).
3. Principles and Strategic Takeaways
[Lecturer Speaking]
Let’s pause to absorb what this simple ratio ($\frac{\varepsilon}{\pi}$) implies for policy and development.
- Non-Price Competitiveness Matters Most: The parameter $\varepsilon$ reflects how much the world wants your exports as global income grows (quality, technological sophistication, brand, reliability). The parameter $\pi$ reflects how quickly your citizens demand foreign goods as domestic income grows.
- The Elasticity Ratio as a Structural Ceiling: If your structural imports grow faster than income ($\pi > 1$) while your exports are income-inelastic ($\varepsilon < 1$), your growth rate must be a fraction of world growth to prevent unsustainable trade deficits.
- Price Adjustments (Devaluation) Won’t Save You in the Long Run: Currency devaluation provides, at best, a short-term price shock. It cannot permanently boost the long-run equilibrium growth rate unless it alters the underlying non-price elasticities ($\varepsilon$ and $\pi$).
4. Real-World Examples & Empirical Evidence
[SLIDE 5: Empirical Case Studies]
| Country / Region | Income Elasticity of Imports (π) | Income Elasticity of Exports (ε) | Predicted Growth (yb) | Actual Growth (y) |
| Japan (1950s–1980s) | Relatively Low (~1.0–1.2) | Very High (~3.0–3.5) | High | High |
| UK (Post-WWII) | High (~1.8–2.0) | Low (~0.8–1.0) | Low | Low |
| Latin America (1980s–1990s) | High (Post-liberalization) | Moderate (Primary commodities) | Severely Constrained | Low/Volatile |
[Lecturer Speaking]
How well does this hold up empirically? Remarkably well across decades of econometric testing.
Example 1: Post-WWII United Kingdom vs. Japan
In the decades following World War II, the UK suffered from a notoriously low ratio of $\frac{\varepsilon}{\pi}$. British manufacturing produced goods with low world-income elasticity ($\varepsilon$), while British consumers eagerly imported high-tech foreign manufactures as their incomes grew ($\pi \approx 2$). Whenever the UK economy expanded, it hit a BoP crisis (“stop-go” policy cycles), forcing the government to cool down the economy.
Conversely, postwar Japan exported high-value, income-elastic consumer electronics and automobiles ($\varepsilon > 3$), while maintaining structural barriers or low domestic propensity for manufactured imports. Japan was able to grow at double-digit rates without running into a balance-of-payments ceiling.
Example 2: The East Asian Tigers vs. Latin America
During the late 20th century, East Asian economies systematically moved up the value chain—transitioning from agriculture to garments, then to electronics, semiconductors, and heavy machinery. In doing so, they explicitly engineered an increase in $\varepsilon$ (their exports became indispensable to expanding global supply chains) and reduced reliance on foreign finished imports ($\pi$).
In contrast, many Latin American economies during the 1980s and 1990s underwent rapid trade liberalization without industrial restructuring. As tariffs fell, their import elasticity ($\pi$) surged. However, their exports remained concentrated in primary commodities (copper, agricultural products), which generally possess low income elasticity ($\varepsilon < 1$). The result? The BoP growth constraint tightened, leading to lower average growth rates and periodic debt/currency crises.
5. Criticisms, Limitations, and Modern Extensions
[SLIDE 6: Criticisms and Counterarguments]
- Is the Real Exchange Rate Truly Neutral in the Long Run? (Crucial role of terms of trade and real undervaluation).
- Capital Flows & Foreign Debt: Ignores capital account dynamics in its basic form.
- Endogeneity of Elasticities: Elasticities ($\pi, \varepsilon$) are treated as exogenous parameters, but they change over time.
- Supply-Side Constraints: What if an economy lacks the productive capacity to meet export demand?
[Lecturer Speaking]
While Thirlwall’s Law offers a compelling framework, it has faced substantial critique from both orthodox and heterodox scholars. Let’s break down the main objections.
Critique 1: Constant Relative Prices & Exchange Rate Effectiveness
Orthodox economists argue that Thirlwall dismisses relative prices too lightly. Neoclassical trade theory contends that if a country experiences a BoP deficit, real depreciation will restore equilibrium via price adjustments.
Heterodox Counter-Response: Empirical studies consistently find that industrial import and export price elasticities are often too low to fulfill the Marshall-Lerner condition strongly enough to drive long-run growth differences. Furthermore, continuous real depreciation can trigger inflationary spirals, eroding real wages without improving the structural trade balance.
Critique 2: Neglect of Capital Account & External Debt (Capital Flows)
The basic law assumes $P X = P^* E M$, meaning trade is balanced. But what about capital inflows? Countries can run persistent trade deficits if financed by Foreign Direct Investment (FDI), portfolio flows, or foreign loans.
Extension (Thirlwall & Hussain, 1982): Scholars extended the model to allow for initial current account deficits financed by capital flows. The extended model shows that capital flows can temporarily allow $y > y_b$, but if external debt-to-GDP ratios grow unadjusted, interest payments on foreign debt eventually tighten the BoP constraint even further, forcing a severe correction.
Critique 3: Supply-Side Factors and Structural Change
Is it realistic to treat supply as purely passive? What if an economy has high export demand ($\varepsilon y^*$), but lacks the physical infrastructure, skilled labor, or energy grid to produce those exports?
Modern multi-sector extensions of Thirlwall’s Law (e.g., Araujo & Lima, 2007) integrate Pasinetti’s structural economic dynamics. They demonstrate that supply-side investments—such as R&D, infrastructure, and education—do matter, but specifically because they transform the structural parameters ($\varepsilon$ and $\pi$), rather than merely increasing capacity in a vacuum.
[SLIDE 7: Summary & Key Takeaways]
- Core Insight: Growth is constrained by the necessity to balance foreign accounts over the long run.
- The Formula: $y_b = \frac{x}{\pi} = \frac{\varepsilon y^*}{\pi}$
- Policy Implication: True economic growth strategies must focus on structural transformation—moving into high-value, technologically sophisticated export sectors ($\uparrow \varepsilon$) while building domestic supply linkages to substitute for unnecessary intermediate imports ($\downarrow \pi$).
- Bottom Line: You cannot grow your way out of a balance-of-payments constraint simply by expanding domestic demand or cutting interest rates; industrial policy and structural change are essential.
[Lecturer Speaking]
To conclude: Thirlwall’s Law teaches us that open economies do not operate in an unconstrained aggregate demand environment, nor are they bound purely by factor inputs. The ultimate boundary condition for long-run expansion is international trade performance.
Thank you. I’m happy to open the floor to questions!
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