Open Economy and Long-Run Growth - Study Notes

Open Economy

  • Week 6 content for MAE307: Economic Policy and Practice.
  • Focus areas: Open Economy concepts, Exchange rates (Nominal and Real), Net Exports (NX), AD and AS in an Open Economy, and Long-run Economic Growth.

Open Economy: Key Questions

  • How open is the Australian economy?
  • Roles of Exports and Imports
  • Role of the exchange rate
  • Openness within the AD–AS framework

Openness: Measures

  • Export + Import (% of GDP) data points shown: 25, 30, 35, 40, 45 (illustrating rising openness over time).
  • Trade Openness (X + M) / Y tracked across years: 1960, 1980, 2000, 2020.
  • Interpretation: Openness increases over time as Australia trades more relative to its GDP.

Definitions of Exchange Rates

  • Exchange rates can be quoted two ways:
    • Foreign currency per unit of domestic currency (e.g., ¥95 / $1)
    • Domestic currency per unit of foreign currency (e.g., $/€)
  • Purpose: Denominate costs/prices in a common currency.
  • Example: Honda price quoted in yen: ¥3,000,000
    • If ¥3,000,000 × $0.0105/¥1 = $31,579
  • Exchange rate (E) is also called the Nominal Exchange Rate.

Exchange Rate Trends (Nominal vs Trade-Weighted)

  • Trade-Weighted AUD/USD series shown (2010m1, 2012m1, 2014m1, 2016m1, 2018m1, 2020m1, 2022m1, 2024m1): AUD/USD movements.
  • Message: Exchange rate movements reflect changes in demand/supply for Australian dollars against a basket of currencies.

Depreciation and Appreciation: Core Concepts

  • Depreciation: A decrease in the value of a currency relative to another currency.
    • A depreciated currency can buy less foreign currency.
    • Example: If the price of USD in EUR terms moves from $1/€ to $1.50/€1, the dollar has depreciated relative to the euro (more dollars needed per euro).
  • Appreciation: An increase in the value of a currency relative to another currency.
    • Example: From $1/€ to $0.90/€1, the dollar has appreciated relative to the euro (fewer dollars needed per euro).
  • Consequences for trade:
    • Depreciation lowers the price of exports relative to imports, potentially boosting NX.
    • Appreciation raises the price of exports relative to imports, potentially reducing NX.

Real Exchange Rate (RER)

  • Definition: RER measures the price of foreign goods relative to domestic goods, both in domestic currency terms.
  • Formula: RER = \frac{E \cdot P_f}{P} where
    • E = Nominal Exchange Rate (domestic currency per unit of foreign currency)
    • P_f = Foreign price level (in foreign currency)
    • P = Domestic price level (in domestic currency)
  • Interpretation:
    • If foreign prices rise relative to domestic prices (foreign inflation higher), domestic expenditure on domestic goods rises relative to foreign goods, affecting NX.
    • A depreciation of the RER (i.e., cheaper domestic goods relative to foreign goods) tends to increase NX.
  • Note: An alternative formulation is RER = \frac{P}{E P_f} depending on the denominator convention.

Real Exchange Rate: Depreciation and Revaluation

  • A depreciation of the RER occurs when the nominal exchange rate (E) depreciates or when foreign prices rise slower than domestic prices.
  • A depreciation tends to increase NX by making domestic goods cheaper relative to foreign goods.
  • When P rises (inflation domestically), the RER can appreciate, potentially offsetting some NX gains.
  • Summary: RER moves with E and relative price levels; it affects NX through import prices and export competitiveness.

Real (Effective) Exchange Rate (REER)

  • REER is a weighted average of bilateral real exchange rates, adjusted by relative price levels.
  • Concept: REER captures the overall competitive position of a country against a basket of trading partners.
  • Historical indices (1995Q1 = 100) show changes in REER over time (1970q1, 1980q1, 1990q1, 2000q1, 2010q1, 2020q1).

Terms of Trade (ToT)

  • Definition: The ratio of export prices to import prices.
  • Time series shown: 1960q1, 1980q1, 2000q1, 2020q1 with ToT values rising/falling over time.
  • Implication: Changes in ToT affect real income from trade and the purchasing power for imports vs. exports.

Open Economy and Aggregate Demand (AD–AS)

  • Mechanism: An increase in RER (i.e., depreciation) tends to decrease imports and increase exports, raising NX.
  • Disposable income (Y − T) affects consumption; higher disposable income raises consumption including imports, which lowers NX.
  • NX depends on RER and the after-tax income gap (Y − T).
  • Common notation in slides: Ye = (Ca − cT + I(r) + G + NX (RER, Y − T)) · mr
    • Where RER is E Pf / P and Y − T captures after-tax income.
    • Note: In the slide, there is also a reference to the domestic demand function Ca − cT (consumption as a function of after-tax income).

Open Economy and AD Shifts due to RER Depreciation

  • If the nominal exchange rate (E) depreciates, the RER depreciates as well (RER = E Pf / P).
  • Result: NX and Y increase, AD shifts to the right, and equilibrium Y (and P) increases.
  • Graphical interpretation: AD shifts from AD1 to AD2 (or similar) as depreciation boosts demand.

Depreciation, RER, and NX: Offset Effects

  • A depreciation that raises Y and P can trigger RER appreciation (as domestic price level P rises), making exports relatively more expensive and imports cheaper.
  • This can cause NX to fall, offsetting part of the initial gain in Y.
  • Result: Partial offset to the initial expansion in output due to higher domestic prices.

Law of One Price (LoP)

  • Assumes no trade barriers and no transportation costs.
  • Statement: Price of a commodity is the same across countries when expressed in a common currency; otherwise, arbitrage will occur.
  • Foreign price in domestic currency: E \cdot Pf = P implies \frac{E \cdot Pf}{P} = 1 (RER = 1).
  • Exchange rate is determined by relative prices (long-run concept).

Purchasing Power Parity (PPP)

  • Aggregate concept: Price levels should be the same across countries when converted to a common currency.
  • Absolute PPP: E = \frac{P}{P_f}
  • Relative PPP: Changes in exchange rates reflect changes in inflation differentials between countries:
    • Formula: \frac{Et - E{t-1}}{E{t-1}} = \pi{AU,t} - \pi{EU,t} where (\pit) is the inflation rate from period t−1 to t.
  • Interpretation:
    • LHS represents exchange-rate depreciation/appreciation.
    • RHS represents inflation difference.
  • Implication: Exchange rate depreciation (appreciation) is determined by relative inflation rates across countries.

Monetary Policy and Exchange Rate

  • Expansionary monetary policy increases the money supply, shifting the AD curve to the right, which raises P (or π) and Y.
  • With higher P, the domestic currency depreciates: E = \frac{P}{P_f}
  • Therefore, expansionary monetary policy leads to currency depreciation.

Summary (Open Economy)

  • Nominal exchange rates: quoted as foreign currency per unit of domestic currency or vice versa.
  • Real exchange rate (RER): price comparison of foreign vs domestic goods in domestic currency; RER = \frac{E P_f}{P}.
  • Depreciation/Appreciaiton effects: Depreciation raises NX and shifts AD to the right, increasing output; price level changes can offset some NX gains.
  • In the long run, exchange rate is determined by the price level across countries.
  • Expansionary monetary policy tends to depreciate the exchange rate.

Long-Run: Economic Growth

  • Question: Why is China or India poorer than Australia but grows faster?

Australia’s Long-Run Living Standards

  • Per capita real GDP (June 2022): \$83{,}678
  • Per capita real GDP (June 1990): \$50{,}832
  • Increase: approximately 1.65 times over 33 years.
  • Average annual growth rate ≈ 1.96\% per year.

Per Capita Real GDP (AUD) Over Time

  • Graphs show: Per capita real GDP (AUD) from 1960 to 2020 across Australia, with values rising overall.
  • Another comparison: GDP per capita (PPP) for Australia over time.

Per Capita Real GDP: AUD vs. PPP

  • Graphs indicate differences between market-based per-capita GDP and PPP-adjusted GDP over 1960–2020.

Long-Run Economic Growth: China (Poor) vs Australia (Rich)

  • China (GDP per capita, constant 2015 US$): 2019 ≈ $10,155.4; 1990 ≈ $905.0 (about 11x increase over 30 years).
  • Australia: 2019 per-capita real GDP ≈ $78,713; 1990 ≈ $49,496; about 1.59x increase over 30 years; average growth ≈ 1.968% ≈ 2.0%.

Why Rich Countries Grow Slower in the Long Run

  • Observation: Rich countries have higher capital stock per worker (K/N).
  • Rich countries experience slower growth due to diminishing marginal product of capital (MPK).
  • Long-run growth is driven by technological progress (A).

Technology and LR Growth

  • Technology shifts the production function: YN = A1 f(KN) vs YN = A0 f(KN) (illustrating technology improvements shift the function upwards).
  • Graphical depiction uses KN and N0, KN, N0 coordinates to illustrate shifts.

Rich vs Poor Countries: Capital Deepening and Convergence

  • Convergence: Poor countries can catch up with rich countries in the long run, achieving similar living standards (Y/N) given similar structural features.
  • Assumes similarity in all respects except capital per worker (K/N).
  • However, empirical convergence is mixed; strong evidence among similar countries (USA and Western Europe) but less across broadly dissimilar economies.

Convergence Across Countries: Historical Evidence

  • GDP per capita (in 2010 US$) shows convergence among some developed economies (UK, Italy, Canada, France, USA, Germany, Japan, etc.).
  • The data table (1870–2010) shows convergence trends among long-run successors.

Convergence in Australian States?

  • Concept: Do poorer Australian states converge with richer states over time?
  • Data: Log of per-capita State Domestic Product, 1990–2021, for NSW, VIC, QLD, SA, WA, NT, ACT, TAS, and Australia as a whole.
  • Question: Observed trends suggest mixed evidence of convergence across states; interpretation depends on time window and methodology.

New Growth Theory

  • Focus areas: Modelling technology and modelling human capital as fundamental drivers of growth.
  • Implication: Growth is not just capital deepening but also knowledge spillovers and human-capital accumulation.

Summary (Economic Growth)

  • Poor countries (low capital-labor ratio) often grow faster than rich countries due to diminishing MPK.
  • Long-run growth is driven by technological progress.
  • Convergence: Poor countries tend to converge with rich ones in the long run, but evidence is mixed; stronger convergence among similar economies.
  • Growth in Australia’s context reflects high capital per worker and technology influences; differences exist compared with China/India.

Notation and Formulas Summary ( Quick Reference )

  • Real Exchange Rate: RER = \frac{E \cdot P_f}{P}
  • Absolute PPP (exchange rate based on price levels): E = \frac{P}{P_f}
  • Relative PPP (inflation differential): \frac{Et - E{t-1}}{E{t-1}} = \pi{AU,t} - \pi_{EU,t}
  • Open economy production (equilibrium output): Ye = (Ca - cT + I(r) + G + NX(E\,Pf/P, Y - T)) \cdot m_r
  • Production function and per-capita form: Y = A F(K,N)\quad ; \quad y \equiv \frac{Y}{N} = f\left( \frac{K}{N} \right)
  • Depreciation/Appreciation examples use currency prices: e.g., from $1/€ to $1.50/€1 indicates USD depreciation; from $1/€ to $0.90/€1 indicates USD appreciation.
  • Growth rates: Australia 1990–2022 approximate annual growth ~1.96\%; China growth historically much higher in per-capita terms over 1990–2019 depending on base.

Connections to Foundational Principles

  • Open economy framework integrates trade, exchange rates, and macro aggregates (AD–AS) to explain how external sector interacts with domestic demand.
  • PPP and LoP connect price levels across borders to exchange rate determination in the long run.
  • Monetary policy transmits to the exchange rate via price level channels and inflation expectations, affecting NX through competitiveness.
  • Long-run growth rests on technology and human capital, not just capital accumulation, explaining why growth rates can diverge across countries with different technology and institutions.

Real-World Relevance

  • Understanding how depreciation/appreciation affects trade balances helps policymakers design exchange-rate regimes and macro stabilization.
  • PPP concepts underpin exchange-rate theories used by central banks and international financial institutions.
  • Growth theory explains why some countries converge over time and others do not, informing development policy and investment decisions.