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Lesson M09.L01: The Savings-Investment Identity in an Open Economy

Module: Savings, Capital Formation, and Economic Growth Level: intro Duration: 30 minutes Learning Objective: Derive the national savings-investment identity for an open economy. Data as of: 2024 Provenance: RBA Education | OpenStax Macro 3e

Explanation

In a closed economy (no trade with the rest of the world), every dollar saved must fund domestic investment: S = I. But Australia is an open economy — we trade goods, services, and capital with the rest of the world — so the identity is richer.

Start from the national income accounting identity:

Y = C + I + G + NX

where Y is GDP, C is household consumption, I is investment, G is government spending, and NX (net exports) equals exports minus imports.

National saving (S) is income left over after consumption and government spending:

S = Y − C − G

Substituting into the GDP identity:

S = I + NX

We can split saving into its private and public components:

S_private + S_government = I + NX

S_private is household saving; S_government is the budget surplus (or deficit if negative). NX equals the current account balance (CA) — a positive NX means Australia is lending to the world; a negative NX means Australia is borrowing.

Australia has historically run current account deficits — NX < 0 — meaning domestic investment exceeds national saving. We borrow the difference from foreign savers. Between the 1980s and 2010s, this deficit averaged around 4% of GDP. Recent commodity booms have pushed Australia into occasional surpluses.

This identity is an accounting truth: it always holds, by definition. Understanding it helps explain why a government budget deficit (lower S_government) can crowd out investment or increase foreign borrowing.

Worked Example

Scenario: In a given year, Australia has the following data (all figures in $billion): - GDP (Y) = $2,200b - Household consumption (C) = $1,320b - Investment (I) = $440b - Government spending (G) = $440b - Net exports (NX) = ?

Step 1 — Calculate NX from the GDP identity:

Y = C + I + G + NX 2,200 = 1,320 + 440 + 440 + NX 2,200 = 2,200 + NX NX = 2,200 − 2,200 = 0

Step 2 — Calculate national saving:

S = Y − C − G S = 2,200 − 1,320 − 440 S = $440b

Step 3 — Verify the identity S = I + NX:

440 = 440 + 0 ✓

Now change the scenario: Suppose the government increases spending to $500b (a deficit of $60b), holding Y, C, and I constant.

S = 2,200 − 1,320 − 500 = $380b NX = S − I = 380 − 440 = −$60b

The government deficit has produced a current account deficit of $60b — Australia must borrow $60b from abroad. This is the twin deficits relationship.

Common Misconception

Misconception: "If Australia invests more, we must be saving more."

Correction: The identity S = I + NX shows that investment can exceed saving if NX is negative — i.e., if we borrow from abroad. Australia consistently invests more than it saves domestically, funding the gap with foreign capital inflows. Higher investment does not require higher domestic saving in an open economy.

Practice Prompts

  1. Why does the savings-investment identity change when an economy opens to international trade? → Answer: In a closed economy, all saving must fund domestic investment (S = I). In an open economy, saving can also flow abroad as net exports (lending) or foreign saving can supplement domestic saving (borrowing), giving S = I + NX. The extra term NX captures international capital flows.

  2. NUMERICAL CALCULATION: Australia reports: Y = $2,500b, C = $1,500b, G = $500b, I = $520b. Calculate (a) national saving S, (b) net exports NX, and (c) state whether Australia is a net lender or borrower. → Answer: (a) S = Y − C − G = 2,500 − 1,500 − 500 = $500b (b) NX = S − I = 500 − 520 = −$20b (c) NX < 0 → Australia is a net borrower from the rest of the world (current account deficit of $20b).

  3. Australia's federal budget swings from a $30b surplus to a $30b deficit (all else equal). Using the savings-investment identity, explain what must happen to NX. → Answer: A $30b shift from surplus to deficit reduces S_government by $30b, reducing total national saving S by $30b. With I unchanged, NX = S − I falls by $30b — the current account deficit widens by $30b. This illustrates the twin deficits hypothesis: fiscal deficits tend to produce current account deficits.

Further Resources