The Goods Market

Saving, Investment & the IS Identity

coreExam · medium

In equilibrium, investment equals saving — private saving S plus public saving (T − G) plus foreign saving (−NX) finance investment. This identity holds by accounting and is an alternative formulation of goods-market equilibrium (Y = Z). Useful for analysing twin deficits, global imbalances, and the saving-investment gap.

Derivation

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The Identity

I = \underbrace{S}_{\text{private}} + \underbrace{(T - G)}_{\text{public}} - \underbrace{NX}_{-\text{foreign}}

Three sources of saving finance investment: private, public, foreign.

Rearranging the National Accounts

Starting from $Y = C + I + G + NX$ :

Y - C - G - NX = I

Split the LHS:

\underbrace{(Y - T - C)}_{S} + \underbrace{(T - G)}_{S^g} - NX = I

Three Regimes

| Regime | Closed/Open | Public Saving | Implication | |--------|-------------|---------------|-------------| | Budget balance | Closed | $T = G$ | $I = S$ | | Twin deficits | Open | $T < G$ | Foreign saving fills gap | | Surplus economy | Open | $T \geq G$ | Funds other countries |

The Twin Deficits Story

A fiscal deficit that raises $G$ without raising $T$ reduces public saving. With private $S$ and investment $I$ relatively stable, the adjustment happens through $NX$ : imports rise, exports fall, CA goes into deficit. The budget deficit "becomes" a trade deficit.

Global Imbalances

Countries with persistent CA surpluses (China, Germany) have $S > I$ . They finance $I$ in the rest of the world. Countries with persistent CA deficits (US, UK) have $S < I$ and import foreign saving.

The identity doesn't tell us why — that's behavioural. But it constrains the possibilities.

Caution

The identity always holds. What it doesn't tell you is causation. The identity is a starting point, not an answer.

Worked Example

Economy data: Y = 100, C = 60, I = 20, G = 20. Taxes T = 25. Compute S, public saving, NX.

From Y identity: NX = Y − C − I − G = 100 − 60 − 20 − 20 = 0. Balanced.
Private saving: S = Y − T − C = 100 − 25 − 60 = 15.
Public saving: T − G = 25 − 20 = 5.
Check identity: I = S + (T − G) − NX = 15 + 5 − 0 = 20. ✓

S = 15, public saving = 5, NX = 0. Investment I = 20 financed by private + public saving. Identity holds.

Common Mistakes

—Confusing accounting identity with behavioural equilibrium — I = S holds by definition, but how it adjusts depends on the model.
—Ignoring foreign saving in open economy — NX < 0 means foreign saving is positive.
—Conflating private and public saving — they're separate components of total saving.
—Forgetting that S uses disposable income (Y − T), not total Y.

Exam Cues

→Identity: I = S + (T − G) − NX. Know all three components.
→Twin deficits: ↑G without ↑T reduces (T − G); I or NX must adjust.
→Closed-economy crowding out: deficit ↓I unless S adjusts.
→Open economy: CA deficit = foreign financing of domestic investment.