Savings Investment Identity

Savings – Investment Identity in a Closed Economy

Take a closed economy with no government. Keynes’s national accounting identity says that S = I — aggregate savings always match aggregate investment ex post. Why? Income either gets consumed or invested, so Y = C + I, and it either gets consumed or saved, so Y = C + S. Subtract one from the other and you land on the equilibrium condition I = Y − C = S.

Open the economy up and you bring in the government and external sectors: Sprivate + Spublic + Sexternal = I. Brazil’s gross saving rate sits around 16% of GDP, far under what East Asian economies like China and Singapore manage (often north of 40%). With domestic savings falling short of the investment the country wants, Brazil usually runs a current-account deficit, importing foreign savings to fund capital formation.

Applications

You see it in macroeconomics teaching (the IS–LM framework, the Solow growth model), in how central banks read external accounts, in sovereign credit ratings, and across policy debates over pension reform, fiscal deficits and the cost of capital. The same identity is what sits behind the “twin deficits” hypothesis, which ties fiscal imbalances to current-account ones.

FAQ

Why must S equal I in a closed economy? Because it’s an accounting identity, not a statement about behaviour. Whatever output isn’t consumed has to end up in the capital stock by definition, inventories included.

Does Brazil’s low savings rate hurt growth? It does. When S stays low for years on end, the real interest rate climbs, productive investment gets crowded out, and the country grows more exposed to external shocks.

What is dissaving? It happens when consumption runs ahead of income — a government in deficit, say, or households spending down their wealth. Savings go negative, and something elsewhere has to make up the gap for the identity to still hold.