The national saving and investment identity is an accounting relationship that connects a country's saving, investment, and trade balance. It shows that any gap between what a nation saves and what it invests domestically must be filled by borrowing from (or lending to) the rest of the world. This identity is central to understanding why trade deficits and surpluses exist and how government policy can shift them.

Factors in Trade Balances

The trade balance measures the difference between a nation's exports and imports of goods and services.

A trade surplus occurs when exports exceed imports (positive trade balance).
A trade deficit occurs when imports exceed exports (negative trade balance).

The current account balance is a broader measure. It includes the trade balance plus net income from abroad (like dividends and interest earned on foreign investments minus payments to foreign investors) and net transfers (like foreign aid and remittances workers send to families in other countries).

Several factors push trade and current account balances in different directions:

Exchange rates change the relative prices of exports and imports. When the domestic currency appreciates, exports become more expensive for foreign buyers and imports become cheaper, which tends to worsen the trade balance. Depreciation has the opposite effect.
Domestic economic growth pulls in more imports as consumers and businesses increase spending on things like construction materials and consumer goods.
Foreign economic growth boosts demand for a country's exports, such as agricultural products or manufactured goods.
Trade policies like tariffs and quotas directly restrict or alter the flow of goods and services.
Capital flows between countries can influence trade balances indirectly by affecting exchange rates and investment patterns.

Factors in trade balances, Trade Balances and Flows of Financial Capital – Principles of Economics: Scarcity and Social ...

Supply and Demand of Financial Capital

Financial capital has two sources of supply:

Domestic saving ( $S_d$ ): saving by households, businesses, and the government within the country
Foreign saving ( $S_f$ ): funds flowing in from international investors and lenders

Total supply of financial capital: $S = S_d + S_f$

Demand for financial capital comes from domestic investment ( $I_d$ ): spending by businesses and government on things like factories, equipment, and infrastructure.

In equilibrium, the supply of financial capital equals the demand:

$S_d + S_f = I_d$

Interest rates are the mechanism that adjusts to bring supply and demand into balance. When demand for borrowing rises, interest rates increase, which attracts more saving (both domestic and foreign) and discourages some investment until the market clears.

Factors in trade balances, Exchange-Rate Policies | Microeconomics

Domestic Saving vs. Trade Balance

The national saving and investment identity can be rearranged to reveal the connection between saving and trade:

$S_f = I_d - S_d$

This says that foreign saving flowing into a country equals the gap between domestic investment and domestic saving. The implications are direct:

When $I_d > S_d$ : The country doesn't save enough to cover its own investment, so it borrows from abroad ( $S_f > 0$ ). This inflow of foreign capital corresponds to a trade deficit. The U.S. is a long-running example: high investment and relatively low saving have been paired with persistent trade deficits.
When $S_d > I_d$ : The country saves more than it invests domestically, so it lends the surplus abroad ( $S_f < 0$ ). This outflow of capital corresponds to a trade surplus. Germany and Japan have historically fit this pattern.

The key takeaway is that trade deficits aren't just about which goods a country buys or sells. They reflect a deeper imbalance between national saving and investment.

National Saving and Trade Deficits

Because $S_f = I_d - S_d$ , any change in domestic saving or investment shifts the trade balance. Here's how each scenario plays out (holding the other variable constant):

If domestic saving increases:

The gap $I_d - S_d$ shrinks.
Less foreign borrowing is needed, so the trade deficit falls (or the trade surplus grows).

If domestic saving decreases:

The gap $I_d - S_d$ widens.
More foreign borrowing is needed, so the trade deficit grows (or the trade surplus shrinks).

If domestic investment increases:

The gap $I_d - S_d$ widens.
More foreign capital must flow in, increasing the trade deficit.

If domestic investment decreases:

The gap $I_d - S_d$ shrinks.
Less foreign borrowing is needed, reducing the trade deficit.

Two major factors drive these shifts in practice:

Government budget balance: A government budget deficit reduces national saving (the government is dissaving). This tends to widen the trade deficit. When budget deficits and trade deficits move together, economists call them "twin deficits." A budget surplus has the opposite effect, boosting national saving and improving the trade balance.
Private saving and investment decisions: These are shaped by interest rates, economic growth, and expectations. Higher interest rates encourage saving and discourage borrowing for investment. Stronger growth and optimistic business sentiment tend to boost investment spending relative to saving.

Open vs. Closed Economies and Balance of Payments

In a closed economy, there's no international trade or financial flows, so domestic saving must equal domestic investment: $S_d = I_d$ . There's no foreign saving to fill any gap.

In an open economy, international transactions create the possibility that saving and investment can diverge. The difference is covered by capital flowing in or out of the country.

The balance of payments is the accounting record of all economic transactions between a country's residents and the rest of the world. Its two main components are:

The current account, which tracks flows of goods, services, income, and transfers
The capital (and financial) account, which tracks flows of financial assets like stocks, bonds, and direct investment

These two accounts must sum to zero. A current account deficit (trade deficit) is always matched by a capital account surplus (net inflow of foreign investment), and vice versa. This is the balance of payments identity in action, and it's just another way of expressing the national saving and investment identity.