National Savings and Investment Identity - Explained

What is the National Savings and Investment Identity?

What is the National Savings and Investment Identity?

The national saving and investment identity provides a framework for showing the relationships between the sources of demand and supply in financial capital markets. The identity begins with a statement that must always hold true: the quantity of financial capital supplied in the market must equal the quantity of financial capital demanded.

The U.S. economy has two main sources for financial capital: private savings from inside the U.S. economy and public savings.

Total savings = Private savings (S) + Public savings (T – G)

These include the inflow of foreign financial capital from abroad. The inflow of savings from abroad is, by definition, equal to the trade deficit.

We can write this inflow of foreign investment capital as imports (M) minus exports (X). There are also two main sources of demand for financial capital: private sector investment (I) and government borrowing. Government borrowing in any given year is equal to the budget deficit, which we can write as the difference between government spending (G) and net taxes (T). Let’s call this equation 1.

Quantity supplied of financial capital = Quantity demanded of financial capital

Private savings + Inflow of foreign savings  = Private investment + Government budget deficit

S + (M – X) = I + (G –T)

Governments often spend more than they receive in taxes and, therefore, public savings (T – G) is negative. This causes a need to borrow money in the amount of (G – T) instead of adding to the nation’s savings. If this is the case, we can view governments as demanders of financial capital instead of suppliers. In algebraic terms, we can rewrite the national savings and investment identity like this:

Private investment = Private savings +    Public savings    + Trade deficit I = S + (T – G) + (M – X)

Let’s call this equation 2. We must accompany a change in any part of the national saving and investment identity by offsetting changes in at least one other part of the equation because we assume that the equality of quantity supplied and quantity demanded always holds. If the government budget deficit changes, then either private saving or investment or the trade balance—or some combination of the three—must change as well.

National Savings and Investment Identity in Budget and Trade Surpluses

The national saving and investment identity must always hold true because, by definition, the quantity supplied and quantity demanded in the financial capital market must always be equal. However, the formula will look somewhat different if the government budget is in deficit rather than surplus or if the balance of trade is in surplus rather than deficit. For example, in 1999 and 2000, the U.S. government had budget surpluses, although the economy was still experiencing trade deficits. When the government was running budget surpluses, it was acting as a saver rather than a borrower, and supplying rather than demanding financial capital. As a result, we would write the national saving and investment identity during this time as:

Quantity supplied of financial capital = Quantity demanded of financial capital Private savings + Trade deficit + Government surplus = Private investment

S + (M – X) + (T – G) = I

Let's call this equation 3. Notice that this expression is mathematically the same as equation 2 except the savings and investment sides of the identity have simply flipped sides.

During the 1960s, the U.S. government was often running a budget deficit, but the economy was typically running trade surpluses. Since a trade surplus means that an economy is experiencing a net outflow of financial capital, we would write the national saving and investment identity as:

Quantity supplied of financial capital  =  Quantity demanded of financial capital

Private savings = Private investment + Outflow of foreign savings + Government budget deficit S = I + (X – M) + (G – T)

Instead of the balance of trade representing part of the supply of financial capital, which occurs with a trade deficit, a trade surplus represents an outflow of financial capital leaving the domestic economy and invested elsewhere in the world.

Quantity supplied of financial capital  =  Quantity demanded of financial capital demand

Private savings = Private investment + Government budget deficit + Trade surplus S = I + (G – T) + (X – M)

We assume that the point to these equations is that the national saving and investment identity always hold. When you write these relationships, it is important to engage your brain and think about what is on the supply and demand side of the financial capital market before you start your calculations.

A rising budget deficit may result in a fall in domestic investment, a rise in private savings, or a rise in the trade deficit. The following modules discuss each of these possible effects in more detail.

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