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10.4: The National Saving and Investment Identity

The close connection between trade balances and international flows of savings and investments leads to a macroeconomic analysis. This approach views trade balances—and their associated flows of financial capital—in the context of the overall levels of savings and financial investment in the economy.

Understanding the Determinants of the Trade and Current Account Balance

The national saving and investment identity provides a useful way to understand the determinants of the trade and current account balance. In a nation’s financial capital market, the quantity of financial capital supplied at any given time must equal the quantity of financial capital demanded for purposes of making investments. What is on the supply and demand sides of financial capital? See the following Clear It Up feature for the answer to this question.

Note: What Comprises the Supply and Demand of Financial Capital?

A country’s national savings is the total of its domestic savings by household and companies (private savings) as well as the government (public savings). If a country is running a trade deficit, it means money from abroad is entering the country and is considered part of the supply of financial capital.

The demand for financial capital (money) represents groups that are borrowing the money. Businesses need to borrow to finance their investments in factories, materials, and personnel. When the federal government runs a budget deficit, it is also borrowing money from investors by selling Treasury bonds. So both business investment and the federal government can demand (or borrow) the supply of savings.

There are two main sources for the supply of financial capital in the U.S. economy: saving by individuals and firms, called S, and the inflow of financial capital from foreign investors, which is equal to the trade deficit (M – X), or imports minus exports. There are also two main sources of demand for financial capital in the U.S. economy: private sector investment, I, and government borrowing, where the government needs to borrow when government spending, G, is higher than the taxes collected, T. This national savings and investment identity can be expressed in algebraic terms:

\[Supply\,of\,financial\,capital=Demand\,for\,financial\,capital\]
\[S + (M – X) = I + (G – T)\]

Again, in this equation, S is private savings, T is taxes, G is government spending, M is imports, X is exports, and I is investment. This relationship is true as a matter of definition because, for the macro economy, the quantity supplied of financial capital must be equal to the quantity demanded.

However, certain components of the national savings and investment identity can switch between the supply side and the demand side. Some countries, like the United States in most years since the 1970s, have budget deficits, which mean the government is spending more than it collects in taxes, and so the government needs to borrow funds. In this case, the government term would be G – T > 0, showing that spending is larger than taxes, and the government would be a demander of financial capital on the right-hand side of the equation (that is, a borrower), not a supplier of financial capital on the right-hand side. However, if the government runs a budget surplus so that the taxes exceed spending, as the U.S. government did from 1998 to 2001, then the government in that year was contributing to the supply of financial capital (T – G > 0), and would appear on the left (saving) side of the national savings and investment identity.

Similarly, if a national economy runs a trade surplus, the trade sector will involve an outflow of financial capital to other countries. A trade surplus means that the domestic financial capital is in surplus within a country and can be invested in other countries.

The fundamental notion that total quantity of financial capital demanded equals total quantity of financial capital supplied must always remain true. Domestic savings will always appear as part of the supply of financial capital and domestic investment will always appear as part of the demand for financial capital. However, the government and trade balance elements of the equation can move back and forth as either suppliers or demanders of financial capital, depending on whether government budgets and the trade balance are in surplus or deficit.

Domestic Saving and Investment Determine the Trade Balance

One insight from the national saving and investment identity is that a nation’s balance of trade is determined by that nation’s own levels of domestic saving and domestic investment. To understand this point, rearrange the identity to put the balance of trade all by itself on one side of the equation. Consider first the situation with a trade deficit, and then the situation with a trade surplus.

In the case of a trade deficit, the national saving and investment identity can be rewritten as:

\[Trade\,deficit=Domestic\,investment – Private\,domestic\,saving – Government\,(or\,public)\,savings\]
\[(M – X) = I – S – (T – G)\]

In this case, domestic investment is higher than domestic saving, including both private and government saving. The only way that domestic investment can exceed domestic saving is if capital is flowing into a country from abroad. After all, that extra financial capital for investment has to come from someplace.

Now consider a trade surplus from the standpoint of the national saving and investment identity:

\[Trade\,surplus = Private\,domestic\,saving + Public\,saving – Domestic\,investment\]
\[(X – M) = S + (T – G) – I\]

In this case, domestic savings (both private and public) is higher than domestic investment. That extra financial capital will be invested abroad.

This connection of domestic saving and investment to the trade balance explains why economists view the balance of trade as a fundamentally macroeconomic phenomenon. As the national saving and investment identity shows, the trade balance is not determined by the performance of certain sectors of an economy, like cars or steel. Nor is the trade balance determined by whether the nation’s trade laws and regulations encourage free trade or protectionism (see Globalization and Protectionism).

Exploring Trade Balances One Factor at a Time

The national saving and investment identity also provides a framework for thinking about what will cause trade deficits to rise or fall. Begin with the version of the identity that has domestic savings and investment on the left and the trade deficit on the right:

\[Domestic\,investment–Private\,domestic\,savings–Public\,domestic\,savings=Trade\,deficit\]
\[I – S – (T – G) =  (M – X)\]

Now, consider the factors on the left-hand side of the equation one at a time, while holding the other factors constant.

As a first example, assume that the level of domestic investment in a country rises, while the level of private and public saving remains unchanged. The result is shown in the first row of Table 1 under the equation. Since the equality of the national savings and investment identity must continue to hold—it is, after all, an identity that must be true by definition—the rise in domestic investment will mean a higher trade deficit. This situation occurred in the U.S. economy in the late 1990s. Because of the surge of new information and communications technologies that became available, business investment increased substantially. A fall in private saving during this time and a rise in government saving more or less offset each other. As a result, the financial capital to fund that business investment came from abroad, which is one reason for the very high U.S. trade deficits of the late 1990s and early 2000s.

Domestic Investment   – Private Domestic Savings   – Public Domestic Savings   = Trade Deficit
I S (T – G) = (M – X)
Up   No change   No change   Then M – X must rise
No change   Up   No change   Then M – X must fall
No change   No change   Down   Then M – X must rise

Table 1: Causes of a Changing Trade Balance

As a second scenario, assume that the level of domestic savings rises, while the level of domestic investment and public savings remain unchanged. In this case, the trade deficit would decline. As domestic savings rises, there would be less need for foreign financial capital to meet investment needs. For this reason, a policy proposal often made for reducing the U.S. trade deficit is to increase private saving—although exactly how to increase the overall rate of saving has proven controversial.

As a third scenario, imagine that the government budget deficit increased dramatically, while domestic investment and private savings remained unchanged. This scenario occurred in the U.S. economy in the mid-1980s. The federal budget deficit increased from $79 billion in 1981 to $221 billion in 1986—an increase in the demand for financial capital of $142 billion. The current account balance collapsed from a surplus of $5 billion in 1981 to a deficit of $147 million in 1986—an increase in the supply of financial capital from abroad of $152 billion. The two numbers do not match exactly, since in the real world, private savings and investment did not remain fixed. The connection at that time is clear: a sharp increase in government borrowing increased the U.S. economy’s demand for financial capital, and that increase was primarily supplied by foreign investors through the trade deficit. The following Work It Out feature walks you through a scenario in which private domestic savings has to rise by a certain amount to reduce a trade deficit.

Note: Solving Problems with the Saving and Investment Identity

Use the saving and investment identity to answer the following question: Country A has a trade deficit of $200 billion, private domestic savings of $500 billion, a government deficit of $200 billion, and private domestic investment of $500 billion. To reduce the $200 billion trade deficit by $100 billion, by how much does private domestic savings have to increase?

Step 1. Write out the savings investment formula solving for the trade deficit or surplus on the left:

\[(X – M) = S + (T – G) – I\]

Step 2. In the formula, put the amount for the trade deficit in as a negative number (X – M). The left side of your formula is now:

\[–200 = S + (T – G) – I\]

Step 3. Enter the private domestic savings (S) of $500 in the formula:

\[–200 = 500 + (T – G) – I\]

Step 4. Enter domestic investment (I) of $500 into the formula:
       
\[–200 = 500 + (T – G) – 500\]

Step 5. The government budget surplus or balance is represented by (T – G). Enter a budget deficit amount for (T – G) of –200:

\[–200 = 500 + (–200) – 500\]

Step 6. Your formula now is:

\[(X – M) = S + (T – G) – I\]
\[–200 = 500 + (–200) – 500\]

The question is: To reduce your trade deficit (X – M) of –200 to –100 (in billions of dollars), by how much will savings have to rise?

\[(X – M) = S + (T – G) – I\]
\[–100 = S + (–200) – 500\]
\[600 = S\]

Step 7. Summarize the answer: Private domestic savings needs to rise by $100 billion, to a total of $600 billion, for the two sides of the equation to remain equal (–100 = –100).

Short-Term Movements in the Business Cycle and the Trade Balance

In the short run, trade imbalances can be affected by whether an economy is in a recession or on the upswing. A recession tends to make a trade deficit smaller, or a trade surplus larger, while a period of strong economic growth tends to make a trade deficit larger, or a trade surplus smaller.

As an example, note in [link] that the U.S. trade deficit declined by almost half from 2006 to 2009. One primary reason for this change is that during the recession, as the U.S. economy slowed down, it purchased fewer of all goods, including fewer imports from abroad. However, buying power abroad fell less, and so U.S. exports did not fall by as much.

Conversely, in the mid-2000s, when the U.S. trade deficit became very large, a contributing short-term reason is that the U.S. economy was growing. As a result, there was lots of aggressive buying in the U.S. economy, including the buying of imports. Thus, a rapidly growing domestic economy is often accompanied by a trade deficit (or a much lower trade surplus), while a slowing or recessionary domestic economy is accompanied by a trade surplus (or a much lower trade deficit).

When the trade deficit rises, it necessarily means a greater net inflow of foreign financial capital. The national saving and investment identity teaches that the rest of the economy can absorb this inflow of foreign financial capital in several different ways. For example, the additional inflow of financial capital from abroad could be offset by reduced private savings, leaving domestic investment and public saving unchanged. Alternatively, the inflow of foreign financial capital could result in higher domestic investment, leaving private and public saving unchanged. Yet another possibility is that the inflow of foreign financial capital could be absorbed by greater government borrowing, leaving domestic saving and investment unchanged. The national saving and investment identity does not specify which of these scenarios, alone or in combination, will occur—only that one of them must occur.

Key Concepts and Summary

The national saving and investment identity is based on the relationship that the total quantity of financial capital supplied from all sources must equal the total quantity of financial capital demanded from all sources. If S is private saving, T is taxes, G is government spending, M is imports, X is exports, and I is investment, then for an economy with a current account deficit and a budget deficit:

\[Supply\,of\,financial\,capital=Demand\,for\,financial\,capital\]
\[S + (M – X) = I + (G – T)\]
 
A recession tends to increase the trade balance (meaning a higher trade surplus or lower trade deficit), while economic boom will tend to decrease the trade balance (meaning a lower trade surplus or a larger trade deficit).

Glossary

national savings and investment identity
the total of private savings and public savings (a government budget surplus)