Savings Investment Identity

Savings Investment Identity for Closed and Open Economies

The savings investment identity for closed and open economies function the same way but one economy allows for international trade to occur where the other does not.

If it is an open economy, it means that the economy engages in trade with other economies. In an open economy, there is the exchange of goods and services in the form of imports and exports which are leakages and injections into the local economy. If it is a closed economy, then there is no trade with any outside countries going on.

Savings Investment Identity in Closed Economy

The savings investment identity in a closed economy includes consumer spending or consumption, government spending, and investment in capital or investments. It does not include imports or exports since they are not available in a closed economy.

In a closed economy, savings are equal to investments. This is because when public and private consumption are subtracted from GDP, or the nation's total output all we have left of the GDP is the output that is not used which means it has been saved. On the other side of the equal sign, we only have investment left.

Savings Investment Identity in Open Economy

The savings investment identity in an open economy will include net exports in the identity since they are capital inflows and outflows of the economy. Imports are considered leakages for the domestic economy because we are sending funds out of our economy into a foreign one to purchase goods. These are inflows of capital. Exports are considered injections into the economy because the domestic economy is collecting foreign funds. Exports are outflows of capital.

For open economies, the components of the savings investment identity are consumption, government spending, investments, and net exports. When added together they also give us the nation's GDP.

In an open economy, the savings investment identity changes depending on if the nation is running a trade surplus or trade deficit. If it has net imports and is running a trade deficit, then foreign countries are investing their savings into the domestic economy. In this case, the investments that the country can make are equal to the amount of domestic and foreign savings combined.

If the nation has net exports, it is running a trade surplus, and it is investing its domestic savings into the foreign economy. We can interpret this as the amount of national savings available being equal to investment and savings gained from the trade surplus combined.

Savings Investment Identity Formula

Let us examine the savings investment identity formula. The first one we will look at is the savings investment identity of a closed economy. The components will be represented as:

\(\hbox{Y = GDP/ Total Domestic Output}\)

\(\hbox{C = Consumption}\)

\(\hbox{G = Government Spending}\)

\(\hbox{I = Investment}\)

\(\hbox{S = Savings}\)

The savings investment identity formula:

\[Y = C + I + G\]

The identity above tells us that every good or service that this economy sells must be consumed, invested in, and bought by the government. But how does this explain the relationship between savings and investment?

If we remove consumption and government spending from both sides of the equation, we isolate the financial portions of the equation. We arrive here:

\[\hbox{Y - C - G = I}\]

Remember that savings equal production (in this case output) minus consumption and government spending. If this is the case, then the equation above is saying that \(\hbox{Y - C - G}\) is savings. Thus we can say...

\[\hbox{S = Y - C - G}\]

And arrive at:

\[\hbox{S = I}\]

Now, let's have a look at the identity if the economy is an open economy. This means we need to incorporate imports and exports.

\(\hbox{M = Imports}\)

\(\hbox{X = Exports}\)

\(\hbox{NX = Net Exports}\)

\[\hbox{Y = C + I + G + (M - X)}\]

Net exports are simply the difference between imports and exports represented as NX. When we include net exports, we are incorporating foreign savings into the identity. Savings are considered leakages out of the economy, just like imports are, because the money that pays for savings and imports is not active in the domestic economy. If there are more imports than exports then, the domestic economy is receiving foreign savings and there is a positive capital inflow or a trade deficit. To the foreign economy, it appears as though they are investing their savings into another economy.

Let's say that \(\hbox{Y - C - G = Savings}_{National}\) and \(\hbox{(M - X) = Net Capital Inflows}\).

Using the equation from earlier, we can say:

\[\hbox{I = (Y - C - G) + (M - X)}\]

The above equation can be read as:

\(\hbox{Investment = Savings}_{National} + \hbox{Net Capital Inflows}\)

If there are more exports than imports, there would be net capital outflows or a trade surplus. Since there are capital outflows that indicate a trade surplus, the domestic economy has extra savings that it can invest abroad. Therefore \(\hbox{Savings}_{National} = \hbox{Investments + Net Capital Outflows}\).

In an open economy, savings do not equal investments, because we have to account for trade.

Savings Investment Spending Identity Macroeconomics

What does the savings investment spending identity in macroeconomics tell us? It helps us understand how savings relate to investments. The level of a country's national savings in macroeconomics determines its wealth and its ability to invest in capital both in the present and in the future. Investing in capital will allow the nation to grow and become more advanced. National savings are a good indicator of a country's financial situation because it indicates how much money a country has that it can spend on new investments. If a nation's savings are low, it can mean that consumption is high or production is low.

When consumption is high, either public, private, or both, it means that private households are spending most of their disposable income and the government is also spending most of the revenue it collects in taxes. If consumers are spending most of their income and so is the government, there is not much money left over for investing in new capital. If production is low, the nation's total output or GDP will also be low. When the output is low, a certain level of consumption and government spending still has to happen regardless so the nation ends up having fewer savings and therefore less investment.

Fig. 1 - Consumption and government spending and savings as a portion of total output. Savings is equal to production.

The savings investment identity has us assume that all money that is saved will be used for investment. The savings can be used for investment right away, or they can be set aside to fund any future investment consumption. In the end, all savings will go towards investments and all investments will have been paid for by savings.

The purpose of having national savings and investments is to be able to encourage economic growth and fund technological advancement. We can think of it on a small scale. If a family is barely producing enough funds to cover their basic consumption, they will not have very much money to set aside to save. Without savings, they cannot invest in a better car, more education, better nutrition, or a house. If they could invest in a reliable car, they could drive to a higher-paying job somewhere else. If they had more education, they would be better qualified for a higher-paying job. Maybe if they owned their house they would not have to move around as much. All of these scenarios show that being able to save up money to then invest, will make you better off in the future, and it is not much different for the national economy. The more money a country can make, the more it can save and invest in buying more capital to increase production.