What do you do with the money that you save? Do you spend it on luxuries or necessities? Or maybe you just keep saving it. But in the end, from a macroeconomic perspective, all the money that is saved in an economy is spent on investments. To better explain this, economists use the savings investment identity. But what is that? This is a good question that we will answer here in this explanation. So, if you are looking for a better understanding of the savings investment identity, you have come to the right place.
Savings Investment Spending Identity Definition
The savings investment spending identity is an identity used in national accounting to prove that the amount of money saved in an economy is the same amount of money that will be invested into new capital. An identity is an equation that is true because of how the variables in the equation are defined. To be considered an identity, the variables on both sides have to be equal. All the money that is saved in an economy is referred to as national savings. It is made up of the total income that is left over after subtracting consumption and government spending. The investments that are referred to in the identity consist of new capital purchases like machinery, or new store inventory. Investments can be thought of as savings that facilitate future consumption.
The savings investment spending identity, also sometimes referred to as the savings investment identity or the national saving and investment identity is an equation showing the relationship between money saved and money invested by an economy.
An identity is an equation that holds true and is equal because of how the variables on both sides are defined.
National savings is often simply referred to as savings and equals the total income of a nation that is left over after subtracting consumption and government spending. Savings is production minus consumption.
Investments refer to the purchase of new physical capital in an economy.
The components of the savings investment spending identity depend on if it is an open economy or a closed economy. For both types, Gross Domestic Product (GDP) is equal to the total income or the total expenditure of the economy. This includes consumer spending, government spending, and investments. These are the only three components when the economy is a closed economy. If it is an open economy, then the identity also includes imported and exported goods and services. In both cases, savings and investments are closely related but the identities vary slightly.
Gross domestic product is one of the main measurements used to understand a nation's wealth and productivity. It can be observed as a country's total income or its total expenditure. To understand how you'll have to read our explanations:
- Gross Domestic Product
- Expenditure Approach
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.
The relationship between consumption and saving goes a lot deeper than what this explanation touches on. To really dig deep, you'll have to read about it in our explanation - Consumption and Savings
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.
Remember, in this case, investments refer to physical capital, not financial capital! When a country imports goods, physical capital is flowing into the domestic economy. When a country exports goods, physical capital is flowing out of the domestic economy.
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.
Trade relationships between nations can become complicated. If you want to really understand how trade works, along with importing and exporting, have a look at our explanations:
- International Trade
- Trade Agreements
- Import
- Export
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:
\[\hbox{S = I}\]
Public Savings versus Private Savings and where Taxes fit in
If we want to dig into the national savings equation a bit more, we can break it apart into public savings and private savings. Public savings is the tax revenue the government has left after it pays all of its expenditures. This means that public savings can be written as:
\[(\hbox{T - G})\]
Private savings are the savings of the individual households, or the income they have left over after consumption and paying taxes. It can be written as:
\[(\hbox{Y - T - C})\]
Since we know that \(\hbox{S = Y - C - G}\), if we account for taxes \(\hbox{(T)}\), we can write national savings as:
\[\hbox{S = (Y - T - C) + (T - G)}\]
The taxes the private sector pays losses from savings is reintroduced as tax revenue earned by the government, which cancels out the two \(\hbox{T}\)'s, leaving us with the original equation of \(\hbox{S = Y - C - G}\) again.
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.
Savings Investment Identity - Key takeaways
- The savings investment spending identity is an equation that illustrates the relationship between a nation's savings and its investments.
- A closed economy does not engage in foreign trade while an open economy does.
- The savings investment spending identity in an open economy is \(\hbox{Investment = Savings}_{National} + \hbox{Net Capital Inflows}\) or \(\hbox{Savings}_{National} = \hbox{Investments + Net Capital Outflows}\).
- The savings investment spending identity in a closed economy is \(\hbox{S = I}\).
- National savings and investments are important for a nation's economic growth and technological advancement.
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