# Does "I" in Y = C + I + G + X - IM refer to the domestic investment?

We know the national income identity: $$Y = C + I + G + X - IM$$.

From many resourses, $$I$$ refers to domestic investment. For example in this link: https://opentextbc.ca/principlesofeconomics/chapter/23-4-the-national-saving-and-investment-identity/

However, in Mankiw's book, it says that $$I= I^d + I^f$$, the summation of domestic investment + foreign investment, as shown in And actually in later pages of Mankiw's book, "I" is referred to domestic investment at many places also.

What does "I" accurately refer to?

I see your confusion that could also apply to $$C$$ and $$G$$ because Mankiw starts from $$\begin{equation} Y= C^d+I^d+G^d+X~~~~~ (1) \end{equation}$$

$$C^d$$, $$I^d$$, and $$G^d$$ have been subjected to the same bit of manipulation'', which is to add and substract the foreign part such that we get the same equality (1).

So the idea here is just that $$I$$, after the manipulation, is essentially equal to $$I^d$$, the domestic investment, because $$I^f$$, the foreign portion, has been substracted from $$I$$ and appears now in import expenditures ($$IM$$). In other words $$I$$, after manipulation, is reinterpreted as domestic investment.

$$\begin{equation} Y= C + I +G +X -IM ~~~~~ (2) \end{equation}$$

I think it safe to say that calling $$I$$ domestic investment is here an "abuse of language"!

The most important is that identities (1) or (2) are consistent with the way we calculate GDP using total value added.

• Hi emeryville, thank you for the quick answer! I don't understand your idea. Why don't we interpret "I" as the summation of I^d and I^f, which is the summation of domestic and foreign investment? I think it is how it is defined in the picture Apr 12 '20 at 7:45
• Hi emeryville, sorry that I still don't understand. We should include the foreign portion I^f in I, because only in this way, it could be cancelled by the corresponding portion in IM, right? Apr 12 '20 at 8:03
• right! but because there is one extra I^f it should be removed somewhere. Recall that your first equation is Y = C^d + I^d + G^d + X, there is no i^f there. Apr 12 '20 at 8:18
• @Johnson does the new answer make more sense? Apr 12 '20 at 8:47
• Hi emeryville, thanks for the update! I'm still confused: if we define (C+I+G) as domestic spending on domestic goods and services and (C~+I~+G~) as domestic spending on foreign goods and services, then Y=C+I+G+X−(C~+I~+G~) is not consistent with equation (1). In this notation, equation (1) is Y=C+I+G+X. Apr 12 '20 at 18:01

I is not the summation of I domestic and I foreign. Think about what is being calculated. Y is the total income or rather expenditure for ‘a country’. Foreign investment is income going to another country, not income to this country. IM represents imports of goods and services from overseas, it also represents a form of investment overseas in employment operations.

The reason why consumption, gov spending and investment are domestic only is because they together calculate the expenditure/ inflows to this country with export and import being the only external sources of inflow and outflow of cash.

Y=C+G+I+X-IM I believe IM stands for IMports btw not investment X imports

• But in the view of income, we should have Y = C^d + G^d + I^d + X, where C^d, G^d and I^d stand for domestic consumption, investment and gov spending on domestic goods and services, and X is the foreign spending on domestic goods and services. Therefore, in order to include IM = C^f + G^f + I^f, we must write Y = C^d + C^f + G^d + G^f + I^d + I^f + X - IM, and thus I = I^d + I^f. Apr 13 '20 at 19:09
• Your saying foreign consumption shoupd be counted... why? Y is the expenditure of a country. Country pays money on imports gains income when it exports. Think of a cash flow statement in business. Apr 13 '20 at 22:24
• Hi JazKaz, I say Y = C^d + G^d + I^d + X from the view of income. C^d, G^d, I^d and X are four income sources. In my notation, C^f, G^f and I^f are domestic spending on foreign goods and services. Apr 14 '20 at 5:40
• Johnson, still domestic spending on foreign goods and services is imports... you would be double counting Apr 14 '20 at 6:08