<p>I see your confusion that could also apply to <span class="math-container">$C$</span> and <span class="math-container">$G$</span> because Mankiw starts from 
<span class="math-container">\begin{equation} Y= C^d+I^d+G^d+X~~~~~  (1) \end{equation}</span> </p>

<p><span class="math-container">$C^d$</span>, <span class="math-container">$I^d$</span>, and <span class="math-container">$G^d$</span> 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).</p>

<p>So the idea here is just that <span class="math-container">$I$</span>, after the manipulation, is essentially equal to <span class="math-container">$I^d$</span>, the <strong>domestic investment</strong>, because <span class="math-container">$I^f$</span>, the foreign portion, has been substracted from <span class="math-container">$I$</span> and appears now in import expenditures (<span class="math-container">$IM$</span>). In other words <span class="math-container">$I$</span>, after manipulation, is reinterpreted as domestic investment. </p>

<p><span class="math-container">\begin{equation} Y= C + I +G +X -IM ~~~~~  (2) \end{equation}</span> </p>

<p>I think it safe to say that calling <span class="math-container">$I$</span> domestic investment is here an "abuse of language"! </p>

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

CC BY-SA 4.0
2020-04-12T07:45:44.870Z
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
Johnson
CC BY-SA 4.0
2020-04-12T08:03:25.943Z
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?
Johnson
CC BY-SA 4.0
2020-04-12T08:18:17.370Z
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.
emeryville
CC BY-SA 4.0
2020-04-12T08:47:38.793Z
@Johnson does the new answer make more sense?
emeryville
CC BY-SA 4.0
2020-04-12T18:01:19.990Z
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.
Johnson
CC BY-SA 4.0
2020-04-12T21:02:05.710Z
Right again! It would be a different approach.to get the final equation Y=C+I+G+(X-IM), the one of interest!
emeryville
CC BY-SA 4.0
2020-04-13T19:12:45.660Z
Hi emeryville, thanks! Why we don't use equation (1), and instead start with Y=C+I+G+X−(C~+I~+G~) where (C+I+G) is domestic spending on domestic goods and services? To me equation (1) makes more sense, since it decompose the national income into different components
Johnson
CC BY-SA 4.0
2020-04-13T19:51:34.313Z
Sorry but I don't get your point. Can you rephrase it?
emeryville
CC BY-SA 4.0
2020-04-14T05:36:36.890Z
Sure, I mean equation (1) is different from Y=C+I+G+X−(C~+I~+G~) (where C+I+G here is domestic spending on domestic goods and services). So I don't understand why we should use Y=C+I+G+X−(C~+I~+G~) (where C+I+G here is domestic spending on domestic goods and services)
Johnson
CC BY-SA 4.0
2020-04-14T07:27:53.907Z
I agree. The most important is to understand the decomposition of Y. You can define identity any way you want as long as (1) all the components are there and (2) this identity gives the same result as the total value added decomposition. Take care.
emeryville
CC BY-SA 4.0
2020-04-12T07:37:47.607Z
2020-04-14T07:59:51.787Z
2020-04-14T07:59:51.787Z
emeryville
<p>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.</p>

<p>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.</p>

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

CC BY-SA 4.0
2020-04-13T19:09:49.280Z
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.
Johnson
CC BY-SA 4.0
2020-04-13T22:24:48.050Z
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.
JazKaz
CC BY-SA 4.0
2020-04-14T05:40:29.367Z
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.
Johnson
CC BY-SA 4.0
2020-04-14T06:08:44.250Z
Johnson, still domestic spending on foreign goods and services is imports... you would be double counting
JazKaz
CC BY-SA 4.0
2020-04-13T13:54:05.003Z
2020-04-13T13:54:05.003Z
JazKaz
<p>We know the national income identity: <span class="math-container">$Y = C + I + G + X - IM$</span>.</p>

<p>From many resourses, <span class="math-container">$I$</span> refers to domestic investment. For example in this link: <a href="https://opentextbc.ca/principlesofeconomics/chapter/23-4-the-national-saving-and-investment-identity/" rel="nofollow noreferrer">https://opentextbc.ca/principlesofeconomics/chapter/23-4-the-national-saving-and-investment-identity/</a></p>

<p>However, in Mankiw's book, it says that <span class="math-container">$I= I^d + I^f$</span>, the summation of domestic investment + foreign investment, as shown in
<a href="https://i.sstatic.net/UV3wd.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/UV3wd.jpg" alt="enter image description here"></a></p>

<p>And actually in later pages of Mankiw's book, "I" is referred to domestic investment at many places also.</p>

<p>What does "I" accurately refer to?</p>

<macroeconomics><gdp><national-income>
Does "I" in Y = C + I + G + X - IM refer to the domestic investment?
Johnson
# Does "I" in Y = C + I + G + X - IM refer to the domestic investment?

(Asked by: username_0 on 2020-04-12)

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
[![enter image description here](https://i.sstatic.net/UV3wd.jpg)](https://i.sstatic.net/UV3wd.jpg)

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?

**Tags:** macroeconomics, gdp, national-income


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## 2 answers

### Answer by username_1 on 2020-04-12. Score: 1

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.

> **Comments:**
> **username_0**: Hi username_1, 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  
> **username_0**: Hi username_1, 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?  
> **username_1**: 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.  
> **username_1**: @username_0 does the new answer make more sense?  
> **username_0**: Hi username_1, 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.  
> **username_1**: Right again! It would be a different approach.to get the final equation Y=C+I+G+(X-IM), the one of interest!  
> **username_0**: Hi username_1, thanks! Why we don't use equation (1), and instead start with Y=C+I+G+X−(C~+I~+G~) where (C+I+G) is domestic spending on domestic goods and services? To me equation (1) makes more sense, since it decompose the national income into different components  
> **username_1**: Sorry but I don't get your point. Can you rephrase it?  
> **username_0**: Sure, I mean equation (1) is different from Y=C+I+G+X−(C~+I~+G~) (where C+I+G here is domestic spending on domestic goods and services). So I don't understand why we should use Y=C+I+G+X−(C~+I~+G~) (where C+I+G here is domestic spending on domestic goods and services)  
> **username_1**: I agree. The most important is to understand the decomposition of Y. You can define identity any way you want as long as (1) all the components are there and (2) this identity gives the same result as the total value added decomposition. Take care.  

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### Answer by username_2 on 2020-04-13. Score: 0

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

> **Comments:**
> **username_0**: 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.  
> **username_2**: 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.  
> **username_0**: Hi username_2, 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.  
> **username_2**: username_0, still domestic spending on foreign goods and services is imports... you would be double counting  

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