<p>GDP data are not reported on individual level so that is not <em>directly</em> possible (at least not without going through the expense of collecting such data).</p>
<p>However, output is equal to income (see Mankiw's Macroeconomics pp 47-77). Consequently, if you want to know median output just look at <em>gross</em> median income, they are equal in reality since the value of your income is value of your output. Due to statistical discrepancy, slight statistical methodological differences and measurement error they might be some discrepancy between situation where per-person output would be observable, but aside of that they should be equal.</p>
<p>PS:</p>
<p>Also, this statement:</p>
<blockquote>
<p>GDP covers more than individual incomes, including services provided by the state, for example.</p>
</blockquote>
<p>is not correct.</p>
<p>GDP can be measured by various ways such as income or spending approach. GDP is by definition sum of all individual incomes or sum of all spending (as these have to be equal), so for closed economy (I use closed economy to save time, the point holds for open one as well):</p>
<p><span class="math-container">$$i+π+w+r=Y=C+I+G $$</span></p>
<p>where <span class="math-container">$i$</span> is all interest income, <span class="math-container">$\pi$</span> all income from profits, <span class="math-container">$w$</span> all income from wages, and <span class="math-container">$r$</span> all income from rent. As you can see this <em>must</em> be equal to all consumption, investment and government spending. So GDP does not measure <em>more</em> than you can get from individual income statistics (at least from the gross one which are the ones often/typically reported).</p>

CC BY-SA 4.0
2021-08-21T11:51:52.857Z
But I get services from the government (infrastructure, security, education etc.), the value of which are not included in my reported income?
Giskard
CC BY-SA 4.0
2021-08-21T11:57:00.463Z
@Giskard but that part of output is captured by taxes you pay, and for GDP transfers do not matter so using median gross income as a proxy for median GDP is completely reasonable.
1muflon1
CC BY-SA 4.0
2021-08-21T12:01:03.333Z
@Giskard also note GDP can be calculated by income approach, so GDP is just sum of all individual gross incomes, sure individual income statistics does not use the same methodology as GDP and might measure it differently - I mentioned all these caveats, but median income should capture median GDP + error
1muflon1
CC BY-SA 4.0
2021-08-21T12:01:41.383Z
If you make the error large enough... surely redistribution affects the *median*.
Giskard
CC BY-SA 4.0
2021-08-21T12:03:10.170Z
@Giskard but that is not captured in standard income statistics, I am not talking about post tax and transfer income but pre-tax and transfer gross income
1muflon1
CC BY-SA 4.0
2021-08-21T12:04:15.247Z
Seems like you are not talking about "median output" as defined in the question? "*GDP covers more than individual incomes, including services provided by the state, for example.*" Perhaps I am missing something.
Giskard
CC BY-SA 4.0
2021-08-21T12:07:50.463Z
@Giskard but state is funded from taxes from gross income. This is why GDP by income approach is $Y= w+i+\pi+r$ and the only adjustment for taxes is for sales taxes, any services provided by the government are just transfers of $w$, $i$ $\pi$ or $r$ between people. Standard income data are reported as gross incomes (sure post tax data exist as well), and those gross incomes in aggregate cover gov spending
1muflon1
CC BY-SA 4.0
2021-08-21T12:09:50.030Z
What I do not understand is why you think that the distribution and hence median is unchanged by gov spending? Mean is a nice operator, if the equation you quote holds for aggregate, it will hold for mean, since it is just a division by $n$. Why would it hold for median?
Giskard
CC BY-SA 4.0
2021-08-21T12:15:01.610Z
@Giskard because the distribution is affected after tax and transfer, not pre-tax and transfers. For example, if we have person A earning 1000 and person B earning 500 and person C=100 and tax rate is flat 300 for A  100 transferred to B, 200 transferred to C, then their gross incomes which are equal to their gross output are still A=1000 an B=500 and C=100 so from that you can get median GDP of 500. Their net incomes will be affected by redistribution as their net incomes are A=700, B=600 and C=400, so this would mess it up, but default incomes are typically reported as market pre-tax incomes
1muflon1
CC BY-SA 4.0
2021-08-21T12:16:32.993Z
@Giskard I edited now the answer to even emphasize that I am talking about gross income if that was not clear
1muflon1
CC BY-SA 4.0
2021-08-21T12:19:22.650Z
@Giskard by the way note, I am not sure if you know about this but for example, all the inequality statistics etc you hear in the media, that is generally based on pre-tax gross incomes and completely excludes redistribution <- as crazy as it might sound this is how those things are *typically* measured
1muflon1
CC BY-SA 4.0
2021-08-21T12:19:41.323Z
Sorry, I guess I just don't enough about how they gather the data. So you are saying, that if I use a free nursery/childcare service provided by the state, the value of this is exactly captured by *my* gross income? And the same is true for a childess person? I.e. the value of this unused service is not included in *their* gross income?
Giskard
CC BY-SA 4.0
2021-08-21T12:21:17.177Z
@Giskard No, what I am saying is that your gross income is equal to your gross product, those two things are equal to each other (they actually have to by standard macro identities so this is purely national accounting necessity that they equal). However, then government gets involved and it severs that equality with taxes and transfers, net post-tax and transfer income has nothing to do with your output anymore
1muflon1
CC BY-SA 4.0
2021-08-21T12:23:18.583Z
I am not sure if you have seen [my earlier comment](https://economics.stackexchange.com/questions/47302/splitting-gdp-between-population/47304?noredirect=1#comment76029_47304)? I am quoting from the question in that comment. OP wants to know what the median is if we include the value of these services. Are you answering that question, or are saying it is not a good question and explaining why?
Giskard
CC BY-SA 4.0
2021-08-21T12:25:42.023Z
@Giskard oh I see, but then that is mistake of the OP, GDP and Gross Income of all individuals **must** equal, by accounting identities, and you can find this in any macro 101 book, so individual incomes do already *indirectly* capture all government spending. To put it as plainly as possible $i + \pi + w + r = Y = C+ I + G$ (for closed economy), so its not possible to measure individual gross incomes and somehow exclude government spending, if you measure all wages profit, interest and rent you automatically measure all consumption investment and gov spending
1muflon1
CC BY-SA 4.0
2021-08-21T12:29:17.163Z
So much effort would have been saved if you had read the comment when I wrote it 20 mins ago...
Giskard
CC BY-SA 4.0
2021-08-21T12:29:42.180Z
@Giskard sorry, I read it but I just misunderstood it, my apologies
1muflon1
CC BY-SA 4.0
2021-08-21T11:38:59.453Z
2021-08-21T12:34:42.903Z
2021-08-21T12:34:42.903Z
1muflon1
<p>When looking at the average incomes in a country it is necessary to distinguish between <em>mean</em> income and <em>median</em> income.  Mean income tends to be distorted by high earners, so typically median income is used.  GDP covers more than individual incomes, including services provided by the state, for example. To look at GDP on an individual level, GDP per capita is used, which seems to suffer from the same problems as mean income.  Has anyone devised a way of splitting GDP among individuals to give a 'median' GDP figure for a country.</p>

<gdp><national-accounts>
Splitting GDP between population
quantropy
# Splitting GDP between population

(Asked by: username_0 on 2021-08-21)

When looking at the average incomes in a country it is necessary to distinguish between *mean* income and *median* income. Mean income tends to be distorted by high earners, so typically median income is used. GDP covers more than individual incomes, including services provided by the state, for example. To look at GDP on an individual level, GDP per capita is used, which seems to suffer from the same problems as mean income. Has anyone devised a way of splitting GDP among individuals to give a 'median' GDP figure for a country.

**Tags:** gdp, national-accounts


---

## 1 answers

### Answer by username_1 on 2021-08-21. Score: 2 | Accepted answer

GDP data are not reported on individual level so that is not *directly* possible (at least not without going through the expense of collecting such data).

However, output is equal to income (see Mankiw's Macroeconomics pp 47-77). Consequently, if you want to know median output just look at *gross* median income, they are equal in reality since the value of your income is value of your output. Due to statistical discrepancy, slight statistical methodological differences and measurement error they might be some discrepancy between situation where per-person output would be observable, but aside of that they should be equal.

PS:

Also, this statement:

> GDP covers more than individual incomes, including services provided by the state, for example.

is not correct.

GDP can be measured by various ways such as income or spending approach. GDP is by definition sum of all individual incomes or sum of all spending (as these have to be equal), so for closed economy (I use closed economy to save time, the point holds for open one as well):

$$i+π+w+r=Y=C+I+G $$

where $i$ is all interest income, $\pi$ all income from profits, $w$ all income from wages, and $r$ all income from rent. As you can see this *must* be equal to all consumption, investment and government spending. So GDP does not measure *more* than you can get from individual income statistics (at least from the gross one which are the ones often/typically reported).

> **Comments:**
> **username_2**: But I get services from the government (infrastructure, security, education etc.), the value of which are not included in my reported income?  
> **username_1**: @username_2 but that part of output is captured by taxes you pay, and for GDP transfers do not matter so using median gross income as a proxy for median GDP is completely reasonable.  
> **username_1**: @username_2 also note GDP can be calculated by income approach, so GDP is just sum of all individual gross incomes, sure individual income statistics does not use the same methodology as GDP and might measure it differently - I mentioned all these caveats, but median income should capture median GDP + error  
> **username_2**: If you make the error large enough... surely redistribution affects the *median*.  
> **username_1**: @username_2 but that is not captured in standard income statistics, I am not talking about post tax and transfer income but pre-tax and transfer gross income  
> **username_2**: Seems like you are not talking about "median output" as defined in the question? "*GDP covers more than individual incomes, including services provided by the state, for example.*" Perhaps I am missing something.  
> **username_1**: @username_2 but state is funded from taxes from gross income. This is why GDP by income approach is $Y= w+i+\pi+r$ and the only adjustment for taxes is for sales taxes, any services provided by the government are just transfers of $w$, $i$ $\pi$ or $r$ between people. Standard income data are reported as gross incomes (sure post tax data exist as well), and those gross incomes in aggregate cover gov spending  
> **username_2**: What I do not understand is why you think that the distribution and hence median is unchanged by gov spending? Mean is a nice operator, if the equation you quote holds for aggregate, it will hold for mean, since it is just a division by $n$. Why would it hold for median?  
> **username_1**: @username_2 because the distribution is affected after tax and transfer, not pre-tax and transfers. For example, if we have person A earning 1000 and person B earning 500 and person C=100 and tax rate is flat 300 for A  100 transferred to B, 200 transferred to C, then their gross incomes which are equal to their gross output are still A=1000 an B=500 and C=100 so from that you can get median GDP of 500. Their net incomes will be affected by redistribution as their net incomes are A=700, B=600 and C=400, so this would mess it up, but default incomes are typically reported as market pre-tax incomes  
> **username_1**: @username_2 I edited now the answer to even emphasize that I am talking about gross income if that was not clear  
> **username_1**: @username_2 by the way note, I am not sure if you know about this but for example, all the inequality statistics etc you hear in the media, that is generally based on pre-tax gross incomes and completely excludes redistribution <- as crazy as it might sound this is how those things are *typically* measured  
> **username_2**: Sorry, I guess I just don't enough about how they gather the data. So you are saying, that if I use a free nursery/childcare service provided by the state, the value of this is exactly captured by *my* gross income? And the same is true for a childess person? I.e. the value of this unused service is not included in *their* gross income?  
> **username_1**: @username_2 No, what I am saying is that your gross income is equal to your gross product, those two things are equal to each other (they actually have to by standard macro identities so this is purely national accounting necessity that they equal). However, then government gets involved and it severs that equality with taxes and transfers, net post-tax and transfer income has nothing to do with your output anymore  
> **username_2**: I am not sure if you have seen [my earlier comment](https://economics.stackexchange.com/questions/47302/splitting-gdp-between-population/47304?noredirect=1#comment76029_47304)? I am quoting from the question in that comment. OP wants to know what the median is if we include the value of these services. Are you answering that question, or are saying it is not a good question and explaining why?  
> **username_1**: @username_2 oh I see, but then that is mistake of the OP, GDP and Gross Income of all individuals **must** equal, by accounting identities, and you can find this in any macro 101 book, so individual incomes do already *indirectly* capture all government spending. To put it as plainly as possible $i + \pi + w + r = Y = C+ I + G$ (for closed economy), so its not possible to measure individual gross incomes and somehow exclude government spending, if you measure all wages profit, interest and rent you automatically measure all consumption investment and gov spending  
> **username_2**: So much effort would have been saved if you had read the comment when I wrote it 20 mins ago...  
> **username_1**: @username_2 sorry, I read it but I just misunderstood it, my apologies  

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