C + S + T = GDP = C + I + G + (X – M)

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DRAFT

The National Income Account Identity (NIAI) is meant to capture the size of a nation's economy, that is: the total value of the spending on goods and services in a nation with an open economy in a year.

Sources of National Income

(§1) GDP = C + I + G + (X - M)

GDP is divided into four broad categories of spending: consumption (C), investment (I), government purchases (G) and net exports (X – M), where X stands for exports and M for imports.

Alternatively, one could say: (§1) lists the sources from which money flows to give people income: people making payments to finance their consumption (C), companies making payments to finance their investments (I), government making payments for the goods and services it buys (G), and foreigners making payments to acquire goods made in our open economy. If more is imported than exported, the term will become negative and net exports drain income out of our open economy. Likewise if government spends less G than it gathers by taxes (T), G will take on a negative value and represent a reduction in national income.

(Frankly, I am not sure why net government spending (G-T) is not explicitly included in (§1) while net exports (X – M) are.) 

Uses of National Income

What is spent in a year is by definition equal to what is received in income in a year. For spending is defined as the transfer of money to a receiver of this money. I spend EUR 1 in buying an apple, ipso facto the seller of the apple receives EUR 1 from me.

In other words, (§1) must be equal in value to the total of money received in that economy in a year.

Now, we can ask ourselves what is a useful way of classifying the uses of all the spending in the economy in a year: what do the receivers of the spent income do with their money? What uses is the spent income put to?

We could use a classification like: "expenditure on apples and all other expenditure". It turns out this is not a good classification, because it leaves out important drivers of an economy, for instance: taxes (T) that need to be paid to the government,

Then how do we capture the remainder of the national income spent in a year in terms of what uses they are put to?

Apart from paying taxes, what expenditures do people make? Well, if we look at the question in the broadest and most comprehensive way, they 

either

• spend their income on consumption,

• save their income, or

• pay taxes with it.

This yields

(§ 2) GDP =  C + S + T  

Spending = Income

Note, in determining GDP, we register all the sales (income) and thus all the purchases (expenditure) attributable to the year in question. Since, by definition, the income earned in a year equals the expenditures made in that year, we may write:

(§3) C + S + T = GDP = C + I + G + (X – M)

The right hand side of the equation lists the sources from which income its received, the left hand side of the equation lists the uses to which the income is dedicated.

A Conundrum and its Solution

When I looked at this equation, I used to scratch my head and wonder how do the terms that appear only on the right hand side of the equation get reflected on the left side of the equation.

Where do net exports end up? Well, I thought, most likely income from net exports will be distributed on the use side, i. e. left hand side of (§3), among consumption (C), saving (S) and taxes (T). Fair enough.

How about income received from government spending (G)? Again, it might find its way into C, S, and even T, when we think of a government employee, who spends most of his money on consumption, saves a little and pays his employer some taxes,

And what happens with investment spending (I). It is the same story with I, for people receive income from selling investment goods and services to companies and use this income to meet consumption expenditures, build up savings and pay taxes.

My Confusion

Still I got mixed up for a reason that I will explain immediately. So confused did I get as to actually consider rejecting the laws of arithmetic.

For, a final doubt remained: is the C on the right hand side the same as on the left hand side?

It must be if the mathematics is to be right, must it not?

But could I convince myself that C is indeed identical on both sides of the equation? I mean, was I able to explain why there cannot be a discrepancy between the Cs?

I spare you the false reckoning to which I subjected

(§3) C + S + T = GDP = C + I + G + (X – M)

Rather, let me explain the false assumption behind my doubt.

I wrongly presumed that it was necessary and possible to deduce from the terms on the right hand side (RHS) the terms S and T on the left hand side (LHS).

No, this is not possible.

From the LHS I know C, which is identical on both sides of the equation. However, if I am given the values of I, G, and (X-M) there is no way that I could tell (from that information alone), how they are allocated between S and T.

The point is rather this: in proposing (§3), we must ask ourselves: are the RHS and the LHS appropriate representations of what they purport to represent: GDP, the national income generated and used within a year.

This in turn reduces to answering two questions. Is the representation 

(a) meaningful, and if so, is it 

(b) complete?

If instead of G, we take "N", the frequency by which I pick my nose, then criterion (a) is not fulfilled. Or if I leave out G, the criterion (b) is not satisfied.

However if both the LHS and the RHS are meaningful and complete, describing (in different ways / from different perspectives) and fully covering the same total of national income, even though in different but compatible ways, we are out of my rather silly conundrum.

If it is true that total national income is exhaustively represented by the use-side of the equation (LHS) and equally so by the sources-side (RHS), then we have in (§3) a valid representation of GDP.

So we have to ask ourselves: (b) is anything left unaccounted for after we have counted all taxes, all savings and all consumption representing these items on the LHS, and counted all consumption, all investment, all government spending and all net exports representing these items on the RHS?

And: (a) do these items and figures make sense?

I am sure the answer to both is no. 

Whether or not nonconformity is a problem is a matter of degree of divergence from our two criteria. In other words: the issue at hand is: do we have an imperfect yet useful model?

The answer appears to be: for a number of purposes — yes.

PS

Presumably we should add a third criterion: (c) mutual compatibility. The RHS and the LHS should contain terms that are  part of a dual system of classification, whose two different branches ascertain all items of national income/expenditure, even though the criteria by which they identify items of national income are different.

You can ascertain the number of spectators in a football stadium by  counting all male and all female onlookers and adding their numbers. You can ascertain that number also by collecting all the tickets sold to them (assuming that everyone has bought a ticket to see the match). Two completely different ways of counting that lead to the same result.