# The Saving-Investment Identity

Last week I explained that the expenditure on what is produced in a country must always equal the income derived from that expenditure, and adding this to the explanation of GDP from the previous week we have the equation:

GDP = C + I + G + (X-M) = Y

(If the letters confuse you, look back over the explanations in the previous 2 weeks.)

Now we’re going to add saving into this.  You may recall that saving is defined as the difference between disposable income and expenditure on consumption (explained here).  But don’t just take this from me – let’s turn to the most authoritative source, the System of National Accounts 2008, published jointly by the World Bank, the International Monetary Fund (IMF), the United Nations, the Organisation for Economic Co-operation and Development (OECD) and the European Commission.

This defines saving as follows (paragraph 9.28, page 182):

“Saving represents that part of disposable income (adjusted for the change in pension entitlements) that is not spent on final consumption goods and services.”

Disposable income is income available to spend, i.e income after paying taxes.  The national income is initially earned by the household and business sectors (government income, taxation, is paid out of the incomes of households and businesses), so saving by these two sectors will be the national income (Y), minus taxation (T), minus the final consumption expenditure of these 2 sectors, which is household expenditure (C).  Expenditure on investment (I) is not included as this is not final consumption.  If we use the letter S to mean saving by households and businesses, we can therefore say:

S = Y – T – C

Re-arranging that with basic algebra we get:

Y = T + S + C

So we now have two different expressions that equal Y, which means that these expressions must equal each other.  Hence we can say:

C + I + G + (X-M) = C + S + T

The Cs on each side cancel each other out.  If we again do some basic algebra we get:

I + (X-M) = S + (T-G)

T is taxation, which is public sector income, so (T-G) is public sector income minus public sector expenditure – in other words it’s public sector saving.  (If G is more than T, which it usually is, we get public sector dissaving – the deficit.)  So the right hand side of this expression adds household and business saving (S) to Government saving (T-G), which gives us the the saving by all sectors in the economy.  This is the total National Saving, which we’re going to call NS.  Hence we get:

I +(X-M) = NS

X-M is exports minus imports, or the balance of payments.  If exports exactly equalled imports then X-M would equal zero.

Hence we can say that in a situation of balanced trade:

I = NS

Expressed in words, investment equals national saving.  This is known as the saving-investment identity.

As with the income-expenditure identity last week, this is not a scientific theory that has been tested empirically and so we know it too be true.  It is a mathematical identity that has been derived logically (using algebra) and so is true by definition of the terms involved:  because of the way we have defined our various terms, it must always be the case that national saving equals investment plus the balance of payments.  Understanding the implications for the economy will therefore depend on how well we understand these terms.

This is a very well known result in macroeconomics.  I’ve spent 3 weeks going through basic introductory macro just to get to this point.  And in fact, everything in the blog so far has been leading up to this.  The opening 16 weeks introducing different economic concepts was designed so that when I introduce this identity you will be able to grasp its significance.  And the following 15 weeks explaining how money works were so that you wouldn’t make the same mistake that every economics textbook, and therefore every conventional economist, does when faced with this identity.

Right now, this might seem like an anti-climax.  But over the next few weeks we will unfold the implications of this identity, and armed with this knowledge we will then examine the functioning of financial markets, and then the significance of everything in the blog will be come clear (hopefully).