Monday, 27 February 2012

Reconciling S = I + (S - I) to the national accounts

There has been what can only be described as astonishing suggestions about MMT's standard sectoral equations, with all sorts of accusations of how MMT doesn't describe saving properly and how it doesn't fit with the System of National Accounts descriptions.

So I thought I'd see if I can put that little canard to bed using everybody's favourite bedtime reading - the UK Blue Book 2011.

MMT uses a sectoral balance approach based on the now familiar sectoral equation.
[1] (S - I) + (T - G) + (M - X) = 0
and this is derived from two GDP equations:
[2] Y = C + G+ I + (X - M)
and
[3] Y = C + S + T
The UK Blue book is based on the ESA95 derivative of the system of national accounts, and describes only equation [2] under the 'Expenditure Approach' in Chapter 1.
Where C = final consumption expenditure by households and NPISH sectors, G = government consumption expenditure, I = investment or gross capital formation, X = exports and M = imports
This is then derived in table 1.2

The values of (S -I), (T - G) and (M - X) are the sectoral net lending figures from the financial account and are showing in table 1.7D under point B.9. Putting those into equation [1] gives you the following
[4]    (117133) + (-150151) + (33018)  = 0
 In dataset CDID terms the equation is as follows:
(EABO+NHCQ+NSSZ+RVFE) + (NNBK) + (NHRB)
where RVFE is the statistical discrepancy.

So the rest of this post is about how to derive those numbers from the UK Blue Book accounts for the year 2010.

First lets put the standard numbers into equation [2] from table 1.2
1458452 = 937906 + 338067 + 224577 + (436796 - 476480)
That is out by 2414 which is the statistical error of the expenditure calculation over the income calculation.

Now we need to slightly adjust this equation. The value for 'I' includes government expenditure on gross capital formation (GCF). So I'm going to move that to 'G' where it belongs in the sectoral view. So we look up the Government GCF  which is P.5 in table 5.1.7 and see that it is the princely sum of 36488. Substituting that in gives:
[5]   1458452 = 937906 + 374555 + 188089 + (436796 - 476480) - 2414
In dataset CDID terms that is:
YBHA = (NSSG)  + (NMRK + NNBI) + (NQFM - NNBI) + (KTMW - KTMX) - RVFD
Equation [2] isn't one of the standard GDP measures in the text, but we can find the elements. We already have 'C'. 'S' is 'UK Gross Saving' with the government sector removed: B.8g from table 1.7D. T is 'General Government Gross Disposable Income' from table 5.1.5. Substituting that into equation [2] gives us:
1458452 = 937906 + (185437 + 98397) + 239670
which is out by 2958 - and that happens to be the difference between the GDP figure and what is called Gross National Disposable Income (B.6*g in table 1.1). So we have:
[6]    1458452 = 937906 + 283834 + 239670 - 2958
In dataset CDID terms that is:
YBHA = NSSG + (NQET - NNAU) + NNAO - dGNDI
and
dGNDI = YBGG - QZOZ - IBJL - YBGF - QZEP 
 Now we combine equation [5] and [6] and shuffle it around into the format for equation [1]
[7]    (283834 + 2414 - 188089) + (239670 - 374555) + (476480 - 436796 - 2958)
(S - I) gets the statistical discrepancy since it has that in equation [4]. dGNDI is to do with foreign income outside the definition of GDP and is assigned to the external sector.

Collapsing [7] down gives us the raw sectoral balances:
[8]    (98159) + (- 134885) + (36726) = 0
Now we need to adjust for the capital transfers at D.9 of table 1.7D and acquisitions less disposals of non-produced non-financial assets at K.2 of table 1.7D, which gives
(98159 + 23806 - 4010 -822)  + (-134885 + 16152 - 32297 +879) + (36726 + 1077 -4728 -57) = 0
 and simplifying that down gives us equation [4] again as expected:
 [4]    (117133) + (-150151) + (33018)  = 0
So the answer to the equation I + (S - I) = S is:
188089 + 117133 = 305222
Not quite as succinct as '42' I admit, but of similar portent.