# [OPE-L:6988] [OPE-L:480] Quantitative measurement of temporal value

Alan Freeman (a.freeman@greenwich.ac.uk)
Tue, 23 Feb 1999 07:40:11 +0000

Thanks to David for his rather generous, I thought, evaluation of the
discussion on price-value equivalence.

I'd like to repay this not by continuing the discussion on price-value
equivalence but by replying to his question to Andrew, because I thought
about it, and I came up with an answer to it. This answer is BTW in my 1997
paper on "Time, money and the quantification of value".

David writes:

"Finally, a question for Andrew. I do not want to go over the whole TSS
terrain again, but the question of empirical measurement of values (even
if only hypothetical) raises one issue I can't resolve. You may identify
*value added* in any period of time with the current labor performed in
that period (leave the heterogeneity problem to one side). But to
estimate *indirect labor time* and gross value, *some* unit value must be
applied to consumed means of production. Even if we are time-sensitive
and want to make this *yesterday's* unit value, the same problem arises
when we try to calculate *that* one, and so on in infinite regress. We
can't use observed money prices of inputs; this would compromise the whole
project, since the idea is to compare values with precisely the observed
price magitudes (and, if Andrew is correct, find them essentially
uncorrelated). Since the TSS approach insists on different market values
at different dates, it is not clear how one could calculate unit values at
a moment of time on these assumptions, even in principle."

My first point is that the problem of infinite regress is a non-problem, or
rather, a different problem. One can pick up any book on difference or
differential equations and find it solved. Provided we have an initial, or
boundary condition, at the start of the process, we can determine values at
all subsequent points in the process. The real issue, therefore, isn't
infinite regress but how to determine the initial condition. If we suppose
that the initial condition is correct, all subsequent calculations of value
are correct by induction.

What I studied in my paper above (I'm not citing it just to make
self-references but because the argument is too long to reproduce here, and
so it's better to study it in the paper concerned) is the following: what
happens if we make an error in the initial condition? What happens if we
begin in 1960 with an estimate of the MEL (the decisive parameter in the
calculation) which is erroneous?

My answer is that this error decays exponentially at an annual rate equal
to the ratio of current constant capital consumption to current output
(C/C+V+S). That's quite a fast rate of decay, around 30% per year. Within
eight years, it's insignificant, by which I mean that it is less than the
error introduced by the mere noise in the data.

Therefore, we don't need, for practical purposes, to regress infinitely;
just to eight years before we want to really start making serious empirical
judgements.

Next point. David writes (re-citing) that

"We can't use observed money prices of inputs; this would compromise the
whole project, since the idea is to compare values with precisely the
observed price magitudes "

But we can use observed money prices of inputs and it doesn't compromise
the whole project. The value of the output is equal to the price of the
input, plus direct labour, and the price of the output is equal to the
price of the output, that is, what it actually sells for. Price and value,
thus calculated, are quite distinct numbers, even for a simultaneous
difference between price and value, thus stated, doesn't reduce to anything
simple or trivial like the difference between time worked and wage paid.
It's a real difference, and it really tells us something.

In order to do the above calculation, of course, we have to reduce money
magnitudes to magnitudes of time, and we do this by using the MEL, which
for any single-system approach (either simultaneous or temporal) is a
universal coefficient of the economy, so that we can use it to convert any
amount of money to an equivalent amount of hours, and vice versa.

We can then use these numbers to check how price and value are related. We
can divide the price of any basket of commodities by its value, both
expressed in the same units of course. If value were identical to price, we
should find that this ratio is one. In fact it isn't; it varies between
around 0.6 and around 1.4, for the UK. Thus there is about 40% deviation of
prices from values. I think the appropriate statistic to report is probably
the standard deviation. I haven't done any study to see what the
distribution is but it looks pretty standard, a bunched centre and two
tails.

If price and value were closely 'correlated', we would find a standard
deviation of close to zero.

Let me illustrate this point because it's quite fundamental. In 1992, I
calculate, the MEL in the UK was #45,540 per worker-year. That is, every
time a capitalist spends a pound, s/he acquires an increment of capital
equal to (1/45,540)year.

Now here's the data and how I use it. This is all to be found in one table
(table 1) in my paper but I'll spread it out here, to make the point
clearer, hopefully.

First, we start from the actual money expenditure of the capitalists in
1992 in each of 9 sectors (could be as many sectors as we want, could be an
individual industry or even an individual capitalist. I haven't included
all sectors)

Row 1 Constant capital consumed, in millions of pounds
sector: 1 2 3 4 5 7 9 10 11
11458 7347 191733 24486 44900 35457 34234 44679 20193

figures in #mn. Legend: 1 Agriculture, hunting, forestry & fishing; 2
Mining & quarrying; 3 Manufacturing; 4 Electricity, gas & water supply;
5 Construction; 7 Transport, storage & communication; 9 Public admin.,
national defence & compulsory social security; 10 Education, health &
social work; 11 Other services including sewage & refuse disposal

Now we can use the MEL to translate these money quantities into years. We
just divide each of them by 45,540 and get

Row 2: Constant capital consumed, in years
sector: 1 2 3 4 5 7 9 10 11
252 161 4211 538 986 779 752 981 443

That's the value of constant capital, using the single-system approach.

Now we find the data that gives the value-added in each sector, namely, the
years of direct labour expended in each sector. This we get from the
employment tables. It yields:

Row 3: direct labour added, in thousands of years
sector: 1 2 3 4 5 7 9 10 11
276 110 4373 238 884 878 1405 3514 2164

Comparing row 2 with row 3 it's pretty obvious that the organic composition
of capital is very variable: in agriculture it is 252/276 and in other
services it is 443/2164

Add row 2 to row 3 and we get the value of output:

Row 4: value output in thousands of years
sector: 1 2 3 4 5 7 9 10 11
528 271 8583 776 1870 1657 2157 4495 2607

This is value output. Is this equal to price? No. Goods don't sell at these
prices, not even these relative prices. To find out what they sell at, we
have to ask the market. The data tells us that the output of each sector
sold at the following prices:

Row 5: observed prices of output in millions of pounds
sector: 1 2 3 4 5 7 9 10 11
22176 19889 305673 38890 73751 81447 72374 111202 61693

Even without converting these prices into hours, we can see that they
cannot possibly equal values. For example the output of sector 2 sells for
hearly as much as the output of sector 1; but its value is only just over
half the value of sector 1.

However, we do need to convert these prices into hours. Here is where the
temporal bit comes in. If we applied the New Solution or the SSS approach,
we would suppose that the new MEL is equal to the old MEL, #45,450. Since
we are temporalists, we don't make this assumption. We calculate the new
MEL using Marx's first equality: total price=total value.

Here things get difficult; my own preference is to use the total price of
stocks and the total value of stocks. However, to simplify the
presentation, let us ignore fixed capital and consider only the 9 listed
sectors. We can then calculate the MEL as follows. The total price of
outputs is, from row 5, in #million:

22176+19889+305673+38890+73751+81447+72374+111202+61693=787,095

which, with the noughts added, is 787,095,000,000
The total value is, from row 4, in thousands of years:

528+271+8583+776+1870+1657+2157+4495+2607=22,994
which, with the noughts added, is 22,994,000 years, not surprising since
the working population is about 25 million.

The new MEL is therefore 787,095,000,000/22,994,000 = #34,305 /year

Now we can use this MEL in one of two ways: we can either convert all the
prices to years, or all the values to pounds. Take your choice: in the
single-system approach, a given quantity of money always represents an
aliquot proportion of years, so it doesn't make any difference.

However, whichever we do, we will most certainly find that prices are
markedly different from values. Let's, out of respect for tradition,
convert money prices to labour years, using the new MEL. This gives:

Row 5: observed prices of output in thousands of years
sector: 1 2 3 4 5 7 9 10 11
646 580 8910 1134 2150 2374 2110 3242 1798

But let's compare this with row 4, values in thousands of years

Row 4: value output in thousands of years
sector: 1 2 3 4 5 7 9 10 11
528 271 8583 776 1870 1657 2157 4495 2607

Same? I think not. Here's the ratios of values in years, to prices in
years, sector by sector

Row 6: ratio of price in years, to value in years
sector: 1 2 3 4 5 7 9 10 11
1.22 2.14 1.04 1.46 1.15 1.43 0.98 0.72 0.69

What do these ratios mean? In the market, for example 1 year of socially
necessary labour time in sector 1 will fetch 1.22 years of socially
necessary labour time in the market. This is the value transferred to this
sector for each year of labour that it sells. Overall this sector
appropriates (646-528) years = 128 years; compared with, for example sector
10 which loses (4495-3242) = 1253 years.

This is real information; it systematically explains the value transfers
effected by the market.

I don't think this 'systematically compromises the whole project'.
Price-value differences really exist and are measurable, so value has an
independent explanatory role. Both prices and values are completely
determinate. The ratio between value and price does not just reduce to any
simple ratio such as ratios of indirect labour and money value added. We
get a quite distinct measure of inflation from the neoclassical measure,
namely the rate of expansion of the MEL. We can systematically define
productivity as the ratio of use-value output to value-output, and thereby
track technical change without reducing it to changes in technical
coefficients. etc etc etc. This value concept therefore has, from my point
of view, genuine and superior explanatory power to magnitudes based on
use-values or so-called 'physical magnitudes'.

It may be objected that this method of calculation provides value estimates
only at yearly intervals, and not at 'any moment in time'. But this
limitation is imposed only by the annual nature of the data; in principle
it can be applied to a time period of any arbitrary smallness, down to
continuous data (though if this limiting process is to converge uniformly
we must base the MEL on stocks of capital not on capital turned over). It
also turns out, a result I find very satisfactory from a mathematical point
of view, that the continuous limit of this process is independent of the
period chosen; we are freed of any dependency on arbitrary accounting
periods.

So, what's the problem?

Alan