Re: Fundamental Flaw of National Accounting

["Per Gunnar Berglund" <pgb@xxxxxxxxxxxxxxxxxx>]

WARNING! LONG POST

In reply to Bruce McFarling:

-----

Bruce wrote:
        I don't mean [commensurate] 'to a degree' as in, "absolutely
conmensurate,
plus or minus a small margin for error and fuzziness around the edges".
I mean 'to a degree' as in 'to a degree: ranging from completely
conmensurate, to completely inconmensurate, and filling the range in
between".  So where you are reading me as saying conmensurate "to
*a very great* degree", I actually intend to say what I have been
saying, "to a degree".

Per:
    Suppose the following: Output, in the vector quantity sense, has
increase from t=0 to t=1 in every component of the vector but one. The
output of "potatoes", a miniscule proportion of aggregate output value, has
diminished. Now, my question to you is: has output as a whole increased or
not? If you say that the components are not comparable to one another, this
would mean that you cannot _strictly_ say that output has increased (let
alone _how much_ it has increased, because _all_ output has in fact not
increased. How would you deal with this?

Bruce:
        You are missing my argument entirely if you read me as hairsplitting
on aggregation techniqes, so it is not surprise if, on reading my argument
in that light, you find it beside the point.  If I have any hairs to split
on aggregative techniques, I will refrain from introducing them until and
unless I am persuaded that your argument holds together.  I do not care
whether the quantity index is generated using initial weights, final weights
arithmatic or geometric mean weights.  The index number problem is
subordinate to the measurement problem.

Per:
What you call a "measurement problem" is really a measure _interpretation_
problem. I don't see your denial that a measure can be erected along the
lines I have proposed. Clearly such a measure _exists_. What you keep
saying, is that this measure is devoid of meaning, and what I keep saying is
that it is meaningful. There is really not much more to it than this. If you
think it is meaningless, feel free to do so. Keep on using your
million-goods vectors in your "macroeconomic" research. I don't suppose you
will be very successful, and again the usefulness is the proof of the
axiomatic pudding. I have found the volume concept to be meaningful, valid
and useful in my work, and I will keep using it.

Bruce:
        You've got my argument upside down, because you *believe* that
a quantity index is a holistic basis for comparison.  That is, your
'holistic' stance is a stance regarding the nature of an index number.
I start out from a holistic stance regarding the economy.  I don't
start out believing that an index number is more than an indicator
regarding the economic system.  GDP is different from a quantity
or price index in this respect, because monetary transactions involve
a common unit -- as a characteristics of our economic systems -- and
GDP is a measure of transactions in that common unit.  GDP is not a
mere indicator of system state -- it one measure of the state of the
economic system.

Per:
    Yes, I do believe that a properly composed volume index is a holistic
basis for comparison, and a holistic basis for the definition of the parts.
You don't think so, and therefore you have no means of clear description of
the state of the macroeconomic system. I certainly don't deny that the GDP
(indeed I don't like the GDP at all) is a "mere indicator of system state".
There are several other indicators, one of which is the volume of domestic
product.
    I guess our South American friends on this list might find it easier to
see the shortcomings of the nominal GDP that you are advocating. You have
not made clear how you would deal with inflation?

Bruce:
        The reductionist's challenge to the holist might be summarised
as: if the characteristic of the system is not in the parts of the
system, where is it?  There are holists who feel no need to provide
a serious response: 'there is obviously something there that isn't
in the parts, and I will talk about that in its own terms.'  The
system perspective is that the challenge must be answered, and that
the answer tends to have the same general form: 'what is not included
within the parts of the system is the *organisation* of the parts of
the system'.

Per:
    Let me pose the holistic issue somewhat metaphorically. You are clearly
Bruce McFarling, and that you have been since you were born. Still the
2-year old Bruce McFarling that once existed is hardly "physically
commensurate" with the Bruce McFarling of today. Still, both you and I would
agree that the "Bruce McFarlingness" of this entity has been increased
rather than watered out in the interlude. (I tremble to think of a 2-year
old with your present properties! :) )  Bruce McFarling is an organic unity,
evolving over time, and fully "commensurate" over time, even though there
are not many cells in him that haven't been replaced since his childhood. It
does indeed seem quite meaningful to compare the 2-year old Bruce McFarling
with the Bruce McFarling of today. The same thing applies to the
socio-economic organism. It does evolve over time, its parts change -- some
are lost, others enter to replace or build up -- but the organism still
remains there and it is a proper object of study as such.
    Moreover, the parts of your body are defined and functioning thanks to
their relation to the whole of you. If some evil bastard was to chop one of
your arms off, it wouldn't be very useful anymore. The "armness" of your arm
would be severely diminished by being severed from the rest of Bruce
McFarling. The same thing applies to the parts of the economic body. Remove
the machine from its place in the equipped machine hall and set it out in
the Sahara desert, and you would find its "machineness" to be greatly
diminished.

Bruce:
        Now if you identify yourself as working with the transaction
principle, your observables are money being transferred in one direction,
accompanied by a corresponding transfer of title to goods or performance
of services.  Whether or not you impute that all back to work in exchange
for the money, that is the observable transaction.  However you attempt
to generate an indicator for the volume of goods and services that
correspond to a given aggregate expenditure, the goods and services are
heterogenous.  There is an identification problem in *measurement* if
you use the price of the goods and services to meaure the aggregate
'volume' corresponding to expenditure, since the expenditure is the
aggregate of price-weighted quantities.  How do we get around this
identification problem?

Per:
    The concept of volume involves relative prices (or values) and changes
in quantitites. Prices come first, as an "exogenous" set of variables, if
you wish. Then comes (changes in) quantities as the choice variable. There
is nothing strange of fishy about this. If we are to sum up the different,
heterogenous (changes in) quantities to an aggregate (change in) volume, we
must use some weighting scheme. The matter at stake here is _what_ weighting
scheme should be used, and why.
    I have argued that we should use relative values as weights, because (1)
that will correspond to intra-personal utility-maximising, and (2) it will
be inter-personally distribution-neutral. Any other weighting scheme must
either be very complicated, since it has to make a difference between the
intra-personal weighting (which must be "plutocratic" to conform with
utility maximisation) and the inter-personal weighting (which should follow
some other principle, mirroring the "social utility" of the activities).
Since we are lacking any objective scheme of inter-personal weighting to
reach a true social utility index, we should make do with the least
arbitrary principle, which clearly is the Marshallian one I have argued.
    As to the parts, they must be defined in relation to the whole. Let me
throw a simple example:
    Suppose there is an economy producing apples and pears. At t=0, 1000
kilos of apples and 1000 kilos of pears are being produced. Apples cost $1
per kilo, and pears $2 per kilo. The nominal "GDP" of this system at t=0 is
clearly 1000 x $1 + 1000 x $2 = $3000. Apples make up one-third of this
"GDP" and pears make up the remaining two-thirds.
    Now suppose that at t=1, apple production is down by 20%, to 800
kilos, while pear production is up 20% to 1200 kilos. Moreover,
prices of apples are up to $2 per kilo, and prices of pears are down to $1
per kilo. The t=1 nominal "GDP" is 800 x $2 + 1200 x $1 = $2800. This would
mean that "output" is down by $200 or 6.7%.
    A (Laspeyres) volume index calculation would yield the following "GDP"
volume growth rate: 0.33 x (-20%) + 0.67 x 20% = +6.7%. The "GDP" volume is
_up_ by 6.7%.
    The t=1 nominal "output" consists of 1600/2800 x 100% = 57.1 % apples
and of 1200/2800 x 100% = 42.9 % pears. Then what is the volume of apples
and pears, respectively, in t=1? The reductionist answer is plain and
simple: Setting apple volume in t=0 to 100 means that apple volume in t=1 is
down to 80. By the same procedure, pear volume is up from 100 in t=0 to 120
in t=1.
    The holistic answer is quite different. Once the apples and pears are
conjoined in the assessment of the whole, the apple volume in t=0 becomes
0.333 x 100 = 33.3 and the pear volume, analogously, 0.667 x 100 = 66.7. At
t=1, the same principle applies: Aggregate "output" in t=1 is set at 106.7.
This aggregate is 57.1% apples and 42.9% pears, yielding index numbers 0.571
x 106.7 = 60.9 for apples and 0.429 x 106.7 = 45.8 for pears. The rate of
increase for apples is thus (60.9 - 33.3)/33.3 x 100% = 82.9%, and similarly
for pears, (45.8 - 66.7)/66.7 x 100% = -31.3%.
    Depending on method, we may reach different answers about the volume
increases: By the reductionistic approach, apples are down 20% and pears are
up 20%, and the aggregate of apples and pears is meaningless. By the
holistic approach, "output" as a whole is up 6.7%, with apples up 82.9% and
pears down 31.3%.
    The interesting thing here is certainly not whether we are using
Laspeyres or Paasche weighting (as explained before, this could be overcome
by using dt time intervals), nor that the reductionist figures differ from
the holist figures. What is important is the approach, and the order of
computation. By taking the holistic approach, the parts are assessed _after_
the whole has been computed, and the development of the parts is seen in the
light of the development of the whole.

Bruce:
        (1) Don't reduce the volume of output -- leave it in its natural
terms.  Then the index number is recognised as nothing but an indicator,
and its accuracy is degraded by changes in the quality and distribution
of the flow.  I view Boulding's approach in this light.  It has much in
common with the conventional approach, and in particular needs updated
to remove a theory of economic behavior (utility maximising theory)
that is inconsistent with a holistic approach.

Per:
    Do as you wish. Keep your million goods vectors if you find that useful.
    Your statement about utility maximisation here is clearly false. There
is nothing to prevent utility functions from being inter-personally
dependent. I take it you make your own decisions -- you are a man and not a
robot. But if you care about other human beings, you might incorporate the
social outcomes of your actions into your own utility function, thus taking
others into consideration when you make your decisions. I thought this had
become standard stuff by now. After all, a lot of time has passed since the
pioneering, excellent work of James Duesenberry on this.

Bruce:
        (2) Shift the focus from the market to the organisations receiving
the expenditure.  Then the output may be identified by expenditure, as
long as there is identification of inputs that is independent of price-
weighted quantities of input.  I view Keynes labor unit in this light.

Per:
Do I read you correctly here? Are you supposing that Keynes did _not_
suggest price-weighting of labour inputs?

Bruce:
        (3) Monkey around with the aggregate of price-weighted quantities
using additional distributions and constraints, and generate a synthetic
measure of volume that we treat *as if* it were an independent measure of
volume -- or, if you prefer the alternative language you suggest, we
treat as 'axiomatic' that the synthetic measure is equivalent to the real
measure -- so that we can act *as if* we have solved the identification
problem.  I view your approach in this light.

Per:
I don't see what is so "synthetic" about the volume measure? Are your
million-goods haystack vectors more "natural" or what? On closer scrutiny
they tend to be quite as "as-if" as anything else. Your "naturalist"
advocacy here only means that you want to avoid abstraction. The truly
naturalist position would be to throw out all abstraction, including such
constructs as "categories", "vectors" and the like. In the end we might just
as well throw out "economics" too, I reckon.

Bruce:
And then all this leads back in a loop back to the questions that I have
posed.

Per:
I think the loop leads back to the numerous questions I have posed in post
after post, and which you
have not answered. Where is your language? Let us see the grammar! What are
your axioms? We need some basis of comparison here.

Bruce:
        If you supposedly have a holistic theory, how do you take
a theory of economic behavior -- the utility maximising theory -- which
is only tractable for a 'society' of atomistic individuals?

Per:
Nonsense! (pardon). Utility maximisation is, again, fully compatible with
social sensibilitity and inter-personal behaviour links. Utility
maximisation is merely a (very reasonable) axiom which says that each
individual, in her own decision-making, tries to make the best out of her
current position. This axiom has no implications about social justice,
atomism or organicism or anything like that.

Bruce:
You can't
seriously expect anyone to be persuaded by your appeal to the mainstream
reliance on utility theory as support for using it while you simultaneously
reject any conclusions of utility theory that are inconvenient to your
purposes.

Per:
If you would be kind enough to spell out exactly what "conclusions" I am
rejecting, I would find it much easier to relate to this accusation. Again,
I feel it is Bruce McCarthy acting here, with sweeping accusations (about
supposedly un-Keynesian "mainstream activities" this time) supported by
"guilt by association" arguments.

Bruce:
The people who will accept the first half (Per doesn't need to
justify using utility maximising theory, because its the most common
theory within economics) will reject the second half (Bruce doesn't need
to do more than point out that the most common utility-theoretical stance
is that interpersonal utility comparisons are invalid, since individual
utility can only be identified to an ordinal scale by individual choices,
and arbitrary changes in the scales used for interpersonal comparisons will
reverse the order of the comparison).  So I take that as nothing but a
rhetorical ploy while you try to work out a more serious response.

Per:
    My dear Bruce, if you would only read what I have been saying. The
volume index does _not_ presuppose any inter-personal comparability of
utilities. I wish that we, in the future, will be able to proceed with valid
inter-personal utility comparisons, but so far I am afraid there are no
working principles laid down for such comparison.
    As to the intra-personal part of the matter, it is easy to show that the
utility-maximising procedure will yield an outcome where relative total
utility of each product stands in direct proportion to the relative sum of
money spent on it. "Plutocratic" weighting, that is.

Bruce:
        If you supposedly have a holistic theory, why is it a *goal* of
your volume index to be invarient with respect to changes in income
structure
(that is, the choice of plutocratic weights).  If you have an indicator that
has this invarience, where is your measure that is invarient to 'volume' and
indicative of income structure?

Per:
    The argument for the invariance principle is that this is the least
arbitrary of all principles.
    There are plenty of methods to assess income distribution, most of which
you must have heard of (Lorentz curves, Gini coefficients, and the like).

Bruce:
        And since the economy is an evolving system, any holistic measure
of the output of the system must recognise that the form of that output and
the utilisation of that output is evolving through time, and so that
degree of conmensurability is eroded steadily over time.  That is a
characteristic of the system, and even an indicator that provides
a relatively accurate comparison of states of the system over a short
period of time will lose either accuracy and/or precision if the comparison
is extended over longer periods of time: accuracy if the comparison is
performed *as if* the economy were not evolving, and precision if
it takes the evolution of the economic system into account (and
in the former case it may be losing a degree of precision in any event,
while in the latter case it may be losing a degree of accuracy in
any event).

Per:
    And in the long run, Bruce McFarling is no longer Bruce McFarling,
because the vast majority of cells composing this evolving structure have
changed?

Bruce:
        So, in short, I see the *economy* in holistic terms, its
just *your indicators* that I see as partially founded on atomistic
models of the economy.  If you view your indicators as equivalent
to the macroeconomy, that would account for the confusion between my
reaction to your indicators and my perspective on the economy and
hence the emergence of McMises.

Per:
    The "equivalence" charge is an interesting one. Yes, I must admit that I
look at the indicator volumes as specifically macroeconomic indicators, even
"equivalent" if you wish. To me, the macro-economy is the forest; to you it
is a large sample of trees. My view is that the trees are the
"microeconomic" part of the matter, and the forest is the specifically
macroeconomic object of study.
    Now, I guess your holism comes in with the causal study, that the trees
are mutually inter-dependent, so to speak. I fully share this view.
    Apart from this "functional holism", or whatever we shall call it, I am
advocating a measurement holism, which means that the trees are assessed in
terms of their being part of the forest (vide the apples-and-pears example
above). I think the trees should be assessed from where they stand in the
woods, and the function they fulfil in there, not from their atomistic
"timber log" point of view.
    I am very happy to find you on the holistic side, and I still hope to
persuade you about the validity, and usefulness of holistic volume
measurement.


Best,
Per

Per Gunnar Berglund
Lilla Sallskapets vag 60
127 61  SKARHOLMEN
SWEDEN

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