Re: PKT digest 1541

[Bruce McFarling <ecbm@xxxxxxxxxxxxxxxxxxx>]

On Mon, 15 Sep 1997 14:00:20 +0200, "Per Gunnar Berglund"
<pgb@xxxxxxxxxxxxxxxxxx> wrote:

>    Since you keep coming back to this basically philosophical question of
>commensurability of aggregates, I will try to state how I perceive your
>view: You say that the aggregates are incommensurate if they don't consist
>of a (virtually) unchanged "internal structure", meaning that they are
>equally composed over time.

        No, I have never said that.  I have argued that aggregates are
conmensurate *to the degree that* there is a basis of comparison between
the items that compose each aggregation.  Obviously, if you develop a
quantity index,[*] and use quantity indices to describe the change
between the two quantity vectors, you are making a comparison between
two quantity vectors that is more precise in some situations than in
others.  But going from an index to a vector is a one-many relation,
and gives rise to what is known in natural sciences as the 'inversion
problem'.  You can, given one of the two vectors, use the relevant
quantity index to compare the two.  How accurate is the comparison?
(coming up with an index that makes different comparisons as accurate
as possible is one way of viewing the index number problem)  If the
change is allometric [equiproportional], a scalar multiplication of
one vector by an appropriately scaled index recovers the other, so that
for allometric changes a quantity index can be a completely accurate
basis for comparison.  Therefore, one way to view the question is to
look at the error vector between the actual vector and the allometric
equivalent that gives rise to the same index comparison, and use that
vector as a measure of the accuracy of the index comparison between
the two quantity vectors.  Of course, then you have a problem of
an appropriate basis for comparison for the individual elements of
the error vector, and different specifications of our error aggregation
may lead to different index numbers showing up as 'most accurate'.
However, it is clear that the *accuracy* of an index comparison of
any given *precision* will vary depending on the changes in structural
composition of the quantity vectors.

        There is no philosophy here, or if there is it is natural
philosophy of the most pedestrian sort.  Various philosophical
question may arise -- is the comparison being made appropriate
to the questions we ought to be asking? is there an ideological
component in the specification of the categories? etc. -- but
from my perspective, the only surprise would be to be told that
conmensurability between aggregates was an "all or nothing"
question.  Even more surprising then, to find that my argument on
the degree to which aggregates are conmensurate taken as if
*I* have been arguing that questions of conmensurability are
of the "all or nothing" sort:

>You say that the aggregates are incommensurate if they don't consist
>of a (virtually) unchanged "internal structure", meaning that they are
>equally composed over time.

        Certainly if they are not entirely conmensurate, but only
conmensurate to a degree, they are also incomensurate to a degree.
How can this be read as saying that they are entirely inconmensurate
unless they are totally conmensurate?  I believe that the latter
position is, in fact, a position of Bruce McMises, someone to which
I have only been recently introduced by Per, but in whose favour I
can report that he casues indigestion to libertarians.


[*] Since volume is not in the Palgrave for Economics, and only appears in
the Palgrave for Banking and Finance in the microeconomic connotation I have
been using, I'll shift to talking about "quantity index numbers" as a term
that is well defined in an external reference, rather than in a vague,
sweeping allusions to 'all macroeconomists' with no references to back it
up.

Virtually,

Bruce McFarling, Ourimbah, NSW
ecbm@xxxxxxxxxxxxxxxxxxx