On Fri, 19 Sep 1997, andrew kliman wrote:
> Paul Cockshott has written: "Whether prices correspond to values is of course
> a different question, and the answer is that on average they do, in the sense
> that they are highly correlated."
>
> In ope-l 5491, I reiterated Alan Freeman's point that aggregate price-value
> correlations are meaningless, and illustrated this by means of an example in
> which the correlation between *unit* prices and *unit* values is 0, but the
> correlation between sectoral aggregates is 1.
>
> In ope-l 5492, Jerry objected that "This doesn't address the issue that Paul
> is posing. Paul asserts
> above *as an empirical matter* that prices and values *are* highly
> correlated."
>
> Actually, it does address the issue quite directly, but I'm glad Jerry raised
> the point, because I now see that I should have provided some more background
> in order to make the issue clearer. Let me try to rectify the situation now.
>
> The "prices" and "values" that Paul asserts to be highly correlated are in
> fact merely the meaningless *sectoral aggregates*. It would be another matter
> entirely were *unit* prices and values highly correlated.
>
> The input/output data which are used to obtain the high correlations simply do
> not permit computation of unit prices and values. The tables provide money
> price aggregates only. It is impossible to obtain unit prices and values from
> them because, first, each sector includes many, physically quite distinct
> use-values, and second, the size of unit prices and values will depend on the
> physical units chosen to measure use-value (grams, kilograms, pounds, tons,
> etc.)
>
> The appropriate methodology to deal with the latter problem is to focus on the
> sectoral price-value *ratios*. The aggregate price of sector j can always be
> written as Pj*Xj, where P is unit price and X is some index of physical
> output. Similarly, the aggregate value is Vj*Xj. Now, *whatever* the
> physical units one chooses to measure physical output, i.e., for *any and
> every* Xj, the *ratio*
>
> Pj*Xj Pj
> ----- = -- .
> Vj*Xj Vj
>
>
> Hence, this ratio will always give the ratio of *unit* price to *unit* value,
> even though the unit prices and values themselves cannot be computed.
>
> The appropriate procedure is then to study how these ratios differ across
> sectors. When values and prices are measured in the same units (labor-time,
> or money, etc.), then the closer the ratios are to unity, the smaller the
> price-value deviations. (If all were unity, then prices would all equal
> values.) Using data for the British economy, Alan found that the ratios are
> generally rather far from unity. He also notes that the *same* pattern exists
> in the more disaggregated data set used by Cockshott, et al.
>
> It is also possible to encapsulate the price-value dispersions in a single
> summary statistic, the mean absolute deviation (MAD) of the price-value
> ratios. Using Alan's data, I computed a MAD of 27%. This is interpreted
> thus: on average, a sector's ("unit") price-value ratio deviates from the
> average ratio by plus or minus 27%. This, IMHO, suggests that prices and
> values differ quite significantly. The 27 0.000000igure is a far cry from what the
> aggregate correlations of .98 or .99 may -- very misleadingly -- seem to
> imply.
>
My coments on this:
1. Petrovich disussed briefely that MAD is better than
correlation coeficients because spurios correlation is present in this
problem. Ochoa adopted MAD in his excelent analysis of value-price
deviations for the US economy. By the way, MAD claculated for Ochoa
are lower than 20%.
2. A MAD of 27 0oes not mean that value and prices
"differ quite significantly" as Andrew assert. The problem of "reasonable
correspondence" between empirical data and a theoretical law is a very
hard one. It is convinient for this "The problem of measuring in
modern physics" of T.S. Kuhn. He showed that there is no rule for
deviations in physics: a very large deviation could be aceptable in
astronomy and not in another sort of problems.
For the Mexican economy MAD of value-price deviations is about 80 0n 1980.
Hence, 27eems low to me.
Un saludo
Alejandro Valle Baeza