From: Allin Cottrell (cottrell@WFU.EDU)
Date: Tue Dec 20 2005 - 21:08:31 EST
On Sat, 17 Dec 2005, michael a. lebowitz wrote: > Paul, > What you are doing is decomposing the rate of profit (and > there could be other variations-- eg., taking into account turnover > insofar as the appropriate rate of surplus value is the annual one), > but is that the same as identifying causes? I for one will answer 'No'; I think Michael has reasonable grounds for skepticism. When we have a quantifiable variable in view -- for example, the rate of profit, or per capita income, or a country's imports -- it is generally possible to produce an "accounting decomposition" of any change in the variable in question. Here are two simple examples: 1) we can decompose a change in per capita income into a change in aggregate income and a change in population. 2) We can decompose a country's imports into a change in the imports-to-GDP ratio and a change in GDP. The examples given show that the quantifiable variable in question need not be inherently "compound" or "complex". In the first case, per capita income seems inherently a complex concept (a ratio); but in the second, the volume of imports seems "simple". An "accounting decomposition" is possible just on condition that the variable in question can be expressed as the product or quotient (or other more complex mathematical resultant of) two or more other quantifiable variables. Consider per capita income. Suppose that in some country over some period, per capita income falls by z percent. Modulo some finagling of percentage changes, we can say, in the accounting sense, that this is due to the extent (x/(x+y)) to an x percent rise in population, and to the extent (y/(x+y)) to a fall in aggregate income of y percent. But wait -- if an economy is "doing OK" we don't expect a rise in population to be automatically accompanied by a fall in per capita income. Rather, we expect aggregate income to rise in line with population, other things equal. So we resist the idea that a rise in population "explains" a fall in per capita income, in a true causal sense as opposed to a merely arithmetical sense. We want to know why aggregate income failed to rise in line with population in this case. Let's return to the rate of profit. As Paul has noted, movements in the rate of profit can be decomposed, in an accounting sense, into movements in (a) the rate of surplus value, (b) the organic composition of capital, and (c) the proportion of total surplus value appearing as profit. Here there are stronger grounds for mapping from an accounting decomposition to a causal decomposition, since the components (a) to (c) relate directly to definite theories proposed by various Marxist writers to account for historical movements in the rate of profit (as opposed to their being merely arbitrary mathematical "components" of the profit rate). Nonetheless, there remain some grounds for skepticism. The "decomposition" approach implicitly assumes that the identified components are mutually orthogonal -- that is, that it makes good sense to consider the counter-factual, "What if A had changed but B had not?" For example: A rise in organic composition was responsible for the fall in the profit rate to the extent of x percent, since if the organic composition had not risen, then -- "other things equal" -- the fall in the rate of profit would have been x percent less. But Marx, for one, linked changes in organic composition and the rate of surplus value, considering them to be joint effects of changes in production methods that substitute fixed capital for labour. (Use machinery in place of living labour: org comp goes up, and so does s/v.) From this point of view, the orthogonality assumption does not hold, and therefore the accounting decomposition does not map directly onto a causal decomposition. Allin Cottrell
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