Andrew remarks:
I wasn't aware until now that the New Interpretation depended on a period
model in this sense. I thought it was meant to be applicable to actual firm-
or aggregate-level (such as the NIPA) accounts. These are generally
constructed on annual or quarterly bases, and prices certainly do change
during the course of a quarter or year.
Duncan replies:
The New Interpretation (at least in my understanding of it) identifies the
flow of value added with the flow of living labor, and is not in principle
limited to any particular model of time (period or continuous). In real
economies production and exchange take place asynchronously, so that
continous time is perhaps the better underlying model. But since the
mathematics of continuous time models is less familiar to many people than
the mathematics of period models, much economic theory (including, for
example, Marx's treatment of simple and expanded reproduction, and his
discussion of the "transformation problem") is carried out on the
assumption of discrete periods. Furthermore, as Andrew points out, economic
data is always collected for particular periods, such as a quarter or a
year.
The usual assumption with regard to periods is that the _average_ levels of
relevant variables, such as prices or value added, through the period is
taken as representing the actual flow. This is, of course, not quite right,
since in real life prices and other economic variables are always changing
within whatever period one may choose, however short. Thus the ratio of the
flow of value added over a year to the living labor time expended during
the year (the New Interpretation MELT) is an average which approximates the
actual path of the MELT in continuous time. The quality of this
approximation depends on how fast the actual MELT might be varying during
the period of the year. If it's varying extremely rapidly, then you might
have to go to a shorter time period to get the time resolution you need.
The use of models based on discrete periods to approximate continuous time
systems is notoriously fraught with conceptual and logical pitfalls,
despite economists' long tradition of reasoning in this way. The pervasive
problem is that variables like output and labor time that are flows in
continous time become stocks in a period model, and it is tempting to add
together stock and flow variables. I believe this is going on in the TSS
definition of the MELT, which wants to add together the values of the
existing stock of commodities and the new production in a period as part of
the definition of the MELT. The only way to protect against the resulting
fallacies (in the mathematical sense) is to consider what happens when the
period becomes shorter and shorter, and, in the limit, becomes an
infinitesimal. Notice that in carrying out this type of analysis one cannot
assume that the _calendar_ time of the period of production shrinks with
the _model_ period. If the period of production is a year, then when we
shorten the period to the quarter, we have to model production as 4 stages
over the 4 quarters in the year, and similarly when we reduce the model
period to a month or a day. The New Interpretation MELT, as the ratio of
flows, adapts to this limiting process consistently, but I'm doubtful
(though willing to be convinced) that the TSS definition can be adapted to
this kind of change in the length of the model period.
The basic methodological premise of period models, however, is that
relevant economic variables like prices, production flows, and so forth
_remain constant_ throughout the period. So if you want to divide up the
year into days, as Andrew does in his example, you either have to average
out the days, or move to an explicit model where the period is a day.
Cheers,
Duncan
Duncan K. Foley
Department of Economics
Barnard College
New York, NY 10027
(212)-854-3790
fax: (212)-854-8947
e-mail: dkf2@columbia.edu