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Hi Jerry,
You asked,
What would be examples of [the use of mathematical models to estimate macroeconomic aggregates]?
A good example would be quarterly GDP data. There would be few countries where there are regular quarterly direct surveys of all production units - the estimates for the main aggregates are in reality often extrapolated from mathematical models using indicator variables, samples and imputations. Quarterly labour force totals are also typically extrapolated from samples. Subsequently, the estimates for the totals are then revised, as more information becomes available.
Actually, if an increasing proportion of national income is property income, and if foreign trade (dominated by multinational corporations trading substantially between their own branches in different countries) increases, GDP is a less and less adequate measure of overall economic activity on its own. In many OECD countries, real growth of total domestic value-adding production is nowadays close to zero, if you take out the "imputed rental value of owner occupied housing" and purely financial activity. In general, Marx's prediction, that in the course of capitalist development more and more products are produced with a smaller and smaller value, does seem to be true.
"The markets" are often very focused on the latest quarterly indicators, but often these are not very reliable. This becomes evident when you compare the first (provisional) releases of the estimates and the final estimates across an interval of let's say 20 or 30 years. The accounts are more insightful if they are disaggregated into their various constituent parts. Marx of course never analysed national accounts in detail, mainly because they did not exist in any comprehensive form, when he lived. (A standard work on the history of national income estimates is by Paul Studenski http://www.nasm.si.edu/research/arch/findaids/studensk/ps_print.html). Funnily enough, modern macroeconomics owes a lot of its concepts to Russian or East European pioneers (think e.g. of Leontief, Von Neumann, Scitovsky and Kuznets).
I noticed a couple of interesting books were published on national accounts analysis recently (haven't had a chance to read them yet):
Utz-Peter Reich, National Accounts and Economic Value (Palgrave, 2001) http://www.palgrave.com/products/Catalogue.aspx?is=0333733916 Andre Vanoli, A history of national accounting (Amsterdam: IOS, 2005) http://www.iospress.nl/loadtop/load.php?isbn=1586034693
Jurriaan
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