Price Index, Monetary Redenomination and Discounting (half-baked)

NOTICE

• still half-baked: DO NOT TRUST THE FOLLOWING

Outlines

• Sometimes total reform of numerical structure of economic quantities needed
• Components of consumer price indexes and of market indexes like Dow Jones need to be changed time after time: there was no GOOG before 2004, no AAPL before 1980. Such components are basis in certain vector space but can not stay adequate over time
• Even monetary redenomination is needed rarely, usually as a process in aftermath of hyperinflation
• In econometrics, time-series data require unit root test. Time-evolution of such data could be non-unitary and should be detrended before calculating correlation. Two pro-cyclical data would have unit root in common, which is equal to inflation rate
• It might not so inadequate to call such act of reform of economic quantities system as renormalization
• Discounting factors, or inflation rates might be called as curvature
• There's no constant approximate wealth functional (and no orthonormal basis) even after discounting of inflation rate (was the key issue in Cambridge capital controversy)
• In other words, space of goods grows: infinite dimensional, not compact and non-separable
• Hence, maximization of certain wealth functional, or intertemporal substitution, might not make sense in long-run

TODO

• find physical analogues of Paasche, Laspeyres, and etc.
• explain what real interest rate is (or is not), and when Irving Fisher's approximation i = r + p (and neutrality of money) breaks
• examine index number requirements with the theory of measurement
• explore relations to FPTs and other well-known results in functional analysis (may take years)