Time Dimension Missing in Macroeconomic Models

One of the magic words of Cambridge macroeconomics is the “short run.” Somehow, the term sweeps all the periods, short or long, under the rug of “moment” (T⁰ in the time dimension). No wonder all “real quantities” are defined with no regard whatsoever to “period.”

             Let us come all the way back to the classical framework of “the market.” One of the first things we do is to define and confine the accounting period. Otherwise, we would never be able to name the “quantity traded” or the “equilibrium price.” To be meaningful, we say for instance that the quantity (q) of apples traded was 10,000 natural units at the average price (p) of half a dollar, over the past week (T^-1, negative dimension for the purpose of accounting only). Apparently, no period, no quantity, no price, no market!

             Now in Cambridge macroeconomics: Is there a way to name in a specific number any of the real quantities including Y, C, I, G, X and M (for imports), and of prices, rates and ratios including i (interest rate), P (price level) and u (unemployment ratio)? Has any Noble laurate ever named an accounting period with regard to his prize-winning model?

             No, never and none at all!

             Fortunately or unfortunately, if we were going to take all the accounting periods into account, no macroeconomic “model” would be feasible: from the basic “Cambridge Quantity equation” (J.R. Hicks, 1937) to the ultra-shiny “IS-LM” and “AS-AD” models (e.g. Paul Krugman and Ben Bernanke) to the sophisticated-most “general equilibrium models” (so many celebs).

             For the sake of convenience, fames and names put all the accounting periods in eternal oblivion. As usual in Cambridge, the Robert Solow model of growth (g≡ ΔY/ Y∙Δt, T^-1) has no time dimension (T⁰)! Long live macroeconomics across the River (T⁰).

             To be sincere and serious about models on stability or growth (T^-1), we would take care of many more periods than the number of symbols. For example,

①   The period to account for the income aggregate: Y, C, I, G or the like 

②   The accounting period for the change in the aggregate

③   The period for enrollment in and retirement from labor force: ΔL

④   The period the change in the unemployment ratio: Δu

⑤   “With full employment granted,” the period for the accumulation and depreciation in the physical capital or land with natural resources: ΔK or ΔN

⑥   The period for “monetary policy”: Δi or Δi_f

⑦   The period for the expansion and contraction of the monetary base

⑧   The period for the change in the money stock: ΔM

⑨   The period to cover the rental rate: wage (for human power) or rent (for physical powers)

⑩   The period to account for the change in the rate

⑪   The period to account for the change in the ratio as of a particular moment: the exchange rate, the auction price or the index

⑫   The accounting period for the average, to represent the typical moment therein: the market price (p), the interest rate (i), the price level (P) or the like

⑬   The period to account for the change in the average: Δp, Δi, ΔP or the like.

 

Would there be a way to align all the different periods in a model? At least as for me as a sheer alien, the answer is, “Absolutely positively no.”

             A General Theory? Huh!