Velocity Wanted: Conveniently in Cambridge

 

“In the short run, we are not all dead.” As such, the rest of us must take the velocity of money (V in macroeconomics) into account as far as the earthly economy is concerned. If history is any guide, by the way, we may learn more from other people’s failures than from their successes. Before looking for velocity, we quickly review how conveniently it is lost in Cambridge Macroeconomics.

Constancy of Velocity. By being assumed to be “constant” as in the “Cambridge Quantity equation,” M= k∙P∙Y, the velocity (V= 1/ k) plays no role whatsoever in macroeconomics. More simply, the velocity does not only lose its citizenship in Cambridge but also its identity rendered by the Classical quantity identity, M∙V≡ P∙Y. By design of macroeconomists, then on, the economy-wide issues are all about M, P, and Y.

             On the other hand, the rest of us are more than well aware that macroeconomics is for the short run, that is, one to two year. Further on, macroeconomists generally believe in “stickiness of prices,” particularly and typically in the SRAS (for short-run aggregate supply) curve, a "constantly" horizontal line to be precise. Oh, yes the price level is outright absent in the IS-LM.

             With both the velocity and the price level constant, macroeconomists now have Y= χ∙M. The conclusion in Cambridge Macroeconomics: Keep running the printing press and that’s it! See, I Told You So, “End the Depression Now!”

Normalization of Velocity. One of the popular hobbies of macroeconomists is “normalization” of anything of convenient choice. Guess what would be the first target of normalization out of the quantity identity. Yours is as good as mine: “Normalize” the annoying thing, or something inconvenient, for the sake of building the so-called theories. [Note: “Normalization” means putting a certain variable to the unity (1).]

             “Arrest and normalize the velocity,” be it constantly normal, normally normal, abnormally normal, or abnormally abnormal (borrowed from Donald Rumsfeld). Now we have M (money stock) x 1 (unity due to normalization)= P∙Y. Monetary policy: While the incremental money ΔM “changes hands” one time (V=1) per annum, the real GDP increases just as much, that is, ΔM= Δ(P∙Y)= ΔY. [Note: When the price level as a variable is assumed “constant,” we have this result Δ(P∙Y)= ΔY.]

             Regretfully, we do not know the meaning of ΔP or ΔY: If anything, the two must be over the time, namely, ΔP/ Δt or ΔY/ Δt. A silver lining as always: Take logarithm of the normalized equation and differentiate it (per time), and we will have m= π+ g, where m for monetary growth, for π inflation and g for economic growth, each in % per annum. [Note: With V being the unity (1), we have log M= Log P+ Log Y and m= π+ g after differentiation.]

             Good news: there is no dimension aberration: all terms equally in % PA. Bad news: The new equation does not have anything whatsoever to do with the IS-LM or AS-AD model. A fatal blow furthermore: The equation m= π+ g in itself is dead false. (The correct one is 2m= π+ g. to which we come back later.)

             With the above said, we as non-macroeconomist keep navigating through for the sake of locating the velocity of money.

             Velocity, the Most Wanted!

 

Her sons: Herman, Lloyd, Arthur, and Fred