Procrustean Art of Backtracking: “Phillips Curve”

 

For the sake of convenience, we copy the following from somewhere else:

 

The Phillips curve relates the inflation rate (π) to the unemployment “rate” (u). Basically, there is dimension aberration: the inflation rate has the time dimension (T-1, or per peiod) while the unemployment rate, a ratio as a matter of fact, does not (T0, or at a moment). In order to link the two, we need a “coefficient” with the time dimension, but finding one may not be easy. To tell the truth, a rate (T-1) can if ever be bridged to a ratio (T0) with a third variable (T1) rather than a constant coefficient.

    The same holds true for any type of level as well. For example, a price level at t1 (Pt1) may be connected to another at t2 (Pt2) with the inflation rate per certain period (π) times a multiple or a fraction (n) of the period; that is, Pt2= Pt1∙(1+ n∙π), where n is a variable in the time dimension (T1).   

    Not to mention, high unemployment (u) is no more shrinking human power (Δu) than a high price (P) is a rising price (ΔP). In the Phillips curve, macroeconomists apparently commit the error of dimension aberration. This mistake is probably caused by the normalization trap due to the granted assumption: the accounting period to be the unity (1). More specifically, π= (ΔP/ P)/ Δt= ΔP/ P, where Δt= 1: then, the time dimension (T-1) conveniently disappears and might be legitimately neglected (T0).

    Back to basics, both the price level and the unemployment ratio are conceptually a number available as of a moment. Therefore, if anything, the change rate in the price level (π) must be compared to the change rate in the unemployment ratio (Δu/ u). With that said, could we still find a curve between the two rates as such? If any, usability of the curve would not be worth the research cost of the discovery.

 

For the sake of verifying a hypothesis, you might cook the data with handy assumptions and metric-free mathematical equations. Who knew “virtual” equaled “real”!

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