Inferring from an Identity

Scott Sumner writes,

To my eyes it looks like “real wages” [(nominal average hourly earnings)/(NGDP/pop)] lead unemployment by about a month or two

Shock me, shock me. Let’s see:

NGDP = RGDP * P = N * (RGDP/N) * W*(P/W)

In words, nominal GDP = employment times output/worker times nominal wages times the price markup.

Solve this for the ratio of the nominal wage to nominal GDP:

W/NGDP = (W/P) * (RGDP/N)/N

In words, Sumner’s “real wage” (the nominal wage divided by nominal GDP) equals the inverse of the price markup times the inverse of productivity times 1/employment. If the price markup and productivity remain about unchanged, then by definition the “real wage” is inversely related to employment.

Scott is fond of saying, “Never reason from a price change.” I say, “Never draw a behavioral inference from an identity.”

4 thoughts on “Inferring from an Identity

  1. Since the wage data Scott uses is collected by survey, no, it is not merely definitional.

    Suppose I was issac newton trying to postulate about gravity. I measure masses and forces abd declare these two things are connected by a universal constant and behave as the inverse square if the distance. Then we have an equation. Kling enters the room and declares: ah well that discovery was just definitional.

    No, recognizing that NGDP decomposes in that way is a discovery because its not obvious there would be a stable relationship.

  2. So, let’s do it this way.
    Nom av hrly wages = Total compensation in the GDP/total hours worked.
    Then (Nominal average hourly wages)/(NGDP/pop) =
    (Total comp/NGDP) / (Tot hrs worked/pop)

    If (Tot comp/NGDP) is fairly constant over this cycle (which it is), all we are looking at here is a correlation between the employment to population ratio and the unemployment rate. I’m with Arnold on this one.

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