Procrustean Art of Backtracking: “Okun’s Law”

 

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

 

[The policy “guidance” called Oku’s law] is sometimes described as g= 3%- 2Δu, where “g” is the percentage increase in GDP [(ΔY/ Y) over two consecutive periods, and Δu is the percentage decrease in human power (Δu≒ - ΔL/L) between two time points apart by a year. The linkage can be justified only when the unemployment ratios at the two points effectively represent the labor input in the respective period. This assumption is counterfactual if in a “cyclical” economy.

      Moreover, this law’s prediction that the percentage gap in GDP is twice (2) as big as the gap in the labor input is the polar opposite of the Solow model’s spirit for the long run: the law of diminishing marginal product of labor puts the number small than the unity (1). Incidentally, the elasticity coefficient is hardly larger than 0.8 for the short or long run if the Cobb-Douglas function is any guide.[1]

 

¿Y qué? Well, 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”!


[1] Assume that the human power (L), or all employees, work for the same hours per annum and that the labor force (F) grows at n% PA. With the unemployment ratio u= (F- L)/F, or L= F∙(1– u), the annual growth in the labor input (ΔL/L)= (F/L)∙(n– Δu– n∙u- n∙Δuhown also Greenspan 2007t                                                                                                     )≒ (F/L)∙(n –Δu)= [1/(1- u)]∙(n– Δu). Now, apply this to the Cobb-Douglas function, Y= A∙Kα∙L1-α, and we get: g= ΔY/Y = [ΔA/A+ α∙(ΔK/K)]+ (1- α)∙(ΔL/L)= [ΔA/A+ α∙(ΔK/K) + n/(1- u)]– [(1- α)/(1- u)]∙Δu, The elasticity (1- α)/(1- u) is probably smaller than 0.8 where α is often thought to be 0.3 and u rarely larger than 0.1, where, with n≒ 0 over a year or less, ΔL/L= - [1/(1-u) ]∙Δu≒ -Δu.

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