Manufacturing Earnings and Cycles: New Evidence

the highest since the Bureau of Labor Statistics first recorded these data in
1956 (Hetrick, 2000).

Average nominal hourly earnings, A, can be defined as a geometric average;
that is

A_t = E^^tW_t¹~^λt                           (8)

where, E is average hourly earnings of overtime workers, W is the average
standard hourly wage rate, and ʌ is the proportion of the total workforce
working overtime. Additionally, given Fair Labor Standard Act regulations
that set maximum weekly standard hours at 40 and the minimum overtime
premium at 1.5, E can be expressed as

E_t = μ_tW_t,                             (9)

where μ is the mark-up required to convert the average standard wage to
average wage earnings. Specihcally, the mark-up is given by

μ_t = (40 + 1.5⅝)∕(40 + ⅝)                  (10)

where V is average weekly overtime hours of overtime workers.

Substituting (9) into (8) and taking logs gives

lnA⅛ = InHh + ʌt In μ_t.                      (11)

If Λ = 0, all workers receive the average standard wage rate and A = W in
(8). If Λ > 0, then A > W due to the fact that a proportion of weekly hours
for a proportion of workers are compensated at the hourly premium rate.⁷

The extent to which A diverges from W depends in (11) on (a) the size of
the average premium mark-up, μ and (b) the proportion of overtime to total
workers, ʌ. Essentially, changes in μ are solely dependent, as shown in (10),
on changes in average overtime hours of overtime workers, V. For the great
majority of workers, the maximum number of weekly hours before premium

⁷In Appendix A, we outline how we derive and construct (8) and the subsequent wage ex-
pressions from Bureau of Labor Statistics data. In our data set, movements in geometric and
arithmetic average wage earnings correspond almost identically, e.g. the simple correlation
is 0.99.

11

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