"Normal" vs "actual" variables in empirical work

Question

In an early OECD study by Deppler and Ripley (1978), the authors distinguish between output per man hour, $OMH$, and what they call "Normal" output per man-hour, $NOMH$.

(table 2, p152)

At no point in the paper do they explain this distinction, which also occurs for the labour cost variables.

In the text (p154) they explain that:

The cyclical component of labor costs is represented by the ratio of actual to "normal" output per man-hour.

This all seems very mysterious to me. Are they talking about a particular reference year value? Or is it a trend component?

Answer 1

"Normal" in this context means "trend" (usually a simple linear trend, but in principle could be a non-linear trend by using for example the Hodrick-Prescott filter device).

Decompose output $Y_t = T_t+Y_{c,t}$, where $T_t$ is the trend component and $Y_{c,t}$ is the cyclical component (note that the cyclical component can be positive or negative). Then

$$OMH_t = \frac {Y_t}{L_t} = \frac {T_t+Y_{c,t}}{L_t}$$

while

$$NOMH_t = \frac {T_t}{L_t}$$

Then the ratio of actual to normal is

$$\frac{OMH_t}{NOMH_t} = 1+ \frac{Y_{c,t}}{T_t}$$

This gives a "mark-up" (or "mark-down" if $Y_{c,t}<0$), on "normal costs" and it is in this sense that it "represents the cyclical component of costs". Namely, this ratio is the gross mark-up or mark-down we need in order to go from "normal" costs to actual costs.