# "Normal" vs "actual" variables in empirical work

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, $NOMH$.

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?

• According to this reference, they are referring to output relative to time trend. To reflect capacity utilization and what not. It is difference between actual and expected output based on past trend.
– Liam
Jun 10, 2017 at 16:05

"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.

• Great stuff. Is $L_t$ the size of the labour force? Jun 11, 2017 at 15:37
• @LondonRob It represents man-hours Jun 11, 2017 at 15:46