Data Note
Output per worker combines hourly productivity with average hours. A numerical decomposition shows how shorter working time can reduce output per person despite an increase in the output produced during each hour.
Higher output per hour can coincide with lower output per worker. The combination arises when average working time falls sufficiently. It does not require a statistical discrepancy: the two productivity measures divide production by different quantities of labor.
The Office for National Statistics identifies output per hour as its preferred labor-productivity measure, because it allows for different working patterns. Output per worker instead divides output by the number of employed individuals. The distinction is particularly relevant when part-time work, overtime or absence changes.
Let denote a consistent volume measure of output, total hours worked and employed people. Then:
Output per worker equals output per hour multiplied by average hours per worker. This is an accounting identity, not an estimate of how a change in working time causes productivity to respond.
Suppose a hypothetical economy initially produces 1,000 output units using 100 workers and 4,000 hours. Output per worker is 10, output per hour is 0.25, and average working time is 40 hours.
In the next period, output rises to 1,020, employment rises to 104, and hours fall to 3,920. Output per worker falls to approximately 9.808, a decline of 1.92 percent. Output per hour rises to approximately 0.2602, an increase of 4.08 percent. Average hours per worker fall to about 37.69, or 5.77 percent below the initial level.
Multiplying the hourly-productivity relative of 1.040816 by the average-hours relative of 0.942308 gives the per-worker relative of 0.980769. Adding the percentage changes gives only an approximation because it omits their interaction.
The identity alone supplies no reason for the change in average hours. It could reflect employees choosing shorter schedules, employers reducing overtime, more part-time recruitment, temporary absence or a shift in activity toward industries with different working patterns. These explanations have different implications for labor demand and household income.
A decline in hours could also coincide with stronger output because the workers who remain have more capital, different tasks or a more favorable industry mix. Conversely, an employer may retain staff during a temporary production interruption. In either case, a short-period productivity movement need not identify a lasting change in technical efficiency.
The measurement question is therefore followed by a composition question. Compare hours and employment within industries, examine actual rather than merely contracted working time, and match the output boundary to the labor input. Using all-economy output with employment from only selected industries does not preserve the identity's intended economic interpretation.
Output per hour helps assess production relative to labor time. Output per worker places that production against the people employed. Neither is equivalent to income per resident. Changes in the employment rate, population, income distribution and cross-border income can alter the relationship between production efficiency and households' resources.
For a firm planning staffing, the appropriate measure may be output per paid hour or a task-specific operational measure. Such a measure should not be presented as identical to the national-accounts productivity series. Paid hours can include time not actually worked, and the business's output unit may differ from the statistical office's volume measure.
A productivity briefing should consequently retain the decomposition rather than choose whichever denominator produces the stronger headline. Showing output, people and hours together reveals whether a change comes from production, employment or working time. That account is more useful for interpreting labor demand than treating the number of workers as a fixed quantity of labor input.