Chapter 11.
Industry Productivity Measures

Labor Productivity Measures
The indexes of output per hour measure the changes in the relationship between output and the hours expended in producing that output. To calculate a labor productivity index, an index of industry output is divided by an index of hours:

where:

=  the index of output in the current year,

= the index of labor input the current year,

t = the current year, and

o = the base year.

For an industry producing a single uniform product or service, the output index is simply the ratio of the number of units produced in the current year divided by the number of units produced in the base year. Similarly, the employee hour index equals hours expended in the current year divided by hours expended in the base year.

More typically, industries produce a number of different products or perform a number of different services. For these industries, output is calculated with a Tornqvist formula:

where:

   = the ratio of output in the current year (t) to previous year (t-1)

n = number of products,

= the natural logarithm of the radio of the quantity product i in the current year to the quantity in the previous year, and    

  ^wi,t = the average value share weight for product i

The average value share weight for product j is computed as:

where:

and price of product i at time t

The Tornqvist formula yields the ratio of output in a given year to that in the previous year. The ratios arrived at in this manner then must be chained together to form a series. If t = 3 and the base year is denoted by o, then

The resulting chained output index, , is used in the productivity formula. The employee hour index for an industry with multiple products is calculated in the same manner as in the single-output case.

The measures of output per hour relate output to one input—labor time. They do not measure the specific contribution of labor, capital, or any other factor of production. The measures reflect the joint effect of a number of interrelated influences such as changes in technology, capital investment per worker, capacity utilization, intermediate inputs per worker, layout and flow of material, skill and effort of the work force, managerial skill, and labor-management relations.

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