5  Measuring quality-adjusted labour input

Multifactor productivity is most often measured using labour and physical capital inputs. The number of hours worked rather than the number of people employed or the number of hours paid is usually the preferred labour input when measuring productivity. This is because the number of people employed does not capture changes in the number of hours worked by each worker nor changes in the composition of part-time versus full-time workers, while the number of hours paid may not accurately capture the number of hours actually worked by salaried workers.

If the number of hours worked is used as the labour input when constructing productivity measures, differences in the human capital associated with each hour worked are not accounted for. Essentially the hours worked by different types of workers are treated as if they were all identical, with differences in the human capital, or the quality of workers subsumed within the productivity measure. For example, the difference in the human capital embodied in the hours worked by a heart surgeon and a school teacher will be ascribed to the productivity measure. Moreover, changes in the human capital of workers owing to further education or greater work experience will be captured by changes in productivity over time.

Productivity analysts are often interested in gauging the contribution to changes in aggregate output from changes in the human capital or the quality of labour inputs. This requires an adjustment for differences in the quality of hours worked by different types of workers. This is done by separately accounting for different types of labour inputs when forming productivity measures.[15]

In section 2, when discussing the economic approach to choosing an index number formula, the aggregate production function was denoted as follows:

where denoted the aggregate number of hours worked, and was calculated by summing over hours worked at the sub-aggregate level (for example industries). It was also outlined that when the production function was given the translog functional form, the continuous time (Divisia) index could be approximated using the Törnqvist index formula.

An alternative specification to the production function presented in equation (23) is the following:

In this specification each of the capital inputs () and each of the labour inputs () are accounted for separately. denotes the alternative measure of multifactor productivity (which is interpreted below). As discussed in section 3, when the productive capital stocks of various asset types are used, the aggregate capital stock measure is formed using the corresponding user cost of capital measures as weights in the index formula. Likewise, when different types of labour inputs are used, income shares for the different types of labour inputs are used as weights in the index formula.

The difference between the multifactor productivity measure () corresponding to the underlying production function in equation (23) and the multifactor productivity measure () corresponding to equation (24) is the latter measure accounts for changes in the composition or quality of labour inputs. This can be seen from the analysis that follows.

Consider the case where the Törnqvist index is used to measure multifactor productivity. Assuming that the aggregate capital stock has been formed using rental prices for different asset types, the multifactor productivity indices can be written as follows:

where is capital’s income share and is labours income share, the total number of hours worked, and a Törnqvist index of aggregate labour input. Furthermore, the labour quality index () can be written as:

This index is the ratio of the aggregate labour input index to an index of total hours worked. This labour quality index is akin to that adopted in work by Jorgenson, Gallop and Fraumeni (1987) and Jorgenson and Fraumeni (1989, 1992).[16]

Finally, substituting equations (25) ,(26) and (27) yields the following index for multifactor productivity:

Equation shows the alternative multifactor productivity index () is simply the original multifactor productivity () adjusted for the quality composition of the labour input.

In forming the alternative multifactor productivity measure () it is necessary to have estimates of labour income shares for the various labour types. Labour shares for the various labour types can be estimated in one of two ways. One approach is to classify the labour inputs into different categories based on the characteristics of various workers and then use the average wage in forming labour shares for the various labour inputs. For example, workers could be classified into various categories based on their level of educational qualification. This approach has been adopted in work by Jorgenson, Gallop and Fraumeni (1987).

An alternative approach is to estimate wage equations econometrically using worker characteristics, such as the number of years worked, as explanatory variables and then use the predicted values from the wage equations to form weights for the various types of labour inputs. This approach has been used by the Bureau of Labour Statistics (1993) when forming their multifactor productivity estimates that accounts for changes in the composition of labour over time (Bureau of Labour Statistics, 1993).