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June, 1988, Vol. 111, No. 6

The role of capital discards
in multifactor productivity measurement

Susan G. Powers

Since the early 1970's, the United States has experienced a marked slowdown in productivity growth, in comparison with the experience of the early postwar years.¹ The slowdown focused increased attention on long-term productivity trends. This article examines a second pattern in productivity growth, prevalent since World War II. Productivity growth increased during business cycle expansions, and decreased during downturns. The cyclical pattern is illustrated in chart 1, using the Bureau of Labor Statistics multifactor productivity measure for the private business sector from 1948 to 1986. The multifactor productivity measure is the ratio of output to combined capital and labor inputs.²

The cyclical pattern in the multifactor productivity measure has not been satisfactorily explained, although various factors that may contribute to such movements have been identified. Change in multifactor productivity is measured as the difference between the growth rate of output and the growth rate of labor and capital inputs.³ Growth in this measure reflects increase in output due to factors other than growth in capital and labor inputs. One of these factors is technical change—the increased efficiency of production resulting from better management or organization of resources and improved technology. However, the multifactor productivity measure also reflects the impact on output of changes in capacity utilization, in the composition of labor, and in economies of scale. In addition, the measure can be affected by errors in the measurement of output and of capital and labor inputs.

One possible explanation for the cyclical pattern of multifactor productivity focuses on the measurement of capital input, specifically, the measurement of capital discards. Capital input in production is defined as the flow of services from the available stock of capital, which is composed of capital assets of various vintages. the stock of capital changes over time as a result of new investment in capital assets, discarding of capital assets, and decay or loss in economic value of existing capital assets. In the BLS framework, capital stock is measured using gross investment data and some assumptions about how capital assets decay and when they are discarded.⁴  The assumption used to estimate when capital assets are discarded does not allow for increases and decreases in discards over the business cycle.⁵ However, capital discards generally increase when the economy is experiencing a slowdown, and decrease when economic activity is at a peak.

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Footnote

1 In the private business sector, growth in labor productivity—output per unit of labor input—decreased from a rate of 2.9 percent annually in 1948-73 to a rate of 1.0 percent in 1973-86. Growth in multifactor productivity—output per unit of combined capital and labor input—decreased from a rate of 2.0 percent in the earlier period to a rate of 0.3 percent in 1973-86. For further information on trends in multifactor productivity, see Multifactor Productivity Measures, 1986, USDL 87-436 (Bureau of Labor Statistics, Oct. 13, 1987).

3 Output is defined as real gross product originating in a given industry, which is net of its intermediate inputs. The multifactor productivity measurement formula is derived from an assumed production relationship: Q(t)=A(t)f(K(t),L(t)), where Q(t) is real output, K(t) is real capital input, L(t) is real labor input, and A(t) is an index of neutral technological progress, or multifactor productivity. Taking the logarithmic differential of this production function with respect to time, and assuming perfect competition and constant returns to scale, a measure of multifactor productivity growth can be derived from observed input and output quantities and prices: 

.             .                          .                          .
A          Q             P^LL    L           P^KK      K

¯      =   ¯      ¯     ¯¯¯    ¯    ¯    ¯¯¯¯     ¯

A          Q             PQ      L            PQ       K

where P^L is the price of labor services, P^K is the rental price of capital services, P is the price of output, and the "dot" notation refers to the rate of change of the variable over time.  The growth rate of multifactor productivity is equal to the growth rate of output minus the cost-share-weighted growth rates of labor and capital inputs.  The cost share of labor input is the expenditure on labor, calculated as the price of output multiplied by the quantity of output, or PQ.  Similarly, the cost share of capital input is calculated as expenditure on capital input, P^KK, divided by total input cost, PQ.  Under constant returns to scale and perfect competition, total input cost is equal to the value of total output.   That is, PQ = (P^LL+P^KK)

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