Chapter 11.
Industry Productivity Measures

Methods and Sources

Output
The output measures used in the industry labor productivity measures are also used in the multifactor productivity measures.

Employee hours
Employee hour indexes are calculated in the same way as those used in measuring industry labor productivity.

Capital
The measure of capital input is based on the flow of services derived from the stock of physical assets. Physical capital is composed of equipment, structures, land, and inventories. Financial capital is excluded. Capital services are estimated by calculating capital stocks; changes in the stocks are assumed proportional to changes in capital services for each asset. Stocks of different asset types are Tornqvist-aggregated, using estimated rental prices to construct the weights for assets of different types.

Capital stocks are calculated using the perpetual inventory method, which takes into account the continual additions to and subtractions from the stock of capital as new investment and retirement of old capital take place. The perpetual inventory method measures stocks at the end of a year equal to a weighted sum of all past investments, where the weights are the asset's efficiency relative to a new asset. A hyperbolic age-efficiency function is used to calculate the relative efficiency of an asset at different ages.

The hyperbolic age-efficiency function can be expressed as:

S _t = (L - t)/(L - (B)t)

where S_t = the relative efficiency of a t-year-old asset
L = the service life
t = the age of the asset
B = the parameter of efficiency decline

The parameter of efficiency decline is assumed to be 0.5 for equipment and 0.75 for structures. These parameters yield a function in which assets lose efficiency more slowly at first, then rapidly later in life.

Stocks of equipment, structures, inventories, and land are estimated separately. Individual price deflators for each asset category are constructed and used to convert the current-dollar investment to constant dollars. Industry-specific service lives are computed for each type of equipment asset for use in the perpetual inventory method.

Current-dollar values of inventory stocks are calculated for three separate categories of manufacturers' inventories: Finished goods, work in process, and materials and supplies. Inventory stocks for each year are calculated as the average of the end-of-year stocks in years t and t-1 to represent the average used during the year as a whole. This is also done with equipment, structures, and land. Current-dollar inventory values for the three categories of inventories are deflated with appropriate price indexes.

Land stocks are estimated as a function of the movement in constant-dollar gross structures stocks for the given industry.

Weights. The various equipment, structure, inventory, and land stock series in constant dollars are aggregated into one capital input measure using estimated rental prices to construct the weights. Rental prices are calculated for each asset as

RP = [(P x R) + (P x D) - (P^t - P^t-1)] x (1- uz- k)/(1- u)

where:

RP = the rental price
P =the deflator for the asset
R =the internal rate of return
D =the rate of depreciation for the asset

P ^t - P ^t-1 = the capital gain term for the asset

1 - uz - k/(1 - u) reflects the effects of taxation where:

u = the corporate tax rate
z = the present value of $1 of depreciation deductions
k = the effective investment tax credit rate

This method of calculating rental prices is similar to that used in calculating multifactor productivity for major sectors of the economy except that no attempt is made to incorporate the effects of indirect business taxes, for which data are lacking at the industry level.

Rental prices are expressed in rates per constant dollar of productive capital stocks. Each rental price is multiplied by its constant-dollar capital stock to obtain current-dollar capital costs which are then converted to value shares for Tornqvist aggregation.

Sources. Industry capital indexes are developed from data published and maintained by the Bureau of the Census and the Bureau of Economic Analysis, U.S.Department of Commerce; and the Office of Employment Projections, Bureau of Labor Statistics. Price indexes are derived from producer price indexes developed by BLS.

Intermediate purchases
The index of intermediate purchases input is a Tornqvist aggregate of separate indexes of change in real materials, services, fuels, and electricity consumed by an industry. With the exception of electricity, for which both price and quantity data are available, the above indexes are calculated by dividing annual current-dollar values by appropriate price indexes to obtain constant-dollar annual estimates. Separate price deflators for materials and fuels for each industry are constructed using detailed price and value data for individual subcomponents of each group. The aggregate deflators are divided into the current-dollar values to derive constant-dollar estimates. The constant-dollar series for each component are indexed by dividing each year's estimate by the base-period aggregate.

Weights. The indexes of change in real materials, services, fuels, and electricity are weighted together with value share weights to derive an aggregate intermediate purchases index. These weights are derived by dividing the current-dollar values of each by the total combined value of intermediate purchases, and averaging these weights at times t and t-1.

Sources. Industry intermediate purchases indexes are developed from data published by the Bureau of the Census and the Bureau of Economic Analysis.

Weights for major input components
The indexes representing quantity change for each of the three major inputs are weighted together to compute the index of combined inputs.The relative weights for each year are derived from total costs for each input. All employee labor costs from Census data are used for the labor weight. The sum of current-dollar values for materials, services, fuels, and electricity constitute the weight for intermediate purchases. The weight for capital is derived by subtracting labor costs and an estimate of purchased services from Census value-added data. These cost shares are averaged at time t and t-1.

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