Technical Notes BLS includes a measure of the effects of changes in the composition of the work force for manufacturing sectors and industries. Labor input in manufacturing sectors and NAICS industry groups is obtained by chained superlative Tornqvist aggregation of the hours at work, classified by age, education, and gender with weights determined by each group’s share of total wages. The labor composition index estimates the effect of shifts in the age, education, and gender composition of the work force on hours worked. Capital Services Capital services are the services derived from the stock of physical assets and intellectual property assets. There are 90 asset types for fixed business equipment, structures, inventories, land, and intellectual property products. The aggregate capital services measures are obtained by Tornqvist aggregation of the capital stocks for each asset type within each of the eighteen manufacturing NAICS industry groupings using estimated rental prices for each asset type. Each rental price reflects the nominal rate of return to all assets within the industry and rates of economic depreciation and revaluation for the specific asset; rental prices are adjusted for the effects of taxes. Data on investment for fixed assets are obtained from BEA. Data on inventories are estimated using data from BEA and additional information from IRS Corporation Income Returns. Data for land in the farm sector are obtained from USDA. Nonfarm industry detail for land is based on IRS book value data. Current-dollar value-added data, obtained from BEA, are used in estimating capital rental prices. Labor Input Labor input in manufacturing sectors and industries is obtained by chained superlative Tornqvist aggregation of the hours at work, classified by age, education, and gender with weights determined by each group’s share of total wages. The labor composition index estimates the effect of shifts in the age, education, and gender composition of the work force on hours worked. Hours at work data reflect Productivity and Costs data as of the December 10, 2019 “Productivity and Costs” news release (USDL-19-2143). The growth rate of labor composition is defined as the difference between the growth rate of weighted labor input and the growth rate of the hours. The growth rate of labor composition in manufacturing may be underestimated due to limitations in the source data. The education proxy does not include training certifications and licensing. The proxy only includes number of years of schooling. Additional information concerning data sources and methods of measuring labor composition can be found in “Changes in the Composition of Labor for BLS Multifactor Productivity Measures, 2014” (www.bls.gov/mfp/mprlabor.pdf). Intermediate Inputs In manufacturing, intermediate inputs consist of energy, materials, and purchased business services, and represent a large share of production costs. Research has shown that substitution among inputs, including intermediate inputs, affects productivity change. Therefore, it is important to account for intermediate inputs in productivity measures at the industry level. In contrast, the more aggregate productivity measures compare "value-added" output with two classes of inputs, capital and labor. Because of these differences in concepts and methodology, productivity change in manufacturing cannot be directly compared with changes in private business or private nonfarm business. Data on intermediate inputs are obtained from BEA based on BEA annual input-output tables. Tornqvist indexes of each of these three input classes are derived at the three-digit NAICS level and then aggregated to the manufacturing sectors. Materials inputs are adjusted to exclude transactions between establishments within the same sector. Combined Inputs The five input indexes (capital services, labor, energy, materials, and purchased business services) are combined using chained superlative Tornqvist aggregation, applying weights that represent each component's share of total costs. Total costs are defined as the current dollar value of manufacturing sectoral output. Most taxes on production and imports, such as excise taxes, are excluded from costs; however, property and motor vehicle taxes remain in total costs. Capital Intensity Capital intensity is the ratio of capital services to hours worked in the production process. The higher the capital to hours ratio, the more capital intensive the production process is. In a production process, profit maximizing/cost-minimizing firms adjust the factor proportions of capital and labor if the price of one factor falls relative to the price of the other factor; there would be a tendency for the firms to substitute the less expensive factor for the more expensive one. In the short run, changes in hours worked are more variable than changes in capital services. Changes in hours worked in business cycles can result in volatility of the capital intensity ratio over short periods of time. In the long run an increase in wages relative to the price of capital will induce the firm to substitute capital for labor, resulting in an increase in capital intensity. Rising labor costs are, in fact, an incentive for firms to introduce automated production processes. Industry estimates of capital to hours ratios can be obtained at www.bls.gov/mfp/mprdload.htm. Sectoral Output The output concept used for multifactor productivity in manufacturing is “sectoral output”. Sectoral output equals gross output (sales, receipts, and other operating income, plus commodity taxes plus changes in inventories), excluding transactions between establishments within the same sector. In contrast, the output concept used for private business and private nonfarm business is “real value-added”. Real value-added output in private business equals gross domestic product less general government, government enterprises, private households (including the rental value of owner-occupied real estate), and non-profit institutions. Real value-added output excludes intermediate transactions between businesses. The output index for manufacturing is constructed using a chained superlative index (Tornqvist) of three-digit NAICS industry outputs. Industry output is measured as sectoral output, the total value of goods and services leaving the industry. The indexes of industry output are calculated with the Tornqvist index formula. This index formula aggregates the growth rates of the various industry outputs between two periods, using their relative shares in industry value of production averaged over the two periods as weights. Manufacturing industry output measures for 2017 and earlier years are constructed primarily using data from the economic censuses and annual surveys of the U.S. Census Bureau together with data on price changes primarily from BLS. These measures have been revised due to new and revised data from the Bureau of Economic Analysis, used in part to construct intra-industry transactions. Manufacturing industry output for 2018 is estimated based on historical relationships between BLS sectoral output, BLS price indexes, and data on industrial production from the Federal Reserve Board. Multifactor Productivity The manufacturing multifactor productivity measures describe the relationship between output in real terms and the inputs involved in its production. Multifactor productivity measures are not intended to capture the specific contributions of labor, capital, or intermediate inputs. Rather, they are designed to measure the joint influences on economic growth of technological change, efficiency improvements, returns to scale, reallocation of resources and other factors of economic growth, allowing for the effects of capital, labor, and intermediate inputs. The multifactor productivity indexes are derived by dividing an output index by an index of the combined inputs of labor, capital services, energy, non-energy materials, and purchased business services. Other information Comprehensive tables containing more detailed data than that which is published in this press release are available upon request at 202-691-5606 or at www.bls.gov/mfp/mprdload.htm. Industry specific contributions to output are available at www.bls.gov/mfp/contributions-to-output.htm. More detailed information on methods, limitations, and data sources of capital and labor are provided in BLS Bulletin 2178 (September 1983), Trends in Multifactor Productivity, 1948-81 and on the BLS Multifactor Productivity website under the title “Technical Information About the BLS Multifactor Productivity Measures” for Major Sectors and 18 NAICS 3-digit Manufacturing Industries www.bls.gov/mfp/mprtech.pdf. General information is available on the BLS Multifactor Productivity website at www.bls.gov/mfp/mprover.htm. Additional data not contained in the release can be obtained in print or at www.bls.gov/mfp. A number of comprehensive tables set up as zip files can be obtained at www.bls.gov/mfp/mprdload.htm. Methods for measuring manufacturing multifactor productivity are discussed in the July 1995 issue of the Monthly Labor Review, "Measurement of productivity growth in U.S. manufacturing”. See www.bls.gov/mfp/mprgul95.pdf.