The importance of output choice: implications for productivity measurement

In this article, we discuss these alternative concepts of output and show how they are related. We then discuss the implications of using the alternative concepts to measure productivity growth. To illustrate these implications, we construct and evaluate productivity measures based on alternative output concepts for the U.S. manufacturing sector and for selected industries within manufacturing. We use a U.S. Bureau of Labor Statistics (BLS) experimental production account for the U.S. manufacturing sector in order to investigate how output choice affects total factor productivity (TFP) in the sector.

Defining productivity and output

Productivity growth relates the growth in output to the growth in the inputs used in the production process. Labor productivity growth compares the growth in output with the growth in labor input and captures gains in output that do not result from additional hours worked. Labor productivity growth can occur because of changes in capital investment, purchased materials and services, economies of scale, worker skills, and production technologies. Labor productivity is often used to evaluate the marginal product of labor and is compared with trends in compensation.¹ Labor productivity growth (LP growth) is commonly expressed as follows:

Total factor productivity (TFP), also referred to as multifactor productivity, compares output with a combination of multiple inputs used in production. Production inputs can include capital (machinery and equipment, computers, structures, intellectual property products, inventories, and land), labor, energy, materials, and purchased services. Because TFP measures the growth in output that does not result from using additional inputs, it is often considered an indicator of technological progress. TFP measures reflect the effects of technical change, increases in general knowledge (for example, new scientific findings), and improvements to management techniques and organizational structure.² TFP growth is commonly expressed as the difference between the growth rate of output and the weighted aggregate of the growth rates of each input to production:

where  is the cost-share weight for input i. This model, developed by Robert Solow in 1957, assumes constant returns to scale, implying that the value of output equals the total cost of all measured inputs and the cost shares sum to 1.³

Productivity estimates can be computed by using any of the three output concepts: gross output, sectoral output, or value-added output. The choice of output concept affects which inputs are explicitly included in the calculation of TFP. Given the relationship among outputs, inputs, and productivity, it is clear that how we define output has implications for addressing different analytical questions.

Output definitions

The broadest measure of output is gross output. Gross output is the total value of goods and services produced by all firms in an industry or sector, regardless of whether these goods and services are sold directly to consumers or sold to other firms as inputs to further production. In the case of gross output, an output is counted when it is sold and then counted again in the value of the product it was used to produce. Thus, a measure of gross output for an economy counts the value of an output multiple times if that output is used in the production processes of other firms.

By contrast, value-added output is a more narrowly defined concept that removes the value of all purchased intermediate inputs from the value of gross output. As such, value-added output reflects only the additional value of transforming intermediate inputs into outputs. Value-added output for the aggregate economy equals the sum of the value-added outputs of all firms; it can also be measured as the value of goods and services that are sold to final consumers.

Sectoral output, which lies between gross output and value-added output, equals gross output in an industry or sector less only those intermediate inputs that are produced within that industry or sector (i.e., intrasectoral transactions). Intermediate inputs used in production that are purchased from outside the industry or sector are not removed. Thus, sectoral output represents the value of output leaving the industry or sector.⁴ By excluding transactions within an industry or sector, sectoral output measures output as if the industry or sector were vertically integrated.⁵

These three measures of output have a direct mathematical relationship, as illustrated in figure 1. Sectoral output equals value-added output plus the intermediate inputs of energy, materials, and services purchased from outside the industry or sector. Gross output equals sectoral output plus the remaining intermediate inputs purchased from within the industry or sector. With the use of nominal data, gross output is greater than sectoral output, which is greater than value-added output. However, the relationship between real trends of these three measures depends on trends in intermediate inputs and price changes.

When we are measuring the total economy, the number of inputs coming from outside the economy declines and sectoral and value-added output converge. The difference between value-added and sectoral output at the level of the total economy depends mostly on the size of imported intermediate inputs. However, if we are measuring the output of a very detailed industry, we would expect most of the inputs to be coming from outside the industry. Thus, for detailed industries, gross and sectoral output are closely aligned.

Value-added output and productivity

Because value-added output can be measured directly by using data on consumption, it is timelier ‎than measures that require data on purchased inputs. Having less demanding data requirements, value-added output is the most common output measure used for measuring productivity, and it can be produced more frequently than productivity statistics based on other output concepts.⁶ Value-added labor productivity (LP_VA) growth is calculated as the percent growth in value-added output less the percent growth in hours worked:

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Value-added labor productivity more closely reflects an industry’s ability to translate labor hours into final income. Labor productivity (output per hour worked) constructed by using value-added output is often used as an indicator of changes in the standard of living.⁷ However, because it omits intermediate inputs, value-added output is sensitive to biases in intermediate-input prices (both import prices and within-industry transaction prices). This simple and easy-to-calculate productivity measure does not tell the whole story. To account for the importance of capital in production, value-added total factor productivity (TFP_VA) growth is expressed as the growth in value-added output less the share-weighted sum of growth in labor and capital:⁸

where K is capital input, L is labor input, and  and  are cost-share weights for, respectively, capital and labor (the “dot” notation on the inputs denotes growth). Energy, materials, and services are absent from this model because they are not components of value-added output; all intermediate inputs of energy, materials, and services have been removed from the measure of output. Given the assumption of constant returns to scale, the value of output equals the summed costs of capital and labor, and the cost shares sum to 1.

Sectoral output and productivity

Sectoral output equals gross output less intrasectoral transactions (i.e., purchases of intermediate inputs that were produced by other firms in the industry or sector). The concept of sectoral output is particularly useful because it describes output in relation to capital, labor, and intermediate inputs purchased from firms outside an industry, rather than only capital and labor. In addition, by removing the value of intrasectoral transactions, sectoral output avoids the double counting of inputs purchased and used for production within the same industry or sector. Sectoral total factor productivity (TFP_SO) growth and sectoral labor productivity (LP_SO) growth are expressed as follows:

In equation (5), , , and are, respectively, energy, materials, and purchased services inputs, all adjusted to remove intrasectoral transactions involving energy, materials, and purchased services inputs; ,  ,  ,  , and  are cost-share weights for the growth rates of, respectively, capital, labor, and the adjusted intermediate inputs of energy, materials, and purchased services. The cost-share weights sum to 1, and the weights on capital and labor in the sectoral-output model of TFP are smaller than those in the value-added model.

For both value-added and sectoral output, changes in labor productivity can be due to changes in technology, capital intensity, economies of scale, management techniques, and the skills of the labor force. The key difference between the two concepts is that while sectoral labor productivity includes the effects of substituting other inputs (energy, materials, and services) for labor, value-added labor productivity does not.⁹ Therefore, labor productivity based on sectoral output will grow with increased outsourcing of labor and purchases of intermediate inputs because the reduction of labor will not be offset by a reduction in output. In the value-added model, outsourcing of labor has a smaller effect on labor productivity because the substitution of purchased services for labor reduces both output and labor input.¹⁰ This differential effect partly explains why the concepts of value-added and sectoral output are useful for answering different analytical questions.¹¹ Value-added labor productivity more closely reflects the ability of an industry or sector to translate labor hours into final income, while sectoral labor productivity measures the efficiency with which an industry transforms labor hours into output.¹²

Gross output and productivity

TFP measures based on gross output relate output growth to the growth in all inputs of production, including capital, labor, and all intermediate inputs of energy, materials, and purchased services. These measures provide a way to observe shifts among all inputs to production by presenting a complete accounting of inputs (regardless of where they are produced). Thus, including all intermediate inputs in the production model can shed light on shifts between primary inputs and purchased intermediate inputs (from within and outside the industry) that accompany efficiency gains.¹³ Because gross output includes the purchase of output for further production within an industry, both output and input values are increased by the same amount—the value of outputs purchased for use as inputs within the industry. This double counting can obscure the relationship between output and inputs and the resulting measurement of productivity for the aggregate economy.¹⁴

Gross total factor productivity (TFP_GO) growth and gross labor productivity (LP_GO) growth are expressed as follows:

In equation (7), ,  ,  ,  , and  are cost-share weights (summing to 1) for the growth rates of, respectively, capital, labor, energy, materials, and purchased services.¹⁵ Given the assumption of constant returns to scale, the value of gross output equals the summed costs of all inputs—capital, labor, energy, materials, and purchased services.

Relationships among productivity measures

Because the three output measures are directly related, the productivity measures based on them are also directly related. These relationships are well known, but it is useful to briefly summarize them.¹⁶

Total factor productivity relationships

From our output definitions above, we know that gross output equals value-added output plus intermediate inputs. It follows that the relationship between gross and value-added TFP growth is a function of the ratio of intermediate inputs to gross output. This relationship can be described as follows:¹⁷

Clearly, gross TFP growth will change proportionally less than value-added TFP growth because nominal value-added output is less than nominal gross output. The difference between the TFP growth rates will increase as intermediate inputs increase (for example, because of an increase in outsourcing) relative to gross output.¹⁸

Similarly, gross TFP growth can also be defined relative to sectoral TFP growth. We know that gross output equals sectoral output plus those intermediate inputs that are purchased from within the industry or sector (i.e., intrasectoral transactions). Thus, the difference between the rate of growth of sectoral TFP and the rate of growth of gross TFP depends on intrasectoral inputs relative to gross output:¹⁹

For narrowly defined industries with most inputs coming from outside the industry and few intrasectoral transactions, sectoral TFP growth will be close to gross TFP growth. As we move from detailed to more aggregate industries or sectors, more inputs will originate inside the industry or sector and the share of intrasectoral inputs in gross output will increase. As a result, gross TFP growth will diverge more from sectoral TFP growth.

Finally, sectoral output can be expressed as value-added output plus intermediate inputs purchased from outside the industry or sector. Thus, by combining equations (9) and (10) and rearranging terms, we can express the relationship between value-added and sectoral TFP growth as follows:²⁰

From equation (11), we see that sectoral TFP growth will change proportionally less than value-added TFP growth. This relationship is a function of the relative share of intrasectoral transactions in gross output compared with the share of total intermediate inputs in gross output.

As we move from detailed industries to more aggregate industries or sectors, intrasectoral transactions will increase while purchases of out-of-sector intermediate inputs will fall. For the most aggregate economic sectors, value-added TFP growth will approximate sectoral TFP growth.²¹ Conversely, as the share of intermediate inputs from outside an industry or sector grows, the difference between value-added and sectoral TFP growth will increase. When outsourcing increases, for instance, total intermediate inputs increase while intrasectoral transactions do not, and value-added TFP grows faster than sectoral TFP. As a result, value-added TFP is more volatile than sectoral TFP in response to changes in the degree of outsourcing and consumption of intermediate inputs.

In summary, the growth rates of the three related TFP series maintain a predictable ordering. Given the absolute value of each growth rate, this ordering is as follows:

Labor productivity relationships

As was the case with TFP growth, the three labor productivity measures directly relate to growth in intermediate inputs:

Unlike the TFP measures, however, the three alternative labor productivity measures are not ordered predictably. This can be explained by reviewing the differences in the output measures used to estimate the labor productivity measures. Value-added labor productivity compares growth in real value earned by capital and labor inputs with growth in labor input; sectoral labor productivity compares growth in real value earned by capital, labor, and intermediate inputs purchased from outside a sector with growth in labor input; and gross labor productivity compares growth in capital, labor, and intermediate inputs purchased from both within and outside a sector with growth in labor input.

Therefore, the order of the three alternative labor productivity measures depends on the relative growth rates of capital, labor, and intermediate inputs purchased from both within and outside a sector. A decline in growth in capital and labor inputs that is offset by larger increases in intermediate-input purchases (whether from within or outside a sector) will result in value-added labor productivity growing more slowly than sectoral and gross labor productivity. And, regardless of growth in capital and labor inputs, the relationship between sectoral and gross labor productivity will vary depending on the relative growth rates of within-sector and out-of-sector purchases of intermediate inputs.

Figure 2 summarizes the relationships among the various elements of the integrated productivity growth model.

BLS output and productivity model

To estimate measures of productivity, we need output and input measures that are consistently defined and independently measured. The choice of output measure depends on several factors, including data availability and analytical purpose. The output measure selected from the growth accounting model’s integrated system of outputs and inputs must be appropriate both for the level of economic aggregation examined and for the analytical purpose of the application. In this section, we discuss some of the output characteristics BLS considers before selecting the most appropriate output concept for use in developing productivity measures for specific purposes.

Aggregate productivity measures

BLS uses value-added output for its business sector productivity measures, including the quarterly labor productivity measure, which is a Principal Federal Economic Indicator. Value-added output is appropriate for highly aggregated sectors because most inputs are purchased from within the sector.²² Also, value-added output is measured with the use of data on consumption (final demand of goods and services), and these data are timely and easily obtained. Data on value-added output (gross domestic product) for the United States are available from the U.S. Bureau of Economic Analysis (BEA) shortly after the reference quarter and are used in constructing BLS quarterly labor productivity measures. Having less demanding data requirements, value-added output is the most used output concept and is particularly useful for making international comparisons. BLS also publishes estimates of TFP growth for business sectors by using value-added output.²³ Because labor productivity and TFP measures are based on the same measure of value-added output, it is possible to decompose the labor productivity measures into contributions coming from capital intensity, the composition of the workforce, and TFP.²⁴

However, unlike sectoral productivity measures, value-added productivity measures do not provide a way to explain shifts between primary and imported inputs or other purchases from outside a sector. Presenting trends in offshoring, as well as purchases of inputs from the government and nonprofit sectors, can provide useful information about economic trends and bridge the value-added and sectoral productivity series.²⁵

Industry productivity measures

For analyses at the industry level, including the manufacturing sector and three- and four-digit North American Industry Classification System (NAICS) manufacturing industries, BLS uses sectoral output to estimate labor productivity and TFP growth.²⁶ The concept of sectoral output best represents the value of output leaving a particular industry. Compared with value-added TFP, sectoral TFP provides a more complete picture of the sources of growth by showing the contributions of energy, materials, and purchased services inputs, in addition to capital and labor.²⁷ Moreover, as intermediate inputs become more important in the production process, the productivity measures using sectoral output will reflect the growth that results from the substitution of intermediate inputs for labor.²⁸ Again, when both productivity measures use the same output concept, it is possible to relate labor productivity to TFP.²⁹

The BEA/BLS integrated industry production account uses a gross output concept because it provides a complete accounting of inputs used in production, regardless of where these inputs are produced.³⁰ Including all intermediate inputs in the production model can shed light on shifts between primary inputs and purchased intermediate inputs from outside and within an industry.

Although measures of gross and sectoral output both include intermediate inputs, sectoral output is comparatively less sensitive to shifts in industry structure due to mergers and split-offs. For example, suppose a single manufacturing plant is restructured into two plants, A and B, such that all the outputs of plant A are consumed by plant B. In this case, industry gross output (and inputs) increases by the output of plant A, whereas sectoral output for the industry (correctly) does not change. This occurs because any outputs produced for consumption within a single plant are not reported to the U.S. Census Bureau as outputs or inputs.³¹ However, after the plant restructuring, the outputs produced by one plant are now counted twice, once as the outputs of plant A and again as a component of the outputs of plant B. Because labor productivity measures do not account for purchased materials and services as inputs, this double counting is particularly problematic. Therefore, measuring labor productivity by using gross output is not advisable.

Comparing productivity measures in U.S. manufacturing

BLS publishes measures of labor productivity and TFP for industries and subsectors of the U.S. business sector.³² We illustrate the impact of using different output measures on related productivity measures by constructing measures of value-added and gross output for the manufacturing sector and 19 manufacturing industries.³³ The method used to construct these measures is consistent with the sectoral-output method used for official BLS productivity measures.³⁴

Data

Table 1 illustrates the data sources used in constructing the three productivity measures for the manufacturing sector and its underlying industries. BLS published measures of labor productivity and TFP for the manufacturing sector and manufacturing industries use the concept of sectoral output. In addition, to remove known sources of bias, BLS measures exclude the output of households and nonprofit institutions; thus, our productivity measures based on value-added and gross output also remove these components.³⁵ All three output measures use value-of-shipments data from the U.S. Census Bureau, as well as BEA data on inputs used in production (energy, materials, and services). Data on intangible outputs are obtained from BEA.

All three measures of productivity use the same estimates of labor and capital services. The labor input for our labor productivity measures is hours worked, produced by the BLS productivity program.³⁶ For our TFP estimates, we use a measure of labor input defined as hours worked adjusted for differences in age, education, and gender and based on the same methodology as that used for BLS published indexes of labor input. Capital input is measured as the flow of capital services from physical capital stock and intellectual property assets.³⁷ Our measures of capital input for the manufacturing sector and its component industries are consistent with BLS published data but have been adjusted to allow for consistency among the three output estimates.³⁸

For the TFP estimates based on gross and sectoral output, we use consistent measures of total intermediate inputs and intrasectoral transactions; there are no intermediate inputs in the calculation of value-added TFP.³⁹

Empirical results

Using the three output measures, we estimate the relationships among output, labor productivity, and TFP for the manufacturing sector and 19 manufacturing industries.

Manufacturing sector: output measures

Chart 1 illustrates the nominal output and input relationships for the manufacturing sector. The height of the bottom bars in the chart depicts the nominal value of capital and labor inputs, or nominal value-added output; the combined height of the lower two bars depicts the nominal value of capital, labor, and out-of-sector intermediate inputs, or sectoral output; and the combined height of all three bars depicts the nominal value of capital, labor, out-of-sector and within-sector intermediate inputs, or nominal gross output. As seen from the chart, the current-dollar data have a predictable relationship: value-added output is less than sectoral output, and sectoral output is less than gross output. However, this is not necessarily the case for the growth rates of the three measures of real output.⁴⁰ Differences in the rates of real output growth depend on the growth rates of intermediate inputs and on the price change for output and intermediate inputs.

Chart 2 presents trends in the three measures of real output for the manufacturing sector for the 1997–2021 period. The chart shows that real gross output decreased at a 0.22-percent annual rate over the 2000–21 period, compared with a 1.20-percent increase for value-added output and no change for sectoral output. In general, the trends for sectoral and gross output are similar, while the trend for value-added output is very different. (See table 2.) Although current-dollar gross output was larger than sectoral and value-added output over the 2000–21 period, real gross output grew at the slowest rate.

Table 2 highlights how changes in within-sector and out-of-sector intermediate inputs may affect the relative growth trends of the alternative output measures. Our data cover two complete business cycles (2000–07 and 2007–19) and two of the most severe U.S. recessions (2007–09 and 2019–20). Over the 2000–21 period, the long-run growth of real gross output in the manufacturing sector was somewhat slower than that of real sectoral output, reflecting a 0.67-percent annual decrease in the rate of real intermediate-input purchases from within the manufacturing sector.⁴¹

Chart 2 also shows real value-added output growing faster than sectoral output. This difference is due to a decline in the real value of intermediate inputs purchased from outside the sector, including purchases of imported intermediate inputs and purchases from service industries and the household and government sectors. As shown in table 2, over the 2000–07 period, real imported and out-of-sector purchases of intermediate inputs were falling at an annual rate of 0.33 percent.⁴² Thus, from 2000 to 2007, real value-added output grew faster, at a rate of 2.60 percent, than sectoral output, which grew at a rate of 1.18 percent. More recently, from 2007 to 2019, this difference in growth rates narrowed, with real sectoral output declining at a rate of 0.49 percent and value-added output declining at a rate of 0.06 percent. Real imported and out-of-sector purchases of intermediate inputs declined at a rate of 1.30 percent in this period.⁴³

In addition, Chart 2 shows that the 2007–09 Great Recession resulted in a decline in all measures of manufacturing output. As shown in table 3, growth in real value-added output fell by 7.15 percent from 2007 to 2009, while growth in real sectoral and gross output fell by 8.54 and 9.30 percent, respectively. The 2007–09 decline in real sectoral output reflects the drop in real value-added output and a 10.19-percent drop in real intermediate inputs purchased from outside the manufacturing sector. The decline in real gross output reflects the drop in real value-added output and a 10.59-percent decline in total real gross intermediate-input purchases.

During the 2019–20 recession, which coincided with the COVID-19 pandemic, real value-added output declined more slowly, by 3.73 percent per year. By contrast, real sectoral and gross output declined more rapidly, by 7.02 and 6.79 percent, respectively. The decline in real sectoral output reflects the fall in real value-added output and an 11.49-percent drop in real intermediate-input purchases from outside the manufacturing sector. The decline in real gross output reflects an 8.90-percent decrease in total real gross intermediate-input purchases, as well as an accompanying decline in value-added output. The path to recovery from the shock of the initial pandemic period is yet to be determined.

Manufacturing sector: productivity

In this section, we compare productivity growth across the three output measures for the manufacturing sector. Table 4 presents trends in labor productivity, output, and hours worked under each measurement framework for the 2000–21 period.

Because we use the same measure of labor input (hours worked) for each of the three labor productivity measures, differences in labor productivity are driven solely by differences in output growth. From 2000 to 2021, hours worked declined at an average annual rate of 1.61 percent, resulting in labor productivity growing faster than output. Like growth for the three output measures, growth in labor productivity was the fastest for the value-added measure and the slowest for the gross-output measure. Chart 3 compares trends in labor productivity by using the three alternative output measures.

Table 5 shows that labor productivity based on value-added output grew at an annual rate of 5.84 percent during the 2000–07 period, increased at a much slower rate of 2.04 percent during the 2007–09 Great Recession, and recovered at a rate of 0.31 percent over the 2009–19 expansionary period. By comparison, sectoral labor productivity grew more slowly in all three periods, at a rate of 4.37 percent during the 2000–07 period, 0.51 percent during the Great Recession, and 0.09 percent during the 2009–19 expansion. Gross labor productivity had the slowest growth prior to the Great Recession, at 3.87 percent per year, and the largest decline during the Great Recession, at 0.32 percent per year. During the 2009–19 recovery period, gross labor productivity grew at an annual rate of 0.23 percent, faster than sectoral labor productivity. Gross labor productivity reflects variation in the value of both within-sector and out-of-sector purchases of intermediate inputs, whereas sectoral labor productivity reflects only variation in out-of-sector purchases of intermediate inputs. In the 2019–20 downturn triggered by the COVID-19 pandemic, value-added labor productivity increased sharply, at a 3.99-percent rate. This reflects a 3.73-percent decline in real value-added output and a 7.42-percent decline in hours worked. Sectoral and gross labor productivity increased slightly—at rates of 0.44 and 0.68 percent, respectively—reflecting declines of 7.02 and 6.79 percent in sectoral and gross output, as well as the decline in hours worked.

For the TFP comparisons, the differences among TFP growth rates are driven both by differences in the growth rates of the alternative output measures and by differences in the change over time in the intermediate inputs of energy, materials, and services; trends in labor and capital are the same for all three TFP measures. Table 6 shows trends in manufacturing TFP, real output, and inputs for the 2000–21 period, by output measure.

Over the 2000–21 period, value-added TFP, which relates value-added output to capital and labor inputs only, grew the fastest of the three measures, at a 1.03-percent annual rate. Sectoral TFP grew at a 0.59-percent rate, which reflects a 0.00-percent growth in output and a 0.59-percent decline in combined inputs, with energy, materials, and services purchased from outside the manufacturing sector declining at a 1.48-percent rate. Thus, the slower growth of sectoral output relative to value-added output is primarily responsible for the difference in TFP growth. The out-of-sector intermediate inputs include purchases from all other sectors, including agriculture, mining and oil and gas extraction, utilities, construction, trade, transportation and warehousing, finance, and service sector industries. Also included are purchases of imported intermediate inputs and purchases from the household and government sectors.

Over the 2000–21 period, the TFP measure based on gross output grew at a rate of 0.41 percent, which is slower than the 0.59-percent rate of TFP based on sectoral output. This difference reflects the combination of slower growth in gross output and a similarly decreasing growth of combined capital, labor, and intermediate inputs used to calculate gross TFP. Total energy, materials, and services purchased by the manufacturing sector declined at a slightly slower rate, 1.09 percent, than did intermediate inputs purchased solely from outside the sector. This difference in growth rates for energy, materials, and services inputs was driven by the material inputs produced and consumed within the manufacturing sector (these inputs are included in the gross-output TFP measures and excluded from the sectoral-output measures). The nominal value of intrasectoral intermediate inputs declined slightly, from 53 percent of total intermediate inputs in 2000 to 51 percent in 2021.

Chart 4 compares trends in TFP indexes based on the three output measures, using 1997 as a base year. In this chart, the decline in TFP during business cycle periods is particularly evident. As seen in table 7, value-added TFP declined more steeply than sectoral and gross TFP during both the 2007–09 Great Recession and the 2019–20 pandemic downturn. The faster slowdown in value-added TFP from 2019 to 2020 reflects a steep decline of 3.73 percent in the growth of real value-added output and a lesser decline of 2.15 percent in the growth of combined capital and labor inputs. By comparison, over the same period, larger decreases in the growth of real sectoral and gross output (7.02 and 6.79 percent, respectively) were offset by respective decreases of 6.18 and 6.27 percent in the growth of combined capital, labor, and sectoral or gross intermediate inputs. The decline in combined capital, labor, and gross intermediate inputs reflects the inclusion of within-sector intermediate-input purchases, which fell by 6.31 percent in 2019–20, compared with a decline of 11.49 percent in out-of-sector intermediate-input purchases.

The annual trends show that movements in gross and sectoral TFP are similar, as is the case for their measures of output. Recall that the difference between gross and sectoral output is represented by the intermediate inputs consumed from within the industry.

Chart 5 presents trends in total, within-sector, and out-of-sector real intermediate inputs for manufacturing from 1997 to 2021. With respect to within-sector intermediate inputs, the chart shows that these inputs exhibited cyclical movements similar to those found in the output measures. The use of intrasectoral intermediate inputs dipped during the 2000–02 period, declined sharply during the 2007–09 Great Recession, experienced a shallow decline from 2015 to 2017, and decreased steeply from 2018 onward. Compared with within-sector intermediate inputs, out-of-sector real intermediate inputs exhibited growth rates with some additional year-to-year variation. In general, however, the trends in growth-rate movements of out-of-sector and within-sector intermediate inputs were similar.

Total intermediate inputs had growth-rate movements that were less pronounced than those of both within-sector and out-of-sector intermediate inputs. The TFP measures using gross output reflect the growth-rate movements of intermediate inputs purchased both within and outside the manufacturing sector. Because movements in the use of within-sector and out-of-sector intermediate inputs were similar, trends in sectoral and gross TFP were also similar.

Manufacturing industries: output

This section explores variations in output, primary inputs (capital and labor), and use of intermediate inputs for 19 manufacturing industries. Table 8 presents the 2021 shares of total, within-industry, and out-of-industry intermediate inputs relative to gross output. The table shows that, in 2021, the share of total intermediate inputs in gross output varied greatly across industries. A low share indicates that production in an industry was more labor or capital intensive, such as in computer and electronic products, where intermediate inputs were only 17 percent of gross output. Generally, manufacturing industries consumed intermediate inputs that were valued at more than 50 percent of the value of gross output. Table 8 shows that petroleum and coal products had the highest share of intermediate inputs in 2021, at 79 percent. Other industries that used large quantities of intermediate inputs were motor vehicles, bodies and trailers, and parts; food and beverage and tobacco products; primary metals; and paper products.

Although the 19 manufacturing industries presented in table 8 used mostly out-of-industry intermediate inputs in 2021, 13 of them used at least 10 percent of intermediate inputs produced by other firms within their industry. The industries with the largest shares of intrasectoral transactions were paper products; food and beverage and tobacco products; and motor vehicles, bodies and trailers, and parts. The industry with the smallest share of within-industry intermediate inputs was printing and related support activities. The relationship between the output share of intermediate inputs and the output share of intrasectoral transactions depends on the level of vertical integration within an industry. By construction, the closer the share of intrasectoral transactions in gross output is to zero, the closer sectoral output is to gross output.

Table 8 also illustrates how these shares have changed over time. The share of total intermediate inputs in gross output for computer and electronic products declined substantially over the 2000–21 period, at an annual rate of 5.76 percent. This industry experienced the largest decline in the share of intermediate-input purchases in the manufacturing sector. From 2000 to 2021, the industry’s share of intrasectoral inputs in gross output declined at an average annual rate of 3.83 percent, while its share of out-of-industry inputs declined at an annual rate of 6.74 percent. By comparison, in motor vehicles, bodies and trailers, and parts, the share of total intermediate inputs grew the fastest, at 0.43 percent per year. The share of out-of-industry intermediate inputs for this industry increased by 0.81 percent per year, while the share of intrasectoral inputs decreased by 0.69 percent annually. Petroleum and coal products experienced the largest average annual increase (2.11 percent) in the share of within-industry intermediate inputs from 2000 to 2021, while the share of out-of-industry inputs for this industry declined. In plastics and rubber products, the share of within-industry intermediate inputs grew by 1.32 percent per year, while the share of out-of-industry inputs declined at an annual rate of 0.03 percent.

Manufacturing industries: productivity

Covering the 2000–21 period, chart 6 presents labor productivity and TFP growth rates—constructed by using value-added, sectoral, and gross output—for the 19 manufacturing industries.⁴⁴ Because all three approaches are based on the same measure of hours-worked growth, the differences in labor productivity growth across the three output concepts mimic the corresponding differences in output growth. As noted earlier, measuring gross labor productivity is complicated by double counting output but only counting hours worked once, which causes gross labor productivity to be upward biased (hence, the measures must be interpreted with caution). However, intrasectoral intermediate inputs are relatively small in manufacturing, limiting the extent of double counting in gross output. For this reason, chart 6 reveals rather similar growth in gross and sectoral labor productivity in each of the 19 manufacturing industries. In most industries, value-added TFP and labor productivity were growing faster than sectoral and gross TFP and labor productivity. Recall from equation (5) that outsourcing results in a faster increase in TFP based on value-added output than in TFP based on sectoral or gross output.⁴⁵ Sectoral and gross TFP are affected by both the decrease in labor input and the increase in intermediate inputs, which results in TFP measures that are less volatile than those measured with value-added output. Finally, chart 6 shows the relative difference in TFP and labor productivity growth over the 2000–21 period for each industry, by output measure.

View Chart Data

Manufacturing industries: examples

The charts and tables below illustrate output and input relationships for three selected industries: computer and electronic products (NAICS 334); motor vehicles, bodies and trailers, and parts (NAICS 3361–3363); and plastics and rubber products (NAICS 326). Over the 2000–21 period, computer and electronic products experienced a decline in both within-industry and out-of-industry intermediate-input purchases; motor vehicles, bodies and trailers, and parts experienced substantially faster growth in out-of-industry intermediate-input purchases than in within-industry intermediate-input purchases; and plastics and rubber products experienced faster growth in within-industry intermediate-input purchases than in out-of-industry intermediate-input purchases.

Using the three alternative output concepts, chart 7 presents nominal output in computer and electronic products. In this industry, the nominal values of capital and labor inputs increased over time, whereas the nominal values of both within-industry and out-of-industry intermediate inputs declined. These growth patterns are reflected in our three output measures. From 2000 to 2021, nominal value-added output increased at an average annual rate of 1.6 percent, while nominal sectoral and gross output declined at rates of 1.2 and 1.7 percent, respectively. (See table 9.) The current-dollar value of intermediate inputs purchased outside the industry declined steadily from 2000 to 2007, at an average annual rate of 5.6 percent; declined more dramatically from 2007 to 2019, at a rate of 11.5 percent; and then increased from 2019 to 2021, at a rate of 1.8 percent. Nominal purchases of within-industry intermediate inputs also declined from 2000 to 2007, at a rate of 6.7 percent. From 2007 to 2019, these within-industry purchases declined more slowly, at a rate of 6.1 percent, and then increased from 2019 to 2021, at a rate of 3.0 percent.

Chart 8 shows the related measures of real value-added, sectoral, and gross output for computer and electronic products. Over the 2000–21 period, real gross output in the industry increased at an annual rate of 0.3 percent, compared with a 5.4-percent increase for real value-added output and a 0.8-percent increase for real sectoral output. (See table 10.) The comparatively slower growth in real gross output reflects both an annual decline of 3.6 percent in real intermediate inputs purchased from within the industry and a much larger decline of 8.2 percent in real intermediate inputs purchased from outside the industry. The current-dollar value of within-industry intermediate inputs declined at an annual rate of 5.5 percent, while the price of within-industry intermediate inputs declined at a rate of 2.0 percent. The faster growth in real value-added output relative to sectoral output can be explained in the same way, by examining growth in intermediate inputs. Recall that sectoral output differs from value-added output by including intermediate inputs purchased from outside the industry.

During the 2000–21 period, real imported and out-of-industry purchases of intermediate inputs declined at a rate of 8.2 percent. This decrease reflects an 8.3-percent decline in the nominal value of out-of-industry intermediate inputs and a 0.2-percent decline in the prices of those inputs. Because real out-of-industry intermediate-input purchases fell substantially from 2000 to 2021, the growth rate of real sectoral output was slower than that of real value-added output. From 2000 to 2007, growth in real value-added output (9.8 percent) was nearly 4 times faster than growth in real sectoral output (2.6 percent). Again, this difference can be explained by examining industry purchases of intermediate inputs by source. Real imported and out-of-industry intermediate-input purchases declined at a rate of 5.0 percent annually. This decrease reflects a 5.6-percent annual rate of decline in nominal purchases of out-of-industry intermediate inputs, whose prices declined at a rate of 0.6 percent annually. From 2007 to 2019, real value-added output increased more slowly, at an annual rate of 3.5 percent, while real sectoral output declined at a rate of 0.5 percent. In this period, real imported and out-of-sector purchases of intermediate inputs declined at an annual rate of 10.9 percent, exhibiting a nominal decline of 11.5 percent and a price decline of 0.6 percent. Over the 2019–21 period, which encompasses the COVID-19 pandemic and related massive federal economic support for industry production, real gross, sectoral, and value-added output saw slow but positive growth of 2.2, 1.9, and 1.9 percent, respectively. Nominal purchases of intermediate inputs also grew, with within-industry purchases increasing at a 3.0-percent rate and out-of-sector purchases increasing at a 1.8-percent rate. Prices of within-industry intermediate inputs increased at a 1.0-percent rate, resulting in positive growth of 2.0 percent for these inputs, while prices of out-of-industry intermediate inputs increased faster, at a 3.9-percent rate, resulting in a decline of 2.0 percent for this category. The larger price increase for out-of-industry intermediate inputs reflects the effects of global production and shipping difficulties that occurred during the initial pandemic years.

Chart 9 displays trends in TFP measures, by alternative output concept, in computer and electronic products for the 1997–21 period. From 2000 to 2021, value-added TFP grew at a rate of 6.2 percent per year, faster than sectoral TFP (3.7 percent) and gross TFP (3.4 percent). (See table 11.) In this period, real value-added output grew at a 5.4-percent rate, an increase offset by a combined decline of 0.7 percent in capital and labor inputs. By comparison, real sectoral and gross output grew at rates of 0.8 and 0.3 percent, respectively, and these increases were offset by respective declines of 2.9 and 3.0 percent in combined capital, labor, and sectoral or gross intermediate inputs. Total input growth was slower for gross TFP than for sectoral TFP, a difference reflecting the inclusion of within-industry intermediate-input purchases, which declined at a rate of 3.6 percent.

In our second industry example, which focuses on motor vehicles, bodies and trailers, and parts, the pattern of use of capital, labor, and intermediate inputs differed markedly from that observed for computer and electronic products. Here, the nominal value of purchases of intermediate inputs from outside the industry increased by 2.2 percent during the 2000–21 period. Chart 10 and table 12 present the relationships between within-industry and out-of-industry intermediate-input growth and output measures for motor vehicles, bodies and trailers, and parts. The share of current-dollar out-of-industry intermediate inputs relative to current-dollar gross output increased steadily in the industry, from 51 percent in 2000 to 61 percent in 2021. By comparison, in computer and electronic products, the share of out-of-industry intermediate inputs relative to gross output declined substantially, from 43 percent in 2000 to 10 percent in 2021. Changes in nominal purchases of within-industry intermediate inputs were more similar between the two industries. In motor vehicles, bodies and trailers, and parts, purchases of within-industry intermediate inputs accounted for 20 percent of gross output in 2000, fell to a low of 15 percent in 2009, and then increased to 17 percent in 2021. In computer and electronic products, purchases of within-industry intermediate inputs initially accounted for 16 percent of gross output, with that share falling to 7 percent by 2021. The share of nominal value-added output in nominal gross output was much smaller in motor vehicles, bodies and trailers, and parts than in computer and electronic products. In the former industry, that share stood at 28 percent in 2000, reached a high of 29 percent in 2003, dropped to a low of 14 percent in 2009 (after the Great Recession), and recovered to 22 percent in 2021. By comparison, in computer and electronic products, the share climbed relatively steadily over time, from 41 percent in 2000 to 83 percent in 2021.

Chart 11 presents measures of real value-added, sectoral, and gross output for motor vehicles, bodies and trailers, and parts from 1997 to 2021. Over the 2000–21 period, real gross output in the industry increased at an annual rate of 0.5 percent, value-added output decreased at a rate of 3.9 percent, and sectoral output grew at a rate of 0.7 percent. (See table 13.) The faster growth in gross and sectoral output (relative to value-added output) resulted from increased growth in real intermediate inputs purchased from outside the industry. Real within-industry intermediate inputs declined at a rate of 0.2 percent, reflecting a 0.7-percent increase in the current-dollar value of those inputs and a 0.9-percent increase in their prices. At the same time, real out-of-industry intermediate inputs grew at an annual rate of 0.5 percent, reflecting a 2.2-percent increase in the current-dollar value of those inputs and a 1.7-percent increase in their prices.

However, the output measures and sources of intermediate inputs for business cycle subperiods reveal a different pattern. From 2000 to 2007, purchases of real intermediate inputs from within and outside the industry declined, resulting in value-added output growing faster than both gross and sectoral output. Real imported and out-of-industry purchases of intermediate inputs fell at an annual rate of 0.1 percent, while nominal purchases of those inputs increased at a rate of 2.5 percent and their prices grew at a rate of 2.6 percent. Real sectoral output grew by 1.2 percent, faster than real gross output (0.9 percent). This difference reflects a 0.4-percent decline in nominal purchases of within-industry intermediate inputs and a slight decline of 0.01 percent in the prices of those inputs. In the 2007–19 period, which includes both the Great Recession and the postrecession recovery, purchases of within-industry and out-of-industry intermediate inputs again showed positive growth because of strong growth in nominal purchases of intermediate inputs and somewhat slower growth in input prices. As a result, both sectoral and gross output grew faster than value-added output. The nominal value of out-of-industry intermediate inputs increased at an annual rate of 2.6 percent, while the prices of those inputs increased by 0.9 percent. The nominal value of within-industry intermediate inputs grew at an annual rate of 2.4 percent, while their prices increased more slowly, at a rate of 1.2 percent. During the 2019–21 period, real value-added output declined by 7.7 percent, and nominal purchases of within-industry and out-of-industry intermediate inputs declined by 5.8 and 1.2 percent, respectively. Prices of within-industry intermediate inputs grew at a rate of 2.0 percent, while prices of out-of-industry intermediate inputs increased at a rapid rate of 3.4 percent. As a result, real within-industry and out-of-industry intermediate inputs declined at rates of 7.7 and 4.4 percent, respectively.

Chart 12 displays TFP trends for motor vehicles, bodies and trailers, and parts over the 1997–21 period. Value-added TFP in the industry grew at a steady annual rate of 5.9 percent from 2000 to the beginning of the Great Recession in 2007, when it plummeted as real value-added output declined sharply, reaching a low point in 2009 before beginning to recover. The dramatic decline in value-added TFP during the 2007–09 recessionary period reflects movements in capital and labor inputs only, with capital inputs in that period declining at a 2.3-percent rate and labor inputs falling at a historically rapid 18.6-percent rate. From 2007 to 2019, value-added TFP declined at an annual rate of 7.9 percent, while sectoral and gross TFP each declined by 0.3 percent. (See table 14.) Over the entire 2000–21 period, real value-added output decreased at a 3.9-percent rate, which was offset by a combined decline of 0.5 percent in capital and labor inputs. This resulted in a 3.4-percent decline in value-added TFP. By comparison, from 2000 to 2021, sectoral and gross TFP grew at rates of 0.4 and 0.3 percent, respectively. Real sectoral output grew at a rate of 0.7 percent, which was offset by combined growth of 0.2 percent in capital, labor, and intermediate inputs from outside the industry, while real gross output grew at a rate of 0.5 percent, which was similarly offset by combined input growth of 0.2 percent.

In our final industry example, we focus on plastics and rubber products. In this industry, purchases of intermediate inputs produced within the industry increased substantially over time relative to purchases of out-of-industry intermediate inputs. (See chart 13.) During the 2000–21 period, nominal value-added output increased at an average annual rate of 1.9 percent, while nominal sectoral and gross output increased at rates of 2.1 and 2.2 percent, respectively. (See table 15.) Over the same period, the current-dollar value of out-of-industry intermediate inputs grew at a 2.1-percent rate, while the value of within-industry intermediate inputs increased by 3.5 percent per year.

Chart 14 presents measures of real value-added, sectoral, and gross output for plastics and rubber products. Over the 2000−21 period, real value-added output increased by 1.8 percent per year, while real sectoral and gross output declined by 0.6 and 0.5 percent, respectively. (See table 16.) Because gross output includes the value of within-industry intermediate inputs, real gross output reflects the additional growth of real intrasectoral transactions. From 2000 to 2021, real intermediate inputs purchased from within the industry increased at a 0.9-percent rate, reflecting annual growth of 3.5 percent in nominal purchases of those inputs and a 2.6-percent increase in their prices. Over the same period, real value-added output grew faster than real sectoral output because of a 1.5-percent decline in intermediate inputs purchased from outside the industry. While nominal purchases of out-of-industry intermediate inputs increased by 2.1 percent, prices for those inputs increased faster, by 3.7 percent.

Looking at business cycle periods, we see that, from 2000 to 2007, real sectoral output declined at an annual rate of 0.6 percent, while real value-added output grew by 0.8 percent. Over the same period, real imported and out-of-industry purchases of intermediate inputs declined by 1.1 percent, while nominal purchases of those inputs increased at a 3.5-percent rate and their prices increased by 4.6 percent. Real gross output declined by 0.3 percent, reflecting growth of 3.0 percent in real within-industry intermediate inputs. This input growth resulted from a 5.8-percent increase in nominal purchases of intermediate inputs and a 2.8-percent increase in the prices of those inputs. In the latest business cycle period (2007–19), real value-added output decreased at a rate of 0.2 percent, while real gross and sectoral output declined by 0.5 and 0.6 percent, respectively. Real imported and out-of-industry purchases of intermediate inputs declined by 0.9 percent, reflecting an increase of 1.0 percent in nominal purchases of those inputs and an increase of 2.0 percent in their prices. Real within-industry purchases of intermediate inputs declined by 0.2 percent, reflecting an increase of 1.8 percent in nominal purchases of those inputs and an increase of 2.0 percent in their prices. Over the 2019–21 period, real value-added output grew at an accelerated rate of 18.5 percent, while real sectoral and gross output both declined, at a 0.4-percent rate. The decline in sectoral output reflects a large decline of 6.4 percent in purchases of out-of-industry intermediate inputs, which resulted from a 4.1-percent increase in nominal purchases of those inputs and an 11.3-percent increase in their prices. Within-industry intermediate inputs declined slightly, at a 0.3-percent rate, reflecting a 5.7-percent increase in purchases of within-industry intermediate inputs and a slightly faster increase of 6.0 percent in the prices of those inputs.

Chart 15 presents TFP measures, by alternative output concept, for plastics and rubber products. From 2000 to 2021, value-added TFP increased at an annual rate of 2.1 percent, while sectoral and gross TFP grew more slowly, both at a rate of 0.5 percent. (See table 17.) The 0.6-percent decline in real sectoral output was offset by a combined decline of 1.1 percent in capital, labor, and intermediate inputs from outside the industry. Similarly, a 0.5-percent decline in real gross output and a combined decline of 1.0 percent in capital, labor, and gross intermediate inputs resulted in a gross TFP growth of 0.5 percent. The similarity between sectoral and gross TFP results from the offsetting effect of sectoral and gross intermediate inputs relative to trends in real sectoral and gross output. Sectoral intermediate input declined at a 1.5-percent rate, while gross intermediate input declined at a 1.3-percent rate. Because both within-industry and out-of-industry intermediate inputs are included in gross intermediate inputs, and because real within-industry intermediate inputs increased at a 0.9-percent rate while real out-of-industry intermediate inputs declined at a 1.5-percent rate, we see a more moderate decline in gross intermediate inputs and a similar gross TFP value.

Summary

Analyzing productivity growth for an industry or sector requires an understanding of how the choice of output concept will affect measured performance. In this article, we have presented an integrated system of output, input, and productivity measures as characterized by the Solow growth accounting model. We have demonstrated the relationships among the three output concepts of gross output, sectoral output, and value-added output and summarized the strengths and weakness of their related productivity measures. Further, we have empirically compared measures of TFP and labor productivity by using the alternative output concepts for the manufacturing sector and selected manufacturing industries. This analysis highlights the bias that may occur in productivity measurement if one ignores the treatment of within-industry transactions. We have also demonstrated that shifts in outsourcing make the choice of output concept even more important.

BLS productivity measures for the manufacturing sector and its component industries use the concept of sectoral output. This concept captures the output that is leaving an industry or sector but is not affected by changes in firm structures within that industry or sector. In addition, the model based on sectoral output approaches the value-added model for the most aggregated industries and the gross-output model for the most detailed industries. Yet, productivity measures based on value-added and gross output may be useful when they fit the data user’s analytical purpose. By constructing an integrated set of productivity measures based on related output measures and by using a consistent framework of outputs and inputs, we hope to provide data users with the broadest and most useful suite of measures for productivity analysis.⁴⁶