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On September 28, 2022, the Bureau of Labor Statistics (BLS) and the U.S. Census Bureau updated an experimental data product, Dispersion Statistics on Productivity (DiSP). This release adds two measures of tail dispersion, the 99-90 range and the 10-01 range. The first release of DiSP was in 2019. DiSP covers all 86 4-digit North American Industry Classification System (NAICS) industries for the years 1987 through 2019. Industry classifications conform to the NAICS 2012 structure. Detailed information on the construction of this data product is available in the working paper, "Dispersion in Dispersion: Measuring Establishment-Level Differences in Productivity," which was published in the *Review of Income and Wealth*.

Researchers at BLS and the Census Bureau recently published a paper in the *International Productivity Monitor* using the DiSP data: "Chaos Before Order: Productivity Patterns in U.S. Manufacturing." This paper combines dispersion data with novel data from the Business Dynamics Statistics (BDS) on establishment and firm entry rates. A hypothesis is examined: in certain industries, periods of innovation are initially associated with a surge in business start-ups, followed by rising dispersion. Only later does productivity grow faster and lastly productivity dispersion declines.

Researchers at BLS and the Census Bureau also published a BLS working paper, “Opening the Black Box: Task and Skill Mix and Productivity Dispersion," using the DiSP data and the Occupation Employment and Wage Statistics (OEWS) to examine the relationship between dispersion in productivity and skills/tasks at the detailed industry level. This paper finds that within-industry productivity dispersion is strongly positively related to within-industry task/skill dispersion.

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Some industries have a wider spread than others between more productive establishments and less productive establishments. This has important implications for how productivity (the ratio of outputs to inputs) changes in the industry as a whole over time. The official industry productivity statistics published by BLS are, after all, the weighted average productivity of all the establishments that make up the industry.

You may have a picture in your mind of how a certain industry’s productivity distribution looks. Are some establishments rising stars of productivity, leaping far above average during times of rapid change, while others struggle to improve productivity? These dynamics lead to a widening distribution. Do most establishments tend to rise and fall together with the business cycle? This pattern might suggest a compressed or stable distribution of productivity.

DiSP provides statistics on establishment-level distributions of real gross output per hour worked and total factor productivity (gross output per unit of combined inputs). The primary data sources include microdata from the Census Bureau's Annual Survey of Manufactures (ASM), Census of Manufactures (CM), and Longitudinal Business Database (LBD). We also use industry-level data from the BLS Current Population Survey (CPS). To improve our understanding of productivity distributions within industries, DiSP includes an array of summary statistics: standard deviations, interquartile ranges (comparing productivity at the 75th and 25th percentiles), and interdecile ranges (comparing productivity at the 90th and 10th percentiles) of the within-industry distributions of establishment-level productivity levels. With this release, DiSP introduces comparisons between the 10^{th} and 1^{st} percentiles and between the 90^{th} and 99^{th} percentiles of within-industry distributions of establishment-level productivity levels. All sample data are frequency weighted. Furthermore, the data set includes activity-weighted versions of these dispersion measures where the weights are based upon the denominator of the relevant productivity measure. As an example, for output per hour worked, the activity weights are defined by hours shares.

BLS and the Census Bureau welcome feedback. In addition, restricted-use microdata are available for qualified researchers on approved projects in the Federal Statistical Research Data Centers (FSRDC).

Note: for measures of *spatial* variation in productivity, please see BLS measures of state productivity.

DiSP differs in substantial ways from other BLS series of labor productivity in 4-digit NAICS manufacturing industries. These diagrams summarize the basic differences in source data, methodology, and the end products. For more information on differences in purpose and the comparability of results, see How are these measures different from other BLS productivity statistics?

For dispersion statistics, we first calculate an establishment’s productivity as revenues (adjusted for price change) per unit of input. The input unit could be hours worked (for gross output productivity measures) or all factor input costs (for our total factor productivity measures). We then take natural logarithms of establishment productivity and subtract the average productivity in its 4-digit industry to get a roughly zero-centered normal distribution around the industry's average productivity.

In the simplified illustration below, assume we rank the productivity levels of all establishments in the industry in a given year and determine that Establishment X is at the 75th percentile of the productivity distribution. There are thousands of establishments in the industry samples, so most will not fall at the critical reference points. Nonetheless, we show another establishment which happens to fall at the 25th percentile of this industry's productivity distribution. The distance between establishments X and Y—i.e., the difference of the log-productivity levels, after normalizing to the industry mean—is the interquartile *range* (IQR). Since **ln(x)-ln(y)** is equivalent to **ln(x/y)**, another way to view the IQR is as the approximate interquartile *ratio*. Taking the exponential of our published log-form IQR statistics, **exp(ln(x/y))** is the same as **x/y**, after accounting for rounding error.

(Note: the weighted mean productivity level of the industry could be higher or lower than that of the median establishment.)

Rather than aggregating up from the microdata, BLS's official industry productivity statistics use revenues from the published data sets of the CM and ASM which have already been aggregated. Hours worked are calculated from BLS sources, not the ASM. Capital services and intermediate inputs data, used in total factor productivity measures, are derived from published data tables provided mainly by the Bureau of Economic Analysis and the Census Bureau.

While productivity levels of establishments vary within a NAICS-defined industry (within-industry dispersion), industries also vary in how much their establishments vary (between-industry “dispersion in dispersion”). Let’s look at productivity dispersion at the level of the manufacturing sector (NAICS 31-33), which comprises 86 4-digit NAICS industries. We consider the full 1987–2019 period in our data sets.

Gross output per hour worked is the productivity dispersion measure closest to the official BLS measure of industry labor productivity, which is *sectoral* output per hour worked. See more information on how these measures differ from other BLS productivity statistics.

Chart 1 shows the distribution, at the manufacturing sector-level, of the industry distributions of gross output per hour worked. Within-industry dispersion is defined here as the interquartile range (IQR) of establishments’ log-productivity levels. The line for “mean” represents the average within-industry dispersion for all 86 manufacturing industries. In 2019, the mean IQR was about 0.95, which means that in the average industry, establishments at the 75th percentile of the average industry's productivity distribution were about *e ^{0.95}* ~ 2.6 times as productive as establishments at the 25th percentile. The industries that rank as 10th most (or least) dispersed are not necessarily the same industries from one year to the next. Rather, they are the industries that have the 10th highest (or lowest) IQR out of the 86 industries for each particular year. The same is true for the 20th most/least dispersed industries.

Be careful about reading too much into the dips and rises of these trend lines over short periods. Because establishments rotate in and out of the ASM sample panels, it is possible that some of this volatility comes from changes in composition. Since establishments are not weighted by hours shares (a.k.a. relative size) in this chart, much of the variance may be explained by the smaller establishments.

For chart 2, establishments are weighted by their shares of their industry’s total hours worked. This reduces the volatility and compresses the upper part of the distribution. Also, it is easier to see now that the mean IQR of all industries rose over time, driven mainly by an increase in the IQR of the industries with greater dispersion.

The BLS Productivity program replaced the term multifactor productivity (MFP) with total factor productivity (TFP) in November 2021. This was a change in terminology only and will not affect the data or methodology used in computing the measures. The use of the term “total factor productivity” will improve the visibility and accessibility of our data and was accompanied by changes to the BLS website and will be adopted in all future productivity news releases.

Charts 3 and 4 display distributions of industries by total factor productivity (TFP) dispersion, using the same rankings as reference points for between-industry dispersion. For chart 4, establishments are weighted by their composite input shares. The measure of within-industry dispersion in both charts is, again, the IQR.

For both charts 3 (unweighted) and 4 (weighted), note the contraction in the vertical axis scale; there is less within-industry dispersion in TFP than in gross output per hour worked. One similarity between the TFP dispersion charts and the labor productivity dispersion charts is that the mean IQR rose between 1987 and 2019.

Comparing chart 4 to chart 3 reveals that (like the first two charts) there is less between-industry dispersion of IQRs when the establishments are weighted by combined input shares.

One goal of the DiSP project is to better understand the relationship between productivity dispersion within an industry and the industry’s overall productivity trend. Here are a pair of examples (charts 5 and 6) from the TFP dispersion statistics (unweighted establishment distributions) that compare the interquartile range to the BLS TFP index for the whole industry. NAICS 3121, Beverages manufacturing (chart 5), had one of the highest IQRs on average from 1987–2019. This industry comprises establishments producing soft drinks, bottled water, ice, beer, wine, and spirits. NAICS 3362, Motor vehicle body and trailer manufacturing (chart 6), had one of the lowest IQRs on average. This industry produces motor vehicle bodies, truck trailers, motor homes, and travel trailers and campers.

For the upper panels of charts 5 and 6, we present the interquartile ranges as approximate ratios of productivity levels, allowing for a more tangible illustration of how productive the 75th percentile establishments are relative to the 25th percentile establishments. The lower panels display overall TFP indexes from the official BLS industry productivity series.

Charts 5 and 6 show that the Beverages industry has larger and more volatile IQR values from 1987 to 2019 compared to Motor vehicle bodies and trailers. Additionally, TFP for Beverages grows from 1987 to 2019, whereas TFP stays relatively steady for Motor vehicle bodies and trailers.

Understanding more about variation in productivity *within* industries can better help us understand variation in productivity levels and change *between* industries. Better knowledge of industry productivity, in turn, can help us better understand productivity in the higher-level aggregates, like the manufacturing or nonfarm business sectors.

Productivity growth and employee compensation are related at the establishment level: highly productive establishments tend to be high-wage establishments. Therefore, differences in productivity dispersion could be related to the distributions of wages and income.

Dispersion statistics are a new way of looking at productivity in official U.S. economic statistics. While the BLS Office of Productivity and Technology publishes official measures of productivity for major sectors and detailed industries, this joint BLS-Census product differs in some fundamental ways:

- A focus on variation within industries rather than industry aggregate averages. The degree to which individual establishments differ from the average is more relevant, to DiSP, than the average itself. Therefore, industry productivity averages are normalized to make it easier to compare distributions.
- More attention to productivity
*levels*than time series. Again, the purpose here is not to compare which industries show the highest levels of productivity, but to study the within-industry distributions. Nonetheless, there are observable time series trends in the DiSP data, such as that dispersion generally rose during the Great Recession, but fell during the recession that followed the dot-com bust. - For the dispersion statistics on gross output per hour worked and total factor productivity, the output series are based on a gross output concept. The official BLS industry productivity statistics use a sectoral output concept. The ASM does not track who products are sold to, or which industries they came from, so it is not possible to remove intrasectoral shipments from DiSP output calculations. (A Monthly Labor Review article explains the importance of intrasectoral measurements in industry productivity series.)
- DiSP data on output and hours worked, aggregated from ASM establishment data up to the industry level, correlate well with BLS official industry-level measures. (This is despite BLS using BLS sources, rather than the ASM, for the hours worked data.) However, labor productivity matches less well because when the output trends differ most from each other does not line up well with when the hours worked trends differ.

Please see the BLS Handbook of Methods for an overview of data sources and methodology in the official industry productivity statistics.

- There are large differences in productivity across establishments within industries. An establishment at the 75th percentile of the labor productivity distribution is more than twice as productive as an establishment at the 25th percentile of the distribution.
- Dispersion is significant in the tails of the productivity distributions. That is, establishments’ productivity levels vary, relative to each other, when we look at groups of the most productive or least productive establishments in an industry.
- Dispersion in productivity has increased between 1997 and 2019.
- Most of the within-industry dispersion in productivity is not accounted for by standard establishment characteristics like business size, age, or location.

BLS and the Census Bureau are exploring ways to expand the coverage to the retail trade sector.

**Last Modified Date: **October 4, 2022