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Productivity
Bureau of Labor Statistics > Productivity > Publications > Articles and Research

Dispersion Statistics on Productivity

A Joint Project

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How does productivity vary by establishment?

On September 28, 2021, the Bureau of Labor Statistics (BLS) and the U.S. Census Bureau updated an experimental data product, Dispersion Statistics on Productivity (DiSP). The first release of DiSP was in 2019. With this release, the DiSP covers all 86 4-digit 2012 North American Industry Classification System (NAICS) industries for the years 1987 through 2018. Industry classifications now 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.

New research

BLS and Census 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 Census Business Dynamics Statistics (BDS) on establishment counts, entries, and exits. 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.

A peek at the patterns underlying industry productivity

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.

    * Note: in manufacturing, establishments are equivalent to plants.

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.

comparision of a high dispersion indsutry and low dispersion industry on a box and whisker plat showing the 25th percentile, average establishment, and 75th percentile.  The low dispersion is much closer together.

 

DiSP provides statistics on establishment-level distributions of gross output per hour worked and total factor productivity (gross output per combined input). 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 introduces an array of summary statistics. These include 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. 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 sets are available for qualified researchers on approved projects in the Federal Statistical Research Data Center (FSRDC) network.

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

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Outlines

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 end product. For more information on differences in purpose and the comparability of results, see How are these measures different from other BLS productivity statistics?

Dispersion Statistics on Productivity

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 (in our total factor productivity measures). We then take natural logarithms of establishment productivity and subtract the average productivity of 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-ordered the productivity levels of all establishments in the industry in a given year and determined that Establishment X is at the 75th percentile. 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.)

Graphic of Establishment X's Productivity feeding industry distribution

 

Official BLS Productivity Statistics for Detailed Manufacturing Industries

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.

Graphic showing Output over Input.  Output aggregates the changes in product line quantities based on shares of industry revenue for all establishments.  Input is the inputs of all establishments.

 

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Summary Charts of Manufacturing Industries

Labor Productivity, 1987–2018

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 1987–2018 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.

 

Line chart of labor productivity dispersion by industry (unweighted ITRs)

 
 

Chart 1 data: labor productivity dispersion by industry (unweighted IQRs)

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 manufacturing industry, in any given year, in which the IQR is at the average for all 86 manufacturing industries. For example, the mean IQR was about 1 in 2018, which means that in the average industry, establishments at the 75th percentile of that industry's productivity distribution were about e 1 ˜ 2.7 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. In particular, because 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.

Line chart of labor productivity dispersion by indsutry (weighted IQRs) 1987-2017

   
 

Chart 2 data: labor productivity dispersion by industry (weighted IQRs)

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.

Total Factor Productivity, 1987–2018

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 input index shares. The measure of within-industry dispersion in both charts is, again, the IQR.

 

Line chart of MFP dispersion by industry (unqeighted IQRs) 1987-2017

 
 

Chart 3 data: TFP dispersion by industry (unweighted IQRs)

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 2018.

Line chart of mfp productivity dispersion by indsutry (weighted IQRs) 1987-2017

   
 

Chart 4 data: TFP dispersion by industry (weighted IQRs)

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

Comparison of High and Low Dispersion Industries

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 higher IQRs on average from 1987–2018. This industry comprises establishments producing soft drinks, bottled water, ice, beer, wine, and spirits. The share of revenues from alcoholic beverage products has increased in recent years, accounting for more than 60 percent of product revenues in the last census. NAICS 3362, Motor vehicle body and trailer manufacturing (chart 6), had one of the lower IQRs. This industry produces motor vehicle bodies, truck trailers, motor homes, and travel trailers and campers.

Bar chart of total factor productivity interquartile range as a multiple for the beverages indsutry, 1987-2017 on top of a line chart of the total factor productivity index of the same time period  with base year of 1987 Bar chart of TFP interquartile range as a multiple for motor vehicle bodies and trailers industry from 1987 to 2017, on top of a line chart of the same years or the TFP index, base year 1987

  

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. Chart 5 reveals that the TFP index and IQR of Beverages were gradually increasing from 1987 until the Great Recession of 2007–2009. In recent years, both TFP and dispersion have returned to roughly their pre-recession levels. Periods of higher interquartile dispersion corresponded to higher TFP growth, suggesting that overall productivity growth, when it occurred, got a major boost from the more productive establishments.

Chart 6, for Motor vehicle bodies and trailers, is flatter in both panels. Establishments at the 75th and 25th percentiles differed less in TFP (top panel). Also, the peaks of the productivity booms were lower, and the troughs of the recessions smaller.

Key questions and answers

Why are BLS and the Census Bureau publishing these measures?

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.

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How are these measures different from other BLS productivity statistics?

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 BLS paper 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.

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What interesting patterns have researchers found so far?

Dispersion patterns in general:

  • BLS and the Census Bureau find productivity dispersion within industries to be as high as, or higher than, other researchers have found.
  • Dispersion increases in the tails of the productivity distributions. That is, establishments’ productivity levels vary the most, relative to each other, when we look at groups of the most productive or least productive establishments in an industry. This is true with or without activity weighting.
  • Dispersion is lower among larger establishments. In other words, smaller establishments vary more in their productivity.

Dispersion patterns by industry:

  • Variation in dispersion between industries ("dispersion in dispersion") is quantitatively less important than dispersion within industries.

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Which industries have the most/least dispersed productivity distributions?

The short answer: it’s complicated. There are many options to consider in comparing one industry’s productivity dispersion to another’s. For example: whether you regard gross output per hour or total factor productivity as the most relevant productivity variable; which percentiles to look at (75–25? 90–10?); or whether to examine weighted or unweighted statistics. (Weighted TFP dispersion statistics are weighted by establishments’ input cost shares; the weighted gross output per hour series are weighted by hours shares.)

The way that industries are defined in the classification system, NAICS, could also be reflected in the productivity dispersion statistics. Although NAICS is designed to group goods (and services) produced by similar production processes, industries may still vary in the heterogeneity of their primary product mix. Some industries may comprise establishments that produce a wider variety of product types between them. Also, some products may be produced under more (or less) standardized systems of production across establishments. If different products of the same industry, or different varieties of a product, are produced under more (or less) efficient production systems, then this might be reflected in wider interquartile or 90–10 ranges at the establishment level.

One ongoing goal of the DiSP project is to compare hypotheses from the research literature to the statistics in the dispersion data sets. It is likely that rapid technological change and changes in market concentration are both related to changes in dispersion patterns. However, there are different hypotheses in the literature for how, and when, this may show up in the productivity dispersion statistics. (Please see the literature review in the introduction of the working paper.)

Productivity dispersion is a growing field of research. We hope that these new public-use data sets help lead to new insights. We are also developing restricted-use data sets for use by researchers in the Federal Statistical Research Data Center network.

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How will BLS and the Census Bureau expand and improve this data product?

Expansion of scope:

  • Bring in data from the Census Bureau’s Longitudinal Business Database on establishment entrances and exits. Changes in the composition of industries, by establishment, are thought to be a major contributor to productivity levels and dispersion.
  • Including industries outside of the manufacturing sector is a possibility. (Access to other microdata sources would be needed.)

Methodology:

  • Continue to study ways of estimating data for establishments that do not report to the ASM, which are typically smaller establishments. The Census Bureau’s imputation methods for missing establishments are designed to yield accurate published aggregates but do not necessarily preserve the distribution or adequately reflect the variability of the underlying microdata.

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