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Dispersion Statistics on Productivity

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How does productivity vary by establishment?

On September 25, 2019, the Bureau of Labor Statistics (BLS) and the U.S. Census Bureau released a new experimental data product, Dispersion Statistics on Productivity (DiSP). Full information is in the working paper, Dispersion in Dispersion: Measuring Establishment-Level Differences in Productivity.

A peek at the underlying patterns of 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.

The first stage of this project is to measure dispersion in manufacturing industries. 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.

Example of two industries, one with high dispersion around the average and the other with low dispersion around the average.

For this initial release, DiSP provides statistics on establishment-level distributions of gross output per hour worked and multifactor productivity (gross output per combined input), for all 86 NAICS 4-digit manufacturing industries from 1997-2015. 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 BLS’s 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’s new measures of state productivity.



Outlines


DiSP differs in substantial ways from other BLS series of labor productivity in NAICS 4-digit 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, please see How are these measures different than BLS’s other productivity statistics?


Dispersion Statistics on Productivity

For dispersion statistics, we calculate an establishment’s productivity, first, as revenues (adjusted for price change) per unit of input. The input unit could be hours worked (for gross output produced) or all factor input costs (in our multifactor productivity measures). We 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.)

Diagram of how interquartile range statistics are calculated.


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 multifactor productivity measures, are derived from published data tables provided mainly by the Bureau of Economic Analysis and the Census Bureau.

Diagram of how official BLS industry productivity statistics are calculated.

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Summary Charts of Manufacturing Industries


Labor Productivity, 1997-2015

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 NAICS 4-digit industries. We consider the full 1997-2015 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 here: How are these measures different than BLS’s other productivity statistics?

Chart illustrating between-industry variation of unweighted dispersion in labor productivity.

Download chart data (XLSX)

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 0.9 in 2015, which means that in the average industry, establishments at the 75th percentile of that industry's productivity distribution were about e 0.9 ≈ 2.5 times as productive as establishments at the 25th percentile. The industries which rank as 10th highest IQR (“10th most dispersed”) or 10th lowest, i.e., ranking 77 of 86, are not necessarily the same industries from one year to the next. 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.


Chart illustrating between-industry variation of weighted dispersion in labor productivity.

Download chart data (XLSX)

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.


Multifactor Productivity, 1997-2015

Charts 3 and 4 display distributions of industries by multifactor productivity (MFP) 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.

Chart illustrating between-industry variation of unweighted dispersion in multifactor productivity.

Download chart data (XLSX)

For both charts 3 (unweighted) and 4 (weighted), note the contraction in the vertical axis scale; there is less within-industry dispersion in MFP than in gross output per hour worked. However, our selected reference industries at the upper part of the distribution (10th and 20th highest IQR) increased their distance from the mean industry more than in charts 1 and 2. In other words, between-industry MFP dispersion is increasing more than for labor productivity.

One similarity between the MFP dispersion charts and the labor productivity dispersion charts is that the mean IQR rose between 1997 and 2015.


Chart illustrating between-industry variation of weighted dispersion in multifactor productivity.

Download chart data (XLSX)

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 MFP dispersion statistics (unweighted establishment distributions) that compare the interquartile range to the BLS MFP index for the whole industry. NAICS 3251, Basic chemical manufacturing (chart 5), had the highest IQR on average from 1997-2015. This industry's product revenues are, according to recent censuses, almost evenly divided between inorganic (mainly petrochemicals) and organic chemicals (such as ethyl alcohol). NAICS 3362, Motor vehicle body and trailer manufacturing (chart 6), had the lowest IQR. This industry produces motor vehicle bodies, truck trailers, motor homes, and travel trailers and campers.

Chart of dispersion in multifactor productivity for the basic chemicals manufacturing industry. Chart of dispersion in multifactor productivity for the motor vehicle bodies and trailers manufacturing industry.

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 MFP indexes from the official BLS industry productivity series. Chart 5 reveals that the MFP index and IQR of Basic chemicals mostly rose and fell at around the same times. Periods of higher interquartile dispersion corresponded to higher MFP 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 MFP (top panel). Also, the peaks of the productivity booms were lower, and the troughs of the recessions smaller. We don't know exactly what happened here. The public-use table of Census-year establishment counts tells us that Basic chemicals stayed roughly the same between 1997 (establishments=2418) and 2012 (establishments=2485). For Motor vehicle bodies and trailers, the establishment count increased slowly between 1997 (establishments=2103) and 2007 (establishments=2215), before contracting by the 2012 Economic Census to 1888 establishments. Further microdata research on the entry and exit of establishments may help tell us more about the high-productivity establishments in Basic chemicals. Were they likely to be newer entrants to the market—or more established?




Key questions and answers

Why are BLS and the Census Bureau publishing these measures?

Understanding more about variations 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 do these measures differ 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 vary 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 multifactor 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 DiSP and BLS output trends differ most from each other does not line up well with when the hours worked trends differ.
  • DiSP MFP data may be less comparable to the official BLS data because of differences in the source data and methodology underlying the capital measures.

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 at 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 adjustments for the employment size of establishments. Dispersion among the most productive establishments (comparing the 99th to the 90th percentiles of an industry) also seems to be increasing over time.
  • 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 multifactor 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 MFP dispersion statistics are weighted by establishments’ input cost shares; the weighted gross output per hour series is 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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Last Modified Date: November 5, 2019