BLS WORKING PAPERS

U.S. Department of Labor

U.S. Bureau of Labor Statistics

Office of Productivity and Technology

Dispersion in Dispersion: Measuring Establishment-Level Differences in Productivity

Cindy Cunningham, U.S. Bureau of Labor Statistics

Lucia Foster, Center for Economic Studies, U.S. Census Bureau

Cheryl Grim, Center for Economic Studies, U.S. Census Bureau

John Haltiwanger, Center for Economic Studies, U.S. Census Bureau

Sabrina Wulff Pabilonia, U.S. Bureau of Labor Statistics

Jay Stewart, U.S. Bureau of Labor Statistics

Zoltan Wolf, New Light Technologies

Working Paper 530

September 2020
Dispersion in Dispersion: Measuring Establishment-Level Differences in 

Productivity

Cindy Cunningham, Lucia Foster, Cheryl Grim, John Haltiwanger, Sabrina Wulff Pabilonia, Jay 

Stewart, and Zoltan Wolf*

September 2020

Abstract: We describe new experimental productivity statistics, Dispersion Statistics on 

Productivity (DiSP), jointly developed and published by the Bureau of Labor Statistics (BLS) 

and the Census Bureau. Productivity measures are critical for understanding economic

performance. Official BLS productivity statistics, which are available for major sectors and 

detailed industries, provide information on the sources of aggregate productivity growth. A 

large body of research shows that within-industry variation in productivity provides important 

insights into productivity dynamics. This research reveals large and persistent productivity 

differences across businesses even within narrowly defined industries. These differences vary 

across industries and over time and are related to productivity-enhancing reallocation. 

Dispersion in productivity across businesses can provide information about the nature of 

competition and frictions within sectors, and about the sources of rising wage inequality across 

businesses. Because there were no official statistics providing this level of detail, BLS and the 

Census Bureau partnered to create measures of within-industry productivity dispersion. These 

measures complement official BLS aggregate and industry-level productivity growth statistics 

and thereby improve our understanding of the rich productivity dynamics in the U.S. economy. 

The underlying microdata for these measures are available for use by qualified researchers on 

approved projects in the Federal Statistical Research Data Center (FSRDC) network. These new 

statistics confirm the presence of large productivity differences and we hope that these new data 

products will encourage further research into understanding these differences. 

*Cunningham, Pabilonia, and Stewart: Bureau of Labor Statistics; Foster and Grim: Center for Economic Studies, 

U.S. Census Bureau; Haltiwanger: University of Maryland; Wolf: New Light Technologies. John Haltiwanger was

also a Schedule A part-time employee of the U.S. Census Bureau at the time of the writing of this paper. Any 

opinions and conclusions expressed herein are those of the authors and do not necessarily represent the views of the 

U.S. Census Bureau or the Bureau of Labor Statistics. All results have been reviewed to ensure that no confidential 

information is disclosed (DRB-FY19-393, DRB-FY19-526, CBDRB-FY20-410). We thank John Earle, Kevin Fox, 

Bernd Görgiz, Bart Hobijn, Mark Roberts, John Samuels, Chad Syverson, the Federal Economic Statistics 

Advisory Committee, the BLS Technical Advisory Committee, and participants at the Conference on Research on 

Income and Wealth and the 2015 Federal Statistical Research Data Center Conference for their helpful comments.

Corresponding author: Cheryl.Ann.Grim@census.gov.
1

1. Introduction

Productivity measures are critical for understanding economic performance in the U.S. 

economy. The Bureau of Labor Statistics (BLS) produces the official labor and multifactor

productivity growth statistics for major sectors and industries in the U.S. These statistics are 

constructed using aggregate industry-level data and can be thought of as changes in the first 

moment of establishment-level productivity (appropriately weighted). That is, these statistics 

show how productivity changes on average within sectors and industries, but they cannot 

provide insight into the variation in productivity levels across establishments within sectors or 

industries.

1

 

To fill this void, BLS and the Census Bureau initiated the Collaborative Microproductivity Project (CMP) to develop and publish experimental statistics on within-industry

productivity dispersion (i.e., second-moment measures of establishment-level productivity) and 

to produce restricted-use research datasets. The public-use statistics developed in this project—

Dispersion Statistics on Productivity (DiSP),

2 which were released for the first time in fall 

2019—cover all 4-digit NAICS industries in the manufacturing sector and are published jointly 

by BLS and the Census Bureau. Restricted-use establishment-level data with micro-based 

estimates of productivity as well as its underlying components (e.g., output and input measures) 

are also available to qualified researchers on approved projects in secure Federal Statistical 

Research Data Centers (FSRDCs).

3

Economic theory and recent empirical evidence suggest the second moments of 

productivity are informative on a number of important dimensions. One of the most important 

 

1 Although usually referred to as industry productivity growth or aggregate productivity growth, these statistics can 

be thought of as the weighted average of within-industry growth rates. 

2 These are available on both BLS and Census Bureau websites at: https://www.bls.gov/lpc/productivitydispersion.htm and https://www.census.gov/disp.

3 For more information on the FSRDCs: http://www.census.gov/fsrdc. An earlier version of this dataset was 

analyzed in Foster et al. (2016a).
2

findings in the literature on micro-level productivity is that large productivity differences across 

establishments exist even within narrowly defined industries.4 For example, using data from the 

1977 Census of Manufactures (CM), Syverson (2004a) found that establishments at the 90th

percentile of the within-4-digit-SIC productivity distribution are about four times as productive 

as those at the 10th percentile.

Syverson’s findings generated considerable interest in the causes and consequences of 

this dispersion. Possible market explanations include curvature of the profit function that 

prevents the most-productive business from taking over an industry, frictions in factor 

adjustments (such as costs of adjusting input factors), barriers to entry and exit, and distortions 

that inhibit the equalization of marginal products across businesses (such as the regulatory 

environment). Drivers of establishment-level productivity variation include differences in 

management skills, the quality of production factors, innovation, and investments in R&D. 

Research has shown that the dispersion of establishment-level productivity varies 

across sectors, by geographic area, and over time. For example, Syverson (2004a, 2004b) shows 

that variation in dispersion across industries and geographic areas is related to product 

substitutability, market structure, and competition. Hsieh and Klenow (2009) argue that both 

cross-country variation and within-country variation in the dispersion of productivity are related 

to distortions that inhibit productivity-enhancing reallocation. Asker, Collard-Wexler, and De 

Loecker (2014) present evidence that the patterns of dispersion reflect the dynamic factor 

adjustment frictions within sectors. The findings in Foster et al. (2016b) suggest that 

productivity differences across establishments may be generated by differences in efficiency 

levels, demand shocks, frictions/distortions, or all of the above. Alternatively, Foster et al. 

(2017a) present evidence that industries experiencing a surge in innovation exhibit a burst of 

 

4 Syverson (2011) provides a survey of this literature.
3

firm entry, followed by an increase in productivity dispersion during an experimentation and 

shakeout phase, followed ultimately by an increase in industry-level productivity. 

Establishment-level productivity differences are also correlated with important 

economic outcomes at the micro level, such as the survival and growth of establishments. There 

is a large literature on the connection between productivity, reallocation and growth (Baily, 

Hulten, and Campbell, 1992; Griliches and Regev, 1992; Foster, Haltiwanger and Krizan, 2001;

Petrin, White and Reiter, 2001; Foster, Grim and Haltiwanger, 2016; Blackwood et. al., 2020; 

Decker et. al., 2020). These studies show that more-productive businesses are more to survive 

and grow. These findings contribute to the perspective that that reallocation—the process by 

which economic activity is allocated to its highest valued use—is an important contributor to 

aggregate productivity growth. 

Productivity dispersion is also important for understanding rising wage inequality, 

which has been shown to be a between-firm phenomenon (Davis and Haltiwanger, 1991; Barth 

et al., 2016; Song et al., 2019; Haltiwanger and Spletzer, 2020). In addition, a number of studies 

have found that high-wage establishments are also highly productive and that rising betweenestablishment dispersion in wages is closely associated with rising between-establishment

dispersion in productivity (e.g., Dunne et al., 2004). Economic theories of search and matching 

provide theoretical justification for the connection between productivity dispersion and wage 

dispersion (e.g., Burdett and Mortensen, 1998). Search and matching frictions create quasi-rents 

for worker-firm matches that make it optimal for high-productivity firms to pay high wages. 

Our results using the DiSP experimental data confirm earlier findings about the large 

differences in productivity across establishments within industries. To preview our results, we 

find that on average, the manufacturing plant at the 75th percentile of the within-industry labor 
4

productivity distribution is more than twice as productive as the plant at the 25th percentile.5If 

we instead focus on multifactor productivity, we find that the 75th percentile plants are almost

twice as productive as plants at the 25th percentile. Underlying these averages, we find 

substantial differences in dispersion across industries. For example, labor productivity 

dispersion in the industry at the 75th percentile of the dispersion distribution is about 1.4 times 

as big as the dispersion in the industry at the 25th percentile. The corresponding multiplier for 

multifactor productivity is 1.2.

The experimental statistics on productivity dispersion are intended to complement 

official BLS data, so it is crucial to understand the relationship between the dispersion of the 

productivity distribution derived from Census Bureau microdata and the statistics from BLS 

built from industry-level aggregates. Section 2 describes BLS productivity measures and 

productivity measures that we construct from Census microdata. Section 3 compares the two 

approaches to measuring inputs, output, and productivity for the manufacturing sector, and for 

4-digit NAICS manufacturing industries. We also compare these measures to data from the 

NBER-CES Manufacturing Industry Database and examine a number of data and measurement 

issues such as imputation and weighting of the microdata. In section 4, we explore the variation 

in industry-level productivity dispersion measures across industries and over time. Section 5 

summarizes our conclusions and describes plans for future work. 

2. Measuring Productivity

Because our primary goal is to create statistics that provide insight to the official BLS 

industry-level productivity measures, it is useful to first describe how BLS constructs its 

measures from published aggregates, and then compare it to our measures that are constructed 

by aggregating Census microdata. 

 

5 We use the terms “establishment” and “plant” interchangeably throughout this paper. 
5

2.1. BLS Industry-level Productivity

BLS publishes quarterly and annual measures of labor productivity for major sectors; 

annual measures of labor productivity for 199 3-digit and 4-digit NAICS industries; and annual 

measures of multifactor productivity for major sectors, 18 3-digit NAICS manufacturing 

industries, 86 4-digit NAICS manufacturing industries, the air transportation industry, and the 

line-haul railroad industry. Productivity growth is measured as the difference between 

percentage changes in indexes of output and inputs (labor and, in the case of multifactor 

productivity, capital and intermediate purchases). BLS does not publish industry productivity

levels, although they are available on request.

BLS industry output is based on a sectoral concept, which measures the value of goods 

produced for sale outside the industry.6 For manufacturing industries, BLS uses published 

Annual Survey of Manufactures (ASM) and Census of Manufactures (CM) data on the total 

value of shipments, which it adjusts to remove intrasectoral transactions and resales, and to 

account for changes in finished goods and work-in-process inventories.

7 This adjusted nominal 

output measure is then distributed to detailed categories of products and services using the mix 

of annual wherever-made product shipments from the ASM. Nominal output in each product 

category is deflated using the appropriate detailed producer price index from the BLS prices

program. These real output measures are then Tornqvist-aggregated into industry output 

indexes. Self-employment revenues for manufacturing firms, which come from Internal 

Revenue Service data, are also added to these output measures. 

BLS measures labor input as the total annual hours worked by all persons in an industry. 

 

6 Sectoral output is less than gross output, but greater than value-added output. In the most detailed industries, 

sectoral and gross output are the same or very close. However, going from very detailed industries to more 

aggregated industries, sectoral output moves closer to value-added output. In the limit, at the aggregate level, 

sectoral output is the same as value-added output, except for imported intermediate inputs. 

7 See https://www.census.gov/programs-surveys/asm.html and https://www.census.gov/programssurveys/economic-census.html. 
6

This measure is constructed by combining data from three BLS surveys: the Current 

Employment Statistics (CES) survey, the Current Population Survey (CPS), and the National 

Compensation Survey (NCS). The CES provides detailed information on the employment and 

average weekly hours paid for production and non-supervisory employees (henceforth referred 

to as production workers).

8 The NCS data are used to adjust CES average weekly hours from an 

hours-paid to an hours-worked basis by removing paid vacation accrued and sick leave taken.

9

To estimate nonproduction worker average weekly hours, BLS uses data from the CPS to 

calculate a ratio of nonproduction to production worker average weekly hours worked, which is 

then multiplied by the adjusted CES production worker hours (worked). Total nonproduction

worker hours are estimated as:

THNP = EmpNP

CES × AWHPCES × hwhpP

NCS ×

AWHNP

CPS

AWHP

CPS × 52 (1)

where EmpNP

CES is nonproduction worker employment from CES, AWHPCES is production worker 

average weekly hours paid from CES, hwhpP

NCS is the hours-worked-to-hours-paid ratio from 

NCS, and (

AWHNP

CPS

AWHP

CPS) is the CPS nonproduction/production hours ratio. CPS data are also used to 

directly obtain hours worked by self-employed and unpaid family workers (Eldridge et al., 

2004).

For multifactor productivity at the 4-digit NAICS level, capital input is based on the 

flow of services from the productive stock of capital. BLS investment data for industries 

combine expenditures on structures and equipment from the ASM with data on investment in 

different types of assets by industry from BEA and the Annual Capital Expenditure Survey 

(ACES). Using a perpetual inventory method, BLS then computes industry-asset level capital 

 

8 Workers in goods-producing industries are referred to as being production or non-production workers and in the 

service-providing industries as nonsupervisory or supervisory workers.

9 Note that this adjustment does not account for off-the-clock hours.
7

stocks from these investment flows. In BLS official multifactor productivity measures, these 

stocks are converted to capital services using industry-asset specific rental prices, and then 

aggregated to the industry level.

For intermediate purchases inputs, BLS combines quantities of materials, purchased 

business services, fuels, and electricity consumed by each industry. The nominal values of 

materials, fuels, and electricity are obtained from the CM and ASM. The values of purchased 

business services are estimated from BEA and Census Bureau data.

2.2 Establishment-level Productivity using Census Data

To measure establishment-level labor productivity, we combine establishment-level 

information from three Census Bureau restricted-use microdata files with public-use industrylevel data from BLS. Given that one of the goals of our research is to shed light on BLS 

industry productivity statistics, we try to match BLS concepts and measures as closely as 

possible. 

Our establishment-level microdata come from the CM, the ASM, and the Longitudinal 

Business Database (LBD). The CM is collected every 5 years in years ending in ‘2’ and ‘7’. 

Data are collected from all manufacturing establishments except those that are very small. For 

these very small out-of-scope establishments, the Census Bureau imputes data using 

administrative records. The ASM sample is a 5-year panel of manufacturing establishments, 

updated every year for births, and data are collected annually. ASM panels begin in years ending 

in ‘4’ and ‘9’, and the probability of selection into the ASM sample is a function of both 

industry and size (generally employment or the value of shipments). Like the CM, the ASM 

does not collect data from very small establishments but accounts for them using administrative 

information. In CM years, ASM data are collected as part of the CM data collection, but for this 
8

analysis we use only the ASM establishments.10 Data are imputed for establishments that do not 

respond or that fail to report some data elements (item non-response); we discuss this further in 

section 2.3. The LBD is a longitudinally linked version of the Census Bureau’s Business 

Register that covers the non-agricultural employer universe of business establishments (see 

Jarmin and Miranda, 2002). The LBD provides us with both high-quality longitudinal links and 

information on the universe of manufacturing establishments, which we use to construct 

propensity-score weights that we use in our productivity calculations. 

Ideally, we would construct an output measure that exactly matches the BLS measure. 

We start by using Census microdata to replicate the value of shipments as closely as possible. 

Specifically, we calculate plant-level real output as deflated revenues, adjusted for resales and 

changes in inventories.11 But we cannot replicate the BLS sectoral output concept because the 

ASM does not collect the information needed to calculate intra-sectoral transactions. Instead, 

we add the value of intra-sectoral transactions back into BLS output measures to make the two 

measures comparable. Thus, we measure plant-level output as:

Qet = (TVSet + DFet + DWet − CRet)/PISHIPit (2)

where TVS = total value of shipments, DFet = FIEet − FIBet and DWet = WIEet − WIBet are 

the changes in finished-goods and work-in-process inventories respectively (FIB, FIE = 

beginning-of-year and end-of-year finished goods inventories and WIB, WIE = beginning-ofyear and end-of-year work-in-process inventories), CR = cost of resales, PISHIP = deflator for 

the value of shipments,

12 and the i, e, and t subscripts index industries, establishments, and 

 

10 The microdata made available in the FSRDCs contains productivity measures for all CM establishments when

productivity calculation is possible.

11 In practice, subtracting resales does not make much difference because they are only a small fraction of revenue.

12 The shipments deflator is constructed as part of NBER-CES data, using price indexes from BEA GDP-byIndustry data. In comparisons to BLS output data conducted in this paper, BLS industry implicit output price 

deflators (as described in 2.1) are used in place of the shipments deflator.
9

years. 

We measure labor input as total hours worked. For each establishment, the ASM collects 

the total number of employees, the number of production workers, and the total number of 

hours worked by production workers. We calculate total annual hours worked by summing 

ASM production worker hours and an estimate of nonproduction worker hours, which we 

calculate using the essentially same methodology as BLS (equation 1) but substituting ASM 

data for CES:

13

 

THet = PHet + ((TEet − PWet) ×

PHet

PWet

× (

AWHNP

CPS

AWHP

CPS)) (3)

where PH = production worker hours, PW = average number of production workers, TE = total 

employment, and AWHNP

CPS

AWHP

CPS = CPS non-production/production average weekly hours ratio.

14 We 

calculate establishment-level log labor productivity as:

lnLPet = lnQet − lnTHet. (4)

Establishment-level multifactor productivity (MFP) in logs is measured as:

lnMFPet = lnQet − αKlnKet − αLlnTHet − αMlnMet − αElnEet, (5)

where Q and TH are real output and total hours as defined above in (2) and (3), K denotes real 

productive capital stock, and M and E denote deflated values of expenditures on materials and 

energy.15 The productive capital stock is constructed using the perpetual inventory method for 

equipment and structures separately.16 The value of M is calculated as the deflated sum of cost 

 

13 Note that it is not necessary to apply the hours-worked-to-hours-paid ratio because establishments are requested 

to report hours worked.

14 These ratios are calculated at the 4-digit industry level. 

15 BLS constructs aggregate MFP using capital services rather than productive stock.

16 We do not include rented capital due to its irregular collection in the ASM. Pre-1986 and post-2006, this 

information is collected annually on the ASM. In the intervening years, this information was only collected in the 

Economic Census. Exploratory analysis for the years when this is available shows rented capital is small and does 

not make much difference to plant-level capital measures. We plan on exploring this further in future research.
10

of materials, the cost of resales and the cost of contract work done for the establishment by 

others.

17 The nominal value of E is obtained as the sum of the cost of electricity and fuels. For 

the CMP data ultimately included in the DiSP data, the two expenditures are deflated using the 

appropriate deflators from the NBER-CES database. We measure the factor elasticities, αK, αL, 

αE, and αM, using the share of expenditures of the corresponding input in total cost in each 6-

digit NAICS industry.

18 For the BLS data comparisons, we use published BLS industry cost 

shares; for the DiSP statistics, we use shares calculated from CMP data.

DiSP does not include value-added-based productivity dispersion for conceptual reasons. 

While there is a market for final demand, a market for value-added does not exist. This 

consideration is irrelevant for the overall economy because value added equals the value of final 

demand at that level of aggregation. However, the relationship between value added and final 

demand is only an approximation at lower levels of aggregation and in order to make inference 

about final goods produced by a plant or industry, not only are the output and input values 

necessary but also the relevant input-output linkages.19 A related issue is that the existence of a 

value-added production function at the establishment-level requires very strong functional form 

assumptions that are likely violated (see Basu and Fernald, 1997). 

2.3 Missing Data and Imputation

 

17 Published ASM measures of value-added are based on the difference between the value of output and a 

composite operating expenses measure inclusive of materials and energy expenditures. We break out the cost of 

materials and energy separately in our MFP measure. The inclusion of contract work implies some aspects of 

purchased services are included in the materials expenditures. However, since 2006, the ASM survey has included 

questions on other operating expenses including leased employees and additional purchased services not included 

in the cost of contract work. We are actively exploring the inclusion of those operating expenses for a supplemental 

multifactor productivity dispersion measure commencing in 2006. Challenges for inclusion of these variables are 

the short time series, item non-response rates, and the treatment of establishments of single-unit versus multi-unit 

establishment firms. Establishments of the latter are less likely to have such additional operating expenses because 

the headquarters establishment of the parent firm may be providing and/or purchasing those services. 

18 See web appendix B in Foster et al. (2016a) for more details. Procedures for extending the output and input price 

deflators are described in this appendix.

19 An additional consideration follows when using the logarithmic transformation to stabilize the variance of 

empirical distributions. This transformation truncates distributions at zero, which leads to biased inference if the 

probability of negative value added is correlated with plant-level characteristics. In other words, negative valueadded may be plausible, for example in intermediate-intensive industries during periods of recession or crises.
11

As noted above, the ASM microdata are subject to item non-response, and these missing 

values are imputed by the Census Bureau. The Census Bureau’s imputation methods are 

designed to yield accurate published aggregates but do not necessarily preserve the distribution 

or adequately reflect the variability of the underlying microdata. There is evidence that certain 

imputation methods may affect microdata analyses. However, there are techniques available to 

mitigate the effects of imputation on dispersion measures. For example, White, Petrin, and

Reiter (2018) analyze dispersion statistics using classification and regression-tree methods. 

Foster et al. (2017b) follow a different approach and address imputation by dropping 

observations with imputed data and reweighting the remaining observations. The results from

these studies suggest that imputation yields lower measured dispersion relative to the case when 

imputation is corrected for. For the purposes of this paper, we consider the entire set of 

observations in the sample and leave further analysis of these issues for future work.

3. Comparing Micro-Aggregated Data to Published Industry Data

In this section, we compare our micro-aggregated estimates to the official data published 

by BLS, covering the 1997–2016 period. Based on earlier work comparing similar business data 

across the two government agencies, we expect that there will be some systematic differences 

between these measures (Elvery et al., 2006). Even though differences in the levels of the micro 

and published first moments do not directly affect our conclusions about dispersion (because we 

sweep out industry-year effects), it is useful to determine how far apart the two sets of estimates 

are. If the first moments are close, then it is more reasonable to think of micro-based second 

moments as measuring variation around the published first moments. As an additional check, 

we compare these two sets of estimates to data from the NBER-CES database. The NBER-CES 

database is used only for comparisons and should be thought of as equivalent to the official 
12

published ASM and CM statistics upon which it is based.20 We start by comparing input and 

output measures, and then we compare productivity measures. 

3.1. Input and Output Measures

Figure 1 shows the total number of employees in the manufacturing sector from the 

different series. The first thing to note is that employment levels based on ASM microdata 

(using ASM sample weights) are significantly lower than the published ASM and BLS estimates 

because they exclude the “non-mail” stratum—small establishments that are not sampled by the 

ASM. The published ASM series includes adjustments for the non-mail stratum and is much 

closer to the BLS estimates. 

To account for these small out-of-scope establishments, we construct an alternative set 

of weights. As noted, the weighted sample total calculated from the ASM (using ASM sample 

weights) is by design not equal to the published total because there are additional adjustments in 

the latter for the non-mail cases. Fortunately, there are some very small establishments in the 

ASM sample each year that are below the thresholds for non-mail cases. This occurs because, 

among the smaller establishments that were selected for the ASM (that is, establishments with 

employment above the threshold), some had fallen below the size threshold by the time that 

they provided data. This implies that there is coverage for all business sizes in the ASM sample 

(e.g., there are ASM establishments in any given year and industry with 1–4 employees even 

though this is typically below the ASM sample threshold). To create an alternative set of 

weights, we use the LBD. Specifically, we define the manufacturing universe using the LBD,

and use LBD data to estimate the probability that an establishment is included in the ASM 

sample, and then use these probabilities to construct inverse propensity score weights (see the 

Appendix for a full discussion of the weighting procedures). This procedure increases the 

 

20 For more information on the NBER-CES Manufacturing Industry Database, see http://www.nber.org/nberces/. 

The NBER-CES series was last updated through 2011 as of September 15, 2020.
13

weights assigned to the “non-mail” establishments so that the propensity-score-weighted (PSW 

hereafter) employment totals are consistent with the LBD.21 Moreover, as can be seen in Figure 

1, the micro-aggregated employment series using PSW yields totals that align with the 

published BLS and ASM more closely than those using ASM weights.

22 This aligns with our 

objective in using PSW as these weights correct for the contribution of the “non-mail” 

establishments in a manner that the ASM weights are not designed to address. 

We next compare total manufacturing output and input growth between the BLS series, 

the CMP–PSW series, and the NBER series (Figure 2).

23 For all three series, we use the BLS 

price deflators for these comparisons, with the exception of capital because BLS does not have 

separate deflators for equipment and structures. We also adjust the BLS output series to make it 

comparable to what we can construct from the ASM by adding the value of intrasectoral 

transactions back into the BLS output series. The BLS and NBER output series track each other 

very closely, while the CMP series deviates from the other two series in some years but exhibits 

the same pattern of growth rates, see Panel (a). Panel (b) compares hours growth rates: the 

growth rates of hours exhibit similar dynamics, except for during the 2005–2007 period, when 

the NBER series diverges. Panel (c) shows capital stock growth rates. All three series exhibit a 

slight downward trend in the late 1990s and are essentially flat starting in the early 2000s. The 

greater year-to-year variation in the CMP series is a due largely to the difficulty of 

implementing the PIM at the establishment level (see below for further discussion). Panels (d) 

and (e) show that for energy and material inputs the three series track very closely.24 

 

21 In addition, unreported results suggest that PSW do a good job matching the industry/year-specific size and age 

distributions of the LBD.

22 We explored the possibility of benchmarking CMP employment (based on the manufacturing universe in the 

Census Business Register) to BLS employment (based on the manufacturing universe in the BLS Quarterly Census 

of Employment and Wages). While this benchmarking, by definition, improves the correlation between labor 

(employment and hours) measures between BLS and CMP, it actually decreases the correlation between BLS and 

CMP output and measures of other inputs, which are both based on the manufacturing universe in the Census 

Business Register.

23 See Appendix A Table A1 for further details about the construction of these series.

24 The cost of purchased services and resales are not included in the materials comparisons.
14

Table 1 shows correlations between the three data sources for inputs and output for the 

total manufacturing sector. The correlations in the top panel are based on total manufacturing 

aggregate time series, while the bottom panel shows the average of the within-industry 

correlations for 4-digit NAICS industries, calculated over the 19 years of the sample. The top 

panel of the table indicates that hours, energy, materials, and output, both in levels and growth 

rates, are highly correlated across the data series (the correlations range from 0.88 to 0.99). 

Average industry-level correlations, shown in the bottom panel, are lower than for total 

manufacturing, but they are still reasonably high for these variables, both in levels and growth 

rates. 

The correlation between the capital series is significantly lower than the correlations 

described above. There are several possible explanations. First, there is a fundamental 

difference in the underlying data. In particular, BLS investment data for 4-digit industries 

combine expenditures on structures and equipment from the ASM with data on investment in 

different types of assets by industry from BEA and the Annual Capital Expenditure Survey 

(ACES). Using a perpetual inventory method, BLS then computes industry capital stocks from 

these investment flows. In contrast, our approach takes investment flows directly from the 

establishment and uses these flows with the perpetual inventory method at the plant level to 

generate capital stocks. Second, given the difference in source data, the BLS investment series 

covers a longer period of time than the micro-aggregated series. The BLS capital stock is built 

up from investment flows that stretch back to 1958 (and longer for some assets). For CMP, we 

initialize new plants using book value, and the earliest book value and investment data that we 

use dates back to 1972. Despite differences in data sources and methodologies, we can conclude 

that the micro-aggregated data are largely consistent with published aggregate data.

3.2. Productivity Growth
15

We calculate productivity growth as the change in the log-productivity for output per

hour and multifactor productivity.

25 Figure 3(a) shows that output-per-hour growth rates for the 

manufacturing sector are broadly similar, with some greater discrepancies in various subperiods 

(e.g., 2003–2009). These differences can be attributed to the differences in data sources and 

methodologies, some of which were illustrated in Figure 2. Despite underlying differences, 

multifactor productivity growth shows remarkable similarity across these data sources, see 

Figure 3(b). Table 2 echoes these findings: the correlations between the series of different data 

sources are highest for multifactor productivity growth.

This comparison of inputs, output, and productivity serves as an important backdrop to 

our new experimental statistics on within-industry dispersion. Although there are some 

differences between the BLS aggregates and the micro-aggregated series, they are close enough 

to each other to allow us to make meaningful inferences about the relationship between withinindustry dispersion and BLS published estimates of industry productivity growth. 

4. Productivity Dispersion

For our analysis of productivity dispersion, we focus on levels rather than growth rates. 

Since we are interested in comparing within-industry dispersion of productivity across 

industries and over time, it is necessary to account for industry differences in average 

productivity. To do this, we calculate establishment-level productivity as the deviation from 

average productivity in that establishment’s 4-digit industry in each year.

26 The interpretation of 

normalized productivity levels is intuitive: they tell us how far above or below the mean the 

establishment sits in the productivity distribution.

 

25 The official BLS productivity series are calculated using percentage changes in the index, and thus the BLS 

series that we refer to here differs from the published series. Additionally, the official total manufacturing 

productivity series is published by the BLS Division of Major Sector Productivity, whereas the data here are 

aggregated from industry data provided by the BLS Division of Industry Productivity Statistics. 

26 These are weighted averages (using our propensity score weights, see appendix) where establishment-level 

productivity is expressed as a deviation from average productivity in that establishment’s 4-digit industry. This 

normalizes productivity across industries and thereby accounts for industry differences in average productivity. 
16

We use the interquartile range (IQR) as our primary measure of dispersion, because it is 

intuitive and easy to interpret. The IQR shows how much more productive an establishment at 

the 75th percentile of the productivity distribution is than an establishment at the 25th percentile

of the productivity distribution. The standard deviation may seem like an obvious alternative to 

the IQR, but, in addition to being harder to interpret, it is known to be more sensitive to outliers

than quantile-based dispersion measures. We also report the 90-10 differential as well as the 10-

1 and 99-90 differentials. 

Table 3 shows the descriptive statistics of the distribution of dispersion measures.

27 The

first entry in the table (0.898) says that in the average industry and year, establishments at the 

75th percentile are about (e

0.898≈) 2.45 times as productive as those at the 25th percentile. 

Establishments in the 90th percentile are about 5.9 times as productive as those at the 10th

percentile. Average dispersion in multifactor productivity is lower.28 Still, establishments at the 

75th percentile are about 1.7 times as productive as those at the 25th percentile using multifactor

productivity measures. This still implies substantial differences in a core measure of business 

performance at the establishment-level within narrowly-defined industries.

Many factors may underlie the observed dispersion in measured productivity across 

establishments in the same industry.29 We define a “wedge” as any mechanism that prevents 

equalization of marginal revenue products across producers. Because the measures of 

productivity dispersion reported here are revenue-based, the presence of widespread dispersion 

is consistent with the presence of some form of wedges. One form is adjustment frictions that 

inhibit businesses from adjusting their scale of operations and specific inputs to changing 

economic conditions. These adjustment frictions may be related to the costs of adopting new 

 

27 We present standard deviations in Table 3 but do not discuss these results.

28 The range for output per hour is somewhat larger than those found by Syverson (2004a)—he found a multiplier 

of about 1.9—but our findings are generally in line with his results.

29 See Syverson (2011) for more detailed discussion of these issues and Blackwood et al (2020) with discussion 

more closely related to the new data product. 
17

technologies or business practices; thus, dispersion in an industry may reflect the gap between 

the frontier establishments and other producers. Additional sources of wedges are market 

distortions such as differences in markups across producers or financial constraints in the same 

industry. Complicating matters is that in the presence of wedges that are correlated with 

fundamentals, the variation in the dispersion will also reflect differences in business 

fundamentals such as technical efficiency and product appeal across businesses, see Blackwood 

et al. (2020). Adjustment frictions are one source of wedges that yields such a correlation. For 

example, an increase in the dispersion in product appeal across producers in the presence of 

adjustment frictions will yield an increase in dispersion of revenue productivity across 

producers (even if the adjustment frictions remain constant). In a similar fashion, dispersion 

may reflect unmeasured inputs. These could include production methods, management 

practices, and the mix of worker types (labor quality). 

It is well beyond the scope of the current paper to determine the relative importance of 

each of these alternative factors. Instead, the objective here is to describe the DiSP data product

and point to its potential for investigating these alternative determinants of dispersion. One of 

the strengths of the new data product is that dispersion measures are provided at a detailed level 

of aggregation by year. Figure 4a summarizes how within-industry dispersion in output per 

hour—measured as the IQR—varies across industries and over time. The mean and median IQR 

are fairly close to each other, but the large differences between the 25

th and 75th percentiles 

indicate that there is a lot of variation in the IQR across industries. For example, in 2002, the 

productivity difference between establishments at the 75th and 25th percentiles is about 100 log

points in the industry at the 75th percentile of the IQR distribution, while this difference is 

approximately 70 log points in the industry at the 25th percentile of the IQR distribution. These 

findings are confirmed by multifactor productivity dispersion, with IQRs of approximately 60 

and 40 log points at the 75th and 25th percentiles, respectively (see Figure 4b).
18

The differences in IQRs suggest that there are factors such as those discussed above 

that generate “dispersion in dispersion,” including differences in shocks, adjustment costs,

distortions, technology, and distributions of capital intensities. In addition, dispersion is rising 

during the period under investigation, more so for multifactor productivity than for labor 

productivity. The rising trend suggests that wedges, and the dispersion in business fundamentals 

underlying the observed dispersion, are changing in systematic ways over time.30 We can also 

see from Figure 4 that although the volatility of (the mean) dispersion is non-trivial, it is 

dwarfed by the variation across industries. Table 4 shows that there is substantial churning in the 

ranking of industries in terms of their dispersion. This finding highlights that not only is there 

dispersion in dispersion but the cross-sectional variation across industries varies over time.

For the remainder of this section, we consider two extensions to our analysis to 

illustrate further the nature of the dispersion. We first examine how our results change when we 

weight establishments using activity weights. Activity weights are generated by multiplying our 

PSWs by an activity measure such as employment or hours. Activity weighting paints a 

potentially different picture of dispersion because there may be differences between the 

dispersion of different size groups.

31 Our second extension is to examine the tails of the 

productivity distribution. There has been great interest in the finding that a substantial portion of 

wage inequality is driven by the upper tail of the distribution and by increasing betweenestablishment wage differentials. Investigating the upper tail of the productivity distribution is 

analogously interesting, as theory and evidence show that the productivity and earnings 

distributions are related. 

 

30 There is an ongoing debate about the source of the rising dispersion in revenue productivity measures. See, e.g., 

Bils et al. (2020), Blackwood et al (2020) and Decker et al. (2020). We do not seek to directly address that debate 

here but note that Decker et al. (2020) find that rising (revenue-based) labor productivity dispersion in 

manufacturing is present in both the ASM survey data used here and in administrative data from the Business 

Register. This finding suggests that rising measurement error is not driving the rising dispersion. 

31 For example, employment-weighted distributions tell us about the productivity of a worker at a given percentile, 

where the productivity of a worker is the average productivity of the establishment where he or she works. 
19

4.1. Activity-Weighted Dispersion Measures

Figure 5 replicates the dispersion measures in Figure 4 using propensity score weights 

that have been reweighted using activity weights, which we will refer to as “activity-weighted” 

or simply “weighted” distributions. For output per hour, the activity weights are defined by 

hours shares (the share of a given plant’s hours of the total hours in its industry) while for 

multifactor productivity they are defined by composite input shares. The main difference 

relative to previous results is that activity-weighted dispersion is smaller and exhibits less yearto-year variation. These findings suggest that although dispersion seems smaller among large 

establishments, it has been rising over the period under investigation, and is likely to be the 

main driver behind the increase in the mean IQR. 

4.2. Dispersion in the Tails

Turning to the tails of the productivity distributions, a distinctive feature of the withinindustry productivity distribution is that mean and median dispersion in the right tail (the 99-to90 ratio) are about the same order of magnitude as the mean and median dispersion in the center 

of the support as measured by the IQR (see Figure 6). This is remarkable given that each tail 

covers only one-fifth as many establishments as the IQR. Comparing Figure 6a to Figure 4a, 

output per hour differences among the most productive establishments are slightly lower than 

differences among those around the average. In contrast, multifactor productivity differences 

among the most productive establishments are larger relative to those in the center of the 

support. In addition, these differences in the right tail of multifactor productivity are rising 

faster: the mean indicates that dispersion in the right tail rose by about 40 log points between 

1997 and 2016 (compare Figures 6b and 4b). The weighted dispersion measures (Figure 7) 

show generally similar patterns but a smaller absolute increase. Also, it is notable that

dispersion in dispersion is substantial in the right tail. 
20

In contrast to the right tail, the left tail (the 10-to-1 ratio) exhibits lower dispersion 

relative to the center. In particular, mean output-per-hour differences among the least productive 

establishments are 20–30 log-points smaller relative to the set of establishments in the middle, 

though exhibit similar volatility (see Figure 8a). Mean multifactor productivity differences in 

the left tail are similarly smaller initially than in the center and exhibit no positive trend, see 

Figure 8b.

32 The weighted dispersion measures (Figure 9) tell a similar story.

These findings highlight the importance of looking at the entire distribution. The IQR is 

a convenient measure that covers half of the distribution. However, there is generally

comparable dispersion in the upper and lower tails as there is in the middle. We also see that 

weighting matters: accounting for size tends to reduce both productivity dispersion and its 

volatility.

4.3 Establishment and Firm Characteristics and Within-Industry Dispersion

Many factors may underlie the substantial dispersion in productivity measures across 

establishments within the same industry as well as the variation in the dispersion measures 

between measures over time. To provide more guidance on the potential driving forces, we 

examine the relationship between productivity and observable establishment characteristics. 

For this purpose, we examine spatial variation (by state), establishment size and age. 

Table 5 shows R2and p-values from F-tests from regressions of establishment-level 

productivity on individual observable establishment characteristics. The first entry of the table 

shows that the variation across 4-digit NAICS industries explains approximately 34 percent of 

the overall variance in establishment-level log output per hour. The explanatory power of the 

other characteristics is similarly significant, but an order of magnitude smaller. The implications 

 

32 The spike in mean dispersion in 1998 is due to transitory changes in the following 4-digit NAICS industries:

3344, 3345, 3341, 3342 and 3351. In these industries, the least productive establishments shifted to the left in 1998 

and then back to right in 1999. The significant changes in production technologies in these industries (factoryless 

manufacturing and offshoring) may explain these transitory dynamics in these years.
21

for MFP are similar, see the lower panel of Table 5. In the right panel of Table 5, we control for 

industry and time variation by removing industry and year effects from the productivity 

measures and find similar results. Our results suggest that differences in size, age, location, time

or even industry classification account for only a fraction of the observed differences in the 

productivity levels across establishments. Further research is necessary to uncover the 

contribution of other factors and our hope is that the DiSP data product will prove useful in this 

regard.

4.4 Description of the Dispersion Statistics on Productivity (DiSP) Data Product 

The new data product, Dispersion Statistics on Productivity (DiSP), which will be 

updated by the two agencies on an annual basis,

33 contains a balanced panel of productivity 

statistics summarizing the within-industry distributions of output per hour and multifactor

productivity.

34 Dispersion statistics include standard deviations, interquartile and interdecile 

ranges of the within-industry distributions of plant-level productivity. All data moments are

frequency weighted; see sections 2.2 and Appendix B.2. In addition, the dataset includes

activity-weighted versions of dispersion measures. The 99-to-90 and 10-to-1 ranges are 

currently under consideration for future releases given the interesting patterns in the right and 

left tails highlighted above.

The data product will be useful in analyzing the relationships between productivity 

dynamics at the plant-level, industry-level and for the entire manufacturing sector. As discussed 

above, many factors may underlie the cross-industry and time-series variation in dispersion. We

anticipate that this new data product will facilitate our understanding of the connection between 

 

33 The timeliness of the data depends on the release of establishment- and firm-level information. In non-Census 

years, the ASM is available in the fall of the subsequent year, while the LBD becomes available in spring of the 

year after. In Census years, microdata become available later. The productivity dataset can be created 

approximately 2–3 months after the underlying microdata becomes available.

34 See both BLS and Census Bureau websites: https://www.bls.gov/lpc/productivity-dispersion.htm and 

https://www.census.gov/disp.
22

micro- and macro-level productivity. A key benefit of making these data available will be to 

allow researchers without access to the confidential microdata to explore the various possible 

causes—and effects—of the differences in within-industry dispersion across industries and over 

time.

5. Concluding Remarks

A growing literature uses micro-level data to examine establishment-level productivity 

dynamics and finds substantial within-industry productivity dispersion. This paper provides an 

overview of a new data product, Dispersion Statistics on Productivity (DiSP), released jointly 

by BLS and the Census Bureau. This new data product provides measures of productivity 

dispersion within narrowly defined industries by year. 

Much of the paper discusses the measurement methodology used to produce this data 

product. We compare inputs and output aggregated from micro-level data, to BLS aggregates at 

the industry and manufacturing-wide level that are part of the official industry and 

manufacturing-level productivity statistics produced and released by BLS. Not surprisingly, we 

find some differences between BLS industry-level data and micro-aggregated ASM data; 

however, in general, we find high correlations between BLS and micro-aggregated outputs and 

inputs (for example, at the total manufacturing level the correlation between the BLS published 

series and the micro-aggregated data for output and hours growth are both about 0.9). 

Using measures of inputs and output, we develop measures of labor productivity (output 

per hour) and multifactor productivity and examine some of their properties. Correlations 

between BLS and micro-aggregated labor productivity growth are also reasonably high and 

especially high for multifactor productivity growth (e.g., at the total manufacturing level the 

MFP growth correlation is 0.94). 

Illustrating the properties of the new data product, we find large within-industry 
23

dispersion in labor productivity: establishments at the 75th percentile are about 2.4 times as 

productive as those at the 25th percentile on average. For multifactor productivity, we find that 

the analogous ratio is 1.7. These patterns indicate enormous differences in measures of business 

performance across plants in the same narrowly defined industry and year. Differences might 

stem from many factors but they highlight both great potential for growth (e.g., if the gaps 

between high- and low-productivity businesses could be reduced) and also possible sources of 

frictions or distortions that are impeding a more efficient allocation of resources. 

A core feature of the DiSP data product is the release of measures of within-industry 

productivity dispersion by detailed industry. We find significant dispersion in within-industry 

dispersion across industries. For the top quartile of industries, the ratio of multifactor

productivity across plants implied by the IQR exceeds 1.7 while for the bottom quartile of 

industries the ratio is lower than 1.4. Dispersion in dispersion over time is small by comparison, 

but it is likely still important. There is rising dispersion in both labor productivity and 

multifactor productivity, which is the source of ongoing debate in the academic literature.

Our results also indicate that average dispersion depends on where we measure it: 

average dispersion is greater as we move further away from the center of the support of the 

within-industry productivity distribution. Specifically, average productivity differences across 

establishments are largest in the right tail. Similar to what we find for average dispersion, the 

dynamics of these measures depend on where we measure productivity differences. We find

evidence that dispersion among the most productive establishments has been increasing during 

our sample period, while differences in the left tail do not show these patterns. This suggests 

that positively trending dispersion found in earlier studies may be a consequence of the 

dynamics of the most productive establishments. Our analysis suggests these patterns are 

sensitive to how dispersion is measured. We find that activity weights generally imply smaller, 

less volatile productivity differences among establishments in the entire distribution. We also 
24

find that, on average, weighted dispersion among more productive establishments shows a more 

pronounced positive trend.

In future work, we plan to explore extending the data product in a number of directions. 

As noted, one active area of exploration is releasing statistics on the tails of the productivity 

distribution. Another area of exploration is to release statistics by additional characteristics such 

as firm age and firm size. Research has shown that young businesses exhibit especially high 

productivity dispersion. This may reflect greater experimentation by young businesses as well 

as greater challenges that young businesses face in changing their scale of operations. 
25

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28

Figure 1. Manufacturing Employment Levels, 1997–2016

Source: “BLS-Employees” is the annual average of the not seasonally adjusted employment in 

manufacturing [CEU3000000001, Current Employment Statistics program]. “ASM Published” 

is the published aggregate employment series from the ASM. CMP denotes micro-aggregated

series using the ASM: CMP-ASM Sample Weighted total employment is calculated using 

ASM sample weights. CMP-Propensity Score Weighted total employment is calculated using 

our estimated inverse propensity score weights.
29

Figure 2. Manufacturing Output and Inputs, 1998–2016

a) Output

 

b) Hours

c) Capital
30

d) Materials

e) Energy

Source: “BLS” is the authors’ calculations from Industry Productivity Program data. “CMP – Propensity 

Score Weight” is the authors’ calculations on the ASM. “NBER” is the authors’ calculations on 

the NBER database 
31

Figure 3. Productivity Growth over Sources and Measures, 1998–2016

a) Output per hour

b) Multifactor productivity

Source: See the notes to Figures 2.
32

Figure 4. Distribution of IQR of Productivity, 1997–2016 

(a) Output per hour

(b) Multifactor productivity

Source: Authors’ calculations on the ASM. Notes: Within-industry productivity moments are created at 

the 4-digit NAICS level, weighted by our propensity score weight. Annual descriptive statistics 

of industry dispersion are unweighted.
33

Figure 5. Distribution of Weighted IQR of Productivity, 1997–2016

(a) Output per hour (hours-weighted)

(b) Multifactor productivity (composite-input-weighted)

Source: See notes to Figure 4.
34

Figure 6. Distribution of 99-90 Difference of Productivity, 1997–2016

(a) Output per hour

(b) Multifactor productivity

Source: See notes to Figure 4.
35

Figure 7. Distribution of Weighted 99-90 Difference of Productivity, 1997–2016

(a) Output per hour (hours-weighted) 

(b) Multifactor productivity (composite-input-weighted)

Source: See notes to Figure 4.
36

Figure 8. Distribution of 10-1 Difference of Productivity, 1997–2016

(a) Output per hour

(b) Multifactor productivity

Source: See notes to Figure 4.
37

Figure 9. Distribution of Weighted 10-1 Difference of Productivity, 1997–2016

(a) Output per hour (hours-weighted)

(b) Multifactor productivity (composite-input-weighted)

Source: See notes to Figure 4.
38

Table 1. Input and Output Correlations between BLS, CMP, and NBER (1997–2016)

BLS/CMP BLS/NBER CMP/NBER

Total Manufacturing

Hours worked, levels 0.986 0.994 0.996

Hours worked, growth 0.930 0.909 0.923

Capital, levels 

-0.184 0.880 0.328

Capital, growth 0.330 0.643 0.585

Energy, levels 0.977 0.997 0.978

Energy, growth 0.958 0.985 0.948

Materials, levels 0.931 0.996 0.963

Materials, growth 0.858 0.992 0.880

Output, levels 0.945 0.996 0.961

Output, growth 0.894 0.993 0.926

Average of 4-Digit NAICS

Hours worked, levels 0.803 0.889 0.883

Hours worked, growth 0.457 0.632 0.599

Capital, levels 0.521 0.714 0.489

Capital, growth 0.265 0.565 0.263

Energy, levels 0.861 0.986 0.841

Energy, growth 0.714 0.714 0.709

Materials, levels 0.837 0.962 0.843

Materials, growth 0.659 0.937 0.661

Output, levels 0.838 0.985 0.850

Output, growth 0.676 0.951 0.675

Source: Authors’ calculations on the ASM.

Table 2. Productivity Growth Correlations between BLS, CMP, and NBER (1997–2016)

BLS/CMP BLS/NBER CMP/NBER 

Labor productivity (Total Manufacturing) 0.705 0.818 0.735

Labor productivity (Average of 4-Digit NAICS) 0.465 0.619 0.660

Multifactor productivity (Total Manufacturing) 0.935 0.991 0.960

Multifactor productivity (Average of 4-Digit NAICS) 0.786 0.896 0.810

Source: Authors’ calculations on the ASM.
39

Table 3. Summary of Within-Industry Productivity Distributions (1997–2016)

Within-Industry productivity moment Mean Standard 

deviation

IQR

Labor Productivity

IQR 0.898 0.290 0.322

90-10 differential 1.773 0.476 0.613

Standard deviation 0.684 0.167 0.222

99-90 differential 0.732 0.279 0.333

10-1 differential 0.550 0.267 0.275

Multifactor productivity

IQR 0.520 0.222 0.205

90-10 differential 1.078 0.393 0.371

Standard deviation 0.460 0.152 0.161

99-90 differential 0.866 0.512 0.546

10-1 differential 0.301 0.181 0.153

Source: Authors’ calculations on the ASM.

Notes: Log labor productivity is calculated as log (output/hours) where hours are BLS-adjusted total 

hours. The 4-digit NAICS industry mean log LP is subtracted off establishment-level log LP. Withinindustry productivity moments are created at the 4-digit NAICS level using propensity score weights. 

Annual summary statistics of these industry statistics are then created weighting each industry equally. 

The numbers shown are means of the annual summary statistic values from 1997–2016 weighting each 

year equally.
40

Table 4. Probability of Transition across Quintiles of the Cross-Industry Distribution of Dispersion 

(annual averages between 1997 and 2016)

IQR IQR (Activity weighted)

Output per hour

1 2 3 4 5 1 2 3 4 5

1 0.63 0.24 0.08 0.03 0.01 1 0.70 0.22 0.06 0.01 0.00

2 0.23 0.41 0.22 0.10 0.02 2 0.22 0.49 0.24 0.04 0.00

3 0.10 0.25 0.41 0.25 0.03 3 0.06 0.25 0.56 0.15 0.01

4 0.03 0.08 0.25 0.44 0.19 4 0.01 0.04 0.14 0.65 0.15

5 0.01 0.03 0.03 0.18 0.74 5 0.00 0.00 0.01 0.15 0.84

Multifactor productivity

1 2 3 4 5 1 2 3 4 5

1 0.64 0.23 0.07 0.04 0.01 1 0.75 0.19 0.03 0.01 0.01

2 0.22 0.42 0.28 0.05 0.02 2 0.19 0.53 0.21 0.05 0.00

3 0.08 0.26 0.40 0.26 0.04 3 0.03 0.24 0.53 0.20 0.03

4 0.04 0.08 0.20 0.47 0.18 4 0.02 0.02 0.20 0.56 0.17

5 0.01 0.02 0.05 0.16 0.75 5 0.01 0.01 0.03 0.17 0.79

Source: Authors’ calculations on the ASM. Rows index quintiles in t-1, columns index quintiles in t.

Probabilities in each table are normalized by column sums, i.e. column elements sum to one, apart from 

rounding.
41

Table 5. Relationship between Productivity and Establishment Characteristics, 1997–2016

Characteristic R

2 Pr > F R2 Pr > F

LogLP LogLP (demeaned)

naics4 0.340 <.0001

year 0.030 <.0001

fipsst 0.010 <.0001 0.0032 <.0001

sizeclass 1 0.020 <.0001 0.0117 <.0001

sizeclass 2 0.022 <.0001 0.0131 <.0001

sizeclass 3 0.023 <.0001 0.0139 <.0001

ageclass 0.013 <.0001 0.0073 <.0001

LogMFP LogMFP (demeaned)

naics4 0.370 <.0001

year 0.002 <.0001

fipsst 0.020 <.0001 0.0062 <.0001

sizeclass1 0.010 <.0001 0.0042 <.0001

sizeclass2 0.012 <.0001 0.0045 <.0001

sizeclass3 0.011 <.0001 0.0044 <.0001

ageclass 0.001 <.0001 0.0009 <.0001

Source: Authors’ calculations on the ASM. LogLP: log labor productivity, LogLP (demeaned): log labor 

productivity, industry and year effects are removed, LogMFP: log multifactor productivity, LogMFP 

(demeaned): log multifactor productivity, industry and year effects are removed, naics4: 4-digit NAICS 

code, year: time identifier, fipsst: Federal Information Processing Standard state code, sizeclass 1: 

employment size class with thresholds 25, 50, 100, and 150, sizeclass 2: employment sizeclass based on 

deciles, sizeclass 3: employment sizeclass with thresholds 20, 50, 100, 250, and 500, ageclass: 

establishment age class with thresholds 1, 2, 3, 4, 5, 10, and 15.
42

Appendix A

Table A1. Summary of Variables Used in Selected Tables and Figures

Table 1 

Correlations

Table 2 

Correlations

Table 3 

Dispersion

Figure 1 

Employment

Figure 2 

Hours

Figure 2 

Output

Figure 3 

Productivity

Comparisons

BLS implicit price 

deflator used for 

all estimates

(except for capital)

yes yes yes yes

Shipments deflator

used to deflate 

output

yes

Cost of resales 

(CR) removed 

from CMP

yes yes yes yes yes

Employees only yes yes N/A

Include BLS 

employees and 

self-employed

(SE) and unpaid 

family workers 

(UFW) in BLS 

data only

yes yes yes N/A yes

CPS 

nonproduction/pro

duction hours ratio 

(even for NBER 

hours)

yes yes yes yes yes

BLS intrasectorals 

included

yes yes yes yes
43

Appendix B

B.1. Properties of ASM samples

The ASM is a 5-year panel of roughly 50,000–70,000 manufacturing establishments. It 

is a sample of establishments drawn from the manufacturing portion of the Census Bureau’s 

Business Register using a probability proportional to size sampling scheme.

35 The largest 

establishments are sampled with certainty and are included in every panel.36 Smaller 

establishments are sampled with a probability less than 1, where the probability increases with 

establishment size (measured by shipments). The smallest single-unit establishments, which are 

part of the “non-mail” stratum, are not mailed a form but they are included in the estimates. Due 

to the desire to reduce reporting burden, the Census Bureau uses administrative records to 

impute payroll, employment, industry and location from the administrative data for the smallest 

single-unit establishments, while total value of shipments are imputed using industry averages.37

The ASM sample is refreshed every 5 years. New ASM panels are drawn from the 

Economic Census and begin 2 years after the Census from which it was drawn (years ending in 

4 and 9). The sample is also updated annually to include new establishments which are 

identified on the Census Bureau’s Business Register. The Business Register is updated with 

information from the Economic Census as well as administrative records from the IRS and the 

Census Bureau’s annual Company Organization Survey. 

Data for the ASM are collected in all years except for years ending in 2 and 7, when the 

 

35 More information about the ASM: http://www.census.gov/manufacturing/asm/.

36 Prior to 1999, certainty units were establishments with 250 or more employees. In 1999, the cutoff was increased 

to 500 employees, and in 2004, it was increased again to 1,000 employees. Currently, the 10 largest establishments 

in an industry are also sampled with certainty. In addition to establishment size, certainty criteria include other 

characteristics such as industry, cell size, or energy use. For example, Computers, Flat-glass, Sugar, and Small 

industries (with less than 20 establishments), or establishments with large inventories, assets, fuel/electric 

expenditures are also sampled with certainty.

37 Non-mail cases are included in the official estimates and have a weight of one. The survey is designed to tabulate 

cases from the mail and the non-mail component. The mail component was not designed to estimate the total 

population. 
44

ASM data are collected as part of the Economic Census. Data on payroll, employment, industry, 

and geography for establishments in the non-mail stratum are obtained from administrative 

records.

38

The ASM sample is designed to estimate unbiased national level estimates of a skewed 

population. For example, in the 2014 ASM panel, large establishments sampled with certainty 

account for approximately 72% of the total value of shipments in the 2012 Census of 

Manufactures; non-certainty establishments are sampled with probabilities from 0.05 to 1.00.39

This sample design implies that the establishment counts in various size bins may not reflect

those calculated from the LBD.

The ASM sample weights, which are inversely proportional to a shipments-based 

establishment size measure could, in principle, be used to correct for the effects of the ASM 

sample design. However, the sample design implies that the weighted sum of shipments from 

the mail stratum only will not match published totals.40

Another important aspect of the sample design is that the composition of establishments 

changes over time and between sample selections. Any weighting procedure aiming at creating 

unbiased estimates of productivity dispersion should account for the fact that the sampling 

probabilities, and therefore the composition of the ASM, change every 5 years. In addition, 

sampling and non-mail stratum thresholds vary across years. 

B.2. Establishment Characteristics and the Probability of Selection into the ASM

The ASM’s sample design has important implications for our analysis. For example, the 

sum of the ASM sample weighted employment or sales might equal total employment or total 

 

38 Federal regulations require the Census Bureau to limit survey response burden.

39 Source - ASM Methodology website, https://www.census.gov/programs-surveys/asm/technicaldocumentation/methodology.html (accessed September 16, 2020).

40 As mentioned above, only the mail component together with the adjustment for the non-mail stratum yields 

unbiased estimates of the total population. See Davis, Haltiwanger and Schuh (1996) for more details.
45

sales. However, it is not clear that the ASM sample weights are appropriate for our analysis. 

This section is devoted to describing our weighting procedure.

To address the effects of the ASM’s sample design, we construct propensity score 

weights using the Longitudinal Business Database (LBD). See Jarmin and Miranda (2002) for 

more details about the LBD. The propensity score weights are constructed from a logistic 

regression in which we model the relationship between plant characteristics and the probability 

that an establishment is selected into the ASM. We start by matching establishments in the ASM 

to LBD establishments by year and “LBD Number.”

41 Our dependent variable is a dummy 

variable that equals one if the establishment is in both the ASM and the LBD for that year and 

zero if the establishment is only in the LBD. For establishments in the non-mail stratum, the 

dummy variable is set to 0.

The set of regressors consists of dummy variables that classify each establishment based 

on its employment and payroll size class, whether the establishment is part of a multi-unit entity, 

the establishment’s industry code, and the interaction between industry and employment size 

effects. Including industry-size interactions allows us to estimate industry-specific size 

distributions. These variables are obvious candidates for our logistic regressions because the 

probability of selection into the ASM sample and the cutoff for the non-mail stratum in the 

ASM vary by industry and size. 

When determining weights, we define industries at the 3-digit NAICS level because the 

interaction of size indicators and more narrowly defined industry codes leads to empty cells in 

smaller industries. Empty-size bins imply that the size distribution cannot be estimated in these 

industries.

42 When the size distribution cannot be estimated for an industry, propensity scores 

 

41 The LBD Number is an establishment identifier that is consistently defined across both datasets. Although 

linking the datasets by LBD Number is straightforward, a small percentage of establishment-year observations do 

not match due to timing issues between the ASM and the LBD.

42 The size distribution cannot be estimated if all establishments are in the same size bin.
46

cannot be calculated because maximum-likelihood estimates of the size effects do not exist. 

Empty cells can, in principle, be avoided by collapsing size bins, combining similar narrowly 

defined industries, or allowing bin definitions to vary across industries. We experimented with 

the number and definition of the size bins and the level of industry aggregation and found that 

using 3-digit industry codes together with 4 size bins allows us to estimate the size distribution 

in every industry and year. Allowing for more heterogeneity by using either industry-specific 

size bins or more narrowly defined industries leads to feasibility problems with the logistic 

regression.

We defined the size bins so that the resulting distribution allows the lowest size bins to 

vary over time. That is, in every year and every industry, the 50th percentile of establishments 

with fewer than 50 employees is used to define bins 1 and 2. For larger establishments, the 

following bins are defined: 50–99, 100–199, and 200+.43 There are 21 3-digit NAICS industries 

in the 2002 classification system, which results in 105 industry specific size distributions. We 

include a continuous size measure in order to allow the weights to vary within these cells. This 

is necessary to account for possible within-cell compositional changes. Adding 5 payroll classes 

and 2 groups related to multi-unit status increases the number of cells to 113.

44

The 2002 change in the industry classification system resulted in missing NAICS-2002 

codes for a nontrivial number of establishments in the LBD between 1997 and 2001. For 

example, the NAICS code is missing if an establishment exited prior to 2002. For these 

observations, we used imputed NAICS codes.45 From 2002 on, NAICS codes are available for 

all establishments in the LBD.

 

43 The payroll size classes are 0–200, 201–500, 501–1000, 1001–5000, 5001+.

44 If we were to use 4-digit industry, the number of cells would increase significantly. There are 86 4-digit NAICS

industries implying 86 different size distributions and 430 industry-size cells. Such an increase in the number of 

cells yields empty size bins in several industries.

45 NAICS codes are imputed using a method described in Fort (2013).
47

Our inverse propensity score weights generate employment counts that do a good job of 

matching the trends and cyclical variation in BLS manufacturing employment, but they do not 

match BLS levels. 

B.3 Comparison of Hours Measures

In this study, we use hours data from ASM, augmented with data from the CPS. 

However, for official estimates of productivity growth, BLS uses the CES as its main source of 

hours data. Although the CES and ASM are establishment surveys, the two surveys differ in 

which hours data they collect and how they collect it. The best information on these differences 

comes from studies completed in the early 2000s (Goldenberg and Willimack, 2003; and Fisher 

et al., 2001). These studies do a nice job of summarizing the differences between the two 

surveys and how those differences affect estimates of hours worked. In this appendix, we 

summarize that research and discuss the implications for comparing our estimates to published 

BLS estimates. 

There are some general differences between the two surveys that are worth noting. First, 

the ASM is an annual survey, whereas the CES is conducted monthly. As a result, the reference 

periods of the two surveys differ. The reference period for the CES is the pay period that 

includes the 12th of the month. The CES collects data on the total number of employees, hours 

for all employees since 2006, the number of production workers, production worker payroll and 

production worker hours. 

In contrast, the ASM has different reference periods for different data elements. For 

production worker employment, the ASM reference period is the pay period that includes the 

12th of the month in the months of March, May, August, and November. These quarterly reports 

are then averaged into an annual number. The ASM collects employment data for Other 

Employees only for the pay period that includes March 12th. The implicit assumption is that 

non-production worker employment does not vary much over the year. Total employment is not 
48

collected directly, but rather is equal to the sum of non-production worker employment in 

March and the annual average of quarterly production worker employment. 

Annual total employment in the two surveys can differ if there are seasonal patterns in 

production worker employment that are missed in the ASM’s quarterly reports or if there is a 

seasonal pattern to non-production worker employment. We examined this issue using monthly 

CES data. Specifically, we calculated the average employment for each quarter using CES data, 

and then calculated the ratio of average quarterly employment to CES employment in the ASM 

reference months (March, May, August, and November). The ratios were very close to 1, 

indicating that estimates of average annual employment are the same whether we use four 

quarterly reports or 12 monthly reports. 

There are greater differences in the hours data collected in the two surveys. First, the two 

surveys use different concepts. The ASM asks employers to report hours worked, whereas the 

CES collects hours paid. The main difference is that the CES hours data include holidays, 

annual leave, and sick leave that were paid but not worked. Thus, we would expect total annual 

hours reported in the ASM to exceed total annual hours in the CES. For productivity 

measurement, hours worked is the correct concept, which is why BLS adjusts the CES data 

using hours-worked-to-hours-paid ratios from the NCS. 

The two surveys also differ in how they ask respondents to report hours. The ASM asks 

respondents to report total annual production worker hours. The CES asks respondents to report 

total production workers for the pay period that includes the 12th of the month. The hours 

reports are converted to a weekly number using conversion factors that vary with the number of 

workdays in the month. Apart from the difference in concept, these two approaches to collecting 

hours data could result in different estimates of total annual hours. Research by Frazis and 

Stewart (2004) has shown that people work longer hours during the week that includes the 12th
49

of the month.46 This would lead to annual hours in the CES being higher than in the ASM and

would offset some of the difference due to the difference in concept. Neither survey collects 

hours data for non-production workers. As noted in the text, nonproduction worker hours are 

estimated using data from the CPS.

 

46 Their research examined the accuracy of CPS hours reports by comparing the CPS hours data to hours data from 

the American Time Use Survey (ATUS). Subsequent research by Eldridge et al. (2019) found differences in some 

years, but not in others.