The Effects of Editing and Imputation on 

Measured Plant-level and Aggregate 

Productivity Growth in a Panel of U.S. 

Manufacturing Plants

Hang J. Kim, University of Cincinnati

Martin Rotemberg, NYU

T. Kirk White, U.S. Census Bureau

(Preliminary and Incomplete)

FCSM Research and Policy Conference, Washington, DC

October 25, 2022

1
The research presented here was conducted while the first two authors were Special Sworn 

Status researchers and the third author was an employee of the U.S. Census Bureau. Any opinions 

and conclusions expressed herein are those of the authors and do not reflect the views of the 

U.S. Census Bureau. The Census Bureau has reviewed this data product for unauthorized 

disclosure of confidential information and has approved the disclosure avoidance practices 

applied to this release (DRB approval number CBDRB-FY2022-CES020-003, DMS subproject 

number 7526913).

2
Plant-level Productivity and Data Cleaning

• Large economics literature uses Census Bureau’s plant-level 

manufacturing data to study productivity and productivity dynamics

• See, e.g., Bailey, Hulten, and Campbell (1992), Olley and Pakes (1992), Bartelsman and Doms

(2000), Foster, Haltiwanger, and Syverson (2008), Syverson (2011)

• Literature mostly ignores fact that large % of Census’s manufacturing 

data are imputed

• Data cleaning done by Census Bureau has huge impact on measured 

cross-sectional productivity dispersion

• White, Reiter and Petrin (2018), Rotemberg and White (2020)

• How does Census data cleaning affect measured productivity growth?

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What We Do in This Paper

• Start with unedited “captured” Annual Survey of Manufactures 

(ASM), 2009-2013

• Use Census Bureau’s edit rules

• Extend Bayesian simultaneous edit-imputation method of Kim, Cox, 

Kerr, Reiter, and Wang (2015) to panel data

• Compare estimates of aggregate productivity growth using:

• Data edited-imputed by Census Bureau

• Data edited-imputed by us using our Bayesian method

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The Annual Survey of Manufactures

• Plant-level survey conducted annually* 

• Sample size: about 50,000 plants

• Universe is U.S. manufacturing sector (about 300,000 plants)

• Certainty sample: 

• large plants, sampled every year

• Probability sample: 

• Small-to-medium plants, sampled with probability proportional to size

• 5-year rotating panels beginning in years ending in ‘4’ or ‘9’

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Variables in the ASM

• ASM 

• Collects (at plant-level) and publishes (at industry level) 55 plant-level 

variables 

• This paper: 

• We focus on 5 variables used for measuring productivity:

• Value of shipments

• Payroll 

• Employment

• Cost of materials

• Capital stock*

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Imputation Rates in the ASM

7

0

10

20

30

40

Value of Shipments Annual Payroll Cost of Materials

Imputation Rates by Variable 

2002-2010 average

% of Observations imputed

0

10

20

30

40

50

60

2003 2004 2005 2006 2007 2008 2009 2010

Imputation Rates for Productivity

ASM years only, 2003-2010

% of plants with imputed data for >=1 variable used to measure

productivity

Source: Foster, Grim, Haltiwanger, and Wolf (2017), table A7
ASM Editing and Imputation Comparison

What Census Bureau does What we do in this paper

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Uses within-year ratio edit rules

Uses year-to-year ratio-of-ratios edit rules

Edits-imputes one year at a time (prior-year data is 

fixed)

Fellegi-Holt editing algorithm (minimizes # of edits)

Uses hierarchy of imputation methods, e.g.,

• Administrative records substitution 

• Uni- or trivariate regression models

• Analyst corrections

Edit rules & imputation models same within NAICS6

Same

Same

Edit-impute 5-year panel simultaneously

Simultaneous Bayesian edit-imputation (chooses 

likeliest variable(s) to edit given the “good” data)

Use truncated Dirichlet Process mixture of normals to 

model joint distribution of 5x5 variables 

Edit rules & imputation models same within NAICS4
Types of ratio edit rules used in the ASM

• Cross-sectional:

XXXXBBjjjj ≤

XXii

YYii

≤ XXXXBBjjjj

• Longitudinal :

jj ≤

XXii

YYii

XXii , −1

YYii , −1

≤ jj

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Census Editing vs. Bayesian Edit-Imputation

(Note: Scatterplots are from Kim et. al (2015) synthetic data)

What Census Bureau does What we do in this paper

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Reported value 

lies outside editrule bounds
Census Editing vs. Bayesian Edit-Imputation

What Census Bureau does What we do in this paper

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Impute value on this line...
Census Editing vs. Bayesian Edit-Imputation

What Census Bureau does What we do in this paper

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...or on this line
Census Editing vs. Bayesian Edit-Imputation

What Census Bureau does What we do in this paper

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Take draws from 

multiple datadriven models of 

the joint 

distribution
Census Bureau Imputation

(includes imputation for non-response)

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Three Versions of ASM Data

• One “final” dataset edited-imputed by Census

• Two versions of data multiply-edited-and-imputed by us:

• “EI lax” data: 

• use the laxest of the ratio-edit bounds within each NAICS4 industry

• “EI strict” data: 

• use the strictest of the ratio-edit bounds within each NAICS4 industry

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Estimates from multiply imputed data

• For each of our models (“lax” and “strict”) and within industry:

• Run an MCMC with a burn-in of 3000 iterations

• Keep 10 implicates with 300 iterations between implicates

• For each implicate-year, estimate aggregate productivity growth

• Compute means and standard errors across implicates

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Aggregate Productivity Growth Rates (annual), 2009-2013 ASM,

Census Final vs. EI “lax” mean

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-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

2010 2011 2012 2013

final EI lax EI strict
Aggregate Productivity Growth Rates (annual), 2009-2013 ASM,

Census Final vs. EI “lax” mean vs. EI “strict” mean

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-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

2010 2011 2012 2013

final EI lax EI strict
Aggregate Productivity Growth Rates (5-year), 2009-2013 ASM,

Census Final vs. EI “lax” mean vs. EI “strict” mean

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-15%

-10%

-5%

0%

5%

10%

15%

20%

final EI lax EI strict
Aggregate Productivity Growth Rates (annual),

Census final vs. EI “lax” with 95% Confidence Intervals

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-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

2010 2011 2012 2013

final EI lax EI lax LB EI lax UB
Aggregate Productivity Growth Rates (annual)

Census final vs. EI “strict” with 95% Confidence Intervals

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-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

2010 2011 2012 2013

final EI strict EI strict LB EI strict UB
Preliminary Conclusions

• The choice of editing and imputation method has a huge effect on 

measured aggregate productivity growth (APG) in U.S. manufacturing

• Uncertainty of APG estimates due to imputation is also large

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Next Steps

• Model validation exercises (training & truth sets)

• Why such big differences between Census final vs. our EI APG measures?

• Are certain industries driving the results?

• Small plants with big survey weights and big growth rates?

• Look at the effect of editing and imputation on :

• Persistence of plant-level productivity (e.g., autocorrelation of TFPR)

• Variability of plant-level TFP “shocks”

• Labor productivity growth

• Association between TFPR and exit

• All of the above by, e.g., firm size

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References

• Foster, Lucia, Cheryl Grim, John Haltiwanger, and Zoltan Wolf. 2017. “Macro and Micro Dynamics 

of Productivity: From Devilish Details to Insights” NBER Working Paper 23666.

• Kim, Hang J., Lawrence H. Cox, Alan F. Karr, Jerome P. Reiter, and Quanli Wang. 2015. 

“Simultaneous Edit-Imputation for Continuous Microdata”, Journal of the American Statistical 

Association, Vol. 110, No. 511.

• Rotemberg, M. and T. Kirk White. 2020. “Measuring Cross-Country Differences in Misallocation” 

CES Working Paper CES-WP-16-50R. 

• White, T. Kirk, Jerome Reiter, and Amil Petrin. 2018. “Imputation in U.S. Manufacturing Data and 

Its Implications for Productivity Dispersion.” The Review of Economics and Statistics.

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