Variance Estimation for Product Sales 

in the 2017 Economic Census: Utilizing 

Multiple Imputation to Account for 

Sampling and Imputation Variance

Matthew Thompson

Katherine J. Thompson

U.S. Census Bureau*

GASP! Workshop

August 24-25, 2018

*The views expressed in this presentation are those of the authors and not 

necessarily those of the U.S. Census Bureau

1
Economic Census Background

 Not strictly a census

 Multi-units and large single-units selected with 

certainty

 Small single-units sampled

2
Economic Census Background

Data Items Collected

“General Statistics”

 Examples: Total receipts, Annual payroll, and 1

st Quarter 

employment

 Complete universe created using administrative records 

and imputation

Product Sales

 Only asked of sampled establishments

 Sample weights used to account for non-sampled 

establishments

 Two types: broad and detail

 Final product sales estimates are produced by calibration 

to stratum-level receipt totals

3
Economic Census Background

Product Sales Data

4

Broad Product 1 Detail Product 1(1) Detail Product 2(1) Detail Product m(1)

Broad Product 2

Broad Product 3 Detail Product 1(3) Detail Product 2(3)

Broad Product k Detail Product 1(k) Detail Product 2(k) Detail Product n(k)

Total Receipts

●●● 

●●● 

●●● 
Research Challenges

 Dedicated Team 

 Short time frame ( 12-15 months)

 Relative inexperience of team members with variance 

estimation

 Magnitude of the problem

  1,000 industries and  8,000 products

 Historical data limitations

 Classification differences (to NAPCS)

 Collection differences (to electronic)

 Unit collection differences (from varied to $1,000)

5
Research Team

Research Team

•  1,000 industries

•  8,000 products

• Broad products

• Detail products

• Calibration Weighting (i.e., poststratification)

6
Research Team

Research Team

•  1,000 industries

•  8,000 products

• Broad products

• Detail products

• Calibration Weighting (i.e., poststratification)

7

Research Team

•  1,000 21 industries

•  8,000 Top 4 products

• Broad products

• Detail products

• Calibration Weighting (i.e., poststratification)
Research Evaluation

Perform simulation studies

 Two initial studies

 Sampling Variance (Recommend: FPBB)

 Variance Due to Imputation (Recommend: ABB)

 Final simulation of recommended method

 Recommendation: FPBB-ABB

8
Finite Population Bayesian 

Bootstrap (FPBB)

9

Sample

Size = nh

Pólya

Sample

Size= 

Nh − nh

Sample

Size = nh

Implicate

Size = Nh
Finite Population Bayesian 

Bootstrap (FPBB)

 Create an implicate by drawing Nh − nh

establishments from the sample with probability for 

the kth selection

ph,k =

wi − 1 +

li,k−1 Nh − nh

nh

Nh − nh +

kh − 1 Nh − nh

nh

 Add the Nh − nh selected establishments to the 

original sample to complete the implicate

10
Approximate Bayesian Bootstrap 

(ABB)

11

Donors

Recipients

FPBB 

Implicate

Recipients

Resampled 

Donors

FPBB-ABB

Implicate
FPBB-ABB

The FPBB-ABB estimate of variance is

V

 

final = V

 

samp +

1

B

V

 

imp

 V 

samp = 1 +

1

B

1

B−1

 b=1

B FPBBAVGb − AVG 2

 V 

imp = 1 +

1

C

1

C−1

 b=1

B c=1

C TOTb,c − FPBBAVGb

2

 B is the number of FPBB implicates 

 C is the number of ABB implicates

12
Implementation Team

Research Team

• 1,000 21 industries

• 8,000 Top 4 products

• Broad products

• Detail products

• Calibration Weighting (i.e., poststratification)

Implementation Team

•  1,000 industries

•  8,000 products

• Broad products

• Detail products

• Calibration Weighting (i.e., poststratification)

• “Non-donors”

• Zero Receipts cases

• Processing time 

13
Implementation Concerns

 Time 

 To prepare the system

 Variance Estimation run time

 Knowledge transfer from research team to 

production programmers and methodologists

 Inflexibility of existing systems

14
Implementation Team

15

Research

Team

Implementation 

Team

Common members (overlap)

• Overlap

• Research team leads

• SAS programmer

• Project Managers w/ functional requirements

• New members

• Subject Matter Experts

• Programmers

• Methodologists
Time & Knowledge Transfer

16
Time & Knowledge Transfer

17

SAS
Time & Knowledge Transfer

18

SAS

Programmer familiar with FPBB-ABB

methodology and participant in 

research team.
Time & Knowledge Transfer

19

New SQL
Time & Knowledge Transfer

20

Existing SQL
Time & Knowledge Transfer

21

Existing SQL

Utilizing existing program and test deck 

saved considerable development and 

testing time.
Time & Knowledge Transfer

22

New SQL
Inflexibility of Existing Systems

23
Inflexibility of Existing Systems

 Existing HDI process fixed:

 Imputation method by imputation cell – Random or NN

 Cell collapsing methodology

 Handling of detailed products

24
Conclusions

 Plan ahead – Involving potential implementation 

team members in the later phases of research 

can be a huge benefit

 Leverage existing resources – Give careful 

thought to areas where existing programs and 

data can be utilized

 Make sure existing systems are well documented 

and well understood.

25
Acknowledgments

Thanks to all of the members of the research 

and implementation teams.

Contact: matthew.thompson@census.gov

26