Differential Privacy 

for Economic Statistics

Margaret Beckom, U.S. Census Bureau

Anthony Caruso, U.S. Census Bureau

William Sexton, Tumult Labs

1

Any opinions and conclusions expressed herein are those of the author(s) and do not reflect the views of the U.S. 

Census Bureau. The Census Bureau has reviewed this data product to ensure appropriate access, use, and 

disclosure avoidance protection [Project No: P-7520953, Disclosure Review Board (DRB) approval number: 

CBDRB-FY23-ESMD002-035].
What will be covered...

• County Business Patterns (CBP) Background

• High-level Overview of Per-Record Differential Privacy (PRDP)

• Accuracy & Privacy

• Future Work

• Outstanding Research 

2
County Business Patterns (CBP)

A Brief Overview on the Program and Current Disclosure Avoidance Methodology

3
CBP Background

• Includes the following estimates

• Counts

• Establishments

• Magnitude

• Employment during the week of March 12

• First quarter payroll

• Annual payroll

• Data is useful for studying the economic activity in small areas

• Current methodology: multiplicative noise

• Applied only to magnitude data

4
A Look into Per-Record DP

How to handle heavy-tailed distributions

5
Objective: Accurately release key economic indicators from heavytailed distributions with modernized privacy protection.

Challenges:

• Differential privacy (DP) provides strong privacy protection but does not 

handle heavy-tailed distributions very well.

• “Per-Record” DP (PRDP) provides high data utility and formal privacy 

protection, but the privacy protection is not as strong as differential privacy.

6
The challenge of applying DP to the CBP: 

How many employees work in ZIP 89506?

7

Source: Google Maps

The example establishments do not imply presence in any Census Bureau database.
Hiding large 

establishments

8

8

Source: Google Maps

The example establishments do not imply presence in any Census Bureau database.
Hiding large 

establishments

9

9

Source: Google Maps

The example establishments do not imply presence in any Census Bureau database.
Overkill for small 

establishments

1

0

10

Source: Google Maps

The example establishments do not imply presence in any Census Bureau database.
Solution: Design a formal privacy framework that provides “sliding” 

protection to establishments.

Protection against “fact-of-filing”: adversaries should not be able to easily infer whether an establishment is represented in the CBP dataset.

Protection against exact inference: adversaries should not be able to deterministically infer exact attributes about an establishment, such as number of employees or annual 

payroll.

Protection for firms: the privacy properties of firms (i.e., collections of related establishments) should be inherited from the privacy properties of their individual 

establishments.

“Sliding” establishment protection: Allow the privacy guarantees to vary by establishment. In particular, allow privacy guarantees to degrade as the influence of an 

establishment grows.

11
Hide small establishments?

1

2

12

Source: Google Maps

The example establishments do not imply presence in any Census Bureau database.
Fully hide small 

establishments

1

3

13

Source: Google Maps

The example establishments do not imply presence in any Census Bureau database.
Hide large 

establishments?

1

4

14

Source: Google Maps

The example establishments do not imply presence in any Census Bureau database.
Split establishments into smaller pieces

1

5

15

Source: Google Maps

The example establishments do not imply presence in any Census Bureau database.
Split establishments into smaller pieces

1

6

16

Source: Google Maps

The example establishments do not imply presence in any Census Bureau database.
Group Privacy for ɛ-DP Algorithms

• ɛ-DP algorithm privacy guarantee extends to groups of size k

• When input databases differ by adding or removing up to k records:

• Output distributions are bounded by k x ɛ

17
PRDP for Establishments

• When input databases differ by adding or removing a particular 

record, r

• Output distributions are bounded by a function P(r) 

• With establishment splitting A followed by DP mechanism M

• P(r) = |A(r)| x ɛ where |A(r)| is the number of pieces record r gets split into

18
Data Utility Comparison

No establishment splitting

• Bias-variance trade off

• Outliers drive noise 

requirements

• Outliers dominate a large share 

of the aggregations

Establishment splitting

• No bias

• Noise requirements can be 

calibrated based on smaller 

establishments

19
Accuracy and Privacy

20
Accuracy and Privacy

• The tradeoff between accuracy and privacy remains.

Less privacy for establishments  More accurate estimates

More privacy for establishments  Less accurate estimates

• Challenge: Find a balance where quality is preserved, and all 

establishments are adequately protected.

21
Median CV of County x 3-Digit NAICS Annual Payroll 

Estimates by Standard Deviation of Noise and Cell Size

Standard 

deviation 

of noise

All

Cell size (number of establishments)

a) 1-2 b) 3-9 c) 10-24 d) 25-99 e) 100+ 

10 0.00 0.03 0.01 0.00 0.00 0.00 

20 0.01 0.07 0.02 0.00 0.00 0.00 

50 0.02 0.17 0.04 0.01 0.00 0.00 

100 0.04 0.35 0.08 0.02 0.01 0.00 

200 0.09 0.69 0.16 0.04 0.01 0.00 

500 0.22 >1.00 0.40 0.11 0.03 0.00 

1,000 0.44 >1.00 0.80 0.22 0.06 0.01 

2,000 0.88 >1.00 >1.00 0.44 0.13 0.02 

5,000 >1.00 >1.00 >1.00 >1.00 0.31 0.04 

10,000 >1.00 >1.00 >1.00 >1.00 0.63 0.09 

20,000 >1.00 >1.00 >1.00 >1.00 >1.00 0.18 

# of cells 187,446 53,264 61,799 32,569 26,901 12,913

22

Median CV

0.00 – <0.05

0.05 – <0.10 

0.10 – <0.15

0.15 – <0.50 

0.50+

Source: Author’s calculations using non-sensitive, simulated County Business Patterns (CBP) microdata.
Median CV of County x 3-Digit NAICS Annual Payroll 

Estimates by Standard Deviation of Noise and Cell Size

Standard 

deviation 

of noise

All

Cell size (number of establishments)

a) 1-2 b) 3-9 c) 10-24 d) 25-99 e) 100+ 

10 0.00 0.03 0.01 0.00 0.00 0.00 

20 0.01 0.07 0.02 0.00 0.00 0.00 

50 0.02 0.17 0.04 0.01 0.00 0.00 

100 0.04 0.35 0.08 0.02 0.01 0.00 

200 0.09 0.69 0.16 0.04 0.01 0.00 

500 0.22 >1.00 0.40 0.11 0.03 0.00 

1,000 0.44 >1.00 0.80 0.22 0.06 0.01 

2,000 0.88 >1.00 >1.00 0.44 0.13 0.02 

5,000 >1.00 >1.00 >1.00 >1.00 0.31 0.04 

10,000 >1.00 >1.00 >1.00 >1.00 0.63 0.09 

20,000 >1.00 >1.00 >1.00 >1.00 >1.00 0.18 

# of cells 187,446 53,264 61,799 32,569 26,901 12,913

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Median CV

0.00 – <0.05

0.05 – <0.10 

0.10 – <0.15

0.15 – <0.50 

0.50+

Source: Author’s calculations using non-sensitive, simulated County Business Patterns (CBP) microdata.
Ensuring Adequate Protection

• PRDP with quality-preserving parameters will provide adequate 

protection for most establishments’ magnitude data.

• Very large establishments will not have adequate protection.

Establishment Employment

#1 75

#2 150

#3 30,000

Total 30,225 30,200 (σ = 22)

24
Relative Protection

pp =

σσ

xx

Standard deviation of

noise added to a cell

Magnitude data for an

individual establishment

25
Relative Protection

pp =

22

30,000

≈ 0.0007

Standard deviation of

noise added to a cell

Magnitude data for an

individual establishment

26
Proportion of Establishments (N=7,960,386)

with Relative Protection* Meeting or Exceeding Selected Levels

Standard 

deviation 

of noise

p ≥ 

0.001

p ≥ 

0.01

p ≥ 

0.02

p ≥ 

0.05

p ≥ 

0.10

p ≥ 

0.15

p ≥ 

0.20

p ≥ 

1.00

10 0.987 0.877 0.792 0.633 0.489 0.402 0.346 0.111

20 0.994 0.932 0.877 0.758 0.633 0.550 0.489 0.191

50 0.998 0.972 0.945 0.877 0.792 0.728 0.676 0.346

100 0.999 0.987 0.972 0.932 0.877 0.831 0.792 0.489

200 1.000 0.994 0.987 0.965 0.932 0.903 0.877 0.633

500 1.000 0.998 0.996 0.987 0.972 0.958 0.945 0.792

1,000 1.000 0.999 0.998 0.994 0.987 0.980 0.972 0.877

2,000 1.000 1.000 0.999 0.998 0.994 0.991 0.987 0.932

5,000 1.000 1.000 1.000 0.999 0.998 0.997 0.996 0.972

10,000 1.000 1.000 1.000 1.000 0.999 0.999 0.998 0.987

20,000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.994

* Relative protection for annual payroll

27

Proportion

0.95+

0.90 – <0.95 

0.85 – <0.90

0.75 – <0.85 

0.00 – <0.75

Source: Author’s calculations using non-sensitive, simulated County Business Patterns (CBP) microdata.
Number of Establishments (N=7,960,386)

with Relative Protection* Less than Selected Levels

Standard 

deviation 

of noise

p <

0.001

p < 

0.01

p < 

0.02

p < 

0.05

p < 

0.10

p < 

0.15

p < 

0.20

p < 

1.00

10 103,250 982,779 1,655,356 2,920,852 4,067,289 4,761,364 5,205,203 7,074,254

20 45,312 542,070 982,779 1,926,842 2,920,852 3,585,832 4,067,289 6,439,113

50 14,304 221,237 441,006 982,779 1,655,356 2,168,765 2,578,852 5,205,203

100 5,651 103,250 221,237 542,070 982,779 1,346,866 1,655,356 4,067,289

200 2,169 45,312 103,250 278,455 542,070 774,739 982,779 2,920,852

500 502 14,304 34,458 103,250 221,237 334,079 441,006 1,655,356

1,000 147 5,651 14,304 45,312 103,250 162,836 221,237 982,779

2,000 42 2,169 5,651 18,995 45,312 73,773 103,250 542,070

5,000 6 502 1,549 5,651 14,304 23,987 34,458 221,237

10,000 2 147 502 2,169 5,651 9,766 14,304 103,250

20,000 1 42 147 737 2,169 3,785 5,651 45,312

* Relative protection for annual payroll

Source: Author’s calculations using non-sensitive, simulated County Business Patterns (CBP) microdata. 28
Number of Establishments (N=7,960,386) 

with Relative Protection* Less than Selected Levels

Standard 

deviation 

of noise

p <

0.001

p < 

0.01

p < 

0.02

p < 

0.05

p < 

0.10

p < 

0.15

p < 

0.20

p < 

1.00

10 103,250 982,779 1,655,356 2,920,852 4,067,289 4,761,364 5,205,203 7,074,254

20 45,312 542,070 982,779 1,926,842 2,920,852 3,585,832 4,067,289 6,439,113

50 14,304 221,237 441,006 982,779 1,655,356 2,168,765 2,578,852 5,205,203

100 5,651 103,250 221,237 542,070 982,779 1,346,866 1,655,356 4,067,289

200 2,169 45,312 103,250 278,455 542,070 774,739 982,779 2,920,852

500 502 14,304 34,458 103,250 221,237 334,079 441,006 1,655,356

1,000 147 5,651 14,304 45,312 103,250 162,836 221,237 982,779

2,000 42 2,169 5,651 18,995 45,312 73,773 103,250 542,070

5,000 6 502 1,549 5,651 14,304 23,987 34,458 221,237

10,000 2 147 502 2,169 5,651 9,766 14,304 103,250

20,000 1 42 147 737 2,169 3,785 5,651 45,312

* Relative protection for annual payroll

Source: Author’s calculations using non-sensitive, simulated County Business Patterns (CBP) microdata. 29
Number of Establishments (N=7,960,386) 

with Relative Protection* Less than Selected Levels

Standard 

deviation 

of noise

p <

0.001

p < 

0.01

p < 

0.02

p < 

0.05

p < 

0.10

p < 

0.15

p < 

0.20

p < 

1.00

10 103,250 982,779 1,655,356 2,920,852 4,067,289 4,761,364 5,205,203 7,074,254

20 45,312 542,070 982,779 1,926,842 2,920,852 3,585,832 4,067,289 6,439,113

50 14,304 221,237 441,006 982,779 1,655,356 2,168,765 2,578,852 5,205,203

100 5,651 103,250 221,237 542,070 982,779 1,346,866 1,655,356 4,067,289

200 2,169 45,312 103,250 278,455 542,070 774,739 982,779 2,920,852

500 502 14,304 34,458 103,250 221,237 334,079 441,006 1,655,356

1,000 147 5,651 14,304 45,312 103,250 162,836 221,237 982,779

2,000 42 2,169 5,651 18,995 45,312 73,773 103,250 542,070

5,000 6 502 1,549 5,651 14,304 23,987 34,458 221,237

10,000 2 147 502 2,169 5,651 9,766 14,304 103,250

20,000 1 42 147 737 2,169 3,785 5,651 45,312

* Relative protection for annual payroll

Source: Author’s calculations using non-sensitive, simulated County Business Patterns (CBP) microdata. 30
Number of Establishments (N=7,960,386) 

with Relative Protection* Less than Selected Levels

Standard 

deviation 

of noise

p <

0.001

p < 

0.01

p < 

0.02

p < 

0.05

p < 

0.10

p < 

0.15

p < 

0.20

p < 

1.00

10 103,250 982,779 1,655,356 2,920,852 4,067,289 4,761,364 5,205,203 7,074,254

20 45,312 542,070 982,779 1,926,842 2,920,852 3,585,832 4,067,289 6,439,113

50 14,304 221,237 441,006 982,779 1,655,356 2,168,765 2,578,852 5,205,203

100 5,651 103,250 221,237 542,070 982,779 1,346,866 1,655,356 4,067,289

200 2,169 45,312 103,250 278,455 542,070 774,739 982,779 2,920,852

500 502 14,304 34,458 103,250 221,237 334,079 441,006 1,655,356

1,000 147 5,651 14,304 45,312 103,250 162,836 221,237 982,779

2,000 42 2,169 5,651 18,995 45,312 73,773 103,250 542,070

5,000 6 502 1,549 5,651 14,304 23,987 34,458 221,237

10,000 2 147 502 2,169 5,651 9,766 14,304 103,250

20,000 1 42 147 737 2,169 3,785 5,651 45,312

* Relative protection for annual payroll

Source: Author’s calculations using non-sensitive, simulated County Business Patterns (CBP) microdata. 31
Decreasing Privacy Loss / 

Increasing Relative Protection

• Second-stage noise

• Added post-PRDP

• Scaled to noisy sums

• Not scaled to the largest establishment in each cell

• Not formally private

• Slow-scaling PRDP

• Noise is added to transformed data

• Greater control over relative noise levels

32
Slow-Scaling PRDP

• Privacy loss grows more slowly as establishment employment size increases

33

Establishment Employment

#1 75

#2 150

#3 30,000

Total 30,225
Slow-Scaling PRDP

• Privacy loss grows more slowly as establishment employment size increases

34

Establishment Employment

#1 75

#2 150

#3 30,000

Total 30,225

Transformation

ff xx = log xx + aa

aa = 1,000

10.349
Slow-Scaling PRDP

• Privacy loss grows more slowly as establishment employment size increases

35

Establishment Employment

#1 75

#2 150

#3 30,000

Total 30,225

Transformation

ff xx = log xx + aa

aa = 1,000

10.349

Gaussian Noise

σσ = 0.1

10.409
Slow-Scaling PRDP

• Privacy loss grows more slowly as establishment employment size increases

36

Establishment Employment

#1 75

#2 150

#3 30,000

Total 30,225

Transformation

ff xx = log xx + aa

aa = 1,000

10.349

Gaussian Noise

σσ = 0.1

10.409

Minimum SD ≈ aaσσ

Minimum CV ≈ σσ
Slow-Scaling PRDP

• Privacy loss grows more slowly as establishment employment size increases

37

Establishment Employment

#1 75

#2 150

#3 30,000

Total 30,225

31,991 (σ = 3,130)

Transformation

ff xx = log xx + aa

aa = 1,000

10.349

Gaussian Noise

σσ = 0.1

10.409

Inverse Transformation

and Debias
Future Work & Outstanding 

Research

A Look into the Future

38
Future Work

• Slow-scaling PRDP

• Parameter tuning

• 95% of cells with 25 or more establishments will have a CV of 10% or less

• Ratios

• Trends

• Extending the work to other data products

• Communication about the methods

39
Outstanding Research

• Protecting sample-based estimates

• Privacy-conserving approaches for firm counts

• Implications for benchmarking

• Privacy-protection algorithms for functions of the data other than sums

• Required privacy protections for product-level statistics

40
Contact Us

• Margaret Beckom

Dissemination Standards Branch

Economic Management Division

Email: margaret.m.beckom@census.gov 

with the subject “Econ Disclosure Feedback”

Phone: 301-763-7522

41