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Variances of Combined Consumer Price 

Index Survey and Alternative data 

Onimissi M. Sheidu

Mathematical Statistician

FCSM 2023
2 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Outline

 Introduction

 Methodology

 Simulation Results

 Conclusion

 Disclaimer: Any opinions expressed in this presentation are those of 

the author and do not constitute policy of the Bureau of Labor 

Statistics.
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Definition

 Consumer Price Index data - a probability survey collected by random 

selection. Use as the study benchmark data

 Alternative data (Corp5) - a nonprobability sample units collected by 

nonrandom process

 Core of the study methodology: Propensity models (create pseudo weight)

 Propensity score - a conditional probability of assignment to treated units 

given individual’s covariate values:e (x)pppppp= pr(S = 1 | X =x).
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 Motivation: 

 Improve reliability and accuracy of computed CPI estimates

 Provide credibility to alternative data estimates (often treated as suspects)

 Enhance CPI data estimates at reduced cost - reduces nonresponse

 Task 

 Gauge accuracy of computed estimates for both blended and Corp5 data

 Benchmarking estimates for both data groups against computed CPI estimates

 Establish outperformance and provide answer on: 

 How best to obtain a more reliable estimates by using blended data
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Data Selection

 Data Sources: 

I. CPI Research database CPI Survey data

II. Alternative (Corp5 data) Non-probability data 

 Data Type : 

 Monthly average prices of gasoline

 Study Period:

 December 2017 – May 2021
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Data Simulation Setups: Six data groups with varying sizes

 Unmixed groups:

I. CPI survey data - Benchmark estimates, TTTTTTTTTT ssssssss42 mmmmmmmmm , NNaa = 114284

II. Corp5 data TTTTTTTTTT ssssssss 42 mmmmmmmmm , NNbb = 380930 

III. Corp5_Adjusted data treated with 1/πi, TTTTTTTTTT ssssssss 42 mmmmmmmmm , nnbb = 266466

 Mixed data sets (CPI data plus Corp5 data): 

I. Mix1 (50% each): CPI data nnaa = 114284, Corp5 data nnbb = 114284, nn = 228568

II. Mix2 (30 -70%): CPI data nnaa = 114284, Corp5 data nnbb = 266466, nn = 380930

III. Mix3 (70-30%): CPI data nnaa = 114284, Corp5 data nnbb = 48992, nn = 163276

 We use composite weights for Mixed data sets
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Figure 1: Weights Adjustment Process (ww00ii = 

11

11−ππii

, ww11 =

11

ππii

,ww

�

=wwjj*wwjj ) 

CPI Survey )

Data

Mixed Data S Alternative 

(Corp5) Data

Final Sample 

Weights × ww0

Composite 

Weights, ΚΚ�ww

County Weights 

× ww1

Analysis 

(Weight 

adjusted S) 

Pseudo 

weights 

wwjj

Adjusted 

Weights ×

Adjustment 

Factor, λλ

Adjusted 

Weights ×

Adjustment 

Factor, 1-λλ
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Figure 1a and 1b: Ex. of Common Support Validation for Model 1 (Mixed 1 Data )

Figure 1a. Lacking Common Support Figure 1b. Valid Common Support 
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Figure 2a & b: Ex. Balance Distribution for the Models covariates (Mixed Data )
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Calculated Composite Weights (ΚΚ�ww )



̂

yy = ∑ iisbb λλ �wwbb yybb + ∑ iisaa

1 − λλ �wwaa yyaa

œ λλ =

nnbb

nn , nn = nnaa + nnbb,

̂

yy - estimated population total 

 here,

œ nnaa = sample size for CPI survey data, 

œ nnbb = sample size for Corp5 data 

 Mixed 1 data: t

̂

y = ∑iεsbb 0.5w

�

biybi + ∑iεsaa

0.5w�

aiyai

 Mixed 2 data: t

̂

y = ∑iεsbb 0.7w

�

biybi + ∑iεsaa

0.3w�

aiyai

 Mixed 3 data: t

̂

y = ∑iεsbb 0.3w

�

biybi + ∑iεsaa

0.7w�

aiyai

 Corp5_Adjusted data: t

̂

y = ∑iεsbb w

�

biybi, 

 given �wwbb = wwbb ∗ ww1 and ww1 = 1/πi ; �wwaa = wwaa ∗ ww0 and ww0 = 1/1−πi
11 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Analysis Method

 Compute Index Area Percent Changes (PCs) for:

 1- month (PC01), 2- month (PC02), 

 6- month (PC06), 12- month (PC12). 

 All gasoline (item) & per gasoline grade (ELI)

 Compute standard errors (SEs) of PCs

 Using:

1) Stratified Random Groups (SRG) 

2) Bootstrap (BT)

3) Jackknife (JK)

 Analyze groups by variance method:

 All-US cities, All Self-representing and Non-self representing areas

9 Nonself rep.

Areas 

(N000)

Areas

(S000)

23 Self 

Rep.

32 Areas (All-US cities,0000)
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Evaluation Method

 Compare resulting values: 

 Among data groups 

 By variance method

 And group by area:

o All-US cities,

o All Self-representing 

o All Non-self representing 

 Verdict: The smaller their 

computed values the better 

 NRMSE values = deciding 

factor

1. AAAA . RR RR ββ (ΘΘ) ,=

ββ (ΘΘ)(tt,tt−kk),ss

θθcc� ,

tt,tt−kk

2. AAAA .DD DDDD. CCCC(ψψ)( ), =

δδ�

θθ(tt,tt−kk),ss

aa

2

θθ�

(tt,tt−kk),ss

aa − σσ�cccccc,tt,tt−kk

2

θθ�cc ,

tt,tt−kk

3. NN NNNNEE θθ̂ ,

aa =

θθ�

(tt,tt−kk),ss

aa − θθcc� ,

tt,tt−kk

2

σσ�cccccc,tt,tt−kk

2

θθ�

( , −kk),

aa - t-month PC for data set s

θθcccc � , , −kk - t-month PC for CPI data (Benchmark estimate)

�σσcc , , −kk

2 - t-month CPI variance estimate

δδ̂

θθ(tt,tt−kk),ss

aa

2 - t-month variance estimate for data s
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Results: One-Monthly SEs for All – US Cities by Data Group (SRG & BT Methods)
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Results: : 12-Month SEs for All – US Cities by Data Groups (BT & SRG Method)
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Results: One-Month NRMSEs for All – US Cities by Data Group (SRG & BT Method)
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Results: One-Monthly NRMSEs for Gasoline for All Self & Non-self-representing Areas
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Results: 12-Month NRMSEs for All – US Cities by Data Groups (SRG & BT Method)
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Results: 12-Month NRMSEs for All – US Cities for Data Groups (JK & BT Method)
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Results: Summary of All Periods calculated NRMSEs for All US Cities for Data sets (12/2017 – 5/2021)

TABLE 1: NRMSE CALCULATION FOR ALL-US AREAS FOR GASOLINE

Period Data 

Group Corp5 Mix 1 (50-50)

Mix 2 

(30-70)

Mix 3 

(70-30)

1 - Month SRG 0.774 1.496 1.494 1.396

BT 0.179 0.467 0.464 0.432

JK 0.397 0.587 0.610 0.604

BT* 0.161 0.231 0.228 0.221

2 - Month SRG 1.329 2.521 2.503 2.350

BT 0.266 0.643 0.637 0.595

JK 0.548 0.798 0.820 0.812

BT* 0.196 0.270 0.266 0.259

6 - Month SRG 3.623 2.850 3.091 2.567

BT 0.495 0.519 0.549 0.463

JK 1.419 0.808 0.934 0.861

BT* 0.308 0.183 0.190 0.172

SRG 6.760 1.293 0.200 1.587

BT 0.807 0.176 0.034 0.234

JK 1.945 0.455 0.124 0.358

BT* 0.446 0.076 0.033 0.085

12 - Month 
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Conclusion and Recommendation

 Study goal: Assess the possible advantage of blending the CPI survey data with alternatively sourced

nonprobability data such as the corp5 data, and to explore the best way to do it.

 The result showed a mix picture especially for 1-month and 2-month estimates, and further exploration

could give a clearer picture.

 Mixed data performed better at longer term (6-month and 12-month) periods.

 Weight assignment is an issue: What weight should be assigned to the mixed data – county or sample

weight?

 With the current way of doing things, we think there is no much benefit in using mixed data except to

give credence to the estimates.

 The study shows that combining CPI survey data with corp5 data could provide better enhancement

when computing at ELI – Area level than at Item level.
Contact Information

21 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Onimissi M. Sheidu

Mathematical Statistician

Statistical Method Division/CPI Survey 

Research and Analysis Branch 

www.bls.gov

202-691-6901

sheidu.onimissi@bls.gov