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

Variance Estimation of Blended Import and 

Export Price Indexes with Census Trade Data

Daniel K. Yang

Office of Survey Methods Research

U.S. Bureau of Labor Statistics

2023 Federal Committee on Statistical Methodology 

(FCSM) Research & Policy Conference, Hyattsville, MD

October 26th, 2023
2 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Overview

I. International Price Program (IPP) Survey

II. Census Trade Data (CTD).

III. Blended Import and Export Price Indexes (MXPI) 

Estimation.

IV. Proposed Bootstrap Approach for CTD.

V. Summary.

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I. International Price Program (IPP) Survey

IPP collects data on U. S. trade with foreign nations and 

produces Import and Export Price Indexes (MXPI).

MXPI measure price changes of U.S. imports and 

exports (a Principal Federal Economic Indicator or PFEI).

IPP Survey: 3-stage sampling design.

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IPP Survey: 3-stage sampling design

1st: stage: 

Establishments 

within Sampling 

Stratum (SS)

2nd: stage: 

Classification Groups 

(CGs/SCGs)

3rd: stage: “item to 

price”

3rd: stage: “item to 

price”

2nd: stage: 

Classification Groups 

(CGs/SCGs)

3rd: stage: “item to 

price”

3rd: stage: “item to 

price”
5 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

II. Census Trade Data (CTD)

Number of publishable detailed MXPI has declined over 

time.

BLS is planning to implement an alternative data source: 

CTD for many commodity product areas.

CTD contains detailed shipment records for nearly all 

imports and exports.

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Impact of Census Trade Data Replacing Direct Data Collection by Panel

(2019 Trade $ Values—in Billions)

Trade 

Type Panel Area

SampleEligible $ 

Value 

Percentage 

Sample-Eligible 

$ Value That 

Is Replaced

Percentage SampleEligible $ Value That 

Is Replaced 

(within Panel)

Percentage SampleEligible $ Value That 

Is Replaced 

(within Trade Type)

Export A Crude Materials 170.4 57%

Export A Food & Beverages 108.8 91% 61% 33%

Export A

Minerals, Chemicals, & 

Rubber 333.9 72%

Export A Miscellaneous 113.1 4%

Export B Machinery 431.8 3% 2%

Export B Vehicles 190.6 0%

Import A Crude Materials 356.3 45% 40%

Import A Food & Beverages 158.0 84% 33%

Import A Vehicles 332.9 20%

Import A Miscellaneous 203.8 28%

Import B Machinery 713.7 17%

28%

Import B

Minerals, Chemicals, & 

Rubber 397.1 46%
7 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Census Trade Data Increases 

Published Detailed MXPI

XPI Admin 

data 

coverage

MPI Admin 

data 

coverage
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Harmonized System Detailed Product 

Categories are Basic Classification 

Group to Calculate Aggregate MXPIs
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Census Trade Data Source 

as Share of Harmonized Product Categories

Index Weight 

Year

Total Number of Harmonized 

Codes in Index

Number of Harmonized Codes 

Represented by Census Trade Data

Percentage of Harmonized Codes 

Represented by Census Trade Data

2019 17,686 8,034 45%

2020 17,627 7,988 45%

2021 17,771 8,108 46%

... ... ... ...

Import End Use Index Harmonized Commodity Classification Codes Representation

Index Weight 

Year

Total Number of Harmonized 

Codes Used in Indexes

Number of Harmonized Codes 

Represented by Census Trade Data

Percentage of Harmonized Codes 

Represented by Census Trade Data

2019 9,006 4,177 46%

2020 8,983 4,180 47%

2021 9,000 4,183 46%

... ... ... ...

Export End Use Index Harmonized Commodity Classification Codes Representation
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Data Source Differences

 IPP Survey Data:

 CTD Administrative Data:

Sampling 

Stratum (SS) Establishment SL - Sampling CGs (SCGs) 

Stratum

Grouping to 

classify items 

under each CG

SL - Index 

calculation of 

admin. data CGs
11 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Data Source Error Type

 IPP Survey Data represents a share of trade across U.S. borders

Sampling error

 CTD Administrative Data represents all trade across U.S. 

borders

Missing data error (some records do not have complete entries)

Outlier exclusion error (some records are excluded because their 

price deviates far from the mean)
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III. Blended MXPI Estimate

 Lohr (2021) blended estimator proposal.

 MXPI will be estimated from dual data sources: IPP Survey and 

CTD admin data.

YY

�

θθ = θθYY

�

1,2

1 + 1 − θθ YY1,2

(2)

 θθ – proportion

 At Stratum-Lower level (SL),

YY

�

ssss θθssss = θθssssYY

�

ssss

1 + 1 − θθssss YY

�

ssss

2

12
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Variance Approximation for Blended MXPI Estimate

 The derivatives of YY

�

ssss θθssss :

∂∂YYssss

∂∂θθssss

= YYssss

1 − YYssss2

, 

∂∂YYssss

∂∂YYssss

1

= θθssss, 

∂∂YYssss

∂∂YYssss

2

= 1 − θθssss

 Taylor Series Linearization (TSL) variance approximation:

VV� YY�

ssss θθssss = YY�

ssss

1 − YY�

ssss

2 2

VV� θθ̂

ssss + θθ̂

ssss

2 VV� YY�

ssss

1 + 1 − θθ̂

ssss

2

VV� YY�

ssss

2 + 1 − θθ̂

ssss

2

VV� YY�

ssss

2 +

2 YY�

ssss

1 − YY�

ssss

2 θθ̂

ssssCCCCCC YY�

ssss

1 , θθ̂

ssss + 2θθ̂ssss 1 − θθ̂ssss CCCCCC YY�

ssss

2 , θθ̂

ssss
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Propagation of Uncertainty 

14

 Groves and Lyberg (2010): 

 Presence of potential error propagation may not be ignored in 

the CTD administrative data.

 Borrowing information from Census improves the estimate.

Error 

Propagation 

Error 

Measurement

Total Survey 

Error
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IV. A Bootstrap Approach for IPP Sample

 Select only directly collected items from CGs and determine 

that they have not been discontinued as of the month being 

calculated.

 Further select items that contribute weights to the MXPI.

 Maintain consistency of sampling population.

 Use simple random sampling with replacement (SRSWR).
16 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

IV. Proposed Bootstrap Approach for CTD

Resampling at CG level for CTD.

Select only “usable” CTD items from CGs. 

Maintain consistency of sampling population.

Use simple random sampling with replacement 

(SRSWR)
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Bootstrap Estimate of Blended Indexes

 Blended SL level estimate at Bootstrap run b:

θθ

̂

bb = (1 − pp

̂

bb )θθ

̂

bb

IIIIII + pp

̂

bb θθ

̂

bb

CCCCCC

 Bootstrap mean and variance estimates of θθssss :

θθ�

ssss =

1

BB �

bb=1

BB

θθ�

bb , vvvv(θθ�ssss) =

1

BB − 1�bb=1

BB

θθ�

bb − θθ�ssss

2

 Bootstrap standard error (SE) and relative SE (RSE) of θθ

�

ssss :

SSSS(θθ̂

ssss) =

1

BB − 1�bb=1

BB

θθ̂

bb − θθ̂ssss

2

, RR (θθ̂

ssss) =

SSSS(θθ̂

ssss)

θθ̂

ssss

× 100
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Summary

Alternative data source (frame) like CTD administrative 

data is here to stay.

Blended estimates present challenges to establishment 

surveys and opportunities to improve.

Researchers need evaluate the complex structure of 

administrative data and the means to access it.

Be adaptive and ...
19 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

THANK YOU!

yang.daniel@bls.gov

Office of Survey Methods Research (OSMR)

Bureau of Labor Statistics