Attachment 22 BLS Working Paper Measuring Export Price Movements with Administrative Trade Data 2019

BLS WORKING PAPERS
U.S. Department of Labor
U.S. Bureau of Labor Statistics
Office of Prices and Living Conditions

Measuring Export Price Movements with Administrative Trade Data

Don A. Fast, U.S. Bureau of Labor Statistics
Susan E. Fleck, U.S. Bureau of Labor Statistics

Working Paper 518
June 2019

All views expressed in this paper are those of the authors and do not necessarily reflect the views or policies of the U.S.
Bureau of Labor Statistics.

Measuring Export Price Movements with Administrative Trade
Data
by
Don A. Fast and Susan E. Fleck
June 2019
Abstract
The International Price Program (IPP) surveys establishments to collect price data of merchandise
trade and calculates import and export price indexes (MXPI). In an effort to expand the quantity and
quality of MXPI, we research the potential to augment the number of price indexes by calculating
thousands, and potentially millions, of prices directly from export administrative trade transaction data
maintained by the Census Bureau. This pilot research requires reconsideration of the long-held view that
unit value price indexes are biased because product mix changes account for a large share of price
movement. The research addresses this methodological concern and identifies others by analyzing two
semi-homogeneous product categories among the 129 5-digit BEA End Use export categories. The results
provide a road map of a consistent and testable approach that aligns with the concepts used in existing
MXPI measures, maximizes the use of high volume data, and mitigates the risk of unit value bias. The
authors then propose one methodological approach and compare more than a dozen indexes constructed
with the methodology against the published IPP export price index benchmarks. Preliminary analysis of
all 129 5-digit BEA End Use categories for exports shows potential for calculating export price indexes
for 50 of the 5-digit classification categories, of which 21 are currently not published.
Don A. Fast is a Senior Economist in the International Price Program. Susan E. Fleck is the Assistant
Commissioner of the International Price Program at the U.S. Bureau of Labor Statistics (BLS). Any
opinions and conclusions expressed herein are those of the authors and do not necessarily represent the
view of the U.S. Bureau of Labor Statistics. We thank Daryl Slusher, Laurence Lang, Dave Mead,
Antonio Caraballo, Sudha Polumatla, Praveenkumar Yerramareddy, Robert Martin, Ilmo Sung, Michael
Havlin, Helen McCulley, Tamar Schmidt, Jeff Blaha, Aric Schneider, Jenny Fitzgerald, Ara
Khatchadourian, David Friedman, Steven Paben of BLS, and Brian Moyer, Ana Aizcorbe, and Jon
Samuels of BEA. Author emails: fast.don@bls.gov, fleck.susan@bls.gov.
The BLS has received prior approval from the U.S. Census Bureau, which affirms that the paper does not
present any disclosure risks and approves this document to be shared.
Use of the data are subject to Agreement No. 2067-2018-001, Memorandum of Understanding (MOU)
between the U.S. Census Bureau and the Bureau of Labor Statistics (BLS).

Measuring Export Price Movements with Administrative Trade Data

Introduction
BLS Import and Export Price Indexes (MXPI) track price changes in internationally traded merchandise
goods. The indexes are used to adjust U.S. net exports and trade balances from current to constant dollars. In
addition, the indexes and the data that underlie them are used to analyze cross-country price competitiveness,
exchange rate pass through effects on domestic inflation, price transmission in the global value chain, and
productivity. For example, Gopinath (2010) uses currency and price data for imports to evaluate exchange
rate pass-through of goods; Clausing (2003) examines taxation impacts on intrafirm trade prices; and
Houseman, Kurz, Lengermann, and Mandel (2011) discuss how U.S. productivity growth can be
overestimated due to offshoring.
The International Price Program’s mission is to maintain and expand the level of detail and quality of import
and export price indexes, but this mission is hindered by the high cost of direct data collection. The limited
amount of product and industry detail impacts the quality of real Gross Domestic Product (GDP) and
international trade balances. Where detailed import and export product indexes are not published, the Bureau
of Economic Analysis (BEA) and the Census Bureau use deflators from parent-level indexes as proxies for
missing detail or turn to domestic Producer Price Indexes (PPI), as a best alternative.
In an effort to expand the coverage and quality of MXPI, BLS is piloting research to use administrative export
trade data provided by the U.S. Census Bureau to calculate detailed price indexes that could supplement
directly collected data. The administrative trade records represent the universe of nearly all export
transactions and have historically been used as the sample frame for the international price survey. The 2.9
million monthly records of export trade dwarfs the 20,000 items in the directly collected international price
survey. Two challenges to using this data source for price indexes are that the data are not available timely
and that prices calculated from administrative data will be, by definition, unit value prices. The known
problem with unit value prices is that they represent the average price of a group of products and not a
specific product. Because unit value indexes reflect price changes of both like-product market factors and
changes in product mix; the methodology is commonly known to distort and bias price movements, especially
for heterogeneous product areas (Alterman 1991).
As described in the 1961 Government Price Statistics Hearing Before the Subcommittee on Economic
Statistics of the Joint Economic Committee of Congress, monthly unit value export and import indexes were
available from July 1933 and were calculated for five broad economic commodity categories (crude materials,
crude food-stuffs, manufactured foodstuffs and beverages, semimanufactures, and finished manufactures).
Aggregate import and export unit value indexes were also available. Additionally, in 1961, as mentioned in
the BLS Handbook of Methods the National Bureau of Economic Research (NBER) had proposed in a report
to the Joint Economic Committee for Congress for the production of import and export prices indexes be
delegated to a federal statistical agency “to obtain the attention and resources for these indexes that we believe
are essential”. Further work (Kravis and Lipsey 1971) showed that unit value indexes showed an upward bias.
They conclude that given the lack of true international price indexes that adjusted wholesale trade price
indexes for classification, weights and coverage, measure price changes better than unit value indexes in their
study. However, they state these wholesale indexes have defects that also cannot be resolved. It was precisely
this quality problem that led the Bureau of Labor Statistics to initiate the international price survey to directly
collect data using a matched-item model approach. The sampled approach replaced and improved upon the
Census Bureau’s unit value import and export price index series.
Maintaining the standard for Principal Federal Economic Indicators requires thoughtful and thorough review
of new methods. Such is the intent of this research. The research develops and evaluates new methods to test
the usability of administrative trade data and the quality of resulting price index measurements. This paper

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Measuring Export Price Movements with Administrative Trade Data
describes the pilot research and the systematic approach to create and evaluate detailed transaction prices and
to calculate and evaluate monthly price indexes. The selection of two semi-homogeneous BEA End Use
export product categories was based on their high degree of homogeneity of the 10-digit product detail, and
also because the two 5-digit indexes had experienced difficulties with respondent cooperation. The first
assumption is shown to be a valid premise for selection, but the second created difficulties in validating the
consistency and quality of the pilot measures.
The paper describes how the approach for selecting items and index methods is motivated by the concepts and
methods of the official MXPI. The numerous permutations of item prices and indexes are analyzed and
evaluated for the quality of the results using all 2015-16 export transaction records for two semihomogeneous product categories, BEA End Use export product categories 00310 (Dairy Products and Eggs)
and 00330 (Vegetables and Vegetable Preparations and Juices). First, item-specific concepts and methods are
described and options for calculating item prices are put forth, analyzing variable choice, consistency and
outliers and their impact on indexes. Second, prices are calculated for the detailed proxy items, and the prices
and price changes are tested for unit value bias within and across months to identify the proxy item that
demonstrates the least bias. Third, the numerous variations of BEA End Use indexes are statistically
compared to select published benchmarks, and the panoply of pilot indexes is narrowed down to those that
best fit the benchmark.

Background
The official MXPI cover nearly all trade in merchandise goods.i The matched-item model is the conceptual
basis of the import and export price indexes. Approximately 20,000 items are priced monthly to calculate both
import and export price indexes. The majority of item prices are directly collected. Some homogeneous
product categories (e.g. export grains uses data from the U.S. Department of Agriculture and import
petroleum uses data from the U.S. Department of Energy) are priced using administrative trade data.
Annually approximately 2,000 establishments across half of all merchandise product categories are sampled
proportional to their weight in trade to provide continuous representative coverage in the baskets of import
and export goods (the full sample covers two years and no more than 4,000 establishments for imports and
exports combined). Cooperative establishments provide prices for precisely-defined items and report the price
of each item over the life cycle of the sample. Up to four panels of item prices are included in the MXPI. A
Laspeyres index formula is used to aggregate item and detailed product groups (also referred to as
classification group) into product and industry strata to the topline import and export goods price index
measures. At the item level a probability-based establishment sample weight is used to calculate the product
group index. Product group to the topline index weights are calculated with 2-year lagged annual trade dollar
values based on product/industry classifications, such that 2019 price indexes are calculated using 2017 trade
weights and classifications.ii
i

Some 10-digit product areas are excluded from MXPI for merchandise goods (e.g. returned goods, used goods, military
goods and firearms). BLS also publishes import and export service price indexes for air passenger and air freight. All
subsequent references to indexes refers to merchandise trade price indexes.
ii

MXPI are published for three classification systems (HS, BEA, and NAICS). A mapping, or “tree” structure is used for
aggregating data and/or weights annually. A concordance is created by taking the relevant year of HTSUSA (imports)
and Schedule B (exports) classification and mapping these classifications to IPP ten-digit classification groups. These
IPP ten-digit classification groups are then mapped to four-digit HS, five-digit BEA, and six-digit NAICS categories and
vertically mapped into higher level indexes.

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Measuring Export Price Movements with Administrative Trade Data
A total of 60 out of 129 5-digit BEA End Use export indexes are presently published. Other indexes do not
meet the publication criteria due to insufficient coverage, potential confidentiality concerns, or dollar value of
trade. Trade in a product or industry category must meet a trade dollar value threshold for an index to be
published. This minimum quality threshold is dependent on the size of the sample that is fielded. The
establishments and items must be sufficient to ensure representativeness while also protecting respondent
identifiable information to support the publication of an index. In the face of finite data collection resources,
an increase in the value of trade or a reduction in data collection resources results in fewer establishments and
items in the survey and negatively impacts index quality. Both published and unpublished product categories
are sampled to assure that the higher levels of aggregation are properly representative of the trade.
The magnitude of observations in the administrative trade data far outnumbers those in the directly collected
data. The volume of usable records would virtually eliminate the risk of disclosure and assure confidentiality,
while also eliminating the bias that accompanies nonresponse. On average, 8,000 prices are collected per
month to support the publication of all export indexes. The average number of monthly observations over the
two-year period considered in this paper nears the export item official count for Dairy and far exceeds it for
Vegetables with 6,839 and 32,430 monthly records respectively. The potential for administrative data to
expand the quantity and improve the quality of price measures, however, faces two hurdles. The first –
whether there is a method to calculate indexes accurately – is the focus of this paper. The second – whether
there is a way to integrate the lagged administrative data into official monthly production – will not be
addressed here, but is not insignificant.

Research Approach
The goal of this research is to determine if the transaction data can be used to calculate accurate indexes that
can be used as a substitute for semi-homogeneous import and export price indexes. Pilot research will focus
on two semi-homogeneous export product categories (stratum) - the BEA End Use export product categories
of “Dairy Products and Eggs” (BEA classification 00310) and “Vegetables and Vegetable Preparations and
Juices” (BEA classification 00330) for 2015 and 2016. Within these product categories in 2016, hundreds of
companies traded close to 3.9 and 7 billion dollars, respectively.
In order to use administrative data for more homogeneous product categories and to blend these indexes with
directly collected data/indexes for more heterogeneous product categories, the selection of data characteristics
should adhere as closely as possible to the concepts used in the official MXPI measures.
The administrative trade data that is the subject of IPP’s pilot research is currently used as the sample frame
for IPP’s sample selection of exports.iii The data are maintained by the U.S. Census Bureau. Regulation
requires exporters to enter information on their shipments on a timely basis. Individual records must be
submitted for each product type in each shipment and include Employer Identification Numbers (EINs) of the
importing and exporting establishments, HTSUSA or Schedule B categories, customs dollar value, quantity,
shipping logistics and other information about the shipment. All goods are classified by ten-digit codes based
upon the Harmonized System (HS), which is based on the six-digit World Customs Organization (WCO)
international Harmonized classification.
This following sections describe item keys used to group trade records by unique characteristics, the method
of calculating prices, weights, and indexes, and the types of concerns that arise when trade data are not

iii

Import administrative data are maintained by the U.S. Customs and Border Patrol agency.

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Measuring Export Price Movements with Administrative Trade Data
consistent, missing, or have outliers. The objective of creating a unique item is to attempt to replicate a
matched item model.

Alternative Products and Prices
The administrative trade data consists of transaction records of goods’ shipments across borders that list many
details of the price, quantity, provenance, and destination of the shipment, for each product category (10-digit
harmonized), and party. A number of the data fields in the record format align with existing concepts used in
defining price characteristics in the official MXPI. We select the variables that most closely align with price
determining characteristics in the international price survey.
For each export establishment, the type of product they trade and the sales price depend on the firm’s
production capacity, the preferences in the market where they are selling the good, and the relationship
between the seller and the buyer. These characteristics of a product and its price are integrated into the
international price survey processing. First, the sample is drawn based upon an establishment’s trade within a
detailed published index level, or stratum, and further selection is done using the 10-digit HS
category/grouping. Business enterprises are identified by EIN (Employer ID Number) or, for Canada,
establishment name. Because one company may have more than one establishment (physical plant), many
establishments may have the same EIN, so survey units are broken out by zip code; this information is used to
initiate contact with an establishment. Administrative data fields– E, Z, and H – correspond with these
sampling characteristics. Second, fixing price characteristics for a product are an important step in defining
the price that the respondent will provide monthly. Different goods are shipped to different countries because
consumer and business preferences differ by country. The official MXPI publish price indexes by country of
destination. The seller-purchaser relation also determines the price. Related trade, e.g. between subsidiaries or
related companies, often has different prices than arms-length trade, ceteris paribus. The unit of measure, e.g.
gross, piece, ton, is also a price determining characteristic that significantly affects the unit price. State of
origin and port code are currently not collected by the IPP. Given the detailed item descriptions that
respondents provide these data are not needed for monthly production, but are helpful in defining a product
for this research. The data fields C, D, S, Q, and R correspond to these price characteristics.
The table below provides data field descriptions from Census’s “2016 Export Net Record Field Names and
Descriptions” along with the abbreviation used in this paper:
Table 1 Export Shipment Characteristics
Abbreviation
E

S
Z
C
D

Variable
EIN

Stateori
Zipcode
Country
Dist_Exp
+
Port_Exp

Variable description
11-digit (USPPI Number) employer identification number (nonCanadian exports).
For Canadian exports where no EIN is provided, the IPP uses the
USPPI Name concatenated with the five-digit ZIP code to create a
proxy EIN.
2-digit state of origin code
5-digit ZIP code
4-digit country of destination code (Schedule C)
2-digit Customs district of exportation (Schedule D)
+
2-digit Customs port of exportation (Schedule D)

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Measuring Export Price Movements with Administrative Trade Data
Q

Qty1_dsg

R

Related

H

HS

2-digit designation code of QTY1 reported (Refer to ‘Attachment A
for a list of designator codes)
In layman’s terms this is the unit of measure for the transaction.
1-digit related/non-related code
'Y' = Parties to the transaction are related
'N' = Parties are not related
10-digit numeric Harmonized Commodity Classification code
(Schedule B)
Note: All keys include HS.

Using these data fields, data are grouped to create item keys. These item keys result in different subgroupings
of the administrative data into unique products, or proxy items. All item keys include the Schedule B code
(H) as part of the unique identifier.
Table 2 Item Keys
Item Keys
ESZCDQRH
ESZQRH
ESQRH
EQRH
QRH
H

Description
EIN, State of Origin, Zip Code, Country of Destination, U.S. Port,
Unit of measure, Related, 10-digit HS
EIN, State of Origin, Zip Code, Unit of measure, Related, 10-digit HS
EIN, State of Origin, Unit of measure, Related, 10-digit HS
EIN, Unit of measure, Related, 10-digit HS
Unit of measure, Related, 10-digit HS
10-digit HS

Looking at BEA classifications 00310 (Dairy products & eggs) and 00330 (Vegetables and vegetable
preparations and juices) one can see how much data exists to support these alternative products and prices.
Table 3 Volume of trade and trade transactions for 2016
Export Indexes,
BEA End Use

No. of annual
trade
transactions
82,100

No. of EINs
with > 50
trades &
> $100k traded
220

No.
10-digit
product
categories
41

00310 - Dairy products &
eggs
00330 -Vegetables and
vegetable preparations and
juices

Annual
trade $
value
$3.8 billion

392,000

950

161

$6.9 billion

The average price for each proxy item defined by an item key was calculated with a weighted geometric
mean. Calculating a geometric mean instead of an arithmetic mean mitigates the impact of outliers, an
important consideration given the volume of data. The records with a missing or imputed quantity, are
excluded from price calculation.
Weighted Geometric Mean

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Measuring Export Price Movements with Administrative Trade Data

𝑛𝑛

1
𝑤𝑤

∑𝑛𝑛

𝑃𝑃 = �
�𝑝𝑝𝑖𝑖 𝑖𝑖 �

𝑖𝑖=1

𝑤𝑤𝑖𝑖

𝑖𝑖=1

Where:
P = Weighted Geomean Price
i = Individual trade transaction
p = Average unit price within a transaction
w = Total dollar value of the unique transaction used as a weight

The prices and price change for each of these item keys are used in the unit value bias analysis later in this
paper. Indexes at both the product category and BEA End Use level are calculated from the proxy items that
comprise an item key. However, in order to compare indexes to the benchmarks – for all pilot indexes –
additional dimensions of index quality are considered below.

Alternative Index Concepts and Methods
Administrative data record patterns of trade by company and product over time. Proxy items are the anchor of
monthly price changes. Tracking the proxy item price change over time, however, is subject to variation and
variability. This section considers the characteristics of trade to identify potential issues of bias in index
methodology and develops a range of options to consider when calculating indexes. These options address
choice of index methodology and quality measurement methodologies related to consistent trade, outlier
management, and missing price imputation. In the subsequent section on Benchmark comparisons, the variety
of indexes based on these different concepts and methods along with the dimension of item keys will be
compared to the Benchmarks for Dairy and Vegetables.
Index Formulas. The fact that the administrative trade data provides current dollar value of trade begs the
question of how we could use this data for index calculation. The official MXPI uses a Laspeyres index
formula, because of the data constraint that current trade weights are not available. The availability of current
period weights in the administrative data expands our options to use a Tornqvist index formula to aggregate
the price data from detailed proxy item to the 10-digit classification group index. In “Economic Theory and
BEA’s release of Alternative Quantity and Price Indexes”, Triplett discusses the benefit of superlative
indexes, which Diewert had previously demonstrated in 1976. Specifically, superlative indexes (Fisher Ideal
or Tornqvist) have an advantage by accommodating for substitution (Triplett 1992). The application of these
ideas for this pilot research is that 10-digit classification group indexes are representative of current trade and
account for substitution.
For this study, two levels of indexes are calculated – the IPP 10-digit classification groups and stratum level
indexes – 5-digit BEA End Use. Two index methods – Laspeyres and Tornqvist – are used to calculate
classification group indexes. Stratum level indexes are calculated using a Laspeyres index formula. Index
values are then compared against benchmarks. Consistency of trade and outlier treatment, as described below,
will only be performed on the Tornqvist indexes based indexes for this study. The two index formulas are
below.
Laspeyres Index

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Measuring Export Price Movements with Administrative Trade Data
∑𝑖𝑖 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑄𝑄𝑖𝑖,0
𝐼𝐼 𝐿𝐿 = �
�∗ 100
𝑡𝑡,0
∑𝑖𝑖 𝑃𝑃𝑖𝑖,0 𝑄𝑄𝑖𝑖,0
Tornqvist Index
𝑃𝑃𝑖𝑖,𝑡𝑡

𝑇𝑇

�𝑊𝑊𝑖𝑖,0 +𝑊𝑊𝑖𝑖,𝑡𝑡 �2

𝐼𝐼𝑡𝑡,0 = �
�
�𝑖𝑖,0�
𝑃𝑃
𝑖𝑖

�∗ 100

Where:
𝑃𝑃𝑖𝑖,𝑡𝑡𝑄𝑄𝑖𝑖,𝑡 𝑡

𝑊𝑊𝑖𝑖,𝑡𝑡 = �
∑

�

𝑖𝑖 𝑃𝑃𝑖𝑖,𝑡𝑡𝑄𝑄𝑖𝑖,𝑡𝑡

𝑃𝑃𝑖𝑖,0 𝑄𝑄𝑖𝑖,0

𝑊𝑊𝑖𝑖,0 = �
∑

𝑖𝑖 𝑃𝑃𝑖𝑖,0 𝑄𝑄𝑖𝑖,0

�

Where:
𝐼𝐼𝐿𝐿 = Laspeyres Index
𝐼𝐼𝑇𝑇 = Tornqvist Index
i = trade transaction
t = Current time period
0 = Base period
P = Price
Q = Quantity
W = Weight (share of trade dollar value)
For any type of index (e.g. Laspeyres, Tornqvist), trade weights are needed to calculate the index values. The
summed dollar value of all observations for each proxy item in the administrative trade data is the proxy item
weight. Using the characteristics that define a proxy item and the IPP’s Schedule B-to-IPP classification
group mappings for the selected period, item weights are calculated using the transaction data. It should be
noted that for index calculation, proxy items map to classification groups. For Laspeyres indexes, 2013 and
2014 annual weights will be calculated at the item level in order to match with the IPP’s current Laspeyres
trade dollar value based index methodology. For Tornqvist indexes, monthly current and previous weights
will be calculated using the total dollar value of the proxy items for the current and previous months.
Proxy item monthly percent changes are calculated as index values using the following formula for Geometric
mean prices:
Index Value

𝑃𝑃𝑡𝑡
𝑡𝑡,0 = �0 �∗ 100
𝑃𝑃

𝐼𝐼

Where:
I = Index value
t = current time period
0 = base time period
P = Price

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Measuring Export Price Movements with Administrative Trade Data

These proxy item values are then aggregated using the proxy item index values and item weights, for both the
Laspeyres and Tornqvist index formulas, to the classification group level.
Index Refinement. The quality and quantity of prices for each proxy item is intertwined with the quality of the
index. Index refinement methods are proposed in this pilot to address two data quality concerns – consistency
of trade and outliers. In the official MXPI sampling process, establishment’s probability of selection is greater
when they historically have traded for more months and quarters. To test how consistent trade affects index
quality, pilot indexes are run both with and without the condition that proxy items have at least six prices each
year (2015 or 2016). If an item does not meet the minimum consistency requirement within the year, all prices
for that proxy item during the year will be removed from the indexes when the condition is imposed.
The pilot indexes are evaluated for the impact of outliers. In the official MXPI price verification process,
prices that are beyond set thresholds (typically 2.5 standard deviations from the historical mean) are identified
as outliers. The price changes may reflect a real market condition, or a change in the product quality, or even
a new item. Each of these situations is treated differently. In the case of outliers in the administrative trade
data; proxy item prices may reflect real market changes or be a price for different good that shares the same
proxy item characteristics. Whether the change is market driven or product mix driven can not be determined.
To test the impact of outliers on index quality, pilot indexes with increasing restrictions on outliers are
calculated. Proxy item price changes that fall outside a set number of weighted standard deviations (either 2
or 3) from the weighted mean are removed as outliers. The analysis of the index quality occurs only after the
outlier price is excluded from index calculation. To carry out outlier identification, the test is calculated
using the following formulas for each classification group based upon the monthly item index value changes:
weighted mean, weighted standard deviation, and the upper and lower price change bounds. The steps in the
process are as follows:
Calculate the weighted mean for each classification group for each month:
𝐼𝐼
∗ � 𝑖𝑖,𝑡𝑡 ��
𝑊𝑊
∑𝑁𝑁
�
𝑖𝑖,𝑡𝑡
𝑖𝑖=1
𝐼𝐼𝑖𝑖,𝑡𝑡−1
𝑊𝑊𝑊𝑊. 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 =
𝑁𝑁
𝑊𝑊
∑
𝑖𝑖,𝑡𝑡
𝑖𝑖=1

Calculate the weighted standard deviation for the classification group for each month:

2
〈𝑊𝑊𝑖𝑖,𝑡𝑡 ∗ �
� 𝐼𝐼𝑖𝑖,𝑡𝑡 �− 𝑊𝑊𝑊𝑊. 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀� 〉
∑𝑁𝑁
𝑖𝑖=1
𝐼𝐼𝑖𝑖,𝑡𝑡−1
𝑊𝑊𝑊𝑊. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = �
𝑁𝑁−1
𝑁𝑁
� 𝑁𝑁 �∗ ∑𝑖𝑖=1 𝑊𝑊𝑖𝑖,𝑡𝑡

Where (for items within a classification group):
I = Item Index value
i = Items with a relative
t = Current time period
t-1 = Previous time period
W = Weight (trade dollar value)
N = Total Number of Item Relatives

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Measuring Export Price Movements with Administrative Trade Data
Calculate the upper and lower price change bounds for the classification group for each month:
𝐿𝐿𝐿𝐿𝐿𝐿𝑀𝑀𝐿𝐿 𝑃𝑃𝐿𝐿𝑃𝑃𝑃𝑃𝑀𝑀 𝐶𝐶ℎ𝑀𝑀𝑀𝑀𝑎𝑎𝑀𝑀 𝐵𝐵𝐿𝐿𝐵𝐵𝑀𝑀𝐵𝐵 = 𝑊𝑊𝑊𝑊. 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 − (𝑀𝑀𝐵𝐵𝑛𝑛𝑛𝑛𝑀𝑀𝐿𝐿 𝐿𝐿𝑜𝑜 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 ∗ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆)
𝑈𝑈𝑝𝑝𝑝𝑝𝑀𝑀𝐿𝐿 𝑃𝑃𝐿𝐿𝑃𝑃𝑃𝑃𝑀𝑀 𝐶𝐶ℎ𝑀𝑀𝑀𝑀𝑎𝑎𝑀𝑀 𝐵𝐵𝐿𝐿𝐵𝐵𝑀𝑀𝐵𝐵 = 𝑊𝑊𝑊𝑊. 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (𝑀𝑀𝐵𝐵𝑛𝑛𝑛𝑛𝑀𝑀𝐿𝐿 𝐿𝐿𝑜𝑜 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 ∗ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆)
Once these standard deviations and limits have been calculated and set in place, indexes are recalculated
excluding item prices for the periods that lie outside of the parent (higher-level) classification group’s bounds.
Thus, the items prices for these months will be imputed.
Imputation of missing data, new data, and nonexistent data. In any time period, when there is a missing price,
cell mean imputation is applied to the item without a price quote. A missing price can occur when an item is
not traded or simply not reported. Cell mean imputation applies the parent’s (higher-level) index percentage
change as the child’s (lower level) proxy item’s price change to continue any index series when no current
price exists..New items’ index values are also initialized based upon their parent’s index values. These new
items can only impact the indexes once they have weights, i.e. an actual value of trade. Indexes are
calculated for classification groups (IPP-created ten-digit classifications closely related to 10-digit Schedule B
codes) based upon the child proxy item data and for strata (BEA classifications 00310 and 00330) based upon
the child classification group data. The structure of indexes is graphically as follows:
Figure 1 Tree Structure
Stratum (Classification Group’s Parent, Item’s grandparent)
|
Classification Group (Item’s Parent, Stratum’s Child)
|
Item (Classification Group’s Child, Stratum’s grandchild)

An analysis of monthly trade by EIN and proxy item shows that establishments regularly export, but the
goods they export are irregularly traded. With irregular, or volatile, trade, records for proxy items are absent
across months. The choice to either impute a price – which over time could lead to index bias – or drop a
proxy item – which could significantly reduce coverage of an index – is a judgmental decision. The analysis
below sets out the approach taken in this research to limit cell mean imputation to under 4 months.
As can be seen in the following table company level EINs vary monthly for 2015 and 2016. Cross-month EIN
is a compilation of comparisons counting the instances of an EIN appearing for the BEA strata in the current
and previous month (e.g. 201501 and 201502), thus being an average of 23 data points. At first glance, one
may think trade is not that volatile since approximately 82% and 78% percent of the companies, respectively,
have trade on a monthly basis.
Table 4 EIN Volatility
BEA
Strata
00310
00330

CrossMonth
EINs
1584
3268

Monthly
EINs

Percentage

1943
4165

82%
78%

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Measuring Export Price Movements with Administrative Trade Data
However, trade transactions are irregular at a more granular level, as demonstrated by the monthly average
number of proxy items used in index calculation for BEA classification 00310 (see table 5). For the more
detailed proxy items, there are two to three times the number of imputed prices for items than there are actual
items. extensive amount of cell mean imputation by a factor of six between new items and estimated this
data, it will be shown that index values exhibit bias due to imputation adjustments. To minimize this bias,
logic was added to price calculation to limit imputation of like-proxy items to three months. This decision
reduces the number of prices used in indexes, because prices in two separate months are needed to start an
index series. Given the total number of prices used in the indexes, the overall impact of having to restart some
item price index series, may not be significant. This balance between imputation bias and the loss of prices in
index calculation is necessary to address the known bias. Volatility still remains in trade/substitution of goods
as demonstrated by the counts, but by applying constraints to cell means, the imputation bias has been
reduced. The descriptive results of this are shown below, and a stand-alone comparison of continuous
imputation vs. constrained imputation is highlighted for Dairy in the benchmark comparison.
Table 5 Item Volatility of Trade for BEA Classification 00310 (Dairy Products and Eggs)
Item Data
New Items
Imputed Items
Items Used in
Calculation

ESZCDQRH ESZQRH ESQRH
886
473
391
4025
2231
1893
1717

1248

1191

EQRH
283
1418
1057

QRH

H

4
24

0
3

85

37

Analyzing the BEA classification 00330 Vegetables with the constraints on imputation logic applied, one can
see that the BEA classification 00330 has significantly more trade, and hence more price data.
Table 6 Item Volatility of Trade for BEA Classification 00330 (Vegetables and Vegetable Preparations and
Juices)
Item Data
New Items
Imputed Items
Items Used in
Calculation

ESZCDQRH ESZQRH ESQRH
3256
1832
1367
14564
8349
6323
5971

4278

3727

EQRH
1065
5047

QRH
14
96

3402

346

H
1
13
148

As demonstrated by the data, both the BEA classification 00310 and 00330 exhibit significant evidence of
trade volatility/substitution. Limiting imputation to three months provides a balance between potential
imputation bias and loss of item price index series.
As with items, if a classification group does not exist, its index value will be initialized based upon its
parent’s index value. Cell mean imputation will be used to continue any index series when data does not exist.
At the classification group level, separate sets of indexes were constructed using both the Laspeyres and
Tornqvist index formulas. At the stratum level (BEA five-digit classification) only the Laspeyres index
formula was used to construct indexes; the strata calculations were limited to the Laspeyres index formula to
replicate existing calculation for IPP’s index methodology. The Laspeyres index formula at the stratum level
used for this test, however, only used 2014 annual fixed weights, as 2013 data were not available.
There is an issue that the IPP will need to address, if this methodology is incorporated into IPP’s production
indexes in the future. The data provided by the Census Bureau contains the Schedule B code that is

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Measuring Export Price Movements with Administrative Trade Data
appropriate for the month where the trade occurred. However the IPP’s mapping structure is lagged, thus not
all Schedule B codes will exist in the IPP’s mapping structure. For this study the Schedule B code changes all
fell in minor revision years, where commonly less than 30 export Schedule B codes of over 8000 are replaced
annually. However, in a revision year hundreds of Schedule B codes can be replaced. Given this study is
performed using non-revision year data, the loss of price and weight data due to unmapped new Schedule B
classifications (and the loss of additional HS data due to related IPP classif group mapping changes) across all
indexes should be significantly reduced. BEA classification 00310 is not impacted by any Schedule B
changes, but BEA classification 00330 had five Schedule B codes that were replaced of over 100 in 2015 with
new Schedule B codes.

Unit Value Bias
The primary issue limiting the use of administrative trade data for price indexes is that the lack of detail
results in an average price of dissimilar goods, and that the price per unit, or unit value, will vary widely
month to month because of the types of goods that are traded. Unit value bias is a valid concern because
changes in the composition of goods in a product area can drive the average price of an aggregate good in a
direction that does not accurately reflect the underlying price trend for that product area. Alterman describes
the concerns and Silver discusses the potential use of unit value indexes with homogeneous goods (Alterman
1991; Silver 2010). The question facing the IPP is whether creating product groupings from detailed
characteristics in the administrative trade data could produce unique enough products that prices and indexes
track market changes in price that can proxy the matched-item model. By choosing semi-homogeneous strata
with homogeneous goods, we expect like-characteristic products to be similar and have similar prices. Unique
items with like-characteristics can be proxied and tracked over time, imitating the matched-item model with
less detailed information but significantly more observations.
In this section we analyze unit value bias in the Dairy and Vegetable trade records data from 201501 to
201612. We use the prices of products created from the item keys described in table 2. Three tests will be
applied to the data including a within month item price dispersion test, a cross-month item percentage change
test, and a price clustering test. For the price dispersion and cross-month tests, the individual monthly results
will be aggregated by category, then the individual monthly categorical numbers (receiving equal weight) will
be combined.

Price Dispersion
Testing the dispersion of prices within a month for each proxy item and month is an important consideration
of price quality. It is measured by the coefficient of variation. The relationship between the mean and the
standard deviation is measured. While variability does not prove unit value bias – because there are examples
such as when prices change due to market conditions between the first and the last of the month - variability
can be an indicator that unit value bias exists. For example if the mean were 100 and the standard deviation
were 80, one would note significant variability in the data. That being said, this specific pricing condition is
not happening across the board on a monthly basis for all goods.
The first test that will be applied to the price data within an item key for a month. If more than one price
exists for a month, the coefficient of variation (𝐶𝐶𝑣𝑣) will be calculated for the item key and month for the price
data.
𝑊𝑊𝑊𝑊. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆
𝐶𝐶𝑣𝑣 = 100 ∗
𝑊𝑊𝑊𝑊. 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

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Measuring Export Price Movements with Administrative Trade Data

𝑊𝑊𝑊𝑊. 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 =

∑𝑖𝑖 𝑃𝑃𝑖𝑖,𝑡𝑡 𝑄𝑄𝑖𝑖,𝑡𝑡
∑ 𝑄𝑄
𝑖𝑖

𝑖𝑖,𝑡𝑡

2

∑𝑁𝑁
𝑖𝑖=1 〈𝑊𝑊𝑖𝑖,𝑡𝑡 ∗ �𝑃𝑃𝑖𝑖,𝑡𝑡 − 𝑊𝑊𝑊𝑊. 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀� 〉
𝑊𝑊𝑊𝑊. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = �
𝑁𝑁−1
∑𝑁𝑁
�𝑁𝑁 �∗ 𝑖𝑖=1 𝑊𝑊𝑖𝑖,𝑡𝑡
Where (for prices for an item for a month):
i = Transaction for a proxy item
t = Current time period
P = Transaction Price
W = Transaction Weight (trade dollar value = Price * Quantity)
N = Total Number of Transactions

For analysis purposes the compiled coefficient of variations will be grouped in five-point range categories.
For each item key there are two columns. The first column is the percentage for that category and the second
column is the cumulative percentage, summing the previous percentage with the new category. Looking first
at the BEA classification 00310 coefficient of variation categories, one notices that the more detailed key
shows the least variability and the least detailed key shows the greatest amount; that is, the more detailed keys
have the highest cumulative percentage (i.e. lower variability) at the lower number categories of the
coefficient of variation. This is naturally expected because more detailed products are likely to represent more
specific types of trade, but the percentage divergence is what is of greater significance. The data shows that
ESZCDQRH through EQRH are all showing significantly less variability than QRH through H. The
cumulative coefficient of variation category of 47.5-52.49 is only 63.6 and 48.6 for QRH and H, respectively,
and at a category of 97.5-102.49 is respectively at 85.2 and 79.7. Item keys ESZCDQRH, ESZQRH, ESQRH
and EQRH are respectively at 87.6, 82.2, 80.6 and 76.8 with a cumulative coefficient of variation category of
17.5-22.49. Given these statistics, one can surmise from the data that item keys QRH and H for the BEA
classification 00310 index are exhibiting significant potential unit value bias.
Table 7 Coefficients of Variation of Transaction Prices for Item Keys within BEA Classification 00310
(Dairy Products and Eggs)

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Measuring Export Price Movements with Administrative Trade Data

C. of V.
Category

ESZCDQRH

ESZQRH

ESQRH

EQRH

QRH

H

Percent

Cumulativ
e Percent

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

0-2.49

45.7

45.7

35.6

35.6

33.3

33.3

29.7

29.7

5.6

5.6

0.9

0.9

2.5-7.49

22.1

67.8

21.7

57.3

21.3

54.6

20.0

49.7

4.2

9.8

0.7

1.6

7.5-12.49

9.8

77.6

12.2

69.5

12.5

67.1

12.7

62.4

3.1

13.0

1.2

2.8

12.5-17.49

5.9

83.5

7.7

77.2

8.0

75.1

8.3

70.7

5.0

18.0

2.0

4.8

17.5-22.49

4.0

87.6

5.0

82.2

5.5

80.6

6.1

76.8

5.9

23.8

4.5

9.3

22.5-27.49

2.7

90.3

3.7

85.9

4.0

84.6

4.7

81.5

5.4

29.3

6.3

15.6

27.5-32.49
32.5-37.49

1.9
1.6

92.2
93.8

2.7
2.2

88.6
90.8

2.9
2.3

87.5
89.8

3.8
2.8

85.3
88.0

7.0
8.0

36.2
44.2

5.5
7.1

21.1
28.2

37.5-42.49

1.3

95.2

1.7

92.5

1.9

91.7

2.2

90.3

7.5

51.7

7.0

35.2

42.5-47.49

0.9

96.1

1.5

94.0

1.6

93.4

1.8

92.1

5.9

57.6

5.8

41.0

47.5-52.49

0.7

96.8

1.0

95.0

1.1

94.4

1.3

93.4

6.0

63.6

7.5

48.6

72.5-77.49

0.2

98.7

0.4

97.6

0.4

97.2

0.5

96.7

1.6

79.8

1.5

71.2

97.5-102.49

0.1

99.1

0.2

98.4

0.2

98.3

0.2

97.9

0.8

85.2

0.7

79.7

> =102.5

0.9

100.0

1.6

100.0

1.7

100.0

2.1

100.0

14.8

100.0

20.3

100.0

Looking at the BEA classification 00330, one sees similar results. Once again item keys ESZCDQRH
through EQRH are showing significantly less variability than item keys QRH through H. However,
comparing the BEA classification 00330 to BEA classification 00310, there is more variation for item
keys ESZCDQRH through EQRH, about the same amount for item key QRH and less variability for item
key H for the BEA classification 00330. The cumulative coefficient of variation category of 47.5-52.49 is
63.6 and 50.9 for item keys QRH and H, respectively, and at a category of 97.5-102.49 is respectively at
85.8 and 82.0. Item keys ESZCDQRH, ESZQRH, ESQRH and EQRH are respectively at 76.9, 72.2, 70.5
and 68.7 at the coefficient of variation category of 17.5-22.49. Once again, the variation in the price data
for item keys QRH and H, flags a valid concern for unit value bias in these areas. Technically, even the
more detailed keys could be demonstrating some unit value bias, but given the limited variation (larger
percentages at the lower number categories for the coefficient of variation) shown in the data and the
known variability in commodity prices the unit value concern is significantly mitigated.
Table 8 Coefficients of Variation of Transaction Prices for Item Keys within BEA Classification 00330
(Vegetables and Vegetable Preparations and Juices)
C. of V.
Category

ESZCDQRH

ESZQRH

ESQRH

EQRH

QRH

H

Percent

Cumulative
Percent

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

0-2.49

30.7

30.7

24.9

24.9

23.6

23.6

22.0

22.0

7.9

7.9

1.0

1.0

2.5-7.49

18.4

49.1

17.5

42.4

16.9

40.5

16.5

38.5

7.8

15.7

1.7

2.7

7.5-12.49

12.3

61.4

12.8

55.1

12.7

53.2

12.6

51.0

5.4

21.1

2.3

5.0

12.5-17.49

8.9

70.3

9.7

64.8

9.7

62.9

9.9

60.9

5.7

26.8

3.5

8.5

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Measuring Export Price Movements with Administrative Trade Data
17.5-22.49

6.6

76.9

7.4

72.2

7.6

70.5

7.8

68.7

6.2

33.1

5.1

13.6

22.5-27.49

4.8

81.7

5.7

77.9

5.9

76.4

6.0

74.7

6.8

39.8

7.3

20.9

27.5-32.49

3.7

85.3

4.3

82.2

4.4

80.8

4.6

79.3

6.0

45.8

7.5

28.4

32.5-37.49

2.8

88.1

3.2

85.4

3.4

84.3

3.6

82.9

5.3

51.1

6.0

34.4

37.5-42.49

2.2

90.3

2.7

88.0

2.8

87.1

3.0

86.0

4.5

55.6

6.5

41.0

42.5-47.49

1.7

92.0

2.0

90.0

2.1

89.2

2.3

88.2

3.8

59.4

5.0

46.0

47.5-52.49

1.4

93.4

1.7

91.7

1.8

91.0

1.9

90.1

4.2

63.6

5.0

50.9

72.5-77.49

0.4

96.7

0.5

95.9

0.6

95.5

0.6

95.0

2.4

78.3

3.1

70.2

97.5-102.49

0.2

98.0

0.2

97.5

0.3

97.3

0.3

97.0

1.2

85.8

2.2

82.0

> =102.5

2.0

100.0

2.5

100.0

2.7

100.0

3.0

100.0

14.2

100.0

18.0

100.0

Cross-Month Comparisons
Another study that was pursued on the data was a cross month item index value percentage change (Index
Short Term Ratio) comparison. For this comparison only non-imputed index values for the current month
were used for the data from 201502 through 201612. Percentage changes were counted by range category,
then equally weighted by month, and these monthly counts were further compiled into aggregate percentage
change range categories. As with the coefficient of variation data, this data will be presented in five point
categories. If significant price changes are confirmed cross month for an item key, it could be a sign that nonmatching items are being priced (product mix is shifting) from month to month. For example, if an item has a
transaction price of $1 this month and has a transaction price of $1000 the next month, it most likely is not the
same item.
For the calculated values that are based upon 23 months of item index percentage change comparisons for all
the item keys for the BEA classification 00310, once again the most detailed item key shows the smallest
month over month percentage change variability in price. As before, each item key receives two percentage
columns, with the second being cumulative. For the 0-2.49 and 2.5-7.49 percentage change categories,
ESZCDQRH through EQRH all out perform QRH through H with cumulative percentage changes for
category 2.49-7.5 with values of 60.7, 56.5, 55.2, 52.5, 44.3 and 49.7, respectively. However, the differences
are not that significant. When the cumulative percentage change category hits 17.5-22.49, H’s cumulative
value has surpassed all other values, excluding ESZCDQRH with a value starting from the detailed key of
85.1, 82.8, 81.9, 80.2, 76.7, and 84.0. Given the high values for the cross month percentage change data for
the BEA classification 00310, there is no observable unit value bias of significance that is demonstrated by
the data.
Table 9 Item Key Percentage Change Comparisons within BEA Classification 00310 (Dairy Products and
Eggs)

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Measuring Export Price Movements with Administrative Trade Data

ESZCDQRH

ESZQRH

ESQRH

EQRH

QRH

H

Percent
Change
Category

Percent

Cumulative
Percent

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

0-2.49

36.2

36.2

31.0

31.0

29.8

29.8

27.6

27.6

19.2

19.2

22.0

22.0

2.5-7.49

24.5

60.7

25.4

56.4

25.5

55.2

24.9

52.5

25.0

44.3

27.7

49.7

7.5-12.49

12.3

73.0

13.2

69.5

13.2

68.5

13.7

66.2

15.3

59.6

17.1

66.9

12.5-17.49

7.3

80.4

8.2

77.7

8.4

76.9

8.7

74.9

9.4

69.0

10.2

77.1

17.5-22.49

4.7

85.1

5.1

82.8

5.1

81.9

5.4

80.2

7.7

76.7

6.9

84.0

22.5-27.49

3.2

88.3

3.7

86.5

3.8

85.7

4.0

84.2

4.3

81.1

4.1

88.1

27.5-32.49
32.5-37.49

2.3
1.9

90.5
92.4

2.5
1.9

89.0
90.9

2.7
2.1

88.4
90.5

2.9
2.3

87.1
89.4

3.5
1.8

84.5
86.3

2.9
1.8

91.0
92.8

37.5-42.49

1.3

93.6

1.5

92.5

1.5

92.0

1.6

91.0

2.0

88.3

1.8

94.6

42.5-47.49

1.1

94.7

1.2

93.7

1.3

93.3

1.3

92.3

1.5

89.8

1.2

95.8

47.5-52.49

0.7

95.4

0.9

94.6

1.0

94.2

1.1

93.5

0.7

90.5

0.3

96.0

> =52.5

4.6

100.0

5.4

100.0

5.8

100.0

6.5

100.0

9.5

100.0

4.0

100.0

Examining the other index area of interest, BEA classification 00330, one finds similar results. For the 0-2.49
percentage change category ESZCDQRH through EQRH, all outperform QRH and H with cumulative
percentage changes with values of 28.8, 25.2, 25.1, 24.1, 18.3 and 19.3, respectively. With the 2.5-7.49
percentage change category, H is outperforming all other item keys excluding ESZCDQRH with values
starting from the most detailed item key of 48.7, 45.6, 45.7, 44.6, 43.3 and 46.8, respectively. By the 7.512.49 percentage change category, H is outperforming all others. The values in the same item key order are as
follows: 60.5, 58.0, 58.3, 57.5, 58.9, and 62.6. Given the data, even if one item key is outperforming another
the values are all high and similar, with no item key presenting an obvious unit value bias of concern.

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Measuring Export Price Movements with Administrative Trade Data
Table 10 Item Key Percentage Change Comparisons within BEA Classification 00330 (Vegetables and
Vegetable Preparations and Juices)
ESZCDQRH

Percent
Change
Category

Percent

Cumulative
Percent

0-2.49

28.8

2.5-7.49

ESZQRH

ESQRH

EQRH

QRH

H

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

Pct.

Cum.
Pct.

28.8

25.2

25.2

25.1

25.1

24.1

24.1

18.3

18.3

19.3

19.3

19.9

48.7

20.4

45.6

20.5

45.7

20.6

44.6

25.0

43.3

27.5

46.8

7.5-12.49

11.8

60.5

12.5

58.0

12.6

58.3

12.8

57.5

15.6

58.9

15.9

62.6

12.5-17.49

8.2

68.7

8.6

66.6

8.7

67.0

8.9

66.3

9.7

68.6

10.9

73.5

17.5-22.49

6.1

74.8

6.5

73.1

6.6

73.6

6.7

73.0

6.7

75.3

6.1

79.6

22.5-27.49

4.6

79.4

5.1

78.3

5.0

78.6

5.1

78.1

5.3

80.7

3.9

83.5

27.5-32.49

3.8

83.2

3.8

82.1

4.0

82.6

4.1

82.2

3.7

84.3

2.9

86.4

32.5-37.49

3.0

86.3

3.2

85.3

3.2

85.7

3.2

85.3

2.3

86.6

2.1

88.6

37.5-42.49

2.5

88.7

2.4

87.7

2.4

88.1

2.5

87.8

2.1

88.7

1.8

90.4

42.5-47.49

1.9

90.7

2.1

89.8

2.0

90.1

2.1

89.9

1.8

90.5

1.6

92.0

47.5-52.49

1.6

92.2

1.7

91.5

1.7

91.8

1.7

91.7

1.4

91.9

1.1

93.1

> =52.5

7.8

100.0

8.5

100.0

8.2

100.0

8.3

100.0

8.1

100.0

6.9

100.0

Clustering
A third method was used to determine if unit value bias exists. Ward’s Minimum-Variance Method was
applied to any proxy item that had 100 or more transactions from 201501 to 201612. Using Ward’s
Minimum-Variance Method the data are clustered for each proxy item to determine how many clusters exist
for each item based upon the transaction prices. The optimal number of clusters for each proxy item should be
one if there is no unit value bias, as the item’s price represents one good only. Valid reasons can exist where
an item exhibits more than one price cluster. For example, a price shock for a good could create two valid
clusters for a proxy item. However, in most conditions one would expect to see one cluster for one item.
The output for BEA classification 00310 is displayed by item key with the number of clusters, the total
number of proxy items that have that number of clusters, and the percentage of items that fall in the number of
clusters.

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Measuring Export Price Movements with Administrative Trade Data
Table 11 Cluster data for BEA Classification 00310 (Dairy Products and Eggs)
ESZCDQRH

ESZQRH

ESQRH

EQRH

QRH

# of
Clusters

Total

Pct.

Total

Pct.

Total

Pct.

Total

Pct.

1
2
3
4
>4

191
29
8
2
2

82.33
12.50
3.45
0.86
0.86

225
48
12
2
5

77.05
16.44
4.11
0.68
1.71

232
46
13
2
3

78.38
15.54
4.39
0.68
1.01

224
39
10
5
2

80.00
13.93
3.57
1.79
0.71

Total

H

Pct.

48
5
3
1
1

82.76
8.62
5.17
1.72
1.72

Total

31
1
1
1
1

Pct.

88.57
2.86
2.86
2.86
2.86

Table 12 Cluster data for BEA Classification 00330 (Vegetables and Vegetable Preparations and Juices)
# of
Clusters

1
2
3
4
>4

ESZCDQRH
Total

Pct.

1003
200
71
22
11

76.74
15.30
5.43
1.68
0.84

ESZQRH
Total

Pct.

1084 79.59
191 14.02
64
4.70
18
1.32
5
0.37

ESQRH
Total

Pct.

1044 78.09
204 15.26
62
4.64
17
1.27
10
0.75

EQRH

QRH

Total

Pct.

Total

Pct.

995
186
61
25
6

78.16
14.61
4.79
1.96
0.47

150
33
9
1
1

77.32
17.01
4.64
0.52
0.52

H
Total

89
19
9
2
0

Pct.

74.79
15.97
7.56
1.68
0.00

Looking at the data one notices that most data for all item keys fall into one cluster. When this data and the
price dispersion (Coefficient of Variation) data are reviewed, based upon the statistical tests for the least
detailed keys (QRH and H) there is a large price dispersion that typically forms one cluster for most items.
For all other keys, once again one typically finds one cluster, but significantly less price dispersion.
Given the three tests, one can state that item keys QRH and H for the BEA classification 00310 and 00330 are
exhibiting significant potential for unit value bias based upon their price dispersions.

Benchmark Comparisons
For this study a range of indexes were calculated for the two dimensions – First on item keys, and then
additionally with options to address potential bias in the measures, including consistency of trade, volatility of
trade, existence of outliers, and the quality differences in Laspeyres and Tornqvist indexes. These options
provide a wide range of measures against which the benchmark measures will be compared. The statistical
tests carried out here are an effort to pin down the index method/item key combination that shows the least
biased and best fit. Data results will be presented using the following index keys, and will be calculated for
each item key to compare against benchmarks. With the benefit of hindsight, the two BEA End Use indexes
that were selected for research based upon their index quality concerns, meant that there were no solid
benchmarks of export price indexes against which to gauge the quality of the administrative price indexes.
Nonetheless, the effort to carry out this work will be a key aspect to validate future research.
Table 13 Index Keys

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Measuring Export Price Movements with Administrative Trade Data
Index
Keys

Description

LL

Laspeyres index formula was used to calculate the stratum lower.
Laspeyres index formula was used to calculate the classification group.

LL4

Laspeyres index formula was used to calculate the stratum lower.
Laspeyres index formula was used to calculate the classification group.
If an item is Cell Mean Imputed for a fourth month, the index is no longer imputed.

LT4

Laspeyres index formula was used to calculate the stratum lower.
Tornqvist index formula was used to calculate the classification group.
If an item is Cell Mean Imputed for a fourth month, the index is no longer imputed.

LT42

Laspeyres index formula was used to calculate the stratum lower.
Tornqvist index formula was used to calculate the classification group.
If an item is Cell Mean Imputed for a fourth month, the index is no longer imputed.
Outliers outside the 2nd standard deviation are removed.

LT43

Laspeyres index formula was used to calculate the stratum lower.
Tornqvist index formula was used to calculate the classification group.
If an item is Cell Mean Imputed for a fourth month, the index is no longer imputed.
Outliers outside the 3rd standard deviation are removed.

LT46

Laspeyres index formula was used to calculate the stratum lower.
Tornqvist index formula was used to calculate the classification group.
If an item is Cell Mean Imputed for a fourth month, the index is no longer imputed.
Only include items in 2015 with at least 6 usable prices in the 12 month period.
Only include items in 2016 with least 6 usable prices in the 12 month period.

LT462

Laspeyres index formula was used to calculate the stratum lower.
Tornqvist index formula was used to calculate the classification group.
If an item is Cell Mean Imputed for a fourth month, the index is no longer imputed.
Outliers outside the 2nd standard deviation are removed.
Only include items in 2015 with at least 6 usable prices in the 12 month period.
Only include items in 2016 with least 6 usable prices in the 12 month period.

LT463

Laspeyres index formula was used to calculate the stratum lower.
Tornqvist index formula was used to calculate the classification group.
If an item is Cell Mean Imputed for a fourth month, the index is no longer imputed.
Outliers outside the 3rd standard deviation are removed.
Only include items in 2015 with at least 6 usable prices in the 12 month period.
Only include items in 2016 with least 6 usable prices in the 12 month period.

Three statistical tests of each of these index keys were run against the benchmarks.




Correlation Coefficients
Root Mean Squared Errors
Mean Absolute Error

Correlation coefficients (r) were calculated for the percentage changes (Short Term Ratios, or STRs) using the
benchmarks’ values for the specified year and month and the related pilot percentage change to determine

Page 18

Measuring Export Price Movements with Administrative Trade Data
how strong the relationship is between the data. For this test a value of one is the preferred value, with values
closer to one showing a strong positive correlation.
�
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∑𝑛𝑛𝑡𝑡=1�𝑃𝑃𝑃𝑃𝑃𝑃𝐿𝐿𝑊𝑊 𝐼𝐼𝑀𝑀𝐵𝐵𝑀𝑀𝐼𝐼 𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡 − 𝑃𝐿𝑃𝑃𝑊 𝐼𝑀𝐵 𝑀𝐼𝑆𝑆𝑆��𝐵𝐵𝑀𝑀𝑀𝑀𝑃𝑃ℎ𝑛𝑛𝑀𝑀𝐿𝐿𝑚𝑚 𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡 − 𝐵𝑀𝑀𝑃ℎ𝑛𝐿𝑀𝑚𝐿𝑆𝑆𝑆 �
𝐿𝐿 =
2 𝑛𝑛 �
�
�
𝐵𝐵𝑀𝑀𝑀𝑀𝑃𝑃ℎ𝑛𝑛𝑀𝑀𝐿𝐿𝑚𝑚 𝑆𝑆𝑆𝑆𝑆𝑆 −�
𝑃�
𝐿�
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𝑊�
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𝐼𝐼 𝑆�
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𝑆𝑆�
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∑𝑛𝑛 �𝑃𝑃𝑃𝑃𝑃𝑃𝐿𝐿𝑊𝑊 𝐼𝐼𝑀𝑀𝐵𝐵𝑀𝑀𝐼𝐼 𝑆𝑆𝑆𝑆𝑆𝑆 − �
∑
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𝑡𝑡=1
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Root Mean Squared Errors were calculated comparing the pilot indexes’ percentage changes to the
benchmark indexes percentage changes. This test is impacted more by outliers given that the numerator is
squared. To minimize the impact of outliers the Mean Absolute Errors can be used. For this test a zero is the
preferred value, with values closer to zero showing less prediction error.
2
∑𝑛𝑛𝑡𝑡=1(𝑃𝑃𝑃𝑃𝑃𝑃𝐿𝐿𝑊𝑊 𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡 − 𝐵𝐵𝑀𝑀𝑀𝑀𝑃𝑃ℎ𝑛𝑛𝑀𝑀𝐿𝐿𝑚𝑚 𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡 )
𝑆𝑆𝑀𝑀𝑆𝑆𝑅𝑅 = �
𝑀𝑀

Mean Absolute Errors were also calculated comparing the pilot indexes monthly percentage changes to the
benchmark indexes percentage changes. For this test a zero is also preferred value, with values closer to zero
showing less prediction error.
∑𝑛𝑛𝑡𝑡=1| 𝑃𝑃𝑃𝑃𝑃𝑃𝐿𝐿𝑊𝑊 𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡 − 𝐵𝐵𝑀𝑀𝑀𝑀𝑃𝑃ℎ𝑛𝑛𝑀𝑀𝐿𝐿𝑚𝑚 𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡 |
𝑀𝑀𝑀𝑀𝑅𝑅 =
𝑀𝑀

Official indexes
Spot prices, Consumer Price Indexes (CPI) (U.S. city average, all urban consumers, not seasonally adjusted),
Producer Price Indexes (PPI), and Import/Export Price indexes (XPI for Export Price Indexes) were all
considered as possible comparative measures. It was determined that the XPI and CPI indexes were the
benchmark indexes of choice for BEA classifications 00310 and 00330 respectively. Given that the Export
Prices indexes are sampled and weighted based upon trade, these indexes in theory should most accurately
reflect trade prices. Even if there are lower response rates in any part of the data collection process, whether
sampling, initiation or on-going collection, one would hope the bias of not receiving what was sampled will
be outweighed by the fact that the sample is trade-based and the indexes are trade weighted. However, there is
a known weighting problem with the IPP BEA classification 00330 index, because the real world monthly
seasonality of vegetable production is much more variable than the classification group trade weight – which
is fixed constant value for the entire year. In a month where the trade is limited at the beginning or end of a
particular vegetable’s season a price change based upon limited trade still receives the annual weight. From a
price setting standpoint for vegetables the price an exporter can charge is impacted by the world price. Given
that domestically most vegetables are available year-round, the impact of this monthly weighting issue should
be mitigated with the CPI index, thus justifying its use as a benchmark.

Results for BEA Classification 00310 (Dairy Products and Eggs)
Below are the results for the statistical test for the BEA classification 00310 using the XPI index as the
benchmark. A CPI proxy index was also tested as a benchmark and was calculated using published CPI
values and aggregated using IPP trade weights. The root mean squared errors and mean absolute errors values
were about the same for the two benchmarks, however, the correlation coefficients that were calculated using
the CPI index percentage changes were not supportive for using this data as a benchmark. It should be noted
that as outliers are removed one would expect these indexes to have lower root mean squared errors and mean

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Measuring Export Price Movements with Administrative Trade Data
absolute errors, since the variance is reduced. However, if bias is introduced when the outliers are removed,
the root mean squared errors and mean absolute errors may not decrease as expected. This should be
considered when reviewing these results.
Table 14 Correlation Coefficients for BEA Classification 00310 using an XPI Index Benchmark
Index
Key
LL
LL4
LT4
LT42
LT43
LT46
LT462
LT463

ESZCDQRH ESZQRH
0.39
0.46
0.61
0.57
0.59
0.59
0.57
0.57

0.33
0.47
0.59
0.60
0.60
0.58
0.53
0.57

ESQRH
0.34
0.52
0.60
0.60
0.62
0.60
0.60
0.58

EQRH
0.35
0.39
0.58
0.57
0.60
0.61
0.64
0.62

QRH
0.18
0.19
0.50
0.52
0.51
0.50
0.52
0.53

H
0.46
0.47
0.48
0.50
0.50
0.48
0.50
0.50

Table 15 Root Mean Squared Errors for BEA Classification 00310 using an XPI Index Benchmark
Index
Key
LL
LL4
LT4
LT42
LT43
LT46
LT462
LT463

ESZCDQRH ESZQRH
2.62
2.56
1.82
1.96
1.88
1.96
2.04
2.07

2.82
2.49
1.90
1.97
1.96
2.03
2.22
2.08

ESQRH
2.64
2.28
1.91
2.00
1.90
2.04
2.07
2.08

EQRH
2.73
2.60
2.00
2.07
2.02
1.99
1.99
2.05

QRH
4.89
4.72
2.61
2.58
2.55
2.59
2.56
2.56

H
2.67
2.66
2.71
2.61
2.61
2.72
2.61
2.61

Table 16 Mean Absolute Errors for BEA Classification 00310 using an XPI Index Benchmark
Index
Key
LL
LL4
LT4
LT42
LT43
LT46
LT462
LT463

ESZCDQRH ESZQRH
2.11
1.97
1.44
1.60
1.50
1.54
1.57
1.58

2.08
1.77
1.35
1.50
1.50
1.48
1.65
1.67

ESQRH
2.06
1.59
1.45
1.47
1.43
1.52
1.52
1.63

EQRH
1.99
1.83
1.57
1.53
1.50
1.53
1.52
1.53

QRH
3.97
3.78
2.07
2.09
2.06
2.10
2.10
2.11

H
2.13
2.12
2.16
2.10
2.10
2.18
2.11
2.11

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Measuring Export Price Movements with Administrative Trade Data
As mentioned previously in the paper, an imputation bias was discovered in the index values when no limits
were placed on how long an item could be imputed. Using a Laspeyres index for classification group index
calculation with similar weighting, one would expect a closer correlation with the XPI indexes. However,
when there are no limits to imputation, these indexes received the lowest correlation coefficients, and the root
mean squared errors and mean absolute errors were generally the higher values. All other data used the 4
month imputation limitation, so this bias should not be an issue of significance for the other index keys.
Analyzing the correlation coefficient data, it is evident that when the Tornqvist index formula is used, the
coefficients are higher, and the root mean squared errors and mean absolute errors are lower, all results
supporting the use of the Tornqvist index formula. With the Tornqvist indexes, new items are being brought
into the indexes on a regular basis, and the weights are also current. These results align the Tornqvist index
closer with the benchmark index. The benchmark IPP index will incorporate new items as they enter the index
and weight them with the lagged trade data that they represent. Additionally, when items are discontinued
they may be replaced in the IPP’s indexes. The Tornqvist indexes address a concern in the literature related to
capturing substitution of goods in the indexes (Moulton 2018).
On the other hand, Laspeyres indexes versus the benchmark showed weaker results; this could be due to the
fact that for the Laspeyres index formula, substitution is not occurring for new goods traded in 2015 and
2016. For the Tornqvist indexes, the root mean squared errors and mean absolute errors generally increased
with the removal of outliers for the more detailed item keys. This is not the expected result when the variance
is reduced. The result raises a concern that the information lost by removing the outliers is adding bias to the
indexes.
From an item key standpoint, the QRH and H keys which previously were identified as having a potential unit
value bias issue are statistically not performing as well as other item keys for any of the statistical tests. This
leaves the four more-detailed item key (ESZCDQRH – EQRH) Tornqvist indexes for further analysis. There
are three index key and item key combinations that stand out. Given that the root mean squared error and
mean absolute error are higher for LT462-EQRH (and these statistics should improve with the removal of
outliers), this option should be eliminated even though it had the highest correlation coefficient. Across the
board the removal of outliers did not have the expected impact on the root mean squared errors and mean
absolute errors, which brings into question if outliers should be removed. Upon comparing the results, the
following two indexes are recommended as the best aligned with the benchmark.

Table 17 Recommended Indexes for BEA Classification 00310
LT4ESZCDQRH
Corr.
Coeff.
RMSE
MAE

LT43ESQRH

0.61

0.62

1.82
1.44

1.90
1.43

Results for BEA Classification 00330 (Vegetables and Vegetable Preparations and Juices)
A similar review was also performed on the BEA classification 00330 export index. For this index area the
XPI did not prove to be a good benchmark with almost all correlation coefficients being negative and of
higher values for the root mean squared errors and mean absolute errors. Given that there is significant

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Measuring Export Price Movements with Administrative Trade Data
monthly seasonality in the weights and the XPI index is constructed using a fixed annual weight, item prices
that should receive minimal index weight when the product is out of the growing season in the U.S. are
receiving greater weight than what is supported by the trade in the given month. This weighting issue is the
likely explanation for this poor match. When the index values are reviewed graphically, one notices that the
XPI indexes values for the first year reflect the test index values (that are later selected). In the second year of
the pilot the data trends show significantly more divergence with generally higher index values and larger
fluctuations in index values.

BEA Classification 00330
115.00

Index Values

110.00
105.00
100.00
95.00
90.00
85.00

Months
IPP

LT4 ESZCDQRH

LT62 ESZCDQRH

LT62 ESZQRH

LT6 ESQRH

LT62 ESQRH

The CPI proved to be a better benchmark, by having consistent demand and steady weights, as consumers can
buy most vegetables at any time during the year in the U.S. Below are the results for the BEA classification
00330.
Table 18 Correlation Coefficients for BEA Classification 00330 using a CPI Index Benchmark
Index
Key
LL4
LT4
LT42
LT43
LT46
LT462
LT463

ESZCDQRH ESZQRH
0.26
0.35
0.39
0.39
0.33
0.47
0.41

0.26
0.29
0.35
0.40
0.37
0.46
0.43

ESQRH
0.24
0.23
0.37
0.34
0.35
0.45
0.38

EQRH
0.29
0.24
0.35
0.35
0.32
0.40
0.38

QRH
0.39
0.48
0.31
0.30
0.37
0.33
0.32

H
0.35
0.37
0.32
0.32
0.26
0.33
0.33

Table 19 Root Mean Squared Errors for BEA Classification 00330 using a CPI Index Benchmark

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Measuring Export Price Movements with Administrative Trade Data

Index
Key
LL4
LT4
LT42
LT43
LT46
LT462
LT463

ESZCDQRH ESZQRH
2.16
1.86
1.79
1.82
1.92
1.69
1.84

ESQRH

2.15
2.02
1.84
1.79
1.79
1.67
1.75

EQRH

2.18
2.13
1.82
1.86
1.84
1.73
1.82

QRH

2.09
2.07
1.82
1.82
1.92
1.79
1.83

H

2.01
1.92
2.03
2.02
2.07
1.99
1.98

2.42
2.37
2.02
2.02
2.50
2.00
2.00

Table 20 Mean Absolute Errors for BEA Classification 00330 using a CPI Index Benchmark
Index
Key
LL4
LT4
LT42
LT43
LT46
LT462
LT463

ESZCDQRH ESZQRH
1.66
1.34
1.34
1.39
1.43
1.33
1.44

ESQRH

1.64
1.60
1.41
1.42
1.41
1.31
1.42

EQRH

1.68
1.68
1.45
1.49
1.40
1.40
1.42

QRH

1.76
1.67
1.45
1.41
1.53
1.44
1.45

H

1.61
1.51
1.50
1.49
1.57
1.47
1.46

1.97
1.94
1.56
1.56
2.04
1.55
1.55

Evaluating the results, LT4-QRH has the highest correlation coefficient and the root mean squared error and
mean absolute error perform better than other keys. However, based upon previous work in the paper, QRH
appears to be impacted by unit value bias. Furthermore, it is surpassed by LT4-ESZCDQRH. Given these
conditions, LT4-QRH is removed from selection. LT462-ESZCDQRH has the second highest correlation
coefficient followed by LT462-ESZQRH and LT462-ESQRH, respectively. LT4-ESZCDQRH and LT46ESQRH stand out, in that without removing outliers they have lower mean absolute error and root mean
squared errors, only insignificantly surpassed by indexes that have outliers removed. LT462-ESQRH has a
better correlation coefficient than both of these. This leaves the following five index keys to consider:
Table 21 Recommended Indexes for BEA Classification 00330
LT4ESZCDQRH
Corr.
Coeff.
RMSE
MAE

LT462ESZCDQRH

LT462ESZQRH

LT46ESQRH

LT462ESQRH

0.35

0.47

0.46

0.37

0.45

1.86
1.34

1.69
1.33

1.67
1.31

1.79
1.41

1.73
1.40

Unlike the 00310 BEA classification, the root mean squared errors and mean absolute errors more often
exhibited lesser values when outliers were removed, as would be expected.

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Measuring Export Price Movements with Administrative Trade Data
Examining the data graphically for these various indexes against the benchmark, they exhibit the same overall
trend. The CPI index has a more pronounced rise to the high point then falls thereafter. At the end of this
movement the index values show limited dispersion.

BEA Classification 00330
115.00

Index Value

110.00
105.00
100.00
95.00
90.00

201612

201611

201610

201609

201608

201607

201606

201605

201604

201603

201602

201601

201512

201511

201510

201509

201508

201507

201506

201505

201504

201503

201502

201501

85.00

Months
CPI

LT4 ESZCDQRH

LT62 ESZCDQRH

LT62 ESZQRH

LT6 ESQRH

LT62 ESQRH

Special Case: Detailed Study of BEA Classification 00310
Given the challenges of finding a solid benchmark against which to compare the administrative price indexes,
there is an alternative way to see how well the BEA classification 00310 index fits the benchmark. An
analysis of the largest classification group in the index - “Concentrated milk and cream in solid form with a
fat content less than or equal to 1.5%” – shows that this classification group carries significantly more weight
than any other classification group index. The indexes from this milk and cream classification group will be
compared to IPP’s unpublished comparable classification group index as the benchmark.
Table 22 Correlation Coefficients for Concentrated Milk and Cream in Solid Form 10-digit classification
group
Index
ESZCDQRH ESZQRH ESQRH
Key
LL
0.70
0.56
0.52
LL4
0.69
0.54
0.53
LT4
0.59
0.64
0.65
LT42
0.62
0.66
0.66
LT43
0.60
0.65
0.66
LT46
0.59
0.63
0.64
LT462
0.61
0.63
0.64
LT463
0.60
0.63
0.65

EQRH
0.56
0.56
0.65
0.65
0.65
0.65
0.65
0.65

QRH
0.15
0.24
0.63
0.64
0.64
0.63
0.64
0.64

H
0.62
0.62
0.62
0.62
0.62
0.62
0.62
0.62

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Measuring Export Price Movements with Administrative Trade Data
Table 23 Root Mean Squared Errors for Concentrated Milk and Cream in Solid Form
Index
Key
LL
LL4
LT4
LT42
LT43
LT46
LT462
LT463

ESZCDQRH ESZQRH
2.93
2.97
3.26
3.12
3.21
3.42
3.29
3.36

3.55
3.60
3.10
3.04
3.07
3.17
3.16
3.21

ESQRH
3.83
3.79
3.20
3.18
3.18
3.26
3.30
3.24

EQRH
3.68
3.66
3.22
3.19
3.19
3.22
3.20
3.21

QRH
6.06
5.37
3.49
3.42
3.42
3.42
3.43
3.43

H
3.54
3.54
3.54
3.54
3.54
3.54
3.54
3.54

Table 24 Mean Absolute Errors for Concentrated Milk and Cream in Solid Form
Index
Key
LL
LL4
LT4
LT42
LT43
LT46
LT462
LT463

ESZCDQRH ESZQRH
2.48
2.50
2.79
2.74
2.82
3.05
2.91
2.98

2.88
2.95
2.57
2.45
2.47
2.62
2.57
2.62

ESQRH
3.02
3.03
2.59
2.52
2.53
2.63
2.64
2.58

EQRH
2.93
2.94
2.58
2.54
2.55
2.60
2.56
2.58

QRH
3.94
3.68
2.75
2.71
2.71
2.71
2.73
2.73

H
2.81
2.81
2.81
2.81
2.81
2.81
2.81
2.81

Analyzing the data, it must be noted that ESZCDQRH using a Laspeyres index at the classification group
level (LL and LL4) best matches the XPI classification group index. Given that IPP methodology uses a
Laspeyres index formula at the classification group level and similar lagged weights, this should not be a
surprise. What is of significance is how the detailed item key ESZCDQRH outperforms the other Laspeyres
item keys. This strengthens the argument that a detailed item key better emulates the matched-item model.
It should be noted that the quality of the classification group Tornqvist indexes is overall closer to the XPI
classification group benchmarks than the Laspeyres classification group indexes. Laspeyres classification
group indexes and QRH and H Laspeyres and Tornqvist classification group indexes in general have the
worst root mean squared errors. When the significance of outliers is minimized using the mean absolute error,
ESZCDQRH indexes joins the Laspeyres classification group indexes (excluding Laspeyres classification
group indexes for item key ESZCDQRH) and QRH and H Laspeyres and Tornqvist classification group
indexes with higher values.
When the milk and cream classification group index is compared to the BEA End Use 00310 index (the
parent), there are significant similarities in the data result. One of the most noticeable differences is for the
Laspeyres index with the ESZCDQRH item key. The BEA classification index 00310 did not exhibit as
strong of a correlation coefficient as did the milk and cream classification group. This is likely an artifact of

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Measuring Export Price Movements with Administrative Trade Data
the accuracy of the IPP milk and cream classification group based upon its sampled coverage. Not all the
classification groups in the index are given the support that the milk and cream classification group receives,
and that is possibly why the parent BEA classification group does not have as high of a correlation
coefficient. One would expect a comparison of two similar Laspeyres indexes to produce similar results.

Lessons Learned, Potential Scope, and Homework
The results of this research creating detailed prices and indexes based on administrative trade data are
promising. Indexes derived and tests conducted as part of the study, substantiate the potential for use of
export transaction data in lieu of directly-collected survey information for semi-homogeneous areas with the
use of appropriate index methodologies. Based upon the limited index areas that were studied (BEA
classification 00310 and 00330), the following general concepts are proposed given the results:
 The Tornqvist index formula should be used instead of the Laspeyres index formula for calculating
classification group indexes due to use of current period weights, which allows for almost immediate product
substitution.
 More detailed item keys show closer approximation to the matched item model, and show less risk of unit
value bias. The most promising item keys ESZCDQRH, ESZQRH, ESQRH and EQRH.
 Additional research and analysis should be performed on measuring the impacts of eliminating outliers
and on consistent exporters. It is difficult to conclusively make a determination on these methodologies based
upon the results.
 More semi-homogeneous areas should be tested and analyzed to ascertain if there is one approach that can
be applied all semi-homogeneous area.
A key objective of this pilot is to determine if this methodology can be expanded to other five-digit BEA
classifications to expand index publication and quality of deflators. Only one of the three statistical tests of
the 00310 and 00330 BEA End Use indexes, the coefficient of variation test, had previously demonstrated
that unit value bias may exist within certain item keys. Given the effectiveness of the coefficient of variation
test, it will be used to determine the potential reach and scope of other export five-digit BEA classifications –
to see whether the approach could potentially apply the pilot’s methodology. The estimates provided give an
approximate idea for how extensively these concepts may be expanded and provides some evidence that these
indexes are not subject to unit value bias.
Starting at the low end of acceptability, given the volatility inherent in the 00330 classification of vegetables,
the coefficient of variation values for item key ESZCDQRH will be used as foundational benchmark to test
the potential scope of indexes that could be covered by this new approach – the assumption being that the
natural price variation in 00330 puts its values at the outer limits of acceptable values. We lowered the
original cumulative percent values for 00330 by five to add flexibility for other volatile classifications that
have similar cumulative percentages but exhibit slightly different rates of increase between coefficient of
variation categories. If the five-digit BEA classification had a cumulative percent that is greater than all the
cumulative percent thresholds for the coefficient of variation categories it would pass the test.
Table 25 Coefficient of Variation Cumulative Percent Thresholds

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Measuring Export Price Movements with Administrative Trade Data

Coefficient of Variation Category

Cumulative Percent Threshold based upon Item
Key ESZCDQRH Coeff. of Var. Values – 5

0-2.49 (0 category)

26.0

2.5-7.29 (5 category)

44.0

7.5-12.49 (10 category)

56.0

17.5-22.49 (20 category)
27.5-32.49 (30 category)

72.0
80.0

42.5-47.49 (45 category)

87.0

Additional tests were done to see if some strata met a reduced benchmark standard using a lower rate of
increase (original cumulative percent values were lowered by ten) for the following categories: 0 and 5, 10
and 20 or 30 and 45. These four tests were run for the following item keys ESZCDQRH, EQRH, and QRH
with the following results summed by the 1-digit BEA 0, 1, 2, 3 and 4 classifications. Each table lists the
number of 5-digit indexes, by BEA classification and test constraint, whether it would pass the coefficient of
variation test. The subtotal of each column sums to 129 in each table, the total number of 5-digit BEA End
Use export classifications.
Table 26 Coefficient of Variation Tests for Item Key ESZCDQRH within Export Five-Digit BEA
Classifications
Five-digit BEA Classification

Pass Coefficient
of Variation - 5
tests

Pass C. of Var. 5 tests with 0 &
5 using -10

Pass C. of Var. 5 tests with 10
& 20 using -10

Pass C. of Var. 5 tests with 30
& 45 using -10

Fail all
Coefficient of
Variation Tests

BEA 0 Classification - Foods,
Feeds, & Beverages

16

0

1

0

1

BEA 1 Classification Industrial Supplies & Materials

27

0

0

3

17

BEA 2 Classification - Capital
Goods

2

0

0

1

30

BEA 3 Classification Automotive Vehicles, Parts &
Engines

3

0

0

0

3

2

0

0

0

23

50

0

1

4

74

BEA 4 Classification Consumer Goods, Excluding
Automotives
Total

Table 27 Coefficient of Variation Tests for Item Key EQRH within Export Five-Digit BEA
Classifications

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Measuring Export Price Movements with Administrative Trade Data

Five-digit BEA Classification

Pass Coefficient
of Variation - 5
tests

Pass C. of Var. 5 tests with 0 &
5 using -10

Pass C. of Var. 5 tests with 10
& 20 using -10

Pass C. of Var. 5 tests with 30
& 45 using -10

Fail all
Coefficient of
Variation Tests

BEA 0 Classification - Foods,
Feeds, & Beverages

9

0

1

0

8

BEA 1 Classification Industrial Supplies & Materials

14

0

0

0

33

BEA 2 Classification - Capital
Goods

0

0

0

0

33

BEA 3 Classification Automotive Vehicles, Parts &
Engines

0

0

0

0

6

0

0

0

0

25

23

0

1

0

105

BEA 4 Classification Consumer Goods, Excluding
Automotives
Total

Table 28 Coefficient of Variation Tests for Item Key QRH within Export Five-Digit BEA Classifications
Five-digit BEA Classification

Pass Coefficient
of Variation - 5
tests

Pass C. of Var. 5 tests with 0 &
5 using -10

Pass C. of Var. 5 tests with 10
& 20 using -10

Pass C. of Var. 5 tests with 30
& 45 using -10

Fail all
Coefficient of
Variation Tests

BEA 0 Classification - Foods,
Feeds, & Beverages

0

0

0

0

18

BEA 1 Classification Industrial Supplies & Materials

0

2

0

0

45

BEA 2 Classification -Capital
Goods

0

0

0

0

33

BEA 3 Classification Automotive Vehicles, Parts &
Engines

0

0

0

0

6

0

0

0

0

25

0

2

0

0

127

BEA 4 Classification Consumer Goods, Excluding
Automotives
Total

Analyzing the results of the testing using different item keys for the coefficient of variation tests, for item key
ESZCDQRH, 50 to 55 five-digit BEA classifications are not demonstrating any clear unit value bias. The
higher technology goods are much less suited for this methodology. For item key EQRH, only 23 five-digit
BEA classifications have indexes that meet the criteria, and for item key QRH, no five-digit BEA
classifications are useable, as all show some unit value bias. As a result, it is clear that with a more detailed
item key, significantly less unit value bias is observed.
Table 29 Publication and Sampling Status for Item Key ESZCDQRH for the 50 Export Five-Digit BEA
Classifications that passed the Cumulative Coefficient of Variation Tests

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Measuring Export Price Movements with Administrative Trade Data

Five-Digit BEA Classification

Unpublished
with only
sampled
items

Unpublished
and contains
non-sampled
items

Published
with only
sampled
items

Published and
contains nonsampled items

BEA 0 Classification - Foods,
Feeds, & Beverages

4

0

8

4

BEA 1 Classification Industrial Supplies & Materials

10

1

10

6

BEA 2 Classification - Capital
Goods
BEA 3 Classification Automotive Vehicles, Parts &
Engines
BEA 4 Classification Consumer Goods, Excluding
Automotives
Total

2

0

0

0

3

0

0

0

1

0

1

0

20

1

19

10

Analyzing the 50 five-digit BEA classifications that met the coefficient of variation’s thresholds, 21 of these
strata are unpublished and 29 are already published. Of these 50 strata, 11 already use some form of nonsampled data, and ten of the 11 are published indexes. This leaves 40 indexes as potential candidates for
administrative trade data index estimation.

Proposed methodology and extension of analysis
The analysis that we have carried out with Dairy and Vegetable BEA End Use export price indexes has led us
to make reasonable judgments about the value and quality of the options we tested. Of the options that were
tested, we determined that the average prices of items showed the best quality when the items were specified
at the greatest level of detail. Furthermore, the best characteristics of calculation were those that:





Limit cell mean imputation to 4 months
Limit observations to those that had traded in at least 6 months of the year
Remove observations whose average price – for a given product within a month – was more than 3
standard deviations from the mean.
Calculate the percent change for each 10-digit detailed product category using a Tornqvist index
formula with same-month weights.

We then apply this methodology to calculate 14 more BEA end use price indexes, the first two of which are
from robust price indexes – soybeans and meat. For these two indexes, the price index constructed with the
proposed methodology and the published export price indexes track each other closely. [Data will be provided
once cleared by Census.]
We subsequently construct price indexes for 12 other price indexes. For those of the 12 for which there exists
a published export price index, we carry out a coefficient of variation analysis. See the list below [data will
be provided once cleared by Census]. Most but not all constructed indexes track the published price index.

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Measuring Export Price Movements with Administrative Trade Data

Index
00100
00300

Description
Soybeans and soybean by-products
Meat, poultry & other edible animal products

00000
00010
00110
00200
00210
00220
00320
00340
00350
00360
01000
01010

Wheat
Rice & other food grains
Oilseeds other than soybeans, and food oils
Corn
Other feedgrains
Other animal feeds, n.e.s.
Fruit and fruit preparations, including fruit juices
Nuts & preparations
Bakery & confectionery products
Other foods and food preparations
Fish and shellfish
Distilled alcoholic beverages

Conclusion
This paper presents a number of options to establish a new methodology for calculating price indexes from
administrative trade data. The primary objective of the testing and analysis was to mitigate the likelihood of
unit value bias in order to establish a systematic approach for calculation. The authors evaluate and identify
the different options and the different tests, and then propose a reasonable methodology that could be
replicated with other indexes.
Proxy item indexes with more detailed item keys exhibit less price dispersion, smaller cross-month price
differences, and greater clustering, which provide reasonable evidence that unit value bias can be addressed
by creating ‘quasi-products’ with detailed item keys. The second dimension of index quality was more
challenging to address, as we identified a systemic approach to compare indexes. But the initial decision to
select product categories that had poor quality indexes – with the intent of ‘filling the gap’ – resulted in
benchmark comparison results that were not definitive. The BEA End Use 00310 Dairy index - with limits on
imputation and with a Tornqvist index formula at the classification level - were a better fit with the
comparable published export price index benchmark. The BEA End Use 00330 Vegetable index constructed
only with consistent exporters where price outliers were excluded had a better overall fit compared to the CPI
benchmark. However, greater root mean squared errors and mean absolute errors for Dairy 00310 were
evidenced when excluding outliers. This outlier related discrepancy deserves further analysis with more
product categories to determine whether excluding outliers typically creates bias.
The addendum to the analysis [data not in this paper] compares the BEA End Use indexes of 14 homogeneous
product areas with the benchmark official export price indexes, using the coefficient of variation test. The
results for the published indexes will be shared.
IPP plans on expanding this pilot beyond the two studied index areas into other homogeneous and semihomogeneous areas for exports and imports. Additionally, we will collaborate with the BEA to calculate and
analyze the impact of multi-year detailed export price indexes not presently published as deflators for GDP.

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Measuring Export Price Movements with Administrative Trade Data
This research would require the expansion of the test index time frame beginning with 2012. Given the
potential increase in the number of detailed BEA indexes the IPP could publish, there may be significant
improvement in accuracy when deflating the import and export GDP numbers, demonstrating the potential
significance of this work. Based on preliminary results, this study suggests that the unit value bias can be
overcome, making administrative trade data for semi-homogeneous products a possible source for calculation
of import and export price indexes.

Gopinath, Gita. 2010. “Currency Choice and Exchange Rate Pass-through,” American Economic Review 100
(1): 304-336.
Clausing, Kimberly A. 2003. “Tax-motivated transfer pricing and US intrafirm trade prices.” Journal of
Public Economics. Volume 87, Issues 9-10, 2207-2223 (September).
Houseman, Susan, Christopher Kurz, Paul Lengermann, and Benjamin Mandel 2011. “Offshoring Bias in
U.S. Manufacturing.” Journal of Economic Perspectives. Volume 25, Number 2, 111-132 (Spring).
Alterman, William. 1991. “Price Trends in U.S. Trade, New Data, New Insights.” Chapter in NBER book
International Economic Transactions: Issues in Measurement and Empirical. Edited by Peter Hooper and J.
David Richardson. National Bureau of Economic Research, Studies in Income and Wealth. Volume 55.
University of Chicago Press 109-143 (January).
Government Price Statistics Hearings Before the Subcommittee on Economic Statistics Of the Joint
Economic Committee Congress of the United States Eighty-Seventh Congress First Session Pursuant to Sec.
5(a) of Public Law 304 (79th Congress) Part 1 January 24, 1961
U.S. Department of Labor, Bureau of Labor Statistics Handbook of Methods. “Chapter 15. International Price
Indexes”, 154-159
Kravis, Irving B., Robert E. Lipsey 1971. “Wholesale Prices and Unit Values as Measures of International
Price Competiveness” Chapter in Price Competitiveness in World Trade
Silver, Mick. 2010. “The Wrongs and Rights of Unit Value Indices.” Review of Income and Wealth. Series
56, Special Issue 1, 206-223 (June).
Triplett, Jack E. 1992. “Economic Theory and BEA’s Alternative Quantity and Price Indexes.” Survey of
Current Business. 49-52 (April). https://www.bea.gov/scb/pdf/national/nipa/1992/0492trip.pdf.
Diewert, W.E. 1976. “Exact and Superlative Index Numbers. Journal of Econometrics” Volume 4, Issue 2.
North-Holland Publishing Company (May).
Moulton, Brent R. 2018. “The Measurement of Output, Prices, and Productivity: What’s Changed Since the
Boskin Commission?” Hutchins Center on Fiscal & Monetary Policy at Brookings, The Brookings Institution
(July). https://www.brookings.edu/research/the-measurement-of-output-prices-and-productivity.

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