Attachment 24 - BLS Working Paper Unit Values for Import and Export Price Indexes – A Proof of Concept

Unit Values for Import and Export Price Indexes
– A Proof of Concept
Don A. Fast and Susan E. Fleck

Big Data for 21st Century Economic Statistics

Abstract

The U.S. Bureau of Labor Statistics’ import and export price indexes (MXPI) are published from an
ever decreasing sample relative to the size of trade. The Principal Federal Economic Indicator has an
opportunity to retain and regain detailed MXPI using unit values calculated from comprehensive
administrative trade data. The unit values from the high-frequency, high-volume source present a
dilemma for official price statistics, given that unit value indexes are known to not track price indexes.
This BLS research proposes a new methodological and statistical approach to identify detailed
homogeneous product categories that show minimal unit value bias to include in the MXPI. The proof of
concept for identifying homogeneous items is based on an analysis of two export products – dairy and
vegetables – for 2015-16. The results provide a prototype and a roadmap for a consistent and testable
approach that aligns with the concepts in official MXPI measures, maximizes the use of high-frequency
data, and mitigates the likelihood of unit value bias. Applying the prototype, 52 of 142 import and 50 of
129 export 5-digit BEA End Use categories are identified as homogeneous using administrative data. This
coverage accounts for 35 and 39 percent of the 2016 value of imports and exports, respectively.
Incorporating unit values has the potential to deepen coverage and support expanded publication of
detailed import and export price indexes.
Don A. Fast is a Senior Economist and Susan E. Fleck is the Assistant Commissioner of the
International Price Program at the U.S. Bureau of Labor Statistics (BLS). We particularly thank Christina
Qiu and Daryl Slusher for their extensive contributions to the final chapter. We recognize and thank these
BLS staff for their research and data support: Jeff Blaha, Antonio Caraballo, Jenny Fitzgerald, David
Friedman, Michael Havlin, Ara Khatchadourian, Laurence Lang, Robert Martin, Helen McCulley, Steven
Paben, Sudha Polumatla, Tamar Schmidt, Aric Schneider, Ilmo Sung, and Praveenkumar Yerramareddy.
We gratefully acknowledge the conference organizers and Jon Samuels for feedback and advice. We have
benefited from comments by Ana Aizcorbe, Alberto Cavallo, John Haltiwanger, Marshall Reinsdorf, and
our discussants, Carol Corrado and Susan Houseman on earlier versions of this research. Author emails:
fast.don@bls.gov, fleck.susan@bls.gov. Use of the export trade data are subject to Agreement No. 20672018-001, Memorandum of Understanding (MOU) between the U.S. Census Bureau and the Bureau of
Labor Statistics (BLS). The BLS has received prior approval from the U.S. Census Bureau, which affirms
that the research results do not present disclosure risks and approves the publication of the results.

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INTRODUCTION
BLS Import and Export Price Indexes (MXPI) track price changes in internationally traded
merchandise goods. The indexes underpin inflation adjustment of U.S. net exports and trade
balances from current to constant dollars. The quality of the indexes is founded on the matched
model and implemented through an establishment survey. The matched model records samegood price differences at the item level and aggregates price changes weighted by product,
company, and trade dollar value shares to all-goods import and export price indexes. For the past
twenty years, 20 to 25 thousand prices of unique items from thousands of companies have been
collected monthly to calculate detailed and all-goods price indexes. Trade has grown and sample
size has been constant and – more recently – reduced. Both trends result in thinner item
coverage, directly reducing the number of detailed indexes of publishable quality. While the toplevel MXPI – principal federal economic indicators – are of consistently high quality, measures
for detailed price indexes are at risk. Symptomatic of this trend is the fact that BLS publishes
only one-third of the most detailed BEA End Use goods price indexes for both imports and
exports.
There exists an extensive source of administrative trade data that – up until now – has been
used only as the sample frame for the international price establishment survey. The price and
quantity information from these administrative records results in an average price or unit value,
i.e., the total dollar value of the shipment divided by the quantity shipped. The 2.9 million
monthly export records dwarf the approximately 24,000 export and import items currently in the
directly collected international price survey. The question analyzed here is whether and which
unit values can be used on a large scale to track price change to bolster the number and improve
the quality of published detailed price indexes and, by extension, the top-level indexes.
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Incorporating unit values on a large scale into a BLS price index is a major methodological
change to existing practices, given that the BLS program was founded in response to critiques of
unit value measures. The BLS established the international price program to directly collect price
data, following significant research conducted by the National Bureau of Economic Research in
the 1960s. The Stigler Commission (Price Statistics Review Committee 1961), a historical series
of import and export price indexes for 11 commodity groups (Lipsey 1963), and an extensive
study on the measurement and calculation of price measures for international trade (Kravis and
Lipsey 1971) described how unit values captured compositional effects of changes in product
mix and different quality of goods and did not mimic price changes. Unit value indexes at that
time were calculated from average values for customs declarations that included value and
quantity. The records were often incomplete, and thus unit values covered no more than a third
of finished manufactured trade and slightly more than half of commodity trade (Kravis and
Lipsey 1971). The ability to determine U.S. competitiveness was hampered because of the poor
quality of these measures. The Census monthly unit value export and import indexes, published
from July 1933 through 1990, were calculated for five broad economic commodity categories
(crude materials, crude food-stuffs, manufactured foodstuffs and beverages, semimanufactures,
and finished manufactures). The first BLS import and export price indexes based on an
establishment survey were published in 1973 as a consequence of this high-profile research to
replace the Census unit value indexes, which BLS also deemed as having substantial unit-value
bias due to lack of detail and the inclusion of heterogeneous products (Alterman 1991).
Since that time, some experts have proposed that unit values for homogeneous goods may
track prices (Mead 2014, Silver 2010). Twenty years ago, Feenstra and Diewert (1997) proposed
that BLS analyze the detailed administrative trade data that are the subject of this chapter, given

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the improvements in coverage, detail and availability at that time. However, BLS had less
capacity than today to address the complexity of the data and the lag in its receipt, and so BLS
did not pursue the project. More recently, Nakamura et.al. (2015) set out both historic
precedence and mathematical formulas to incorporate unit values into official price indexes as a
viable alternative to address substitution and other biases.
The proof that unit values could be used in price indexes is in the doing, and BLS has begun
research to evaluate the aforementioned administrative trade transactions. The administrative
trade data are reported by type of export product per exporter per vessel per day, based on the
detailed Harmonized System (HS) classification with more than 5,000 merchandise good
categories. The transaction records include dozens of data fields. The data provide the
opportunity to evaluate whether and which grouped transactions with a range of price differences
are homogeneous, essentially addressing Nakamura et. al.’s ‘impediment 2’ to the adoption of
unit values – “the question of if and when auxiliary product unit attributes should be used in
forming index basket product definitions”. (Nakamura et. al. p. 54).
The basic questions are 1) whether the data source can be used to calculate unit values and 2)
how to select and group the attributes of these transactions into homogeneous products. The first
question is more easily answered than the second. The approach we use allows for multiple
transactions per product at multiple prices to calculate a unit value with current prices and
quantities per time period. The second question is how to differentiate heterogeneous from
homogeneous product categories – and thus unit values – with the attributes in the trade data in
addition to the detailed HS product category (called here 10-digit HS). Many researchers use the
trade data to calculate their own price or price index comparisons. For example, unit values are
calculated for cross country comparisons, using 10-digit HS product categories (Feenstra et.al.

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2009, Feenstra and Romalis 2014). Impacts of import prices on welfare in the United States
group the 10-digit HS with one or two data characteristics to calculate more detailed unit values.
For example, Broda and Weinstein (2006) estimate the impact of product variety changes on
prices and welfares by including country of origin in their import indexes. Hottman and
Monarch (2018) create an import price index that includes the foreign supplier ID and map out
the welfare impacts of import price changes on select consumer profiles. Kamal and Monarch
(2017) analyze the reliability of the trade data in the context of U.S.-foreign supplier relations.
These one-time research projects show the potential to calculate unit values and to group
transactions into products. But we know of no work that evaluates the reliability of, bias in, or
homogeneity of unit values calculated from the trade data. To consider the trade data as a source
in official statistics, these topics have to be addressed.
There is limited precedent using unit values as prices in the import price index in the
international price program. A crude petroleum import price index is currently calculated using
unit values derived from the U.S. Department of Energy (DOE) petroleum transaction import
records. i The DOE administrative data source is more reliable than survey data in the face of
low company response rates and the price volatility of this heavily traded product. Furthermore,
crude petroleum import records provide fairly detailed product information. In contrast, the
administrative trade transaction records do not have consistently similar product and transaction
information across the thousands of categories, in part because of the regulatory nature of trade.
Many of the 10-digit HS product categories are composed of differentiated goods, which means
that unit values grouped only by HS product are likely to be heterogeneous and not track product
price trends. In the face of the uneven detail of administrative trade data, is it possible to move

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beyond a ‘special case’ use of unit values, such as in crude petroleum, to a more comprehensive
approach?
Key to the decision of whether and how to use unit values from the administrative trade data
is having sound criteria for deciding when and how they can be applied. BLS requires a
consistent and transparent approach to evaluate 1) whether a product category is homogeneous
and, relatedly, 2) to what degree unit value bias exists in the entry level item and the published
index level. The potential to use unit values for the MXPI statistics faces two hurdles. The first –
evaluating and establishing a proof of concept to select homogeneous categories and 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 – is not insignificant, but will not
be addressed here.
In this paper, we outline both concepts and methods for using administrative trade data to
produce unit values and unit value indexes. Using 2015-16 export transaction records for dairy
and vegetables, we test six different ways to group characteristics in the administrative records
into entry level items (ELIs). Entry level items are the products in the index basket for which
prices are tracked across time periods, and which form the base unit of price change for price
indexes. Unit values for these ELIs are described and analyzed. Prices and price changes (short
term ratios, or STRs) are tested for unit value bias within and across months to identify the
groupings—or item keys—that result in the least bias. ELI prices then are aggregated using a
Tornqvist index formula to produce the 10-digit HS price indexes that are the building blocks for
the official product price indexes (Harmonized and BEA End Use) and industry price indexes for
imports and exports.

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For this research, applying a modified Laspeyres index formula, we use the 10-digit HS unit
value price indexes to form 5-digit BEA End Use indexes, and then compare those indexes to
existing BLS official price indexes as benchmarks for quality. A natural question is how our
indexes compare to BLS’s published BEA End Use export price indexes. Those published price
indexes are used to deflate imports and exports in GDP, meaning that differences in index values
would result in revisions to GDP if the unit value indexes were adopted. The comparative
analysis of the unit value indexes and the benchmark indexes leads us to propose a prototype unit
value index approach. The promising first results we obtain provide a road map for
comprehensively evaluating all import and export price indexes for homogenous categories.

THE RESEARCH APPROACH
Maintaining the standard for Principal Federal Economic Indicators when considering new
concepts or methodology requires thoughtful and thorough review. This research evaluates
which 10-digit HS categories are homogeneous and whether a more detailed grouping of
attributes is necessary to mitigate compositional effects of shipping contents on the resulting unit
value. The simplest case is one in which all or some 10-digit HS unit values provide as good a
measure of price change as the published import and export price indexes.
Two principles guide the methodological approaches in this research – to evaluate item
homogeneity, and to improve the index where possible. The research develops and evaluates new
methods to identify homogeneous products and to calculate unit value prices and indexes with
administrative trade data, using a small subset of export data for two years (2015-2016) for two
product areas – dairy and eggs (BEA End Use Classification 00310), and vegetables, vegetable
preparations, and juices (BEA End Use Classification 00330). ii We selected these two product
categories for two reasons - because the 10-digit HS product groups that comprise each BEA
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End Use product area appear relatively homogeneous and because these indexes historically had
been of uneven quality. The issues generally have stemmed from an insufficient number of
representative businesses voluntarily participating in the survey, resulting in an insufficient
number of prices, incomplete representation of sampled products, or inadvertent exclusion of
large traders. Precisely because of the quality issues, the official XPI for these product categories
may be an imperfect benchmark to validate the consistency and quality of the pilot index
measures.
Defining Homogeneity. Moving from a matched model price to homogeneous product unit
values requires consistency of definition of product attributes, sufficient transactions to group by
similar product attributes, and persistence over time of transactions with those same attributes.
Before using a homogeneous unit value in a price index, it is necessary to define what a
homogeneous product is. Nakamura et. al. (2015) consider primary attributes of products as the
only necessary characteristics to define a unit value. However, in the administrative trade data,
many 10-digit HS product category include a mix of different products. Given that international
trade transactions are more logistically complex and depend on well-defined sales contracts in
order to be backed by a letter of credit from a financial institution (Amiti and Weinstein 2009),
we expect that the non-price characteristics in the administrative records can provide additional
information to define products. That is, similarity of the transaction characteristics that define a
sale are expected to signal similarity of products and purchasers.
Transactions should be grouped to minimize differences in product attributes and also
maximize substitutability among the products in the included set. Price-setting research tells us
that the prices of homogeneous products vary over time. In studies of exchange rate pass-through
spanning nearly 100,000 goods in the international price survey from 1994 to 2005, Gopinath

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and Itskhoki (2010) and Gopinath and Rigobon (2008) demonstrate that homogeneous goods
experience both more frequent and larger price changes than differentiated goods. They attribute
these differences to larger elasticities of demand by consumers contributing to greater costs of
price stickiness for producers. Thus, in the case of homogeneous goods, unit values allow for
substitutability among similar products with different prices. As Nakamura et. al. (2015)
propose, such unit values may more accurately represent import and export prices than a single
price observation for the product from one sampled establishment. Additionally, the unit value
indexes calculated from the unit values are expected not to demonstrate the “product replacement
bias” of matched models delineated in Nakamura and Steinsson (2012), where frequent product
turnover results in no price changes across months for 40% of imported items.
What are the shared attributes that help define homogeneity? Rauch (2001) notes that business
networks linking country of origin and country of destination play an important role in market
share, price, and trade volume of goods. Furthermore, Clausing (2003) describes how intra-firm
trade and country impact price-setting. This research leads us to suspect that 10-digit HS product
categories on their own are likely to be too broad for unit value indexes to demonstrate the
characteristics of homogeneous products. To group transactions with a greater level of specificity
than the 10-digit HS product categories, we take into account price and non-price trade
characteristics that separate goods into unique bins or groups of substitutable products. Given the
high frequency of transactions in trade data, each bin is likely to have more than one transaction.
In other words, we aim to increase what we call intra-item substitutability by grouping
transactions by as many attributes that define the purchaser-seller relationship while assuring
persistence over time of transactions with those same attributes. To objectively evaluate the

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different groupings of products and their price dispersion, we use the coefficient of variation
(described below) to compare the different product groupings.
Better Measures. Mismeasurement of trade impacts other indicators such as real GDP and
productivity. The matched model has been criticized for measuring price changes of the same
good only, and missing prices for new goods and different quality goods (Feldstein 2017).
Nakamura et al. (2015) and Bridgman (2015) also describe sourcing substitution and trade cost
biases, especially for import price indexes, arguing that official price indexes are upwardly
biased.
The ability to account for new products and disappearing products and product varieties is a
benefit of the new method because the current values for all items are available and can be
integrated into a superlative unit value index. More specifically, the Tornqvist index is known to
adequately address substitution bias and can be implemented with the proposed unit value
indexes (Diewert 1976). It is important to note that the lag in collection of new goods and the
lack of current weights to account for changing tastes and trading patterns are not inherent in the
matched model method, but are related instead to the resources available for timely data
collection. The administrative data expand the ability to account for new goods, to exclude
products that are no longer traded, and to use current weights in a superlative index to account
for substitution. Furthermore, the use of multiple transactions at multiple prices addresses the
criticism of Nakamura et al. (2015) that single items may not be representative of a product when
multiple prices are present in a population.
The prices and indexes calculated and presented here are based on the two principles
described above. They are tested and evaluated for the degree of homogeneity and the existence
of unit value bias. Basic parameters are established as a result of this research to 1) define

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homogeneous unit values and items, 2) test item homogeneity, 3) identify appropriate BLS price
indexes as benchmarks for comparison, and 4) propose the concepts and methods to use for
survey production. These parameters provide the roadmap to systemically evaluate homogeneity
at the item and index levels.

UNIT VALUES and UNIT VALUE BIAS
Defining Unit Values. The point of departure for the research is to establish the 10-digit HS
product category as the starting point for evaluating unit values. This level of detail is naturally
occurring in the administrative trade data, as records are HS-specific. iii Given the fact that the
10-digit HS are also the strata from which MXPI indexes are sampled and calculated, this level
of detail provides the most convenient entry point to blend the unit values into the statistical
production process. Our research tests the premise that the 10-digit HS product categories are
homogeneous, and products grouped with more attributes are more homogeneous, thus
establishing a range of homogeneity from fewer products with fewer attributes to more products
with more attributes. Unit values are then calculated for this range of products within each 10digit HS product, in which each entry level item is actually a product group, and each entry level
item price is a unit value.
Whereas the simplest case occurs when the item key—the list of price-determining
characteristics that defines the item—contains only the 10-digit HS code (H), other item keys
include additional attributes that are similar to price-determining characteristics in the
international price survey. The attributes used in the item keys are: HS commodity classification,
EIN (establishment ID number) for the exporting company, zip code, state of origin, domestic
port of export, country of destination, related or arms-length trade iv and unit of measure. The
data fields for HS, EIN, and zip code correspond with the sampling unit (multi-stage sampling
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for the directly collected international price survey allocates price quotes across establishments at
the 10-digit HS product category level). The data fields for state of origin, port of export, country
of destination, related or arms-length transaction correspond to production and/or market
relations between exporter and foreign consumer. Most of these descriptors also are collected in
the survey as price-determining characteristics. For measurement consistency, the unit of
measure (e.g. gross, piece, ton) also is included. Each item key specification results in a different
set of unique items, or ELIs, with the same attributes grouped by the same shared characteristics.
The unit value is calculated at the level of the transaction. The unit value can be represented as
a transaction i of a unique item j in month t, where j is composed of a 10-digit HS code H, and is
further defined by an array of price characteristics, item key K. Transaction i involves the trade
of z actual items, where z is the number of actual items traded in transaction i. The unit value
price of a transaction i is the average of prices for actual items traded in i, or
(𝑗𝑗,𝑡𝑡),𝐻𝐻
𝑝𝑝𝐾𝐾𝑖𝑖

(i)

=

(𝑗𝑗,𝑡𝑡),𝐻𝐻
𝑖𝑖,𝑧𝑧

∑z∈𝑖𝑖 𝑝𝑝𝐾𝐾

,

𝑧𝑧

(𝑗𝑗,𝑡𝑡),𝐻𝐻

where z can alternatively be represented as 𝑞𝑞𝐾𝐾

𝑖𝑖

.

For all like-transactions of a given K that comprise the unique item j, the price of item j is
represented as a weighted geometric mean of unit value transaction prices which yields:
(ii)

𝐻𝐻
𝑝𝑝(𝑗𝑗,𝑡𝑡)

(𝑗𝑗,𝑡𝑡),𝐻𝐻
(𝑗𝑗,𝑡𝑡),𝐻𝐻
∙𝑙𝑙𝑙𝑙�𝑝𝑝𝐾𝐾
��
𝑖𝑖
𝑖𝑖
(𝑗𝑗,𝑡𝑡),𝐻𝐻
∑𝑖𝑖∈𝐾𝐾 𝑤𝑤𝐾𝐾
𝑖𝑖

∑𝑖𝑖∈𝑗𝑗�𝑤𝑤𝐾𝐾

= 𝑒𝑒𝑒𝑒𝑒𝑒 �

�

where normalized transaction-level weights are represented as
(𝑗𝑗,𝑡𝑡),𝐻𝐻

𝑤𝑤𝐾𝐾𝑖𝑖

(𝑗𝑗,𝑡𝑡),𝐻𝐻

= ∑z∈𝑖𝑖 𝑝𝑝𝐾𝐾𝑖𝑖,𝑧𝑧

.

The quantity of item j is represented as a sum of transaction quantities:

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(𝑗𝑗,𝑡𝑡),𝐻𝐻

𝐻𝐻
(iii) 𝑞𝑞(𝑗𝑗,𝑡𝑡)
= ∑𝑖𝑖∈𝐾𝐾 𝑞𝑞𝐾𝐾

𝑖𝑖

.

Taking an experimental approach to test different specifications of items supports the
objective to identify the best unit value measure. For the unit value tests, we use the price
changes of actual transactions based on attributes for six item key specifications.
Testing Unit Value Bias. To test for unit value bias, one must consider the price
characteristics of a homogeneous item. Homogeneous items are close, if not perfect, substitutes.
Thus, in a competitive market, they would be expected to have similar price levels and be
affected by the same market conditions over time. For multiple transactions of one product, we
call this condition intra-item substitutability. If there is no supply or demand shock or large
exchange rate fluctuation, one would expect a homogeneous product’s within-month prices to
group close to a mean, and its cross-month prices to show smoothness. For an item that faces a
market shock, prices may cluster around more than one mean price. Although some HS 10-digit
product categories experience more variable prices both within and across months, the large
majority of items display little price change between months. Efforts to define homogeneity in a
consistent way lead us to apply three types of test to the prices and price changes of items for the
six item key specifications. Of these tests – the price dispersion test, an across month item
percentage change test, and two price clustering tests – the first shows the most promise.
The price dispersion test was conducted on the actual unit values for dairy and vegetables
transactions. The coefficient of variation (CV) is the ratio of the weighted standard deviation of
prices within a month to the weighted mean; lower percentages indicate less variability in the
ELI. Even though findings from the trade literature report price variability in homogeneous
products, we assume there is a degree of within-month price variability for an item beyond which
an item is not homogeneous. The CV test allows us to identify a frontier of price variability
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beyond which a group of transactions comprising an item should not be considered
homogeneous. This test fits with findings from the trade literature that similar products from a
producer are priced similarly. The intra-month intra-item unit values for each of the six item keys
were evaluated for all 24 months. Results are shown for dairy unit values only, as vegetables
trend similarly. The bins in Figure 1 specify ranges of CVs. The least detailed item keys that
exclude the company identifier (EIN, or ‘E in the legend) result in a concave cumulative
distribution, in which the vast majority of ELIs present with high variability of within-month
prices, which implies poor intra-item substitutability. About 60 percent of dairy products had a
CV of less than 52.5 percent for the two item keys that exclude EIN. When the company
identifier is added to the ELI specification, prices cluster closer to the mean – 60 percent of the
ELIs that include the company identifier had a CV less than 12.5 percent. Furthermore, the most
detailed item key, which includes company identifier and country of destination, experiences the

Cumulative Percentage

Figure 1. Coefficient of Variation Test
Dairy Products and Eggs, 2015-16
100
90
80
70
60
50
40
30
20
10
0

10-digit HS

HQR

E-HQR

E-HQRS

E-HQRSZ

E-HQRSZCD

NOTE: Letters correspond to these non-price transaction characteristics: EIN (E), 10-digit HS (H),
Unit of Measure (Q), Related Transaction (R), State of Origin (S), Zip Code of shipper (Z),
Country of Destination(C), Domestic Port Code (D)

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least price dispersion for each good. The wide dispersion and variability shown in the item keys
that exclude the EIN demonstrate more unit value bias than for the item keys that include that
characteristic.
Another test of homogeneity looks at the month over month percentage change in price.
Monthly price changes are grouped into price variability bins for all months. Following on past
price-setting research that price variability across months is not expected to be large, any such
price change across months for item keys could indicate that the ELI may not represent the same
good. Looking at the cumulative results for dairy and vegetables, both show 75-85 percent of
ELIs with less than 22.5 percent monthly price changes. These results do not reveal intra-item
substitutability improvements with additional item key attributes and are not informative for item
key selection or unit value bias.
Two types of price cluster tests are applied to the price data for the ELIs. The first method
minimizes the variance in the price cluster created (Ward Minimum Variance Method) and the
second method minimizes the distance in the price clusters created (SAS Clustering Method 1).
Assuming no price shocks and no unit value bias, the optimal number of clusters for each ELI
should be one, as the item’s unit price should reflect intra-item substitutability. The Ward
Minimum Variance Method was applied to price clusters for all ELI that had 100 or more
transactions during the two year period. The clustering results show that all item keys for both
vegetables and dairy saw around 80 percent of their ELIs falling within one cluster. When using
SAS Clustering Method 1, results are sensitive to price cluster distance. When EIN is included in
the item key, the ELIs fall in one cluster around 60-63 percent of the time, compared to 31-40
percent of the time when it is excluded. These results suggest that including EIN in the item key
increases intra-item substitutability. Yet when outliers are removed at the second standard

15

deviation from the mean, ELIs had one cluster around 78-91 percent of the time, demonstrating
no definitive difference from the simplest case of 10-digit HS unit values.
The results of the coefficient of variation test align with the expectation of intra-item
substitutability, showing that the more detailed ELIs have more similar within-month unit values.
This test has strong explanatory power and is used to evaluate item homogeneity.

BENCHMARKING UNIT VALUE INDEXES WITH BLS PRICE INDEXES
Having selected ELIs that have intra-item substitutability and established an index
methodology, we consider the options for calculating the least biased unit value indexes and then
compare the resulting indexes to existing BLS price indexes. As set out in the introduction, we
compare the unit value indexes for 5-digit BEA End Use categories to appropriate price index
benchmarks in order to evaluate the potential impact of their adoption on GDP revisions. The
data we analyze are voluminous and many choices must be made in producing the unit value
indexes. We apply different assumptions for index calculation, imputations, and outliers to
produce a wide range of results, then compare the resulting unit value indexes for dairy and
vegetables with official benchmarks. The most obvious benchmarks for the unit value indexes
would be the official export price indexes based on the BEA End Use classification, but we have
selected two product areas whose official export price indexes are not of the highest quality. For
this reason, we consider other benchmarks.
Unit Value Index Calculation Methods. Unit value indexes are calculated at the level of 10digit HS strata. This procedure generally provides an opportunity to incorporate current weights.
The problem of missing prices is addressed both for the regular continuation of an ELI in the
index and also as it relates to consistency of establishments’ trade. The likely problem of outliers
that arises with high-frequency low-detail data is also addressed.
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Tornqvist index formula. The long term relative (LTR) of the 10-digit HS stratum is the entry
point for blending data. For official price indexes, company weights are used to aggregate ELI
price changes to the 10-digit HS product category, and then trade dollar weights for 10-digit HS
categories, lagged two years, are used to aggregate the LTRs and map them into the BEA End
Use price index and other classifications. Because current period weights are available in the
administrative trade data, the unit value ELIs can be aggregated into their corresponding 10-digit
strata. The 10-digit HS unit value Tornqvist indexes then are aggregated into the BEA 5-digit
index using official estimation procedures. The Tornqvist index is superior to a Laspeyres index
because it accounts for the introduction of new goods, disappearing goods, and changes in trade
volumes (Diewert 1976, Triplett 1992). The baseline case is to use the 10-digit HS stratum unit
value as the entry level item.
Using the current period weights, the 10-digit HS stratum is represented by a Tornqvist index
comprising all unique items j:

(iv) 𝑅𝑅𝐻𝐻,𝑡𝑡 = ∏𝑗𝑗∈𝐻𝐻 �
𝐻𝐻
where 𝑊𝑊(𝑗𝑗,𝑡𝑡)
=∑

𝐻𝐻
𝑝𝑝(𝑗𝑗,𝑡𝑡)

𝐻𝐻
𝑝𝑝(𝑗𝑗,𝑡𝑡−1)

𝐻𝐻
𝐻𝐻
𝑝𝑝(𝑗𝑗,𝑡𝑡)
𝑞𝑞(𝑗𝑗,𝑡𝑡)

𝐻𝐻
𝐻𝐻
𝑗𝑗∈𝐻𝐻 𝑝𝑝(𝑗𝑗,𝑡𝑡) 𝑞𝑞(𝑗𝑗,𝑡𝑡)

.

�

𝐻𝐻
𝐻𝐻
𝑊𝑊(𝑗𝑗,𝑡𝑡−1)
+𝑊𝑊(𝑗𝑗,𝑡𝑡)
2

These calculations differ from existing methodology, not only because we are using unit
values, but also in the use of current weights to account for item turnover. The opportunity to
apply the Tornqvist index to the unit values addresses a common criticism of the official indexes
– that they do not sufficiently account for substitution of new items. v
Missing prices, consistency of trade and outliers. In order to evaluate the unit value indexes,
methods must be adopted to address the problems of missing prices, inconsistent trading, and
outlier observations.
17

Index calculation requires two months of actual prices to establish an item in the index. Once
an item is established, imputation fills in the gaps when the item is not traded or its price is of
questionable quality. vi Even though 80 percent of the dairy and vegetable establishments in the
two-year dataset are traded every month at the 5-digit BEA product level, the items traded each
month vary considerably, resulting in many missing prices. Missing prices become even more
prevalent as attributes are added to the item key, because each ELI has fewer transactions and
experiences more turnover. Imputation is used to maintain items in the index, but there is a point
at which imputation negatively impacts index quality. To minimize the negative impact that
continuing imputed prices over time has on the indexes for the 10-digit HS strata, imputation is
suspended for items that have no transaction recorded after three months. Beyond that point, the
price imputations overwhelmed the count of unit values calculated directly from transaction
records by more than two to one.
Establishments with inconsistent trade are excluded from the sample for the official MXPI to
focus on respondents that can provide monthly prices. Inconsistent trade manifests itself in the
administrative trade data in the form of a trade off at the item level between defining the item
more precisely and experiencing more missing prices. The decision whether or not to include
inconsistently traded items in the 10-digit HS unit value indexes has implications for index
quality. Including inconsistently traded items increases the use of imputation, but excluding
items that are not consistently traded could bias unit values by not accounting for new goods.
Thus, two variations are tested for the unit value calculations—retain all items regardless of
consistency of trade and exclude items that are traded less than half the year. Both approaches
preserve the 3-month imputation rule set above.

18

The decision whether or not to eliminate outliers is of particular importance for unit value
index calculation. In the official MXPI, an outlier price is flagged to evaluate the validity of
monthly price change, but an outlier in the unit value of the transaction cannot be evaluated in
the same way. It may represent an error or a different product being traded. Three unit value
index calculations are considered—retain the outlier; recalculate the unit value with an imputed
price when the price change falls outside the two-standard-deviation band; or recalculate the unit
value with an imputed price when the price change falls outside the three-standard-deviation
band.
We nest outlier treatment within the two conditions of restrictions on consistent trade.
Combined, these variations create six alternatives to calculating unit value indexes. Table 1
shows the index calculation methods from the least constrained to most constrained options
regarding truncation of ELIs, and the statistical comparison of these alternative indexes against
BLS price indexes. All methods use the Tornqvist index formula and impute missing prices for
up to three months. The first three calculation methods include all items, and the last three
calculation methods exclude items that are not consistently traded.
Benchmark Comparisons. The comparison of the unit value indexes against BLS official
price indexes as benchmarks helps narrow down the proof of concept – of six different item keys
that define the ELI and six different methodological approaches to calculate the unit value
indexes – to a prototype. The 5-digit BEA End Use unit value indexes for dairy and vegetables
are calculated from the 10-digit HS strata with the methods used for the official MXPI, and these
indexes are then compared with a BLS price index as a benchmark. Holding all else equal, the
company identifier significantly improves the correlation and reduces the root mean squared
error. More detailed item keys show a closer fit than the baseline case of the 10-digit HS ELI.

19

The differences between the index calculation methods of including or excluding consistent trade
and treatment of outliers are not as clear-cut.
Because the two product groups were chosen due to quality concerns, the XPI for dairy and
vegetables for this time period were respectively unpublished and had low coverage. Thus the
best benchmark against which to measure the unit value indexes was not necessarily the XPI.
Export Price Indexes, spot prices, the relevant Consumer Price Indexes for all urban consumers,
and the relevant Producer Price Indexes (PPI) were considered as possible benchmarks for unit
value indexes. The unpublished XPI was chosen as a benchmark for dairy – even though the
index was unpublished due to insufficient company representativeness, there were a sufficient
number of prices in the index. Although consumer prices are systematically different from export
prices, meaning that the CPI is generally not the best comparative benchmark, it was chosen as
the benchmark for vegetables due to seasonal weighting concerns with the official vegetable
XPI.
Correlation coefficient comparison. Correlation coefficients assess how closely indexes
calculated from administrative data track changes in benchmark price indexes, where an estimate
of 1 suggests perfect alignment. We apply the six variations of the unit value index calculations
for each of the six selected item keys. The benefits of unit value indexes are realized with more
detailed item key specifications than the 10-digit HS level, but there is a possibility that item key
specifications with too much detail may be “over-fitted” – understating intra-item substitution
and missing price changes of high-volume or price-variable products. Additionally, truncating
outliers may introduce bias if outliers represent real price shocks.
Generally, correlation coefficients for dairy unit value indexes are higher than correlation
coefficients for vegetable unit value indexes, i.e. dairy unit value indexes do a better job of

20

tracking the price trends in the benchmark index. For dairy, correlation coefficients remain
consistent across different treatments of outliers and trade consistency. Correlation coefficients
vary more for vegetables, pointing to a less consistent time series. Dairy correlation coefficients
significantly improve after including company identifier in the item keys, with correlation
coefficients being on average 0.090 higher than correlation coefficients of indexes excluding the
company identifier, or EIN. Adding other attributes to define products resulted in correlation
coefficients that were 0.002 lower on average. The large increase in dairy correlation coefficients
in item keys that include the EIN implies that product differentiation may occur at the firm level
for items in the dairy category. This pattern, however, is not reflected for vegetables. Comparing
vegetable products with item keys that include and exclude the EIN, the correlation coefficients
are on average 0.012 lower than correlation coefficients excluding the EIN. This statistic is of a
smaller magnitude than the average 0.020 correlation coefficient increase with the addition of
non-EIN attributes in vegetable item keys.
Our assessment of the impact of index calculation methods on the correlation coefficient is
less informative. Dairy unit value indexes mirror the unpublished XPI benchmark, no matter the
index calculation method, when the EIN attribute becomes part of the item key. The vegetable
unit value indexes do not track the CPI benchmark to any large degree.
Root mean squared error/mean absolute error comparison. Root mean squared error and
mean absolute error measure differences between calculated and benchmark price indexes. We
interpret these measures as an indication of accuracy. Large differences are more heavily
weighted in root mean squared error than in mean absolute error. An error value of 0 implies
perfect similarity between unit value and benchmark price indexes. As can be seen in Table 1,
across index calculation variations, the dairy unit value indexes display larger error than the

21

vegetable unit value indexes compared to their respective benchmarks. For both indexes, error
measures trend downwards as item keys become more detailed, implying that accuracy increases
when more attributes are used to create items, regardless of index calculation methods.
Table 1. Unit Value Index Comparison to BLS Price Indexes, Dairy and Vegetables, 20152016
Exclude Company Identifier

Dairy U.V.Index

Tornqvist index w/ 3 month
imputation
+ exclude outliers 3rd Std.
+ exclude outliers 2nd Std.
Tornqvist index w/ 3 month
imputation + consistent trade
+ exclude outliers 3rd Std.
+ exclude outliers 2nd Std.
Tornqvist index w/ 3 month
imputation
+ exclude outliers 3rd Std.
+ exclude outliers 2nd Std.
Tornqvist index w/ 3 month
imputation + consistent trade
+ exclude outliers 3rd Std.
+ exclude outliers 2nd Std.
Vegetable U.V.Index
Tornqvist index w/ 3 month
imputation
+ exclude outliers 3rd Std.
+ exclude outliers 2nd Std.
Tornqvist index w/ 3 month
imputation + consistent trade
+ exclude outliers 3rd Std.
+ exclude outliers 2nd Std.
Tornqvist index w/ 3 month
imputation
+ exclude outliers 3rd Std.
+ exclude outliers 2nd Std.
Tornqvist index w/ 3 month
imputation + consistent trade
+ exclude outliers 3rd Std.
+ exclude outliers 2nd Std.

Include Company Identifier (EIN)

+ transfer
+ company
10-digit HS price + unit
identifier
measure

+ state of
origin

+ zip code
of shipper

Correlation Coefficient

+ country of
destination +
U.S. port

0.48

0.5

0.58

0.6

0.59

0.61

0.5
0.5

0.51
0.52

0.6
0.57

0.62
0.6

0.6
0.6

0.59
0.57

0.48

0.5

0.61

0.6

0.58

0.59

0.5
0.5

0.53
0.52

0.62
0.64

0.58
0.6

0.57
0.53

0.57
0.57

Root Mean Squared Errors / Mean Absolute Errors
2.71 / 2.16

2.61 / 2.07

2.00 / 1.57

1.91 / 1.45

1.90 / 1.35

1.82 / 1.44

2.61 / 2.10
2.61 / 2.10

2.55 / 2.06
2.58 / 2.09

2.02 / 1.50
2.07 / 1.53

1.90 / 1.43
2.00 / 1.47

1.96 / 1.50
1.97 / 1.50

1.88 / 1.50
1.96 / 1.60

2.72 / 2.18

2.59 / 2.10

1.99 / 1.53

2.04 / 1.52

2.03 / 1.48

1.96 / 1.54

2.61 / 2.11
2.61 / 2.11

2.56 / 2.11
2.56 / 2.10

2.05 / 1.53
1.99 / 1.52

2.08 / 1.63
2.07 / 1.52

2.08 / 1.67
2.22 / 1.65

2.07 / 1.58
2.04 / 1.57

Correlation Coefficient
0.37

0.48

0.24

0.23

0.29

0.35

0.32
0.32

0.30
0.31

0.35
0.35

0.34
0.37

0.40
0.35

0.39
0.39

0.26

0.37

0.32

0.35

0.37

0.33

0.33
0.33

0.32
0.33

0.38
0.40

0.38
0.45

0.43
0.46

0.41
0.47

Root Mean Squared Errors / Mean Absolute Errors
2.37 / 1.94

1.92 / 1.51

2.07 / 1.67

2.13 / 1.68

2.02 / 1.60

1.86 / 1.34

2.02 / 1.56
2.02 / 1.56

2.02 / 1.49
2.03 / 1.50

1.82 / 1.41
1.82 / 1.45

1.86 / 1.49
1.82 / 1.45

1.79 / 1.42
1.84 / 1.41

1.82 / 1.39
1.79 / 1.34

2.50 / 2.04

2.07 / 1.57

1.92 / 1.53

1.84 / 1.40

1.79 / 1.41

1.92 / 1.43

2.00 / 1.55
2.00 / 1.55

1.98 / 1.46
1.99 / 1.47

1.83 / 1.45
1.79 / 1.44

1.82 / 1.42
1.73 / 1.40

1.75 / 1.42
1.67 / 1.31

1.84 / 1.44
1.69 / 1.33

22

Similar to correlation coefficient trends, error decreases most significantly for dairy when EIN
is added into the item key, a trend that is not observed for vegetables. Mirroring the previous
correlation coefficient analysis, root mean squared error decreases by 0.555 points on average
after inclusion of EIN into the dairy item key, compared to a decrease of 0.029 points on average
for inclusion of a non-EIN attribute. For vegetables, root mean squared error decreases on
average by 0.126 points after EIN inclusion into item keys, compared to a decrease of 0.047
points on average for inclusion of a non-EIN characteristic. For dairy, the lowest level of error is
found using the most detailed item key with the least restrictive index calculation method; for
vegetables, the lowest level of error is found using the most detailed key with the most
constrained index calculation method. Both findings corroborate those based on the correlation
coefficient analyses.
Though the unit value dairy index tracks the benchmark index better than the unit value
vegetable index tracks its benchmark, the vegetable index comparison has smaller errors,
indicating greater accuracy. Both correlation coefficient and error analysis point to similar
methodologies to optimize accuracy and mirroring of benchmarks, most especially, for both
indexes, the inclusion of EIN in the item key but also the stronger treatment of outliers for the
vegetable index.

AN INITIAL PROTOTYPE FOR UNIT VALUES and UNIT VALUE INDEXES
Coefficient of variation, correlation coefficient, and error analysis yield a prototype for unit
value specification and unit value index calculation. Regarding the best specification for the ELI,
the most prominent result is the importance of company identifier in the item key. The
coefficient of variation results show the product prices based on the most detailed item key are
23

the least variable in price and the most homogeneous. Results including the EIN but not
necessarily other attributes were robust across the correlation coefficient, root mean squared
error, and mean absolute error analyses.
Regarding the index calculation methods, results are not as clear-cut. Because neither of the
benchmark indexes was a published export price index, it is possible that results are not
consistent when unit value indexes are compared to the benchmarks. Whereas the least
constrained index method calculation - retaining outliers and not truncating ELIs that are
inconsistently traded – provides a best fit for dairy, vegetables require a more rigorous treatment
of outliers and consistency in trade. It is possible that the differing success of particular methods
reflects differing market forces for the two cases. In particular, price and quantity changes are
more variable with seasonal items like vegetables, making price outliers less informative of
general price trends.
To proceed with a prototype index calculation method, we make two strong assumptions in
order to test other BEA 5-digit export indexes composed of homogeneous products that also have
published XPI benchmarks. First, we assume that the three-month imputation rule sufficiently
addresses any inconsistencies in trade, and thus, do not impose limits on ELIs that are
inconsistently traded. Second, though dairy unit value indexes are most accurate without
elimination of outliers, we proceed on the basis that it is prudent to treat price outliers, assuming
that they likely are due to differences in product mix in the shipment or incorrect transaction
records. Thus, we apply the Tornqvist index to a data set with no more than three months’
imputation for missing prices and additionally replace outlier prices outside the third standard
deviation band with imputed values.

24

We apply the prototype ELI—the most detailed item key—to evaluate homogeneity of all 5digit BEA End Use export product categories, based on the homogeneity of their ELIs. We then
calculate select unit value indexes with the prototype calculation method and compare then with
published XPI benchmarks. Homogeneity is evaluated as the level of intra-item substitutability,
where less price-dispersion indicates more homogeneity. Price dispersion is calculated through
the coefficient of variation test. To limit the presence of non-impactful problematic outliers, we
use the coefficient of variation for prototype vegetable unit values as an upper bound on the
coefficient of variation for a homogeneous category. Using this criterion, we identify 50 export
and 52 import 5-digit BEA End Use unit value indexes as homogeneous. We calculate three 5digit BEA end use export indexes—meat, soybeans and animal feed—based on the prototype and
evaluate the results against published XPIs with extensive price quotes. The indexes for soybeans
and animal feeds show a high degree of accuracy when assessed using correlation coefficients,
and the indexes for meat and animal feeds closely track published XPI benchmark indexes.
Table 2. Unit Value Index Comparison to Published Export Price Indexes, 2016
BEA End Use Export
Classification
Meat, poultry, and other
edible animal products
Soybeans and soybean
by-products
Animal feeds

Correlation Coefficient

RMSE

MAE

0.1657

1.677

1.128

0.9116

2.927

2.349

0.9519

0.918

0.744

CONCLUSION
Our findings hold the promise that it may be possible to blend unit value indexes with directly
collected survey data to calculate MXPI. Defining homogeneity and addressing unit value bias
are essential to this approach. We establish that the best approach to defining homogenous items
involves adding attributes to the 10-digit HS product grouping to create more detailed items and
25

limiting the price dispersion allowable for an item to be considered homogeneous. We identified
an inverse relationship between the number of attributes used to define an item and the price
variability among the transactions that comprise the item’s unit value. While having more
attributes and less price variability means that items are more homogeneous, it also means that
there is a greater risk of the items not being traded consistently, as number of transactions that
comprise that item’s unit value for a month is lower and the prevalence of missing prices across
months is greater.
Establishing an index methodology that works with unit values also is essential to blending
unit value indexes into the MXPI. The availability of prices and quantities allowed us to use a
Tornqvist index to address substitution bias. We established imputation to account for missing
prices and addressed outliers. These new methods were tested by comparing the unit value
indexes against benchmark price indexes to evaluate their similarities and differences. The three
tests we conduct to determine unit value index accuracy and tracking of benchmarks with 36
variations of item key and index calculation method show that EIN and other non-price
characteristics more precisely define a homogeneous good. The most detailed item key shows the
least price dispersion, most accuracy, and best benchmark tracking. There was no clear result for
which index formula provided the most comparable index, but the groundwork is laid for the
next round of comparisons.
Future research will assess unit value indexes from 2012 to 2017 for all 50 export and 52
import 5-digit BEA End Use categories that have sufficiently low within-category price
dispersion as to be considered homogenous. The results will be used to validate a prototype for
ELI specification and index calculation that consistently provides strong results. As part of this
research, options for systematically identifying over-fitted and under-fitted indexes will be

26

explored. Indexes’ impact on net trade and GDP as well as on top-level price indexes also will be
evaluated. Much work remains to be done, but we are encouraged by the results obtained thus
far.

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Import crude petroleum prices are derived from the administrative records of crude petroleum imports collected by
the U.S. Department of Energy. Detailed product categories are grouped by product and transaction characteristics
(i.e. gravity, crude stream, and country of origin) and average weighted prices are incorporated into the price index.
ii
The administrative trade data are collected through an electronic interface that exporters and importers use to
directly enter data on trade transactions. The U.S. Census Bureau collects and cleans the export data to calculate
official international trade measures, after which the data are transferred to the BLS.
iii
For a given shipment, each company must submit an individual record for each product as defined by the 10-digit
harmonized schedule classification (Schedule B for exports, and HTSUSA for imports). Thus, each record pertains
to only one Employer Identification Numbers (EIN) and one shipment. The record includes total dollar value,
quantity, company, transportation, and geographic information on provenance and destination of goods and shipper.
iv
Related trade is an intra-firm transaction that takes place between a parent and an affiliate.
v
BLS research has previously proposed using the Tornqvist index to blend secondary data sources with the matched
model where current period weights are available (Fitzgerald 2017).
vi
Missing item price values are imputed by applying the percent change of the item’s parent 10-digit stratum to the
item’s price in the previous month. However, the actual month-to-month price percent change for an item may not
be the same as the month-to-month price percent change for its parent classification level, which is an estimation
error associated with imputation.
i

28