The price change represented by an index number is usually
expressed as a percent change rather than as simply the change in
the level of the index. The percent change in an index from
Period 1 to Period 2 is calculated as:
((Index Period 2 / Index Period 1) x 100) -100.
As an example, December, 1999 with an index level of 110.4 is compared to March,
2000 with an index level of 115.4 by:
((115.4 /110.4) x 100) - 100 = 4.5%.
In this case the price index has increased 4.5%. The
information that the index level changed 5 index points
(115.4-110.4) is less useful because index point changes are
affected by the level of the index in relation to its base year period while percent
changes are not.
A price index is a statistical tool used to measure price changes over time.
The simplest index of price change is a percentage that shows how a price occurring
in one time period differs from a standard or base
period price. To express price change in the form of an index number, the
comparison price, P1, is divided by the base period price,
P0, to form a ratio P1/P0. This ratio is called a
price relative. A simple index number is obtained by multiplying the price relative
by 100. Thus the formula for a simple index number is
Index = ( P1/P0) * 100 = (Comparison Price/Base Price) * 100.
When the prices of many different commodities are to be added together to form
an aggregate index, a method must be used
to account for the relative importance of the different prices used in the index.
For example, if the value of steel in export trade is twice the value of aluminum
in export trade it is desirable in an aggregate index of prices that the price
of steel have twice the affect as an equal change in the price of aluminum.
This relative importance of the various items in the aggregate index is accounted
for by assigning different weights to the different items. Therefore the two
basic elements used in calculating price indexes are prices
and weights. The International Price Program uses export and import trade
values as weights.
There are many types of weighted aggregate price indexes. The International
Price Program uses a modified form of the Laspeyres
Index. The main feature of the Laspeyres Index is that fixed base period
quantities are used to aggregate prices. This feature means that the quality
of goods and services is fixed, new goods do not appear, and the prices of goods
that disappear must be observable. Because these implications are not consistent
with the actual workings of the economy, adjustments to the Laspeyres Index
must be made.
International Cost of Living Comparisons
Information on international cost of living comparisons is
available from the following sources:
- The U.S. State Department produces quarterly report indexes on Living Costs
Abroad, Quarters Allowances, and Hardship Differentials. The
telephone contact is 202-663-1121.
- The Organisation for Economic Cooperation and Development
(OECD) publishes information on Prices and Purchasing Power Parities.
- The Penn World Tables, compiled by the University of Toronto,
contain international economic information at http://datacentre.chass.utoronto.ca/pwt/index.html
- The BLS Division
of International Labor Comparisons has produced studies in the past
examining international cost of living comparisons.
International Price Program
In 1961, a report on Federal Price Statistics prepared by the
National Bureau of Economic Research (NBER) for Congress' Joint
Economic Committee suggested that responsibility for compilation
of export and import price indexes be assigned to a federal
statistical agency "to obtain the attention and resources
for these indexes that we believe are essential." A further
study undertaken for the NBER by Professors Irving Kravis and
Rober Lipsey gave a greater impetus to the Project. In their
study, eventually published as Price Competitiveness in
World Trade, Kravis and Lipsey outlined both the need
for such measures and the feasibility of producing them. In the
meantime, the BLS, largely because of its expertise in the
development of other price measures, had also begun research on
the feasibility of producing export
and import price indexes. Thus, the
International Price Program (IPP) was established in 1971.
IPP uses market sale prices and transfer
prices which are market related for calculating export and import
price indexes. Transfer prices that are not market related are
not used for index calculation but are kept for research
The majority of prices used in calculating import price
indexes are quoted FOB (Free On Board) Foreign Port. This
excludes duties, insurance and other extra charges to bring a
good into the United States. The majority of prices used in
calculating export price indexes are quoted FAS (Free Along Ship)
U.S. Port. This includes inland freight, insurance and other
charges to get the good to the carrier exiting the United States
but not afterwards. The prices are quoted at national boundaries
since the export and import price indexes' primary function are
as deflators of the export and
import volumes used in the U.S. national accounts figures. While
the International Price Program prefers exit point price bases,
point of origin or entry point price bases are used if they are
the industry standard.
Quality and Price Factor Adjustments
When an item whose price is
used in index calculation has a modification to one of its features and that modification is
reflected in its price, a "link" price is created in
order to compare the item's price in the period with the
modification to its price in the period before its modification.
The creation of an adjusted or link price is often referred to as
a quality adjustment. One requirement for creating a link price
is that the item must remain unchanged in its class, general
function, or purpose; otherwise, the price series is restarted.
Some examples in which an item has had a change made to one of
its features but the nature of the item and the factors which
determine price remain similar are: (1) A woman's short-sleeved
cotton blouse which is now long sleeved, (2) a formerly uncoated
plain aspirin which is now coated for easier swallowing, and (3)
a luxury sedan previously equipped with only a driver's side
airbag which is now equipped with both driver's and passenger's
side airbags. Link prices are also set for changes in unit of
sale specification (e.g., change from price per item to price per
dozen), for non-market discounts, and for changes in price basis.
To calculate a valid link price, the amount of the price
change (a positive or negative amount) associated with the new or
different feature must be quantified. For example, a car sold for
$10,000 in September is sold for $11,000 in October. If improved
paint has increased the cost of the car by $400 and the remaining
$600 increase in the price of the car is the company's normal
annual market increase then the link price is $10,600.
When a link price is set the item's price series is continued.
If information is not available to quantify a change in the item
description then a link price cannot be calculated and a
replacement if available is required. With a replacement, the old
item's price series ends and the new item's price series begins
with a more accurate starting point.
Every six months, the International Price Program resamples 25%
of its goods import/export universe. In the realm of international
trade, the appearance of new goods and the disappearance of other
goods presents a serious problem that requires the International
Price Program to resample its universe frequently. The volatility
in traded goods arises from changes in domestic prices, as well as
changes in the prices of foreign goods and changes in exchange
Unit Value Indexes versus Price Indexes
In 1961, before the creation of the International Price Program, The
Stigler Report produced by the National Bureau of Economic Research
stated, "Specification price data, such as those from the BLS Producer
Price programs should be used more extensively as deflators in the absence
of positive evidence of their unsuitability in individual instances. This
recommendation represents a change in order of preference from the present
practice which provides for using unit values except where they seem unreasonable."
Unit value indexes do not take into
account changes in a product's specifications when
measuring price change. For instance, the addition of
passenger side air bags to a car would cause an increase
in the unit value index since the index reflects changes
in the full cost of an item. The price index controls for
changes in specifications and would not indicate an
increase in the index in the above example as long as the
basic good as specified has not changed in price.
Unit value indexes reflect changes in product mix at
the finest level of detail independent of price change.
For instance, the unit value index would decrease in the
case of a shift from luxury cars to economy cars within a
product category even when all the prices for each item
The published data for unit value indexes do not
represent the entire U.S. export and import universe. For
the last year in which data were available the unit value
was calculated for 56% of all imports and 46% of all
The unit value index is only published at the one
digit level of aggregation.
Volatility in International Trade
Import and Export Price Indexes are very sensitive to the
changing composition of world trade. The International Price
Program reweights its index aggregation structures for goods every year
at the stratum level.
Below the stratum lower, the
weights used in aggregation are based on the sample design. These
weights are primarily based on the value of imports (or exports)
for a given company in a specific product category. The
International Price Program resamples each
quarter of the goods import/export universe every two years.
The history of petroleum imports serves as a good example of the impact of
changes in trade composition on the movement of price indexes. The relative
importance of petroleum imports to the U.S. economy has shifted considerably
in the past. In 1980, following OPEC induced shortages, the dollar value of
petroleum imported into the U.S. was 75.5 billion dollars. At that time, petroleum
imports accounted for approximately 31.3% of the nation's total imports. Five
years later, as Americans used fuel more efficiently and adopted alternative
energy sources, petroleum imports, valued at 51.3 billion dollars, dropped to
14.9% of imports. When the annual change in the All Imports price index from
December, 1985, to December, 1986, was first published using 1980 weights, the
index fell 8.7%. However, when the series was recalculated based on 1985 weights,
the All Imports index covering the same twelve month period increased .3% primarily
as a result of the change in the relative importance of petroleum imports!
The weights used in aggregating
import and export price indexes are taken from two sources
depending on the level of aggregation. At the stratum level of aggregation, the
trade weights for goods are based on U.S. import and export shipment values
as reported by the Bureau of Census. Trade weights at the
stratum level of aggregation for services are derived from a variety of other sources.
The trade weights used in aggregating import and export
price indexes are updated every year at the stratum level for goods, and are updated every
five years for most services. Weights are
assigned to each category of commodities or services, called a classification group, for the
specific base year. The
classification groups and their associated trade weights are
combined into lower level strata,
which in turn are aggregated into higher
level strata within each of the classification systems. The
aggregation process continues to the "All Imports" or
"All Exports" level. The larger the trade weight
assigned to a particular lower level stratum, the greater the
influence of any price shifts of that stratum on the aggregate.
Below the stratum lower level, the trade weights used in
aggregating indexes are based on the sample
design and are updated every six months for 25% of the goods
import/export universe. Each item
falls into a single weight group,
which is mapped into a classification
group, which in turn is aggregated to a stratum lower within each of the classification systems.
Last Modified Date: September 11, 2017