### Index Interpretation

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.

### Index Construction

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:

(1) The BLS Division of International Labor Comparisons has produced studies in the past examining international cost of living comparisons.

(2) 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.

(3) The Organisation for Economic Cooperation and Development (OECD) publishes information on Prices and Purchasing Power Parities.

(4) The Penn World Tables, compiled by the University of Toronto, contain international economic information at http://datacentre.chass.utoronto.ca/pwt/index.html.

### 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 purposes.

### Price Bases

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.

### Sampling

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 rates.

### 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 remained constant.

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 exports.

The unit value index is only published at the one digit level of aggregation.

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!

### Weights

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.