Constructing special Consumer Price Indexes (CPIs) and their percent changes : U.S. Bureau of Labor Statistics

An official website of the United States government

The .gov means it's official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you're on a federal government site.

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Bureau of Labor Statistics > Consumer Price Index > Publications > Factsheets

Constructing special Consumer Price Indexes (CPIs) and their percent change

The Bureau of Labor Statistics (BLS) calculates many special aggregate indexes that are available in our online databases. Examples include all items less food and energy, all items less energy, and all items less food.

Occasionally, a user needs to estimate a price change that is not published by BLS. For instance, suppose a user needs a CPI series for ‘services less energy services and shelter’. This can be done by estimating a special index, in this case, services less energy services and shelter. It is important to remember that this estimate will not be an official CPI, though it can be used to estimate changes in prices for item categories not published by BLS.

When creating a special index, the relative importance of published indexes is a key component. To reflect the differences in the average expenditures on various items purchased, weights are assigned to each item. As the prices of the individual items change, the ratio of weight of each item to the weight of all items is reported as the item’s relative importance. The relative importance for each published index component is available for December of each year in the relative importance tables, or monthly in supplemental press release tables 6 and 7.

The first step in making a special index is to calculate an adjusted relative importance for the component being removed from services less energy services, in this case shelter. Calculate the index relative for the relevant period by dividing the index value for the month of interest (here December 2022) by the index value for the initial period (here December 2021). Multiply this index relative by the relative importance of the index in the initial period (here December 2021).

An example using the December 2021 relative importance data and the December 2022 and December 2021 CPI-U shelter component indexes for the U.S. city average (1982-84=100) is given in table 1.

Table 1, updating shelter relative importance
Month	Relative Importance	Index Value	Index relative	Product of initial-period RI and index relative
December 2021	32.946	341.241
December 2022		366.868	1.075	35.420

The same calculation using the same periods for the other index, in this case services less energy services, is given in table 2.

Table 2, updating services less energy services relative importance
Month	Relative Importance	Index Value	Index relative	Product of initial-period RI and index relative
December 2021	57.583	359.559
December 2022		384.906	1.070	61.642

As shown in table 3, the next step is to calculate the inital relative importance of the unofficial ‘services less energy services and shelter’ index. This is done by subtracting the original relative importance of shelter from the original relative importance of the services less energy services index.

Table 3, finding intial relative importance for 'services less energy services and shelter'
Item	Relative Importance, December 2021
Services less energy services	57.583
Shelter	32.946
Services less energy services and shelter	24.637

Table 4 shows the same calculation with the adjusted relative importance for the ending month.

Table 4, finding ending relative importance for 'services less energy services and shelter'
Item	Relative Importance, December 2022
Services less energy services	61.642
Shelter	35.420
Services less energy services and shelter	26.222

The final step is to calculate the percent change in ‘services less energy services and shelter’ between the two periods. To do this, first divide the updated relative importance for the ending period, December 2022, by the relative importance for the initial period, December 2021. Doing this yields 26.222/24.637, which is equal to roughly 1.0643.

Thus, one could estimate that prices for ‘services less energy services and shelter’ rose 6.4 percent from December 2021 to December 2022. As mentioned before, this is an estimate and does not represent an official BLS index.

The relative importance of a component is its expenditure or value weight, expressed as a percentage of the total for all items within an area. These ratios represent an estimate of how consumers would distribute their expenditures over time.

Relative importance ratios cannot, however, be used as estimates of current spending patterns or as indicators of changing consumer expenditures in the intervals between weight revisions, because consumption patterns are influenced by factors other than price change. These factors include income, variations in climate, family size, preferences, and the availability of new and different kinds of goods and services.

Additional information

Additional information may be obtained from the Consumer Price Index Information Office by email or calling 202-691-7000. Information on the CPI's overall methodology can be found in the BLS Handbook of Methods.

Last Modified Date: February 9, 2023