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

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. This page shows how to calculate an aggregate series using data available on the CPI website.

When creating a special index, the weight 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. The cost weight of an item represents the expenditure, in dollars, on that item based on data collected as part of the Consumer Expenditure (CE) survey. Here, we use cost weights based on the U.S. all items cost weight rounded to the nearest hundred million dollars, and multiplied by the published relative importance values.

As a basic example, consider the expenditure class beverage materials including coffee and tea (SEFP), which is an aggregate of coffee (SEFP01) and other beverage materials including tea (SEFP02). In order to calculate the percent change in the aggregate series, we use the cost weight for the components in the weight update period (here we are using December 2022), as well as the index value for December 2022 and our period of interest, here January 2023.

First, we calculate the index relative for January 2023 for each component series. This is done by dividing the index value for the January 2023 by the index value for December 2022. Next, we update the cost weights for our component series using the index relative. To do this, we calculate the product of the cost weight for December 2022 and the index relative for January 2023, resulting in a new cost weight for January 2023.

The cost weight for an aggregate series is the sum of the cost weights for that aggregate’s component series. To find the cost weight for the beverage materials including coffee and tea aggregate, we sum the cost weights for coffee and other beverage materials including tea. Once this is done, we can calculate the percent change between these two cost weights to find the percent change in our aggregate series between December 2022 and January 2023.

This example is shown in table 1.

Occasionally, a user wishes to estimate a price change that is not published by BLS. For instance, suppose a user would like 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.

This can be using the same methods as the beverage materials including coffee and tea example above, with an additional step. Since ‘services less energy services and shelter’ is not an officially published CPI item category, we first define it.

The CPI item aggregation page lists the definitions of published CPI item categories. In table 2, the definitions of services less energy services and shelter are given. Note that these differ slightly from those presented on the item aggregation page, because some of the series used as basic items in the estimation of published CPI series are not themselves published. Where this is the case, the expenditure class which contains those item categories is used instead. Once we have these definitions, we define ‘services less energy services and shelter’ as all of those items which are listed in the definition of services less energy services except for those which are also included in the definition of shelter. This definition is also shown in table 2.

Now following the same steps as in the simple beverage materials including coffee and tea example, we calculate ‘services less energy services and shelter’. This is shown in table 3.

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: October 23, 2023