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Consumer Price Index

## 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. 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.

Table 1: Construction of beverage materials including coffee and tea (SEFP)
Item Code Item Title Cost Weight, December 2022 Index level, December 2022 Index level, January 2023 Index Relative, January 2023 Percent Change, January 2023 Cost Weight, January 2023 Percent Change in CW, January 2023

SEFP

Beverage materials including coffee and tea 139.208 141.512 1.017 1.7

SEFP01

Coffee 17367000000 234.473 239.827 1.023 2.3 17763561301

SEFP02

Other beverage materials including tea 9638685000 150.794 151.576 1.005 0.5 9688670090
Total 27005685000 27452231391 1.7

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.

Table 2: Composition of selected CPI aggregate items
Item Item Title Components

SASLE

Services less energy services SEEB01, SEEB02, SEEB03, SEEB04, SEEB09, SEEC01, SEEC02, SEED03, SEED04, SEEE03, SEEE09, SEGC, SEGD01, SEGD02, SEGD03, SEGD04, SEGD05, SEGD09, SEHA01, SEHB01, SEHB02, SEHC01, SEHC09, SEHD01, SEHG01, SEHG02, SEHP01, SEHP02, SEHP03, SEHP04, SEHP09, SEMC01, SEMC02, SEMC03, SEMC04, SEMD01, SEMD02, SEMD03, SEME, SERA02, SERA04, SERB02, SERD02, SERD09, SERF01, SERF02, SERF03, SERF09, SETA03, SETA04, SETD01, SETD02, SETD03, SETD09, SETE, SETF01, SETF03, SETF09, SETG01, SETG02, SETG03, SETG09

SAH1

Shelter SEHA01, SEHB01, SEHB02, SEHC01, SEHC09, SEHD01

n/a

'Services less energy services and shelter' SEEB01, SEEB02, SEEB03, SEEB04, SEEB09, SEEC01, SEEC02, SEED03, SEED04, SEEE03, SEEE09, SEGC, SEGD01, SEGD02, SEGD03, SEGD04, SEGD05, SEGD09, SEHG01, SEHG02, SEHP01, SEHP02, SEHP03, SEHP04, SEHP09, SEMC01, SEMC02, SEMC03, SEMC04, SEMD01, SEMD02, SEMD03, SEME, SERA02, SERA04, SERB02, SERD02, SERD09, SERF01, SERF02, SERF03, SERF09, SETA03, SETA04, SETD01, SETD02, SETD03, SETD09, SETE, SETF01, SETF03, SETF09, SETG01, SETG02, SETG03, SETG09

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.

Table 3: Construction of services less energy services and shelter
Item Code Item Title Cost Weight, December 2022 Index level, December 2022 Index level, January 2023 Index Relative, January 2023 Percent Change, January 2023 Cost Weight, January 2023 Percent Change in CW, January 2023

SEEB01

College tuition and fees 103941495000 916.495 916.002 0.999 -0.1 103885582903

SEEB02

Elementary and high school tuition and fees 26745180000 956.645 956.719 1.000 0.0 26747248838

SEEB03

Day care and preschool 49409115000 340.174 342.261 1.006 0.6 49712244642

SEEB04

Technical and business school tuition and fees 2257710000 268.689 269.401 1.003 0.3 2263692714

SEEB09

Unsampled tuition, other school fees, and childcare 6599460000 1.000 0.0 6599460000

SEEC01

Postage 5470605000 354.565 356.967 1.007 0.7 5507665604

SEEC02

Delivery services 868350000 392.261 416.625 1.062 6.2 922284700

SEED03

Wireless telephone services 125476575000 48.750 48.732 1.000 0.0 125430245188

SEED04

Residential telephone services 21014070000 145.719 148.163 1.017 1.7 21366518116

SEEE03

Internet services and electronic information providers 84229950000 81.332 82.159 1.010 1.0 85086416934

SEEE09

Unsampled information and information processing 607845000 1.000 0.0 607845000

SEGC

Personal care services 52708845000 322.018 322.717 1.002 0.2 52823259358

SEGD01

Legal services 20840400000 405.211 405.211 1.000 0.0 20840400000

SEGD02

Funeral expenses 14675115000 370.228 371.990 1.005 0.5 14744957239

SEGD03

Laundry and dry cleaning services 12330570000 211.187 212.302 1.005 0.5 12395671477

SEGD04

Apparel services other than laundry and dry cleaning 2344545000 248.369 250.111 1.007 0.7 2360989071

SEGD05

Financial services 15109290000 385.656 395.285 1.025 2.5 15486536441

SEGD09

Unsampled items 6599460000 1.000 0.0 6599460000

SEHG01

Water and sewerage maintenance 65734095000 639.319 646.581 1.011 1.1 66480766064

SEHG02

Garbage and trash collection 26050500000 565.185 570.412 1.009 0.9 26291422819

SEHP01

Domestic services 22837605000 205.307 206.259 1.005 0.5 22943502022

SEHP02

Gardening and lawncare services 27439860000 236.999 1.000 0.0 27439860000

SEHP03

Moving, storage, freight expense 9204510000 199.717 200.770 1.005 0.5 9253040416

SEHP04

Repair of household items 9725520000 325.578 319.469 0.981 -1.9 9543034692

SEHP09

Unsampled household operations 6512625000 1.000 0.0 6512625000

SEMC01

Physicians' services 161078925000 415.611 415.197 0.999 -0.1 160918470452

SEMC02

Dental services 79627695000 560.198 563.582 1.006 0.6 80108703715

SEMC03

Eyeglasses and eye care 27266190000 199.607 198.971 0.997 -0.3 27179312802

SEMC04

Services by other medical professionals 45501540000 255.471 255.438 1.000 0.0 45495662422

SEMD01

Hospital services 168459900000 383.150 385.064 1.005 0.5 169301430076

SEMD02

Nursing homes and adult day services 16151310000 263.996 269.002 1.019 1.9 16457577738

SEMD03

Care of invalids and elderly at home 12764745000 146.138 148.486 1.016 1.6 12969836224

SEME

Health insurance 66862950000 189.070 182.312 0.964 -3.6 64473042473

SERA02

Cable, satellite, and live streaming television service 75112275000 544.717 547.509 1.005 0.5 75497270276

SERA04

Purchase, subscription, and rental of video 10159695000 70.416 71.145 1.010 1.0 10264875891

SERB02

Pet services including veterinary 46543560000 306.453 310.869 1.014 1.4 47214254563

SERD02

Photographers and photo processing 3299730000 131.904 135.521 1.027 2.7 3390213408

SERD09

Unsampled photography 86835000 1.000 0.0 86835000

SERF01

Club membership for shopping clubs, fraternal, or other organizations, or participant sports fees 58787295000 155.473 156.205 1.005 0.5 59064078107

SERF02

Admissions 38033730000 428.825 433.278 1.010 1.0 38428679454

SERF03

Fees for lessons or instructions 15977640000 368.247 372.114 1.011 1.1 16145422857

SERF09

Unsampled recreation services 20493060000 1.000 0.0 20493060000

SETA03

Leased cars and trucks 63129045000 110.411 111.465 1.010 1.0 63731684351

SETA04

Car and truck rental 11028045000 184.218 175.721 0.954 -4.6 10519379732

SETD01

Motor vehicle body work 4949595000 399.411 401.172 1.004 0.4 4971417726

SETD02

Motor vehicle maintenance and servicing 50016960000 321.717 322.869 1.004 0.4 50196060072

SETD03

Motor vehicle repair 35949690000 234.246 240.662 1.027 2.7 36934352325

SETD09

Unsampled service policies 4949595000 1.000 0.0 4949595000

SETE

Motor vehicle insurance 218042685000 648.771 658.513 1.015 1.5 221316832330

SETF01

State motor vehicle registration and license fees 24140130000 190.938 192.801 1.010 1.0 24375667516

SETF03

Parking and other fees 17019660000 221.243 224.454 1.015 1.5 17266674045

SETF09

Unsampled motor vehicle fees 1823535000 1.000 0.0 1823535000

SETG01

Airline fares 50972145000 268.519 264.629 0.986 -1.4 50233718132

SETG02

Other intercity transportation 4254915000 163.190 161.377 0.989 -1.1 4207643961

SETG03

Intracity transportation 12591075000 340.709 336.875 0.989 -1.1 12449387573

SETG09

Unsampled public transportation 347340000 1.000 0.0 347340000

n/a

"Services less energy services and shelter" 2064154785000 2072656742460 0.4