Consumer price index


A consumer price index is a statistical estimate of the level of prices of goods and services bought for consumption purposes by households. It is calculated as the weighted average price of a market basket of consumer goods and services. Changes in CPI track changes in prices over time. The items in the basket are updated periodically to reflect changes in consumer spending habits. The prices of the goods and services in the basket are collected from a sample of retail and service establishments. The prices are then adjusted for changes in quality or features. Changes in the CPI can be used to track inflation over time and to compare inflation rates between different countries. While the CPI is not a perfect measure of inflation or the cost of living, it is a useful tool for tracking these economic indicators. It is one of several price indices calculated by many national statistical agencies.

Overview

A CPI is a statistical estimate constructed using the prices of a sample of representative items whose prices are collected periodically. Sub-indices and sub-sub-indices can be computed for different categories and sub-categories of goods and services, which are combined to produce the overall index with weights reflecting their shares in the total of the consumer expenditures covered by the index. The annual percentage change in the CPI is used as a measure of inflation. A CPI can be used to index the real value of wages, salaries, and pensions; to regulate prices; and to deflate monetary magnitudes to show changes in real values. In most countries, the CPI is one of the most closely watched national economic statistics.
The index is usually computed monthly, or quarterly in some countries, as a weighted average of sub-indices for different components of consumer expenditure, such as food, housing, shoes, and clothing, each of which is, in turn, a weighted average of sub-sub-indices. At the most detailed level, the elementary aggregate level, detailed weighting information is unavailable, so indices are computed using an unweighted arithmetic or geometric mean of the prices of the sampled products. These indices compare prices each month with prices in the price-reference month. The weights used to combine them into the higher-level aggregates and then into the overall index relate to the estimated expenditures during the preceding whole year of the consumers covered by the index on the products within its scope in the area covered. Thus, the index is a fixed-weight index but rarely a true Laspeyres index since the weight-reference period of a year and the price-reference period, usually a more recent single month, do not coincide.
Ideally, all price revalidations are accepted, and the weights would relate to the composition of expenditure during the time between the price-reference month and the current month. There is a large technical economics literature on index formulas that would approximate this and that can be shown to approximate what economic theorists call a true cost-of-living index. Such an index would show how consumer expenditure would have to move to compensate for price changes so as to allow consumers to maintain a constant standard of living. Approximations can only be computed retrospectively, whereas the index has to appear monthly and, preferably, quite soon. Nevertheless, in some countries, notably the United States and Sweden, the philosophy of the index is that it is inspired by and approximates the notion of a true cost of living index, whereas in most of Europe it is regarded more pragmatically.
The coverage of the index may be limited. Consumers' expenditure abroad is usually excluded; visitors' expenditure within the country may be excluded in principle if not in practice; the rural population may or may not be included; certain groups, such as the very rich or the very poor, may be excluded. Savings and investment are always excluded, though the prices paid for financial services provided by financial intermediaries may be included along with insurance.
The index reference period, usually called the base year, often differs both from the weight-reference period and the price-reference period. This is just a matter of rescaling the whole time series to make the value for the index reference period equal to 100. Annually revised weights are a desirable but expensive feature of an index; the older the weights, the greater the divergence between the current expenditure pattern and that of the weight reference period.
It is calculated and reported on a per region or country basis on a monthly and annual basis. International organizations like the Organisation for Economic Co-operation and Development report statistical figures like the consumer price index for many of its member countries. In the US the CPI is usually reported by the Bureau of Labor Statistics.
An English economist by the name of Joseph Lowe first proposed the theory of price basket index in 1822. His fixed basket approach was relatively simple as Lowe computed the price of a list of goods in period 0 and compared the price of that same basket of goods in period 1. Since his proposed theories however were elementary, later economists built on his ideas to form our modern definition.

Calculation

For a single item

For a single item, the CPI can be calculated as:
or
where 1 is usually the comparison year and CPI1 is usually an index of 100.
Alternatively, the CPI can be performed as:
The "updated cost" is divided by that of the initial year, then multiplied by one hundred.

For multiple Items

Many but not all price indices are weighted averages using weights that sum to 1 or 100.
Example: The prices of 85,000 items from 22,000 stores, and 35,000 rental units are added together and averaged. They are weighted this way: housing 41.4%; food and beverages 17.4%; transport 17.0%; medical care 6.9%; apparel 6.0%; entertainment 4.4%; other 6.9%. Taxes are not included in CPI computation.
where the terms do not necessarily sum to 1 or 100.

Weighting

Weights and sub-indices

By convention, weights are fractions or ratios summing to one, as percentages summing to 100 or as per mille numbers summing to 1000.
On the European Union's Harmonized Index of Consumer Prices, for example, each country computes some 80 prescribed sub-indices, their weighted average constituting the national HICP. The weights for these sub-indices will consist of the sum of the weights of a number of component lower level indices. The classification is according to use, developed in a national accounting context. This is not necessarily the kind of classification that is most appropriate for a consumer price index. Grouping together of substitutes or of products whose prices tend to move in parallel might be more suitable.
For some of these lower-level indices detailed reweighting to make them be available, allowing computations where the individual price observations can all be weighted. This may be the case, for example, where all selling is in the hands of a single national organization which makes its data available to the index compilers. For most lower level indices, however, the weight will consist of the sum of the weights of a number of elementary aggregate indices, each weight corresponding to its fraction of the total annual expenditure covered by the index. An 'elementary aggregate' is a lowest-level component of expenditure: this has a weight, but the weights of each of its sub-components are usually lacking. Thus, for example: Weighted averages of elementary aggregate indices make up low-level indices.
Weight averages of these, in turn, provide sub-indices at a higher, more aggregated level and weighted averages of the latter provide yet more aggregated sub-indices.
Some of the elementary aggregate indices and some of the sub-indices can be defined simply in terms of the types of goods and/or services they cover. In the case of such products as newspapers in some countries and postal services, which have nationally uniform prices. But where price movements do differ or might differ between regions or between outlet types, separate regional and/or outlet-type elementary aggregates are ideally required for each detailed category of goods and services, each with its own weight. An example might be an elementary aggregate for sliced bread sold in supermarkets in the Northern region.
Most elementary aggregate indices are necessarily 'unweighted' averages for the sample of products within the sampled outlets. However, in cases where it is possible to select the sample of outlets from which prices are collected so as to reflect the shares of sales to consumers of the different outlet types covered, self-weighted elementary aggregate indices may be computed. Similarly, if the market shares of the different types of products represented by product types are known, even only approximately, the number of observed products to be priced for each of them can be made proportional to those shares.

Estimating weights

The outlet and regional dimensions noted above mean that the estimation of weights involves a lot more than just the breakdown of expenditure by types of goods and services, and the number of separately weighted indices composing the overall index depends upon two factors:
  1. The degree of detail to which available data permit breakdown of total consumption expenditure in the weight reference-period by type of expenditure, region and outlet type.
  2. Whether there is reason to believe that price movements vary between these most detailed categories.
How the weights are calculated, and in how much detail, depends upon the availability of information and upon the scope of the index. In the UK the retail price index does not relate to the whole of consumption, for the reference population is all private households with the exception of pensioner households that derive at least three-quarters of their total income from state pensions and benefits, and "high income households" whose total household income lies within the top four per cent of all households. The result is that it is difficult to use data sources relating to total consumption by all population groups.
For products whose price movements can differ between regions and between different types of outlet:
  • The ideal, rarely realizable in practice, would consist of estimates of expenditure for each detailed consumption category, for each type of outlet, for each region.
  • At the opposite extreme, with no regional data on expenditure totals but only on population and only national estimates for the shares of different outlet types for broad categories of consumption the weight for sliced bread sold in supermarkets in the Northern region has to be estimated as the share of sliced bread in total consumption × 0.24 × 0.7.
The situation in most countries comes somewhere between these two extremes. The point is to make the best use of whatever data are available.
Due to differences in weightings in the consumer basket, different price indices may be calculated for groups with various demographic characteristics. For example, consumer price indices calculated according to the weightings in the consumer basket of income groups may show significantly different trends.