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The Consumer Price Index and other
price indexes
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Why has the CPI gained such notoriety compared to other price indexes?• It is one of the most closely watched economic indicators
because of the devastating affect inflation can have on the economy.
• The CPI is important because a rise, especially in the Core estimate might push the Bank of Canada to raise interest rates in an effort to prevent inflation from getting out of hand.
• It is also important because a number of benefits such as the Canada Pension Plan, Old Age Security, private pension plans and some contracts such as labour contracts have a “cost of living” provision tied to the CPI.
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The CPI: Generic Definition
• A consumer price index (CPI) measures changes in the price level of consumer goods and services purchased by households. It is a measure of the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.
• The CPI is a statistical estimate constructed using the prices of a sample of representative items whose prices are collected periodically.
• Sub-indexes and sub-sub-indexes are computed for different categories and sub-categories of goods and services, being combined to produce the overall index with weights reflecting their shares in the total of the consumer expenditures covered by the index.
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The CPI: Generic Definition (cont’d)
• It is one of several price indices calculated by most national statistical agencies.
• The annual percentage change in a CPI is used as a measure of inflation.
• Two basic types of data are needed to construct the CPI: price data and weighting data.
• The price data are collected for a sample of goods and services from a sample of sales outlets in a sample of locations for a sample of times.
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The CPI: Generic Definition (cont’d)
• The weighting data are estimates of the shares of the different types of expenditure in the total expenditure covered by the index.
• These weights are usually based upon expenditure data obtained from expenditure surveys for a sample of households or upon estimates of the composition of consumption expenditure in the National Income and Product Accounts.
• Although some of the sampling of items for price collection is done using a sampling frame and probabilistic sampling methods, many items and outlets are chosen in a commonsense way (purposive sampling) that does not permit estimation of confidence intervals.
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The CPI: Generic Definition (cont’d)
• 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, clothing, each of which is in turn a weighted average of sub-sub-indices.
• At the most detailed level, the elementary aggregate level, (for example, men's shirts sold in department stores in Ottawa), detailed weighting information is unavailable, so indices are computed using an unweighted arithmetic or geometric mean of the prices of the sampled product offers.
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The CPI: Generic Definition (cont’d)
• 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 a 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, very similar to a true Laspeyres index.
• Ideally, the weights would relate to the composition of expenditure during the time between the price-reference month and the current month.
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The CPI: Generic Definition (cont’d)
• There is a large technical economics literature on index formulae which would approximate this and which 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.
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The CPI: Generic Definition (cont’d)
• Nevertheless, in some countries, notably in 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 (constant utility) 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.
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The CPI: Generic Definition (cont’d)
• Saving 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, for the older the weights the greater is the divergence between the current expenditure pattern and that of the weight reference-period.
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The CPI: Generic Definition (cont’d)
• It is one of several price indices calculated by most national statistical agencies.
• The annual percentage change in a CPI is used as a measure of inflation.
• Two basic types of data are needed to construct the CPI: price data and weighting data.
• The price data are collected for a sample of goods and services from a sample of sales outlets in a sample of locations for a sample of times.
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The CPI: Canada
• The Consumer Price Index (CPI) is an indicator of changes in consumer prices experienced by Canadians. It is obtained by comparing, over time, the cost of a fixed basket of goods and services purchased by consumers.
• Since the basket contains goods and services of unchanging or equivalent quantity and quality, the index reflects only “pure” price change.
• Price movements of the goods and services represented in the CPI are weighted according to the relative importance of goods and services in the total expenditures of consumers.
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The CPI: Canada
• Each good or service is considered to be an element in a fictitious basket, and price movements are assigned a basket share or weight commensurate with the proportion of total consumption expenditure they account for.
• For example, Canadians as a whole spend a much larger share of their total expenditures on rent than on milk. As a result, a 10% price increase in rental rates will have a greater impact on the All-items CPI than a 10% increase in the price of milk.
• CPI basket shares have recently been updated at four year intervals; the data to specify them are obtained primarily from the Survey of Household Spending (62-202-X).
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The CPI: Canada
• Release dates of the CPI for the coming year are published in advance, usually with the release of the CPI for October.
• They can be found in the Daily and in the publication "The Consumer Price Index" (62-001-X, free), available online from the "Key resource" module of our website under "Publications".
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The Canadian CPI: The definitive measure of the rate of inflation, why?
• It describes in general what has been happening to prices for goods and services which we, as consumers, are acquiring from day to day in the market place.
• It is available on a monthly basis and with only a short lag following the end of each month.
• Can be broken down into many components, so that movements in the total index can be explained in terms of changes in specific components.
• It is available for each major urban area and also for each province.
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The Canadian CPI: Target Population
• The target population of the CPI consists of families and individuals living in urban and rural private households in Canada.
• People living in collective households, such as members of communal colonies, prison inmates, and chronic care patients in hospitals and nursing homes are excluded from the target population.
• Students in higher-education programs living full-time in residence are not considered to be living in collective households and are part of the target population.
• Students are not part of their parents' households if they live less than 30 days a year with them.
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The Canadian CPI: Target Population
• Also excluded are people living on Indian reserves and official representatives of foreign countries and their families.
• Part-year households - households whose members were part of other households at the beginning of the year, or who have moved to Canada since the beginning of the year - are part of the target population (their exclusion used to be a problem for the CPI)
• Base period: The time base is the period for which the CPI equals 100; currently this is the year 2002.
• Collection period: For most products, prices are collected in the first three weeks of the reference month.
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The Canadian CPI: the Goods and Services
• The universe of goods and services consists of all consumer goods and services that can be associated with a retail price, that is, goods and services for which a price can be associated with a specific quantity and quality.
• Many public goods and services provided by governments, and for which there is no market price, are excluded since they cannot be associated with a retail price.
• For example, health services received through the health insurance system are excluded, as are life and disability insurance premiums.
• Drugs, medical supplies, dental care, and eye care goods and services purchased by the general population are included, since these goods and services can be associated with retail prices.
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The Canadian CPI: the Goods and Services
• In establishing the universe of goods and services for the CPI, no effort is made to isolate "luxuries" or "necessities", and none are omitted on moral grounds.
• For instance, some may regard the use of tobacco and alcohol as undesirable. However, these products are included in the product universe of the CPI because they represent a legitimate and relatively significant expenditure for many Canadians.
• Prices used in the CPI are final prices paid by consumers, after discounts, but inclusive of excise and sales taxes and any other indirect taxes paid by consumers.
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The Canadian CPI: Sampling
• Price collectors collect most price data using technical descriptions or specifications for the selected goods and services in the CPI sample.
• These are referred to as representative products. • The specification for a representative product contains:
(1) a description (e.g., "frozen French fried potatoes, regular, crinkle or shoe string cut"); (2) acceptable units of measure; (3) frequency of pricing (e.g., monthly); (4) quality requirements (e.g. "Grade A or Fancy"); and (5) description of unacceptable varieties (e.g., "super fries, super chips, dollar chips").
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The Canadian CPI: Sampling
• Representative products in the price survey may represent larger groups of similar products.
• Market intelligence and research by CPI product specialists are used to select and define representative products.
• As much as possible, interviewers track the price of the same products through time.
• However, a review of sales shares is conducted periodically to ensure that the sample of products continues to be representative.
• If a product fails to meet sales-share criteria, it is removed from the survey and replaced by another product with higher sales.
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The Canadian CPI: Sampling
• The CPI price sample is obtained from a judgmental (or purposive) selection of geographical areas, representative goods and services, and types and locations of retail outlets, except as noted below.
• Purposive sampling: The researcher chooses the sample based on the products they think would be appropriate for the study.
• The CPI price sample is obtained from a judgmental selection of geographical areas, representative goods and services, and types and locations of retail outlets, except as noted below.
• The timing of price collection during the month is predefined. The extent and quality of the sample is constrained by budgets and the information available on which to base the sampling process.
• The timing of price collection during the month is predefined. • The extent and quality of the sample is constrained by budgets and
the information available on which to base the sampling process.
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The Canadian CPI: Sampling
• There are about 600 goods and services identified to represent the price movement in 170 basic goods and services classes.
• Sample goods and services are chosen on the basis of representativeness and expected continuous availability.
• The geographical distribution of the sample varies by product. • The most geographically dispersed price samples are for goods
and services whose prices are likely to be heavily influenced by local market conditions (e.g., locally determined prices such as rents, water charges, local transit fares, and property taxes).
• In contrast, prices, such as car registration fees or postage fees, are collected from provincial or national agencies.
• The All-items CPI, at the Canada level, is based on an annual sample of over 875,000 price quotes.
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The Canadian CPI: Data sources
• Responding to this survey is mandatory.• Data are collected directly from survey respondents,
extracted from administrative files and derived from other Statistics Canada surveys and/or other sources.
• The price survey collects prices of a large, representative set of consumer goods and services. The frequency of collection of prices of any particular good or service varies depending on the nature of the goods and services.
• The prices of most of the goods and services surveyed for the CPI are collected monthly, usually in the first three weeks of the reference month.
• Gasoline prices are collected in four weeks of the month.
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The Canadian CPI: Data sources
• The prices of some goods are observed less frequently than monthly, since their prices tend to change less often.
• The prices of most food items are observed every month. Bus, train and taxi fares are collected twice a year. University tuition fees, property taxes and automobile registration fees are collected once a year.
• However, when prices change outside of the scheduled time of collection, a special sample of prices may be collected.
• Prices of seasonal goods (e.g. winter coats), which appear in the market place for only a few months of the year, are only observed in the months in which the product is available in sufficient quantities.
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The Canadian CPI: Data sources
• Over 90 percent of the price quotes used in the construction of the CPI are collected by personal visits to selected retail outlets.
• For products such as newspapers, cable television services, men's haircuts, fuel oil, and restaurant meals, prices are collected over the telephone and at least once a year, by personal visits.
• Some types of information are collected via the Internet.
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The Canadian CPI: Imputation
• Imputation is sometimes used in the CPI in instances when no prices are collected. This can happen for several reasons.
• Firstly, not all goods and services covered in the price survey are collected every month: (e.g., lawn mowers or snow suits), goods whose prices are relatively stable (e.g., parking fees), and some services whose prices change only once a year (e.g., university tuition fees).
• Secondly, the prices of some products are not collected in some geographical areas, usually because the quantities available to consumers in those areas are too limited to merit the cost of collecting price data (e.g., fuel oil in Alberta).
• Thirdly, prices may be imputed in cases where prices are missing in a given month, when they are out of stock or otherwise not available, or because the prices collected are of questionable quality.
• Finally, adjustments to captured price data are made in cases where the characteristics of a product have changed and this may be affecting its price. This is referred to as quality change, and steps are taken to account for it so that only pure price change is used to calculate the CPI.
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The Canadian CPI: Seasonal adjustment (a note)
• You can have a S.A. CPI. • Economic time series such as the CPI (or the unemployment rate) are made up
of four components:– St: The seasonal component– Tt: The trend component– Ct: The cyclical component– It: The error, or irregular component.
• Unlike the trend and cyclical components, seasonal components, theoretically, happen with similar magnitude during the same time period each year.
• The seasonal component of a series are often considered to be uninteresting in their own right and to cause the interpretation of a series to be ambiguous.
• By removing the seasonal component, it is easier to focus on other components.
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The Algebra of the CPI
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Schematic of the CPI
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MAJOR COMPONENTS
Basic Class
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Weighting Diagram of the CPI
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• http://www.statcan.gc.ca/imdb-bmdi/document/2301_D48_T9_V1-eng.htm
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New Goods Bias
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• The CPI tends to overstate inflation because of the following biases:– New goods bias– Quality change bias– Outlet substitution bias– Commodity substitution bias
• See: http://www.frbsf.org/econrsrch/wklyltr/el97-16.html
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The commodity substitution bias
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• If the CPI was a true COLI...
• u is almost impossible to measure • The Laspeyres price index is an upper bound to a COLI• The Paasche index is a lower bound.• The Fisher index (geometric average of the Laspeyres and
Paasche indexes) is a good approximation of a COLI.
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The CPI biases
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• Bank of Canada research suggests that the above four main sources of bias, taken together, cause the Canadian CPI to overstate increases in the cost of living by about 0.6 per cent per year.
• Which menas that if the annual rate of change in the CPI is 2.6%, the the bias corrected CPI would be 2.0%.
• This is somewhat below most estimates in other countries.• In the United States, the measurement bias is estimated to
be around 1 per cent.
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Recommendation of the Boskin Commission
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• To the Economists and Statisticians– “These professions should treat training in data collection, data
analysis, and interpretation more seriously and give it more space and attention in the standard curriculum. There should be more emphasis on measurement and sampling issues in the training of economists and statisticians. Effort should also be put into improving the ties between professionals in government and their academic and business colleagues. The academic world needs to be cognizant of the important work done by its colleagues in government who provide them with much of the "raw material" for their subsequent analyses and show more appreciation of their efforts and understanding of the constraints under which they are laboring”.
– http://www.ssa.gov/history/reports/boskinrpt.html#cpi8
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Housing: a challenging area for index number compilers.
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• The treatment of Owner-occupied housing (OOH) is not unanimous among statisticians.– Not so for rents: this service is readily priced and it is
this cost, the “opportunity cost” to the consumer that is priced.
– Opportunity cost: What he or she sacrifices by living in the rental unit.
• “The concept of consumption (recall we are measuring a CPI) implies that the standard of living depends on the consumption of housing services, and not on the purchase of houses. I think that is not controversial...” (Jack E. Triplett, 2001).
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Housing: a challenging area for index number compilers.
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• According to economists, the CPI should measure the opportunity cost faced by Owner-occupiers.
• Two views on the opportunity cost– User cost (UC): sell the house, earn interest on the owner’s
capital thus released, and buy it back a year later, making an allowance for its physical depreciation.
– Rental equivalence (RE): let the house to someone else for a year, in which case the cost is the rent that could be obtained for it. According to economists, the CPI should measure the opportunity cost faced by Owner-occupiers.
• There is no directly observable price, and also no directly observable monthly or annual expenditure weight.
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Housing: a challenging area for index number compilers.
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• Four objections to the RE approach1.Publicly subsidized housing and rents controls: changes
in rents may not measure monthly dwelling costs for owner-occupied dwellings very well.
2.Owner-occupied and rental housing are different markets and their prices do not move together.
3.Rental market is 'thin'.4.Pricing using the rental equivalence method is an
imputation.2.Many countries use the rental equivalence method: USA,
Japan, and Norway.
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Housing: a challenging area for index number compilers.
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• The user cost approach.
• ct:monthly cost of providing housing of specified characteristics
• Pt:is the price of the house itself• d:rate of depreciation• i:appropriate interest rate for housing investment. • Pt - Pt-1: capital gain (or loss) from holding the property for
one period.
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Housing: a challenging area for index number compilers.
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• Criticism of the user cost.– Capital gains, which reduce the cost of providing housing,
are volatile, and when capital gains are high (which will happen when house prices are accelerating), they may be large enough to create negative user cost.
– Central banks seldom like to see the price they control (interest rates) included in the CPI.
• Another solution is to include only the price change of housing. • Including house prices only in the CPI overstates the cost of
housing to owners during a period of rising house prices, and understates it if house prices fall.
• Conclusion: There is no satisfactory solution.
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Housing: The Canadian approach
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• Owned accommodation– Mortgage interest cost– Homeowners’ replacement cost– Property taxes– Insurance– Maintenance and repairs– Other homeowner expenses
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More price statistics
• See Statistics Canada (www.statcan.gc.ca)• Table 326-00092
Average retail prices for gasoline and fuel oil, by urban centre, monthly (cents per litre)
– http://www5.statcan.gc.ca/cansim/a05?lang=eng&id=3260009
• Latest CPI release:
– http://www.statcan.gc.ca/daily-quotidien/110921/t110921a1-eng.htm
• Table 326-00121 Average retail prices for food and other selected items, monthly (dollars)
– http://www5.statcan.gc.ca/cansim/a05?lang=eng&id=3260012
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More price statistics
• Table 326-00151 Inter-city indexes of retail price differentials for selected groups of consumer goods and services, annual (index, combined city average=100)– http://www5.statcan.gc.ca/cansim/a05?
lang=eng&id=3260015• Import and export price indexes:
– http://www5.statcan.gc.ca/cansim/a05?id=2280047&stByVal=3&lang=eng
• IPPI– http://www5.statcan.gc.ca/cansim/subject-sujet?
themeID=2786&spMode=tables&lang=eng
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More price statistics
• Table 326-00151 Inter-city indexes of retail price differentials for selected groups of consumer goods and services, annual (index, combined city average=100)– http://www5.statcan.gc.ca/cansim/a05?lang=eng&id=3260015
• Import and export price indexes:– http://www5.statcan.gc.ca/cansim/a05?
id=2280047&stByVal=3&lang=eng• IPPI
– http://www5.statcan.gc.ca/cansim/subject-sujet?themeID=2786&spMode=tables&lang=eng
• Service price index– http://www5.statcan.gc.ca/cansim/subject-sujet?
themeID=3967&spMode=tables&lang=eng
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