Publications

The Canadian Consumer Price Index Reference Paper

Chapter 1 – Introduction to the Canadian Consumer Price Index

Warning View the most recent version.

Archived Content

Information identified as archived is provided for reference, research or recordkeeping purposes. It is not subject to the Government of Canada Web Standards and has not been altered or updated since it was archived. Please "contact us" to request a format other than those available.

Archived

This page has been archived on the Web.

Skip to text

Text begins

1.1 The Canadian Consumer Price Index (CPI) is an indicator of the change in consumer prices. It measures price change by comparing through time the cost of a fixed-basket of consumer goods and services. Since the basket contains products of unchanging or equivalent quantity and quality, the index reflects only "pure� price change.

Availability and Uses

1.2 The CPI is released every month, about three weeks after the price observation period. A variety of CPI time series statistics for different product classes and geographical areas are available without charge on the Statistics Canada Internet site by means of CANSIM, Statistics Canada's on-line database, and via analytical publications.Note 1

1.3 The index is used for an assortment of different purposes by various users. One of its most important uses is by governments, businesses and individuals to adjust selected contractual or legislated payments in line with inflationNote 2. By linking a stream of future payments to the CPI, it is possible to ensure the purchasing power represented by those payments is unaffected by the average change in consumer prices that may occur.

1.4 For more than two decades the Bank of Canada has based its monetary policy approach on inflation targeting, aiming to hold the rate of inflation, as measured by the CPI, between one and three per cent. In addition, the federal and provincial finance ministries frame their fiscal policies in terms of the income and expenditure accounts which, in turn, are reliant for their calculation on the CPI, among other statistical data sources. The CPI is regularly and widely reported by the news media and is the standard measure of inflation used by most Canadians.

1.5 The CPI itself compares prices in the current month, t, to prices in the index reference period, where the index is set arbitrarily to 100. For many purposes it is also useful to calculate month-over-month changes or 12-month changes, comparing prices in the current month to those in the immediately previous month or the same month one year earlier. contributions to percentage change are also useful because they provide the influence of changes in sub-aggregate indices to changes in aggregate indices. In Statistics Canada's CPI publications, all indices and percentage changes are rounded to one decimal place.

1.6 For more on the availability and uses of the Canadian CPI, and on the interpretation of percentage changes and contributions to change in the CPI and the effect of statistical rounding on the index, refer to Chapter 2.

Scope of the Index

1.7 The CPI does not purport to measure the average movement of prices for all products bought and sold in Canada. Rather, its scope is limited to the prices of goods and services purchased by households in Canada. Moreover, the purchases of most, but not all households are in scope. The few exceptions include soldiers on military bases, people living on First Nations reserves and institutionalized persons, such as prison inmates and persons in long-term care facilities. In addition, households living in the rural areas of the three northern territories, outside Yellowknife, Whitehorse and Iqaluit, are deemed out of scope due to the difficulty and cost of monitoring prices in those remote regions.

1.8 Many products are out of scope for the CPI. For example, the prices of raw materials and other intermediate products purchased by manufacturers as inputs to their production processes are not included. Nor are the prices paid by governments for office equipment, consulting services and other products. Likewise the prices paid by businesses in other countries for exported Canadian goods and services are excluded. The CPI is all about the prices paid by households for consumer goods and services.

1.9 Financial products such as equities and bonds are not included either, even though they might be purchased by consumers, since they are considered financial investments rather than consumer goods or services. Nevertheless the prices of the services that facilitate the purchase of such financial assets, such as banking and brokerage charges, are in scope. Illegal products, such as non-prescription narcotic drugs, and a few legal products such as gambling services are also excluded, because of the practical or conceptual difficulties they present.

1.10 The CPI aims to measure average transaction prices throughout the entire reference month. Prices reflected in the index are those actually paid by Canadians to purchase consumer goods and services, including the impact of any discounts or sales and excise taxes that may apply, such as the Goods and Services Tax. Accordingly when tax rules or rates change, the index is affected. The index does not include personal income taxes because these are not associated with the purchase of any particular product.

1.11 Chapter 3 provides a more thorough explanation of the CPI scope.

Classifications

1.12 The CPI covers a wide range of goods and services and a large geographical area. It does this by using classifications of products and geography. The product classification contains 691 product classes that together account for all products in scope for the CPI calculation. The geographical classification has 19 area strata representing the ten provinces, with four in Ontario, three in Quebec, two in British Columbia and one in each of the others, plus the Primary Census Agglomeration (PCAs) of Yellowknife, Whitehorse and Iqaluit. The CPI is built up from price indices for elementary aggregates, which are pairings of product and geography classes from these two classifications. For more information about the product and geography classifications and the associated elementary aggregates, see Chapter 4 and Appendix B.

Sample Strategy

1.13 Households engage in millions of transactions every month. Most of the prices involved in these transactions are in scope for the CPI. However, since it is not practical to observe the prices in all transactions, a statistical sampling approach is required. That approach involves a general sampling strategy for most prices combined with more specialized strategies for some specific product classes.

1.14 General sampling for the CPI occurs in three stages. In the first stage, a set of representative geographical collection areas is selected, first in terms of census sub-divisions (which are essentially municipalities) and then in terms of specific census tracts within the chosen sub-divisions (which are like neighbourhoods within municipalities). The sampling of census sub-divisions (CSDs) and tracts is done with population counts serving as weights.

1.15 The second stage is the selection of representative outlets from the CPI outlet frame. The degree of "representativeness� of outlets is assessed using a variable such as annual sales revenue. In the third stage a set of representative products (RPs) from each of the product classes is chosen to characterize all the products in that class and to be collected in the outlets selected at the second stage. The product sample is not probabilistic because there is no comprehensive sampling frame for all consumer transactions.

1.16 At the outlet sampling stage, the goal is to identify sales by product class by type of outlet (large retail stores, small retail stores, Internet sales, and so on), in order to identify which types of outlets account for the largest proportion of consumer purchases. That done, specific outlets can be selected in which to observe the prices of specific RPs. For a few product classes, where national or provincial pricing predominates, prices are collected via the Internet or through other means not involving direct collection in stores. However, in most instances prices are obtained locally in retail stores.

1.17 From each product class a small sample of RPs is chosen to characterize all the products in that class. Ideally the selection of RPs would be chosen probabilistically, with associated weights reflecting the relative importance of each product within the class. This would require a products "frame� – a comprehensive and up-to-date list of products with associated expenditure values – from which to select and weight the sample of collected prices. Frame information of this kind is available for a few selected product classes, but is presently unavailable for most product classes. For this reason, the selection of RPs for most product classes is done judgmentally, with emphasis on products that are known to be among the most popular with consumers.

1.18 For a few product classes, no sampling is required because it is possible to observe all transaction prices for the entire product class. This is substantially the case for passports, passenger vehicle permits and driver's licenses. Cut-off sampling is used in some instances. The profiles method is used where the market normally prices product bundles instead of individual products and the bestsellers method is used for products where prices are based on the intangible characteristics, such as novelty of the content.

1.19 The sample size is limited by budgetary considerations. Given a particular sample size, the optimal allocation of sample across product/outlet pairs is a challenge. Key factors entering into decisions about this allocation are the volatility of the product price, the basket weight for the product class in question and the associated collection cost. The more volatile a product's price, the greater its basket weight and the lower the marginal cost of price quote collection, the larger will be the price sample for that product category.

1.20 Chapter 5 provides more details on the sampling strategy for the CPI.

Price Collection

1.21 Most of the price quotes used to calculate the CPI are collected in the sampled outlets in various locations across the country. The collection is done by employees, known as interviewers, supervised by the Statistics Canada Regional Offices. Each month Statistics Canada headquarters sends a sample request to the interviewers, who collect the requested price quotes, record them in Computer-Assisted Personal Interview (CAPI) devices and transmit the data to headquarters in Ottawa for further processing.

1.22 Back at headquarters the observed prices are reviewed for conformity with the sample request, checked for unusual or 'outlier' values and corrected if necessary, adjusted for quality changes where appropriate (as explained in Chapter 7) and generally made ready for the CPI calculation.

1.23 For more about the price sample collection and processing procedures, see Chapters 5 and 7.

Calculation of the Consumer Price Index

1.24 The calculation of the CPI is done in two steps. The first, termed the lower level calculation, involves calculating price relatives, using a matched-model approach, and then averaging them together to obtain elementary price indices. The second step, referred to as the upper level calculation, involves the estimation of aggregate price indices as weighted averages of the elementary price indices.

1.25 The lower level calculations are mostly done using an implicitly weighted geometric mean equation, referred to as the Jevons formula. There are some exceptional cases, however, where alternative formulas are used. Some of the more significant among these special cases are the elementary product classes for mortgage interest charges (explained in Chapter 10), dwelling rents, property and automobile insurance, banking services and post-secondary education services (see Chapter 6 and Appendix B).

1.26 The upper level calculations are done using a fixed-basket Lowe formula, which applies fixed quantity weights to the elementary price indices in order to aggregate them. The basket weights determine the relative importance of different product classes and geographical regions in the All-items CPI.

1.27 The structure and methodology of the CPI are technically complex and the summary just given omits many details. A fuller description is provided in Chapter 6. In addition, the mathematical formulas for the aggregation of the CPI are listed in Appendix A.

Quality Change and Adjustment

1.28 The CPI aims to measure 'pure' price change and it does this via the 'matched-model' approach to sampling. However, what happens when a given sampled product is no longer carried by a particular outlet, or when the outlet in which the product's price is collected has closed its doors? In this kind of situation a substitute product or a replacement outlet must be chosen and price change in the affected month must be adjusted for any quality difference that may exist between the new and the old products.

1.29 Adjustments for quality change are often fraught with difficulty and pose a demanding challenge for index compilers. A variety of different methods are employed depending on the circumstances.

1.30 For some products there is no significant possibility of quality change and for these, no adjustments are needed. Examples include products like electricity, natural gas, motor gasoline and refined sugar and flour. For some packaged products, the quality is unlikely to change significantly but the quantity in the container may increase or decrease. When this happens, the observed price change is adjusted to standardize for quantity. Examples of this standardization treatment include cereals, laundry detergents and candy bars. The more difficult cases of quality adjustment involve such products as automobiles, high-tech goods, items of clothing and many types of services. These products involve more substantial changes in the inherent quality of the product over time as a result of technological innovation, changes in fashion or other factors.

1.31 A thorough discussion of how quality change is dealt with in the CPI is provided in Chapter 7. As explained there, a variety of methods are used for the various product classes. Among these are implicit techniques, such as direct price comparison, overlap pricing, overall mean imputation, and link-to-show-no-change. Where implicit adjustment is not feasible, various explicit quality adjustment methods, including hedonic modeling, the option cost method or expert judgment are used. The table in Appendix B includes a column showing the quality adjustment method used for each published product class.

Weights and Basket Updates

1.32 The product and geographical classifications, discussed in Chapter 4, are important to many aspects of the CPI. They offer users of the index considerable detail that is helpful in analyzing inflationary trends. They provide a foundation for the price sampling strategy, as discussed in Chapter 5. In addition, they are central to the "fixed basket� concept that underlies the CPI upper level calculation.

1.33 To grasp the fixed basket concept consider the following story. A person enters a store, fills a shopping basket with various products and pays for these items at the cash register. The following month the person goes back to that store and buys the exact same quantities of the same goods and services. In other words, the person buys a "fixed basket� of goods and services. The cost of the products bought in the second month divided by the cost of the identical items purchased in the first month is an aggregate price relative. Defining a price index starting value of 100 in the first month, the price index will change in the second month to 100 multiplied by the aggregate price relative just computed. This is what is meant by a fixed basket concept. The CPI is essentially a fixed basket index of this type, except that the CPI "basket� contains not just a few specific products, but rather all the in-scope goods and services purchased by households in Canada.

1.34 Each of the elementary classes has a fixed quantity weight that is used as part of the CPI aggregation process – that is, to combine the elementary price indices into the All-items CPI. However, data on consumer expenditures is much easier to obtain than data on quantities purchased. Since the Lowe formula can be expressed in terms of quantities, expenditures or expenditure shares, the aggregate expenditures for each elementary class are used. These expenditures are a product of the unobserved quantities and the observed prices. In order to maintain the fixed quantity nature of the index, the expenditures used in the calculation have to be price-updated according to observed price changes.

1.35 The CPI expenditure weights are estimated primarily from data taken from Statistics Canada's Survey of Household Spending (SHS), which is conducted annually and yields statistical estimates of household expenditure by product class and region, about eleven months after the reference year. Of course, household expenditure patterns are in constant flux in response to demographic change, the economic cycle, shifting relative prices and other factors. The current practice is to measure the household expenditure weights comprehensively for a 12-month period, and to refresh these estimates every two years. When the weights are recalculated in this way, the process is referred to as a "basket update�.

1.36 The CPI is a sequence of fixed basket indices, each with its own unique classification structures and basket weights, which have been chain linked together. At present the basket updates occur every two years or so, but in the past they were carried out less frequently. Appendix C provides a detailed chronology of the various baskets implemented since the CPI began in 1913. The 100-year time series for the CPI, which is available on CANSIM, is really a chain-linked series of many CPIs.

1.37 It is important to distinguish between the weight reference period, the index reference period and the price reference period. The first of these is the period from which the CPI expenditure weights are taken. The index reference period is the period in which the index is arbitrarily scaled to equal 100. Currently, for the Canadian CPI this is 2002. The choice of index reference period has no effect on percentage changes in the index. Users can easily change the index reference period by simply rescaling the index accordingly. Statistics Canada also maintains a few alternative CPI series on CANSIM with different index reference periods, for the convenience of users. Finally, the price reference period is the period that prices are being compared with. It appears in the denominator of price ratios and is typically designated as period 0.

1.38 Chapter 4 provides a more thorough discussion of the CPI classification systems, while Chapter 8 focuses on the weights and basket updates as well as the index base period.

Reliability and Uncertainty

1.39 Statistical error is, of course, the difference between the unknown "true� value and the measured value. The CPI is a sample-based statistic and like all such statistics, is subject to several types of error. The error can occur either during the lower level calculations or as part of the upper level calculations.

1.40 Statistical bias arises when the expected average result over many samples differs from the "true� value. In the case of the CPI, bias can occur for several reasons. When statisticians need to replace one product with another and they make an associated quality adjustment, statistical bias might be introduced if the method for doing so had a persistent tendency either to underestimate or to overestimate the true extent of quality change. Bias might also be inherent in some editing procedures, although of course Statistics Canada strives to avoid any such bias.

1.41 Sources of potential bias are associated with new product introductions and outlet substitutions. New product introduction bias occurs when innovative products appear on the market and are not reflected in the CPI product sample in a timely manner. A number of steps are taken to guard against this bias, but it is difficult to avoid entirely, especially given the CPI's matched-model pricing methodology. Outlet substitution bias occurs when new stores enter the market offering lower prices and thereby inducing consumers to switch outlets. Again this is a difficult source of potential bias to avoid completely, but efforts are made to refresh the outlet sample periodically to minimize this kind of bias.

1.42 Sampling variance is an error characteristic that is very different from statistical bias. It refers to the extent of dispersion of estimates, over many samples, around the "true� value. In a statistical context, larger samples will yield lower variance. Efficient statistical estimation means minimal variance given the sample size. It is quite possible to have a zero bias and a positive variance. However, the only way to achieve a zero sampling variance is to measure the entire target population which, in the case of the CPI, is not possible.

1.43 Most Statistics Canada surveys report numerical estimates of the size of the sampling variance. These provide users of the statistics with an indication of statistical reliability. Thus, when a particular statistical estimate is released, the variance might be used to calculate what the "true� value is expected to be within certain specific numerical boundaries 19 times out of 20. As explained in Chapter 5, however, this is not possible for the CPI because, since product sampling is almost always done judgmentally rather than randomly, sampling variances cannot be calculated.

1.44 The CPI may also be subject to non-sampling errors of various kinds. Clerical and transcription errors fall into this category, although there are a number of checks and balances in the CPI monthly production process that aim to detect and correct any such errors. Another source of non-sampling error is errors and omissions in the business frame (list) that is used in selecting the sample of outlets for price collection. Again, efforts are made to minimize such errors, but it is nearly impossible to keep the list of retail businesses constantly up to date and without error.

1.45 Another notable source of potential error in the CPI applies to the elementary aggregates that are estimated by imputation rather than by direct price measurement. There are several residual classes in the CPI product classification, typically containing a wide variety of distinct goods and services, yet having comparatively small basket weights. Price change for these elementary aggregates is estimated indirectly, by imputation, as a cost saving measure. The expense of direct price measurement in these cases would be unjustified given their small basket weights and heterogeneous character.

1.46 Prices change with the passage of time and as they do, consumers tend to substitute goods and services that have become relatively cheaper for ones that have become relatively more expensive. For example, if pork prices have risen less rapidly than beef prices, there is an incentive for consumers to buy more pork and less beef. This phenomenon tends to make the basket weights out of date as time goes by. It causes a problem called substitution bias that influences the CPI upper level calculation.

1.47 Ideally the basket weights would reflect purchasing patterns of consumers in both periods for which prices are being compared. In other words, if the index is comparing two particular months, the weights would reflect the purchasing patterns of consumers in those two months. This is not presently feasible. In fact, the weights come not from the two months where prices are compared, but from some period (typically a year) prior to the price reference period (0) and price observation period (t). This is the main source of substitution bias in the CPI. Normally the closer is the time period from which the weights are calculated to the two months being compared, the smaller will be this source of bias. When, in 2013, Statistics Canada increased the frequency with which the basket weights are updated from once every four years to once every two years, this reduced substitution bias.

1.48 In addition, the upper level calculations are affected by statistical error in the SHS, which is used to estimate the basket weights.

1.49 Chapter 9 gives a much fuller discussion of the CPI's reliability, error properties and statistical bias.

Treatment of Owned Accommodation

1.50 Owned accommodation is an important component of the CPI, with a large basket weight, which poses especially difficult conceptual and methodological issues. There is no international consensus on how best to define and measure the price of owned accommodation and countries have adopted a variety of approaches. This makes international comparisons of inflation challenging.

1.51 The difficulty in this case stems from the fact that owned accommodation can, for some purposes, be thought of as a capital good rather than consumption good. Like all capital goods, it provides a stream of services over a lengthy period of time. Statistics Canada's approach is to measure the impact of price changes on the costs incurred by homeowners while they own a home. These costs include mortgage interest, replacement cost (depreciation), property taxes, home and mortgage insurance, maintenance and repairs, and other expenses. The first three of these cost categories account for three quarters of the total owned accommodation basket weight.

1.52 The owned accommodation price index is explained in Chapter 10.

Seasonal Products

1.53 Some of the products whose prices are measured by the CPI are highly seasonal, both in terms of the quantities purchased each month by consumers and in terms of the prices retailers charge at different times during the year. This is true for fresh fruit and vegetables, some kinds of clothing and certain recreational services, for example.

1.54 The basket weights applicable to seasonal products are, just as for non-seasonal products, estimated using annual household expenditure statistics. They are, therefore, not seasonal even though the monthly purchases by consumers can vary considerably through the year. Indeed, for some products in some months consumer purchases are zero – Christmas trees in July, for example. Statistics Canada deals with such cases by imputing the price movement based on that of similar in-season products. The fact that actual purchases of seasonal products in a given month can be very different from the purchases that are reflected in the yearly basket weights is another source of statistical bias in the CPI. This bias is likely to average near zero for the year as a whole, but can be significant in month-over-month comparisons. Bias is discussed in Chapter 9.

1.55 A related matter is the fact that monthly changes can be substantially influenced by seasonal factors. For any given month-over-month percentage change, users of the index often find it advantageous to distinguish between the part that is attributable to normal seasonal causes and the remaining non-seasonal part. The seasonal part is predictable and, therefore, less interesting. The non-seasonal part reflects the underlying trend in prices as well as any special temporary factors, and is more noteworthy.

1.56 Seasonally adjusted indices reflect price change after seasonal fluctuations are removed. Statistics Canada provides seasonally adjusted versions for the All-items CPI, the eight major aggregates and four of the special aggregates. These indices are adjusted independently, which implies they are not consistent in aggregation, and these indices are also subject to revision over time, unlike the unadjusted indices which are not revised.

1.57 The influence of seasonality on the CPI is discussed in Chapter 10.

History of the Canadian Consumer Price Index

1.58 Canada's CPI has a century-long history. Not surprisingly, the index has been improved greatly over that lengthy period. The interval between basket changes was reduced in several steps, from 13 years the first time the basket was updated in 1926 to just 2 years currently. The estimates of the basket weights were much enhanced by the introduction of the Family Expenditure Survey for the year 1938. The scope of the index has been broadened several times, in a number of ways. The sample size has risen, fallen and risen again, reflecting changing budgetary priorities. In addition, while the index was often revised during its first few decades, starting with the postwar period, the policy has been to eschew statistical revisions of the unadjusted statistics, as a convenience to users.

1.59 For more on the history of Canada's CPI, see Chapter 11 and Appendix C.

Notes

Date modified: