Chapter 2 – Availability and Uses

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• Availability of Information
• Interpreting Percentage Changes
• Contributions to Price Change
• Rounding in the Consumer Price Index
• Uses of the Consumer Price Index

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Availability of Information

2.1 The All-items Consumer Price Index (CPI), various aggregate indices as well as special aggregate indices are produced and published each month for Canada, the provinces, Whitehorse and Yellowknife. Additionally, the All-items CPI and the Shelter price index are produced and published for sixteen cities.^Note 1 The All-items CPI is the only index published for Iqaluit.

2.2 The monthly CPI series for the eight major aggregates at the Canada level are also available seasonally adjusted. Each year with the release of the December CPI in January, annual average indices are produced for all of the published monthly indices. Annual average indices are calculated as the unweighted arithmetic average of the 12 monthly indices within the year. The monthly and annual average indices for the All-items CPI for Canada are available in chain-linked series back to 1914. Indices for other geographies and/or aggregates are available starting from various periods as they entered the CPI statistical program.

2.3 In addition to the monthly and annual CPI series, average retail prices (not price indices) for food and other selected items for Canada and average retail gasoline and fuel oil prices for eighteen cities^Note 2 are estimated and published monthly.

2.4 Inter-city indices of price differentials of consumer goods and services are produced and published once a year for eleven cities.^Note 3

2.5 All monthly CPI statistics are available at 8:30 am EST on the day of the release. The release is typically on the third Friday of the month following the price observation period. For example, the CPI for price observation period January 2014 was released on February 21^st 2014.

2.6 At present, there are three main vehicles for the release of the CPI data:

• 2.6.1 The Canadian Socio-Economic Information Management System (CANSIM)^Note 4
• 2.6.2 The Daily^Note 5
• 2.6.3 The Consumer Price Index publication^Note 6

2.7 CANSIM is Statistics Canada's key socioeconomic database in which users can easily access a large range of statistics free of charge. CANSIM contains many more CPI series than either The Daily or the CPI publication.

2.8 The Daily is Statistics Canada's main release bulletin and the Agency's first line of communication with the media and the public. The Daily provides an overview of the monthly CPI statistics while focusing on the indices which had the most notable upward or downward contributions to the year-over-year (12-month) and monthly percentage changes in the CPI.

2.9 The CPI publication includes the same text and graphs contained in The Daily as well as a lengthy list of statistical tables and information on the quality, concepts and methodology of the CPI.

2.10 Once published, the official CPI statistics are not revised. Seasonally adjusted price indices are the only CPI series which are revised. Those data are revised one month after release and then each year with the January CPI, the past 36 months of seasonally adjusted data are revised.

Interpreting Percentage Changes

2.11 The CPI is a composite price index, which compares prices for consumer products in various price observation periods (which can be months or years), to prices in the index base period (also referred to as the index reference period). The CPI is arbitrarily set to equal 100 in the index base period. Therefore, all index values express price change in percentage terms in comparison to the index base period. For example, if the index is 123.4, that means prices have increased 23.4% since the base period. The current index base period of the CPI is 2002.

2.12 The CPI base period can easily be changed by multiplying all CPI series by a constant conversion factor equal to 100, divided by the average index for another specific time period. This is known as rebasing an index. Period to period price change will not be impacted by rebasing an index.^Note 7

2.13 Other common time comparisons that are made with the CPI include:

• 2.13.1 month-over-month percentage changes which compare price indices in a given month to price indices in the preceding month (e.g. November compared to October).
• 2.13.2 year-over-year (12-month) percentage changes, which compare price indices in a given month to price indices in the same month of the preceding year (e.g. November 2012 compared to November 2011).
• 2.13.3 annual average percentage changes, which compare two consecutive annual average price indices.

2.14 Special aggregate indices are calculated and published monthly and on an annual basis for Canada, the provinces, Whitehorse and Yellowknife.

2.15 Special aggregates are different combinations of the elementary aggregate indices. They often exclude certain product classes, in order to provide users with supplementary information on how consumer prices are changing. These indices provide alternative measures of consumer price inflation.

2.16 When a special aggregate index excludes certain product classes, their corresponding weights are removed from the total. As a result, the shares of the remaining goods and services increase in relative importance.

Contributions to Price Change

2.17 A fixed-basket composite price index for a given aggregate $I_A^{0:t}$  is made up of price indices $I_i^{0:t}$ and weights $w_i^0$  for the sub-aggregates that are contained in the given aggregate.^Note 8 Therefore it is possible to explain a given aggregate's price change (month-over-month or 12-month) in terms of the influence exerted by its particular sub-aggregates. Analyses of this kind are referred to as contributions to percentage change. Contributions explain how many percentage points of the aggregate percentage change come from a given sub-aggregate. For example, the gasoline index (a sub-aggregate) contributed 0.5 percentage points to the 1.0 percent change in the All-items CPI.

2.18 The influence exerted by a given sub-aggregate on a composite price change depends on both its price change and on its importance in the basket, as measured by its weight. Calculating contributions to composite price change across chained baskets requires additional steps.^Note 9

2.19 Any composite price index that relates to one fixed basket can be written as a weighted arithmetic average of the corresponding indices for all its constituent sub-aggregates. In other words, the aggregate index $I_A^{0:t}$  that expresses the change in prices between period 0 and t is a weighted mean of all the indices $I_i^{0:t}$  expressing the change in prices during the same period for all its constituting sub-aggregates.

$$I_A^{0:t}={\displaystyle \sum _{i=1}^n{I}_i^{0:t}\times w_i^{0b}}$$

(2.1)

Where: $w_i^{0b}\equiv \frac{p_i^0{q}_i^b}{{\displaystyle \sum _{i=1}^n{p}_i^0{q}_i^b}}$  is the hybrid expenditure share,^Note 10
$p_i^0$ is the price for sub-aggregate i in period 0;
$q_i^b$  is the quantity for sub-aggregate i in period b, and;
n is the number of sub-aggregates in the aggregate A.

2.20 Using (2.1), it is possible to decompose the monthly price change of the aggregate index between t-1 and
t $\left(\frac{I_A^{0:t}}{I_A^{0:t-1}}-1\right)$ in terms of the monthly change of its sub-aggregates.^Note 11 By construction, the weighted sum of all the sub-aggregates' monthly price changes will be equal to the monthly price change of the aggregate.

$$\left(\frac{I_A^{0:t}}{I_A^{0:t-1}}-1\right)=\frac{I_A^{0:t}-I_A^{0:t-1}}{I_A^{0:t-1}}=\frac{{\displaystyle \sum _{i=1}^n\left(I_i^{0:t}-I_i^{0:t-1}\right)w_i^0}}{I_A^{0:t-1}}$$

(2.2)

Where:

$\frac{\left(I_i^{0:t}-I_i^{0:t-1}\right)w_i^0}{I_A^{0:t-1}}$ represents the contribution of each sub-aggregate i to the aggregate A.

2.21 The share of the basket weight $w_i^{0b}$ of the sub-aggregate index i, together with the size and direction of its price change will determine the size and direction of its contribution to the percentage change in the aggregate index A. An increase/decrease in a sub-aggregate index will most often translate into an upward/downward contribution to the aggregate index percentage change.^Note 12 The sum of the contributions of all sub-aggregates of the All-items CPI is equal to its overall rate of change (monthly or 12-month).

2.22 The difference in contributions gives the impact of a sub-aggregate on the difference in the percentage change of its aggregate index. This is commonly referred to as acceleration or deceleration and is obtained by subtracting the contribution in period t-1 from the contribution in period t. For example, assuming that the gasoline index contributed 0.5 percentage points in period t-1 to the 1.0 percent change in the All-items CPI and in period t contributed 0.7 percentage points to the 1.4 percent change in the All-items CPI, it can be interpreted that the gasoline index contributed 0.2 percentage points (0.7 – 0.5) to the 0.4 percentage point acceleration (1.4 – 1.0) of the All-items CPI between periods t-1 and t.

2.23 The analysis provided by Statistics Canada in the various release items for the CPI is based on an understanding of the contributions of sub-aggregate indices to the monthly or 12-month percentage change in the All-items CPI or another aggregate index.

Rounding in the Consumer Price Index

2.24 During the different steps of their construction all CPI indices are calculated to several decimal places. However, consistent with international practice, indices are rounded to one decimal place when they are published. Percentage changes (monthly, 12-month and annual average) in Statistics Canada publications are always calculated with the published rounded indices. They are also rounded to one decimal place. That way, users can always replicate the published percentage changes.

2.25 As a result of these two stages of rounding, a small amount of accuracy in percentage changes may be lost. Therefore, small fluctuations (+/- 0.1) in the percentage changes of indices should be interpreted with discretion.

2.26 Another side effect of rounding indices is that at times there could appear to be inconsistencies between the percentage changes in aggregate indices and their sub-aggregate indices. For example, the rounded percentage change of an aggregate index may not be centered among the rounded percentage changes of its sub-aggregate indices.

2.27 The loss of precision due to rounding is amplified when indices are of small value. Therefore, rebasing an index, which generally results in smaller index values for the past, can reduce the precision of calculated percentage changes. For example, with an index base period of 1914=100, a 0.1 percent increase in the All-items CPI from 1914 to 1915 would translate to an index value of 100.100, rounded to 100.1. However, with an index base period of 2002=100, the rebased 1914 index value would be 6.0. The same 0.1 percent increase in the All-items CPI from 1914 to 1915 translates to an index value of 6.006, rounded to 6.0. Therefore, rounding indices reduces the precision for percentage changes for periods in the past. Loss of precision in historical figures should be considered when deciding to rebase an index.

Uses of the Consumer Price Index

2.28 The CPI, as a composite price index, is an official measure of consumer price change through time. It is of interest to governments, unions, business organizations, research institutions and very large segments of the general public. Undoubtedly, the CPI is one of the most widely-known, quoted and used statistical series in Canada. Its prominent profile, while indicative of wide acceptance, also poses problems because the CPI cannot serve all uses perfectly and equally well. Users are advised, therefore, to approach the CPI with discretion, especially when using it for purposes that lie outside of its main focus.

2.29 The CPI is often used to adjust incomes, wages or other payments to maintain previous purchasing power in the face of changing consumer prices. In some cases, periodic changes to specific payments are made using a built-in adjustment factor, in which the CPI rate of change is applied either wholly or in part. This is currently the case, for example, for government payments resulting from such social programs as the Canada and Quebec Pension Plans, Old Age Security and the Guaranteed Income Supplement. Some labour-management contracts also contain cost-of-living adjustment clauses, by which wages and salaries are tied to the CPI in a variety of ways. Even more frequently, the CPI serves as a point of reference in wage and salary negotiations without being applied as a built-in adjustment factor. Many other financial arrangements make reference to the CPI in adjusting the terms of payment.^Note 13 Finally, it is likely that many Canadians monitor the CPI to judge how their incomes (or expenditures) are keeping pace with consumer price change.

2.30 As an adjustment factor, whether it is used automatically or as a point of reference, the CPI has come to affect most Canadians, and it plays an extremely important role in the economic and social affairs of the country. The CPI, for example, is a good indicator of changes in the purchasing power of the consumer dollar. However, the index does not dictate what the specific adjustments should be to wages and other forms of income. It is up to the contracting parties to determine the proportion of changes in purchasing power that should be compensated for. The following should be considered by those who use the CPI as an income adjustment factor.

• 2.30.1 The CPI is an indicator that relates, by definition, to a specified target population, may not reflect the experience of a particular group within this population. However, it is unlikely that the differences between the average change in consumer price indices for the target population and those for any other broad segment of the Canadian population would be large over the long run.^Note 14
• 2.30.2 The CPI, by construction, is not a Cost-of-living-Index (COLI) and while it may serve as a close approximation for one, it does not take into account some aspects or concepts which would typically be included in a COLI.^Note 15 For example, it does not include the effect of changes in the external environment, such as incidence of disease and natural disaster or crime levels, which may affect the demand for certain goods and services with little or no effect on prices. Additionally, as an asymmetrically weighted, fixed-basket index the CPI does not, in a timely manner, account for consumer substitutions among purchased products.^Note 16

2.31 The CPI is often used as a general indicator of inflation in Canada. An analysis of the CPI, in conjunction with analyses of other statistical series, can reveal fundamental trends in the economy. The CPI therefore plays an important role in the formulation of policies and in economic forecasting. The comparison of current changes in the CPI to changes in the past, and to the behavior of similar indices in other countries, helps analysts to evaluate the effectiveness of many economic policy decisions. Although the CPI is often used as a general indicator of inflation, it is worth underlining some important limitations in this respect.

• 2.31.1 The CPI is not a comprehensive measure of price change at the final stage of economic transactions. This is because the index does not take into account some elements of the final use of goods and services in the country, such as the consumption of government services, capital formation or exports.
• 2.31.2 The mortgage interest cost index in the owned accommodation component of the CPI reflects not only current price changes, but also past changes by means of a moving weighted average of price changes over multi-year periods.^Note 17

2.32 The Implicit Price Index for domestic final expenditures in the Canadian System of National Accounts (CSNA), being free of the above limitations in addition to being calculated with a symmetrically weighted index formula, is a more comprehensive indicator of overall inflation. It is, however, released quarterly, two months after a given quarter, relates to non-market as well as market segments of the economy and relies on imputed prices for some important components, notably owner-occupied housing. It is also subject to revisions over several years as more statistical information becomes available.^Note 18

2.33 The importance of the CPI as a general indicator of inflation has become more apparent since February 1991, when the Bank of Canada switched to an inflation targeting regime with the All-items CPI as its target indicator. While the CPI has always been a key statistical measure used by the Bank of Canada in determining its monetary policy, the adoption of an inflation targeting regime increased the attention given to the CPI as a general indicator of inflation.

Notes