# The Canadian Consumer Price Index Reference Paper

Chapter 2 – Availability and Uses

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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 } The All-items CPI is the only index
published for Iqaluit.

**2.2 **The
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 } are estimated and
published monthly.

**2.4 **Intercity
indices of price differentials of consumer
goods and services are produced
and published once a year for fourteen cities.^{Note }

**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 Wednesday of the month following the price observation period. For example, the CPI for price
observation period November 2018 was released on December 19th 2018.

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

**2.6.1**The Statistics Canada Website^{Note }**2.6.2***The Daily*^{Note }

**2.7 ***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.

**2.8 **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.

**2.9 **Contrary
to the official CPI, the three Bank of Canada’s preferred measures of core
inflation, CPI-trim, CPI-median and CPI-common, are subject to revision. For
CPI-median and CPI-trim, this results from the fact that these measures are
based on seasonally adjusted price index series. For CPI-common, revisions are
due to the statistical technique used as a factor model is estimated over all
available historical data.

## Interpreting Percentage Changes

**2.10 **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.

**2.11 **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 }

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

**2.12.1**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).**2.12.2**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).**2.12.3**annual average percentage changes, which compare two consecutive annual average price indices.

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

**2.14 **Special
aggregates are different combinations of elementary aggregates. 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.

**2.15 **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.

**2.16 **The
Bank of Canada’s preferred measures of core inflation (CPI-trim, CPI-median and
CPI-common) are based on the disaggregation of the All-items CPI into 55
exhaustive and mutually exclusive components.^{Note } The CPI-trim measure excludes CPI components whose rates of change in a given
month are located in the tails of the distribution of price changes. This measure
helps filter out extreme price movements that might be caused by factors
specific to certain components. In particular, CPI-trim excludes 20% of the
monthly variations in weighted prices at both the bottom and top of the
distribution of price changes, and thus it always removes 40% of the total CPI
basket. The components excluded from the CPI-trim calculation can change from
month-to-month, depending on which ones are extreme in a given month. This
approach differs from traditional a priori exclusion-based measures
which, every month, omit a pre-specified list of CPI components. The CPI-median
measure corresponds to the price change located at the 50th percentile (in
terms of the CPI basket weights) of the distribution of price changes in a
given month. This measure helps filter out extreme price movements specific to
certain components. This approach is similar to CPI-trim as it eliminates all
the monthly variations in weighted prices at both the bottom and the top of the
distribution of price changes in any given month, except the price change for
the component that is the midpoint of that distribution. The CPI-common measure
tracks common price changes across categories in the CPI basket.

## Contributions to Price Change

**2.17 **A
fixed-basket composite price index for a given aggregate is made
up of price indices

**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 } ^{ }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’s 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 }

**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.

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 }

${p}_{i}^{0}$
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 $t$
in terms of the monthly change of its sub-aggregates.^{Note } By
construction, the sum of all the sub-aggregates’ monthly price changes will be
equal to the monthly price change of the aggregate.

$$\left(\frac{{I}_{A}^{0:t}}{{I}_{A}^{0:t-1}}-1\right)=\frac{{I}_{A}^{0:t}-{I}_{A}^{0:t-1}}{{I}_{A}^{0:t-1}}=\frac{{\displaystyle \sum _{i=1}^{n}\left({I}_{i}^{0:t}-{I}_{i}^{0:t-1}\right){w}_{i}^{0}}}{{I}_{A}^{0:t-1}}\text{\hspace{1em}\hspace{1em}\hspace{1em}(2.2)}$$

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 } 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 centred 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.

**2.28 **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

**2.29 **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.

**2.30 **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 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 } Finally, it is likely that many Canadians monitor the CPI to judge how their
incomes (or expenditures) are keeping pace with consumer price change.

**2.31 **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.

**2.31.1**The CPI is an indicator that relates, by definition, to a specified target population, and therefore 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 }^{ }**2.31.2**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 }For example, it does not include the effect of changes in the external environment, such as the 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 }

**2.32 **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 behaviour 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.

**2.32.1**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.**2.32.2**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 }

**2.33 **The
Implicit Price Index or the chain Fisher 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 }

**2.34 **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. Again,
to help it achieve this target, the Bank of Canada defined a set of preferred measures
of core inflation that are calculated and published by Statistics Canada. The
purpose of these measures is to reflect persistent price movements by eliminating
transitory or sector-specific fluctuations in some components of the CPI.

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