# The Canadian Consumer Price Index Reference Paper

Chapter 10 – Treatment of Owned Accommodation and Seasonal Products

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## Concepts Surrounding the Treatment of Owned Accommodation

**10.1 **The treatment
of owned accommodation is one of the most difficult problems encountered when
constructing
consumer
price indices. There is probably no other component that is treated in so many
different ways by
statistical
agencies of various countries. The different treatments are in response to both
the complex nature
of
homeownership, which creates problems in identifying and measuring price
changes associated with
homeownership,
and the diversity of users’ requirements with respect to the Consumer Price Index (CPI).^{Note }

**10.2 **Conceptually,
an owner-occupied dwelling may be regarded as either a capital good or a consumer good, or both. Statistical
agencies that adopt the former view exclude owned accommodation from their
consumer
price
indices. In other words, no effect of price changes associated with the cost of
purchasing and using
owned accommodation is reflected in the CPI.

**10.3 **Agencies that
regard owner-occupied dwellings as consumer goods have several options. One
approach is
to treat owner-occupied dwellings the same way other durable goods are treated in the CPI, that is, by
using the value of net purchases of dwellings in a specified year to derive the basket weight of the
index and purchase prices of dwellings to measure price changes for the owned
accommodation component.

**10.4 **A second
approach is to take into account the shelter services that are provided by
owned accommodation.
Since
these services, in themselves, are not objects of market transactions, their
price movement can only
be
imputed from other series, such as the rent price index. When this rental equivalence approach is strictly applied, the basket
weight assigned to the owned accommodation component is based on the estimated rental value of
owner-occupied dwellings. The rental equivalence approach has the merit of
being consistent
with the conventional treatment of owned accommodation in the “Personal expenditure
on consumer
goods and services”
component of the Canadian System of National Accounts (CSNA).^{Note }

**10.5 **Thirdly, the
statistical agencies of several countries represent the price movement of the services
provided
by
owner-occupied dwellings with indicators that estimate the effect of price
changes on the cost of using dwellings. However, not all countries use the same
cost elements. When this user cost approach is applied, the basket weight
assigned to owned accommodation is derived from actual or imputed cost elements (imputations may be made
for unobserved costs such as the forgone interest on the homeowner’s capital invested in the
dwelling). Some countries decline to include any imputed cost components in the
owned
accommodation index. Only expenses involving actual cash disbursements are thus
included, so this approach is referred to as a money outlays variant of the user cost approach.

**10.6 **The owned
accommodation component seems to be a good illustration of the truism that no
single series of
consumer
price indices can serve well all purposes for which the CPI is commonly used.
For example, the
rental
equivalence approach is fully satisfactory when indices are to be used for
deflating the current dollar series within the “Personal expenditure on consumer
goods and services”
component of the CSNA. This is because the estimated rental value of
owner-occupied dwellings is conventionally included in that statistical program. Similarly,
if a consumer price index is intended to measure retail price changes, then the
movement
of
current prices of dwellings (and possibly, the movement of current mortgage
interest rates) ought to be reflected in the index of owned accommodation.

**10.7 **Neither of
these approaches, however, seems to be particularly suitable for measuring the
effect of price
changes
on the purchasing power of the consumer dollar. The use of the rental
equivalence approach for
this
purpose is questionable, because the purchasing power of homeowners is neither
directly dependent on
rent
changes nor is it necessarily correlated with these changes, especially in the
short-to-medium term. The
use
of current changes in dwelling prices is not appropriate for the above purpose
either, because most
homeowners
continue to pay for their dwellings many years after the purchase. Accordingly,
the
purchasing
power of homeowners at any time is affected by price levels in the dwelling’s
purchase year,
rather than just by those in the current year.

## Treatment of Owned Accommodation in the Consumer Price Index

**10.8 **The treatment
of owned accommodation in the CPI does not truly conform to the basic
definition of the CPI as a price index associated with a fixed basket of products
purchased by the target population. Moreover, owned
accommodation is not treated in the CPI in the same manner as other durable
goods. This special
treatment
is justified by the fact that owner-occupied dwellings have, in general, much
longer useful lives,
higher
values and more complicated terms of payment than other durable goods. Although
these differences
are
of a quantitative rather than of a qualitative nature, they are
important enough to be taken into account in the computation of the CPI. For
instance, mortgage credit is generally considered to be an integral part of purchasing a
home, so it would not be ideal to disregard the effect of changing mortgage
interest costs on
the
overall shelter price index. In addition, since mortgage payments for purchased
dwellings are spread over
many
years, it is desirable to take into account not only their current, but also
their previous prices in order to produce an appropriate indicator of
price-induced changes in the purchasing power of the consumer dollar. These problems
seem to affect other durable goods, including high-value goods such as
automobiles, to a
lesser extent.

**10.9 **The
treatment of owned accommodation in the CPI follows neither the money outlays
approach nor the
opportunity
cost approach. The owned accommodation index is not a money outlays index
because of its
replacement
cost component, depreciation being an imputed cost rather than an actual
expense. The owned
accommodation
index is not consistent, either, with an opportunity cost approach because it
excludes other
imputed
elements that are generally regarded as part of the opportunity cost, such as
forgone interest on
invested capital and capital appreciation.

**10.10 **It follows that
the solution to the treatment of owned accommodation is a matter of determining
the principal
purpose(s)
that the CPI is designed to serve. There are several, sometimes competing, uses
of the CPI.^{Note } As with the
rest of the index, the approach taken with respect to owned accommodation must
attempt to
find
balance between the purposes for which it serves. The treatment of owned
accommodation in the CPI
serves
well the purpose of providing an adequate indicator of price-induced changes in
the purchasing
power
of the consumer dollar. In particular, it is meant to measure the impact of
price changes on a selection of costs specific to homeowners.

**10.11 **The price index
for the owned accommodation aggregate class, like those for other CPI classes,
is
calculated
as a weighted average of elementary indices. Each elementary index represents
the price
movement
for a given element of homeowners’ costs. These costs relate to the stock of
dwellings that is
identical
or equivalent to the stock actually owned by the target population at the end
of the basket reference
period. Thus, the indices
for owned accommodation measure price-induced changes in the cost of using a fixed stock of
dwellings, while, for other CPI classes, they measure price-induced changes in
the cost of
buying
a fixed basket of goods
and services. Six homeowners’ costs are included as elementary indices under the
owned accommodation aggregate class:

- mortgage interest cost
- replacement cost
- property taxes
- homeowners’ home and mortgage insurance
- homeowners’ maintenance and repairs
- other owned accommodation expenses

**10.12 **Except for the mortgage
interest
cost and
the
replacement cost
index, the basket weights of the owned accommodation components are purely derived from the household expenditures
reported in the Survey of Household Spending (SHS).

**10.13 **The replacement
cost basket weight is partially derived from SHS while the weights of the mortgage
interest cost is estimated using administrative data supplemented by SHS data.

**10.14 **The basket
weight for replacement cost, considered equal to the annual depreciation of the
stock of owner-occupied dwellings, is estimated to be 1.5% of the estimated
market value of this stock at the end of basket reference year.^{Note } The estimated
market value of the stock of owner-occupied dwellings is derived from SHS.

**10.15 **The basket
weight for the mortgage interest cost is the total interest paid on mortgages
by Canadian households. In the Canadian CPI, it represents the interest portion
of the mortgage payments made by homeowners on the principal dwelling.^{Note } To estimate its value, administrative data, namely banks’ financial statements,
collected and published by the Office of the Superintendent of Financial Institutions
(OSFI) and SHS data are used.

**10.15.1**Based on OSFI data, Statistics Canada estimates the effective interest rate paid on residential mortgages as the ratio of banks’ residential mortgage income divided by the banks’ total residential mortgage loans in the basket reference period.**10.15.2**The SHS mortgage balances, as reported by SHS, is then multiplied by this effective rate to derive the CPI mortgage interest weights.

**10.16 **The **mortgage
interest cost **index is intended to measure price-induced
changes in the amount of
mortgage
interest owed by the target population. There are two price factors that
contribute to these
changes
through time. First, changes in dwelling prices affect the initial amount of
debt; hence they also
affect
the amount of principal outstanding in subsequent periods. Second, given the
amount of principal
outstanding,
the amount of mortgage interest payments is determined by changes in the price
of credit (that
is, mortgage interest rates). Consequently, the mortgage interest cost index
(with the price observation period $t$
and the price reference period $0$
) is defined as a product of two indices
(10.1).

$${M}^{0:t}={H}^{0:t}\times {I}^{0:t}\text{\hspace{1em}\hspace{1em}\hspace{1em}(10.1)}$$

where:

${H}^{0:t}$ is an index that estimates the effect of changes in dwelling prices on the amount of principal outstanding, assuming a fixed stock of mortgaged dwellings and constant conditions of their financing; and

${I}^{0:t}$ is an index that estimates the effect of changes in interest rates on the amount of mortgage interest owed, assuming a fixed amount of principal outstanding.

**10.17 **The index ${H}^{0:t}$
is derived by
comparing the average level of dwelling prices in the 25-year interval prior to
the price observation period ($t$
) of
the index with the average level of dwelling prices in the 25-year interval
prior to the price reference period ($0$
).^{Note } The
procedure is based on the assumption that the dwelling price at the time the
debt was initially contracted affects the amount of principal outstanding at
any given time. Hence, the total amount of principal currently outstanding for
the population of homeowners depends on dwelling prices from all the past
periods in which their
mortgages were initiated.

**10.18 **We assume a
standard mortgage amortized over 25 years (300 months) at a fixed rate. The index ${H}^{0:t}$
is defined as
follows (10.2):

$${H}^{0:t}=\frac{{\displaystyle \sum _{g=1}^{300}NHP{I}_{t-g}\left({\gamma}_{g}\times {\phi}_{g}\right)}}{{\displaystyle \sum _{g=1}^{300}NHP{I}_{0-g}\left({\gamma}_{g}\times {\phi}_{g}\right)}}\text{\hspace{1em}\hspace{1em}\hspace{1em}(10.2)}$$

where:

$NHP{I}_{t-g}$ and $NHP{I}_{0-g}$ are the New Housing Price Index respectively for month $t-g$ and month $0-g$ ;

${\gamma}_{g}$ represents the proportion of principal that remains to be paid on a mortgage initiated $g$ months ago. This proportion is based on a standard mortgage amortized over 300 months at a fixed interest rate; and

${\phi}_{g}$ is the proportion of households that hold a mortgage initiated $g$ months ago. This information is taken from the SHS and would be the only data coming from that survey. It is approximated as of the date on which the household moved into the dwelling.

**10.19 **The index ${I}^{0:t}$
is derived using two administrative
data sets. The first one is produced by the Bank of Canada and provides the
amounts of new mortgage loans as well as the corresponding interest rates for
the nine largest banks. This dataset allows for monthly update of the mortgage
loans by term and covers a large spectrum of interest rates, including variable
rates and over 5 years fixed rates. The second source of data is the banks’
financial statements collected and published by OSFI.

**10.20 **It is assumed
that the amount of mortgage interest cost at any given time (${A}_{t}$)
depends on interest rates at the time
when the current mortgage agreement was contracted. Hence, it is only through
new and renegotiated mortgage contracts (${L}_{t}$
) that the current interest rates affect
the amount of mortgage interest currently owed by the population of homeowners.
A standardized mortgage interest cost function reflects this assumption by considering
the initiation and renegotiation of mortgages.

**10.21 **For any month *t*,
the standardized function for the interest payment ${A}_{t}$
is derived in two steps according to
(10.3).

$${A}_{t}={\displaystyle \sum _{j=1}^{9}\underset{\begin{array}{c}\text{Amountofintereston}\\ \text{NEWlending}\\ \text{bybank}j\end{array}}{\underbrace{\left({L}_{j,t}\times {r}_{j,t}\right)}}}+{\displaystyle \sum _{j=1}^{9}\stackrel{\begin{array}{l}\text{AmountofinterestpaidonNON}\\ \text{}\text{NEWlendingissuedbybank}j\text{}\end{array}}{\overbrace{\left[\left({B}_{j}-{L}_{j,t}\right)\times {r}_{j,t-1}^{eff}\right]}}}\text{\hspace{1em}\hspace{1em}\hspace{1em}(10.3)}$$

where

${A}_{t}$ is the amount of interest paid in month $t$ ;

${L}_{j,t}$ is the amount of new loans issued by the bank $j$ in month $t$ and is obtained from an administrative database produced by the Bank of Canada;

${r}_{j,t}$ is the interest rate negotiated by bank $j$ in period $t$ for its new mortgage loans and is obtained from the Bank of Canada administrative data source;

${B}_{j}$ is the balance of mortgage loans issued by the bank $j$ that remains fixed throughout the reference period of the CPI basket to ensure that changes in ${A}_{t}$ are solely the result of changes in interest rates and in the distribution of mortgage loans by term; this is taken from the bank's statement, as provided by the OSFI; and

${r}_{j,t-1}^{eff}$ is the effective interest rate in the previous month ($t-1$ ) for bank $j$ . It is calculated by establishing the ratio between the interest amount for the previous month and the loan balance.

**10.22 **From (10.3),
the index ${I}^{t-1:t}$
which measures the
impact of changes in mortgage interest rates on interest amounts, can be calculated
according to (10.4).

$${I}^{t-1:t}=\frac{{A}_{t}}{{A}_{t-1}}\text{\hspace{1em}\hspace{1em}\hspace{1em}(10.4)}$$

**10.23 **The **replacement
cost **index relates to that portion of owner-occupied dwellings that is
assumed to be
consumed.
This is represented by the worn-out structural portion of housing (depreciation
of housing) or
the
amount a homeowner must spend to maintain the home’s market value. The price
index for the
replacement cost is derived
by taking the total value of homes owned in Canada at the end of the basket
reference year
and adjusting the total each month by changes in house prices as reflected by
the New Housing Price Index,^{Note } exclusive of land.

**10.24 **The **property
tax** index measures changes through time in the amount of taxes levied on a
constant sample of dwellings in
selected municipalities. This sample of property taxes paid, obtained from
administrative
sources,
is used to obtain an estimate of the average property tax by city. This enters as
the price in the
current and previous periods’ unit value index calculation.^{Note } Changes in property taxes are reflected once a year, in the October CPI.

**10.25 **The **homeowners’
home and mortgage insurance** index measures changes through time in the cost
of
insuring
a fixed stock of dwellings against a specified combination of perils. This cost
varies not only with
changes
in insurance rates for given property values, but also with changes in the
values of the properties
covered
which result from movements in dwelling prices. Consequently, the insurance
index is estimated
by multiplying the following two indices:

**10.25.1**One that measures the change in the value of the replacement cost of properties using a third-party insurance data base (estimated quarterly); and**10.25.2**One that measures the change in insurance rates by comparing the cost of identical policy profiles using data from insurance companies in the sample.

**10.26 **The elementary indices
for homeowners’ maintenance and repairs as well as other owned accommodation expenses are estimated using the standard approach for calculating elementary price indices.^{Note }

## Treatment of Seasonal Products

**10.27 **The use of the fixed-basket
concept to construct consumer price indices creates difficulties when the
actual consumption pattern in the price observation period differs markedly
from that of the basket reference period. In the case of monthly indices,
problems may arise due to the seasonality of the quantities consumed of many
goods and services. Some products are subject to seasonal variations in their
supply. These include various services, such as golf memberships or downhill
ski lift tickets that are only available for a few months every year. Other
products are subject to seasonal variations in demand. These include many
articles of clothing, such as bathing suits and winter coats. Whatever the
cause, any good or service that experiences seasonal fluctuations in its
quantity purchased should be considered a seasonal product.

**10.28 **The CPI is based
on a fixed-basket, constructed from consumer expenditure data for one year. The
representativeness of an annual fixed-basket index in any one particular month is adversely affected if seasonal
products are part of the basket. In a fixed-basket index, a seasonal good or
service will have the same quantity weight in the basket for all months of the
year. That quantity will be inappropriately small in the product’s in-season
months and inappropriately large in its off-season months. For example, golf
membership will be under-weighted in June’s CPI, and over-weighted in
December’s.

**10.29 **The treatment
of seasonal goods and services is a contentious issue. One effective way of
dealing with seasonal products in a fixed-basket index with weights from a
calendar year is to avoid the inclusion of highly seasonal products in the
sample, that is goods or services for which quantity consumed would fall to
zero in any particular month(s) of the year. For example, rather than including
golf memberships which are unavailable in the winter months, instead the CPI
could measure price change of indoor rock climbing passes which are available
all year round.

**10.30 **The main
problem with this approach is that it may diminish the representativeness of
certain indices in certain months. For example, while the CPI aims to measure
price change for all in-scope consumer products, it must inevitably be based on a sample of product offers (POs) for a
relatively small number of representative
products^{Note } that are considered to be representative of all goods and services within a
particular elementary aggregate. The problem appears if the price movements of
the all-year product, such as indoor rock climbing passes, are not
representative of the price movements of all products included in the
elementary aggregate. This can become particularly problematic in a country
with very distinct seasons, such as Canada, where seasonal products may make up
a large proportion of consumer spending. Not including the price movements of
seasonal items could lead to some elementary price indices being
unrepresentative of price change experienced by the target population for that expenditure
category.

**10.31 **Another option
for dealing with the challenges associated with seasonal products is to have separate
fixed-quantity baskets for all months of the calendar year (seasonal baskets).
That is, to calculate the January index using only the quantities consumed in
January, the February index using only the quantities consumed in February, and
so forth. Then a seasonal product would have an appropriate quantity weight in
every month’s index of the year. Annual indices for seasonal products would be
calculated as weighted averages of monthly indices so in-season months would be
more heavily weighted than off-season months in calculating the annual price
movement. If a good or service was a seasonally disappearing product, it would
not be part of the basket in a month when it is not available in the market.

**10.32 **The major
disadvantage of an index with seasonal baskets is that it does not provide a
measure of pure price change for intra-annual price movements, such as quarterly or monthly changes. First,
consider the fixed-basket index with calendar year weights. If the price of
every collected PO showed no change in a given month, the index would also show
no change. Additionally, if the prices of some collected POs in this
fixed-basket index change in a given month, the percentage change of the All-items CPI (or another
aggregate index) will lie between the minimum and maximum percentage changes of
the corresponding sub-indices. By contrast, if the price of every PO in an
index with seasonal baskets showed no price change
from month to month, that index may still register an increase or a
decrease due to changes in the quantities of the monthly seasonal baskets. Additionally,
the monthly percentage change of an All-items CPI (or another aggregate index)
with seasonal baskets could sometimes stray outside the minimum and maximum percentage
changes of its respective sub-indices.

**10.33 **Finally, the
determination of seasonal basket weights, like all basket weights, is based on
consumption patterns from periods in the past and consequently would not take
into account abnormal seasonal fluctuations in current periods. For instance, if
bad weather conditions in the current period were to impact certain fruit or
vegetable crops thereby delaying their availability in the market, seasonal
baskets based on past expenditure periods would not account for this.

**10.34 **The CPI has
used two methodologies to deal with seasonal products. From 1961 to April 1973 the
CPI series for seasonal food products were based on seasonal-basket formulae.^{Note } From April 1973 forward all aggregate price indices are calculated using a
fixed-basket Lowe price index formula with calendar year weights. Price
movements for highly seasonal products are imputed in their out-of-season
periods.

**10.35 **In the current
CPI practice, highly seasonal products are identified as such and in the months
when their quantity purchased is believed to approximate zero, their price
movements are imputed. Examples of products identified as highly seasonal
include gas barbeques, lawn mowers, winter jackets and boats. Out-of-season
imputations are done at the level of elementary aggregates. The imputed price movement
is taken from the aggregate class that is located above the out-of-season
product in the CPI classification.

**10.36 **In the months
when indices for out-of-seasonal products are imputed, the price movement for
the aggregate index would be exactly the same as if the seasonal product were
not part of the basket. Essentially, the basket weights of out-of-season goods
and services are redistributed among the remaining in-season products so in
this respect, out-of-season imputation, although carried out within the
parameters of a fixed-basket index with calendar year weights, gives results
similar to the seasonal-basket approach.

**10.37 **Imputing prices
for out-of-season products also helps dampen sharp movements in the index that
can occur when moving from one season to the next. This is because the price
movement of the product is extrapolated over the out-of-season period rather
than being treated as posting no price change. The extent to which
out-of-season imputations reduce inter-seasonal shifts in the index depends on
the correlation between the price movement of the highly seasonal products and
the price movement of the aggregate class that is the source of the imputation.

**10.38 **It should be
clearly understood that the objective of out-of-season imputation is not to
obtain a proxy index that mirrors the price behaviour of the seasonal product
in its out-of-season months. In many cases, the true price movements of
products in their out-of-season months are quite volatile as they are not
subject to predictable changes in supply or demand.

## Seasonal Adjustment of Price Indices

**10.39 **Month to month
movements in the CPI can sometimes be the result of seasonal price changes. For
example,
between
January and March travel packages typically see price increases as more people
tend to travel out
of
the country in the winter and over the March break. While these price changes
are valid, in that consumers often experience higher prices for travel tours in
the winter months, they are part of a usual pattern of price increases
brought on by raised demand. They are likely to be reversed when demand weakens
again.
Accordingly,
for some purposes these price changes might not be interpreted as consumer
price inflation.
The practice of seasonal adjustment is used to isolate and then remove seasonal price
movements from indices to get a better picture of “true” or “underlying” consumer
price inflation in the economy.^{Note }

**10.40 **Statistics
Canada uses the statistical program X12 ARIMA to seasonally adjust the All-items
CPI and 12
other aggregate indices at the Canada level.^{Note } Each month the current index is seasonally adjusted and at the same time the
previous month’s seasonally adjusted index is open to revision. Additionally,
each January the last 36 months of seasonally adjusted data are reviewed and
revised if necessary.

**10.41 **Statistics
Canada does not seasonally adjust every CPI series. The headline CPI figure is an
unadjusted
estimate.
This is due, in part, to the fact that many users consider the year-over-year
percentage change in
the
All-items CPI to be a good general indicator of consumer price inflation.
Year-over-year changes, by their very construction, neutralize seasonal
movements and do not require seasonal adjustment.

**10.42 **The other
reason for the limited production of seasonally adjusted CPI data is the
properties of the index
aggregation
formula (Lowe) used to compile the upper level of the CPI. To counteract the
potential for
residual
seasonality in aggregate indices, Statistics Canada employs a direct or
independent seasonal
adjustment
method, meaning that seasonally adjusted CPI series are not derived from their
respective
seasonally
adjusted sub-indices. While this practice reduces the likelihood of having
residual seasonality in
the
series, it also poses a few challenges when using the seasonally adjusted CPI
data. First, direct seasonal adjustment prevents consistency in aggregation.
Since the All-items CPI is adjusted independently of the eight major aggregates, its movements
can be inconsistent with those of its component indices. Second, by directly
seasonally adjusting the All-items CPI and major components, the capacity to
analyze or interpret contributions to percentage change is lost.

**10.43 **Despite the
challenges with seasonally adjusted price indices, seasonal adjustment provides
many useful
benefits to users of price indices.^{Note }

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