#
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 1}

**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 2}

**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 during 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 ofthe 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 3} 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** Basket weights for these cost elements, except for replacement cost, have been derived from household expenditures reported in the Survey of Household Spending (SHS) for the basket reference period. 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 2013.^{Note 4}

**10.13** 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).

$${M}^{0:t}={H}^{0:t}\times {I}^{0:t}$$

(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.

**10.14** 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 5} 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. The index of the effect of dwelling prices reflects this assumption, although with some further qualifications.

**10.15** Prices from various past periods do not equally affect the current total amount of principal outstanding. Dwelling prices from remote periods normally have less influence than do prices from more recent periods because, in general, the older the mortgage the larger the proportion of debt that has already been paid off. This pattern is evident in the distribution of principal outstanding by mortgage age, derived from household expenditure data estimated in the SHS. The pattern is reflected in the index by using weights inferred from this distribution. They decrease with the age of the mortgage, giving less importance to dwelling prices from earlier periods.

**10.16** The actual distribution of principal outstanding by mortgage age, however, depends not only on this general rule of decreasing importance, but also on various conditions prevailing in specific past periods such as the price level of dwellings, the volume and quality of the stock of dwellings mortgaged and the conditions of mortgage financing.^{Note 6}

**10.17** The effect of varying price levels is removed by converting the amounts of principal outstanding reported in the basket reference period to the basket reference period price level, whatever the period of mortgage initiation. The resulting figures represent the unpaid portions of the dwelling stock that were initially mortgaged in those past periods, expressed in volume (quantitative) terms. This price-corrected distribution, after further smoothing to remove the effect of other irregular factors, is used as a model to derive weights assigned to mortgages of various ages.^{Note 7}

**10.18** Due to this design, the variation of the index${H}^{0:t}$
which estimates the effect of changes in dwelling prices is not affected by non-price factors such as changes in the volume and quality of the stock of mortgaged dwellings or in the proportion of debt that is paid off on mortgages of equal age. The index represents a special case of a fixed-basket price index, which may be presented as follows (10.2).^{Note 8}

$${H}^{0:t}=\frac{\frac{{\displaystyle \sum _{g=1}^{300}{\overline{p}}^{t-g}\times {q}_{g}}}{{\displaystyle \sum _{g=1}^{300}{q}_{g}}}}{\frac{{\displaystyle \sum _{g=1}^{300}{\overline{p}}^{0-g}\times {q}_{g}}}{{\displaystyle \sum _{g=1}^{300}{q}_{g}}}}=\frac{{\displaystyle \sum _{g=1}^{300}{\overline{p}}^{t-g}\times {q}_{g}}}{{\displaystyle \sum _{g=1}^{300}{\overline{p}}^{0-g}\times {q}_{g}}}$$

(10.2)

Where:

$g$ is the age of the mortgage debt, between 1 and 300 months (25 years), counted from the time of the initial mortgage contract to the price reference period 0;

${\overline{p}}^{t-g}$
and ${\overline{p}}^{0-g}$
are the average dwelling price levels in periods *t-g* and 0*-g*, respectively, for a stock of dwellings that is equivalent to that with mortgages of age *g* in the model distribution; and

${q}_{g}$
is the implicit stock of mortgaged portions of dwellings with loans of age *g*, estimated according to the model distribution and expressed in volume terms.

**10.19** The index ${I}^{0:t}$
is derived from a standardized function of mortgage interest cost, by comparing its values in the price observation period (*t*) and in the price reference period (0). The function is standardized by assessing the mortgage interest cost with respect to a constant amount of principal outstanding. Due to this property, the function varies only with the effect of interest rates.

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

**10.21** The first value of the standardized mortgage cost function was calculated for the basket reference period. It was inferred from data reported by homeowners on principal outstanding at the end of the basket reference year and on interest rates applicable to their mortgages during consecutive months of that year. In addition, the above amounts of principal outstanding at the end of the basket reference year and the standardized amounts of mortgage interest cost inferred for that month were grouped by the expiration month of the mortgage contracts, again as reported in the SHS of the basket reference year.

**10.22** For any observed month subsequent to the basket reference year, the standardized mortgage cost function is derived in a recursive way, from figures already established for the preceding month. The initiation and renegotiation of mortgages in the month preceding the observed one are first simulated. The amount of principal outstanding that is assumed to have been entirely paid off^{Note 9} is reintroduced to represent the newly created mortgages. Also, the amount of principal corresponding to contracts that are assumed to have expired is reintroduced to represent the renegotiated mortgages. New mortgage terms^{Note 10} and current interest rates^{Note 11} are then applied to those two amounts of principal outstanding. In this way, the standardized mortgage interest cost for the observed price reference month is estimated on mortgages that are assumed to have been created and renegotiated in the preceding month.

**10.23** For the remaining mortgages whose contracts are considered to be unchanged, the standardized mortgage interest cost is simply carried over from the preceding month. This completes the estimation of the standardized mortgage interest cost function for the observed month. The standardized mortgage cost function can be presented by the following, recursive formula (10.3).

$${A}^{t}={A}_{old}^{t-1}+{\displaystyle \sum _{1,3,5}^{}\left[\left({B}_{new}^{t-1}+{B}_{renew}^{t-1}\right)\times {f}_{(1,3,5)}\right]}\times {r}_{1,3,5}^{t-1}$$

(10.3)

Where:

${A}_{}^{t}$
is the amount of the standardized mortgage interest cost in the price observation period *t*, estimated with respect to all mortgages;

${A}_{old}^{t-1}$
is the amount of the standardized mortgage interest cost in the period *t*-1, estimated with respect to the mortgages that did not change (not newly initiated or up for renewal);

$\left({B}_{new}^{t-1}+{B}_{renew}^{t-1}\right)$
is the total amount of principal outstanding in period *t*-1, estimated with respect to the mortgages newly initiated and renewed;

${f}_{(1,3,5)}$
is the fraction of principal outstanding that represents contracts with *1,3,5 *year terms among newly created and renewed mortgages; and

${r}_{1,3,5}^{t-1}$
is the current mortgage interest rate in period *t*-1 for contracts of 1, 3 and 5 year terms.

**10.24** 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 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 12}

**10.25** 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 13} Changes in property taxes are reflected once a year, in the October CPI.

**10.26** 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:

**10.26.1**One that measures the change in the value of the replacement cost of properties using a third-party insurance data base (estimated quarterly); and**10.26.2**One that measures the change in insurance rates by comparing the cost of identical policy profiles using data from insurance companies in the sample.

**10.27** 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 14}

## Treatment of Seasonal Products

**10.28** 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.

**10.29** 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.

**10.30** 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.**
**

**10.31** 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 consumer products in-scope it must inevitably be based on a sample of product offers (POs) for a relatively small number of representative products^{Note 15} 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.

**10.32** 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.

**10.33** 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.

**10.34** 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.

**10.35** 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 16} 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.**
**

**10.36** 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.

**10.37** 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.

**10.38** 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.

**10.39** It should be clearly understood that the objective of out-of-season- imputation is not to obtain a proxy index that mirrors the price behavior 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

**10.40** 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 17}

**10.41** 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 18}> 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.**
**

**10.42** 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.

**10.43** 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.

**10.44** Despite the challenges with seasonally adjusted price indices, seasonal adjustment provides many useful benefits to users of price indices.^{Note 19}

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