# The Canadian Consumer Price Index Reference Paper

Glossary

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Term | Description |
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Acceleration | A larger (faster) rate of change of an index from one period to another. The opposite of deceleration. |

Acquisitions approach | An approach to the timing of price collection corresponding to the period in which the good or service is obtained by the consumer, that is, when the legal ownership of the good passes to the consumer. |

All-items CPI | The total (highest-level aggregate) in the CPI product classification. The index which is commonly used to calculate “inflation”. |

Annual average price index | The unweighted arithmetic average of 12 consecutive monthly price indices from January to December. |

Annual average percentage change | The percentage difference between two consecutive annual average prices indices. |

Asset | An economic resource. Anything capable of being owned or controlled to produce value and that is held to have positive economic value. |

Asymmetrically weighted | Refers to a price index formula where the weights used to aggregate elementary price indices do not give equal weight to both periods of price comparison. For this reason an asymmetrically weighted price index formula does not represent the spending patterns of consumers over both periods of price comparison and is therefore subject to substitution bias. The Laspeyres, Lowe and Paasche formulae are asymmetrically weighted price indices. |

Basic class (aggregate) | The lowest level in the intersection of the product and geography classifications at which the quantity weights are kept fixed for the duration of the basket. |

Basket update | The process of replacing a basket (fixed-quantity weights) by another one that is more recent. |

Basket weight | Expenditures from a given reference period used to estimate quantities consumed for upper level aggregation of elementary price indices. |

Bestsellers method | A common method for estimating price change for goods that are highly ‘fashionable’ and have highly intangible content that consumer’s value. The price estimation method currently used for the Books and other reading material (excluding textbooks) elementary index in the CPI. |

Bias | Errors which are systematic, meaning they lead to persistent over- or under-estimation of the phenomenon being measured. |

Capital good | A durable good that is also an asset. |

Chain-linked index | An index spanning more than one basket that has been calculated using the chain-linking procedure. |

Chain-linking | The process of chaining a fixed-basket index to another fixed-basket index in order to create a continuous time series. This process ensures that period-over-period percentage changes in a chain-linked index will only reflect price change and not changes in the fixed quantities. |

Classification | An exhaustive and mutually exclusive structure for categorizing a domain. In the CPI, classifications are used primarily for the product and geography domains. They are used for weighting and aggregating elementary prices indices and also serve as a basis for stratifying the sample of prices collected. |

Collection area | A geographical sampling unit. For the CPI it corresponds to a Census Sub-Division and is similar to a “municipality”. |

Composite price index | An index designed to express, in one number, average price change for multiple products and/or geographies. |

Computer-Assisted Personal Interview (CAPI) | A survey approach where interviewers ask questions guided by a computer screen and enter the responses into the computer, where those answers are checked for consistency and from which the encrypted responses are ultimately transmitted to headquarters. |

Consumer goods and services | Products purchased for consumption by a household. |

Contribution to percentage change | The percentage points that a change in a component index account for in the percentage change of an aggregate index. It is a tool used by Statistics Canada to understand and summarize movements in the CPI. |

Cost-of-Living Index (COLI) | An index designed to measure changes in the cost of maintaining a given level of well-being for a group of consumers. |

CPI survey frame | A set of units from which a CPI sample is drawn. |

Cut-off sampling | A survey sampling method in which parts of the universe are excluded from sample selection. The method is used by Statistics Canada in the sampling of prices for various elementary aggregates where only partial frames are available. |

Deceleration | A smaller (slower) rate of change of an index from one period to another. The opposite of acceleration. |

Direct price comparison | A method used to compare the prices of exiting and entering Product Offers (POs) in the CPI sample when there is no perceptible quality difference. The price of the entering PO is compared directly with the price of the exiting PO and no quality adjustment is made. |

Durable good | A good that is not fully consumed in a short period of time (roughly one year). It provides utility over a long period of time. |

Economic Region | A standard geographical unit, defined by Statistics Canada, for analysis of regional economic activity which corresponds to a grouping of Census Divisions. |

Eight major aggregates (components) | The highest level of aggregation in the product classification of the CPI below the All-items level. |

Elementary aggregates | The lowest level in the intersection of the product and geographical classifications of the CPI for which expenditure weights are normally available. They consist of similar groupings of products in a geographical stratum. They are the starting point of the upper level aggregation using the fixed-basket Lowe formula. |

Elementary price indices | Price indices corresponding to elementary aggregates. In the CPI they are typically calculated using a Jevons formula. |

Explicit quality adjustment | Various methods of directly adjusting an observed price to account for the estimated quality difference between exiting and entering Product Offers in the CPI sample. |

Fixed-basket index | The ratio of the cost of a specified basket of goods and services in a price observation period to its cost in a previous period. The Dutot, Lowe, Laspeyres, Paasche, Marshall-Edgeworth and Walsh formulae yield fixed-basket price indices. |

Geographical stratum | The lowest geographical level in which expenditure weights are used in the construction of the CPI. The geographical strata also serve as sampling areas within which Product Offers are collected for the CPI. |

Hedonic quality adjustment | A statistical method for estimating how the price of a Product Offer (PO) is affected by its characteristics. It is a common method used to estimate the effect of quality change on price movement at the time of PO substitution. |

Hybrid expenditures | The value corresponding to the hypothetical cost of an elementary aggregate, in which quantities and prices are derived from different periods. The quantities normally come from the basket reference period and the prices from another period. |

Imputation | The process of replacing missing data with estimated values. In terms of the CPI it involves estimating the price movement of an elementary aggregate by proxy, using the price movement of a donor class. |

Index reference period (index base period) | The period in which an index is arbitrarily set equal to 100. |

Link month | The month in which a new fixed-basket index is chained to an old fixed-basket index. |

Link-to-show-no-change | A method which forces a price relative of 1 (no price change) when a new (entering) Product Offer (PO) replaces an old (exiting) PO in the CPI sample. |

Lower level calculation | The first stage of CPI calculation, which involves computing price indices for elementary aggregates. In the case of the CPI this is typically done using a ratio of geometric average prices (Jevons). |

Matched-model | A method for measuring “pure price change” by keeping constant all quality characteristics across time, except for price. This is the standard method for measuring price change in elementary aggregates in the CPI. |

Money outlays | A variant of the user-cost approach for measuring owned accommodation in a CPI where only expenses involving actual cash disbursements are included. |

Month-over-month change | A price change between one month t and the preceding month t-1. |

Outlet | The interface between a supplier of products and the consumer. It may be a store, a catalogue, a website etc. |

Overlap pricing | A method of quality adjustment based on the difference in price between exiting and entering Product Offers (POs) when both can be observed simultaneously. |

Plutocratic weights | Expenditure weights in which each household in the target population contributes its own spending to the total spending weight for the target population. The basket weights for the CPI, which are derived primarily from the Survey of Household Spending, follow this approach. Opposite of democratic weights. |

Price observation period | One of the periods for which an index has been compiled. Also widely used to mean the later of the two periods being compared. Appears in the numerator of price ratios. It is typically designated as period t. |

Price reference period | The period that provides the prices to which all other periods are compared. Appears in the denominator of price ratios. It is typically designated as period 0. |

Price-updating | A procedure whereby the quantities of an earlier period are revalued at the prices of a later period. The result is hybrid expenditure weights. This procedure is necessary in order to hold quantities constant when expenditures (not quantities) are the only source of data available for deriving basket weights. |

Product Offer (PO) | The presentation of a particular good or service, with an associated price, by a retailer to a purchaser. Used in the CPI as a proxy for the final transaction price paid by consumers. |

Profiles method | A method for estimating price change for an elementary aggregate where prices for bundles of services (rather than individual products) are compared over time. |

Pure price change | The change in the price of a product of which the characteristics are unchanged; or the change in the price after adjusting for any change in quality. |

Quality adjustment | An adjustment to remove from the observed price change the contribution attributable to changes in a product's characteristics. |

Rebasing | The process of changing the index reference (base) period. As an arithmetic operation it does not affect the rate of price change between any two index points. |

Rental equivalence | The estimation of the hypothetical rents that would be payable by owner-occupiers on the basis of market rents payable for renter-occupied accommodation of the same type and location. |

Representative Product (RP) | The definition of a narrow class of products for which the average price change is expected to be representative of the average price change of an elementary aggregate. |

Sample | A set of data collected to represent a population. |

Sampling unit | An element considered for selection in some stage of survey sampling. |

Scope | The set of products and geographies and the target population for which the CPI is intended to measure price changes. |

Seasonal adjustment | A procedure for removing regular recurring intra-annual fluctuations from a time series in order to reveal its underlying trend, cyclical and irregular movements. |

Seasonal product | Products that are either not available for purchase during certain periods of the year or are available but subject to regular and significant fluctuations in the quantities available and/or purchased. |

Special aggregate index | An index for different combinations of elementary price indices, excluding certain product classes. These indices provide supplementary information on aggregate price change. |

Substitution bias | Generally understood to be the bias that arises from the use of asymmetrically weighted fixed-basket index formulae. Occurs because quantities are held constant while consumers change their purchasing patterns in response to relative price changes. |

Symmetrically weighted | Refers to a price index formula where the weights used to aggregate elementary price indices refer to both periods of price comparison. For this reason a symmetrically weighted price index formula represents the spending patterns of consumers over both periods of price comparison and is therefore not subject to substitution bias. The Fisher, Törnqvist-Theil, Walsh and Marshall-Edgeworth formulae are examples of symmetrically weighted price indices. |

Target population | The people or group of people whose consumption expenditures are in the scope of the CPI. |

Target Product Offer (TPO) | The specification of a Representative Product (RP) to an outlet. The TPO acts as the sample intention for the CPI. |

Unit value index | A method for estimating price change for an elementary aggregate where the quantity-weighted average transaction price for homogenous products is compared over time. |

Upper level calculation | The second stage of CPI calculation, which involves aggregating elementary price indices using a fixed-quantity weighted arithmetic average formula (Lowe). |

User cost | The estimation of the cost of using a fixed asset or durable good. The current approach used in the CPI for owned accommodation. |

Weight (basket) reference period | The period from which the expenditures, used to derive the quantity weights of the CPI basket, are taken. |

Weight adjustment | A procedure to obtain monthly hybrid expenditure weights when annual expenditures are used in the calculation of monthly price indices. |

Source: Statistics Canada, Consumer Prices Division. |

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