The Canadian Consumer Price Index Reference Paper
Chapter 7 – Quality Change and Adjustment

7.1 The Canadian Consumer Price Index (CPI) aims to measure pure price change, thus excluding price changes that are due to differences in the quality of products bought by consumers. It achieves this mostly through the matched-model approach which tracks unchanging products in the same outlets, thus holding all variables constant except for the month when prices are observed.

7.2 The universe of products bought and sold in the marketplace changes over time. Updating the sample for any given elementary aggregate is inevitable in order to maintain its representativeness. As products in the market change, observed product offers (POs) may change. This means that the matched-model framework at times does not hold, and therefore price changes could reflect a mixture of price and quality differences. In order to measure pure price change, quality adjustments are performed.

7.3 There are multiple techniques, implicit (indirect) and explicit (direct), available to account for quality differences between exiting and entering POs. This chapter will present the different methods used in the CPI.^Note 

7.4 It is not always necessary or possible to adjust for quality change when a PO must be replaced in the CPI sample. There are various reasons why adjusting for quality change may not be required and a direct price comparison between entering and exiting POs is the best option. Direct price comparison, an implicit method of quality adjustment, is the simplest approach used in the CPI.

7.5 The CPI employs the direct price comparison method when there is no perceived difference in quality between entering and exiting POs. This method assumes that POs are equivalent in terms of quality.  

7.6 The use of the direct price comparison method for these elementary indices is not likely to lead to any systematic bias in the CPI because the majority of these indices fall under one of the following categories.

• 7.6.1 No appreciable quality change: Many items like gasoline, electricity or natural gas are essentially of the same quality over long periods of time.
• 7.6.2 Non-market services: Most government-regulated services, such as university education, local transportation or passports, do not receive any treatment for quality change. While it could be argued that the quality of these services may change through time, this is likely to happen very slowly and is difficult to measure. These services are also not available in a competitive market so little can be said about the market valuation of the quality features that are implied.
• 7.6.3 Bestsellers method: In the case of popular media, such as books, movies or DVDs, it is common international practice to simply aggregate the prices of the top bestsellers and compare the result to that for the previous period’s bestsellers, even if these best sellers are different in the two periods. This is because the novelty of the product’s content is what is being sought out by consumers, rather than any tangible physical characteristic such as number of pages or quality of the binding, to take books as an example.
• 7.6.4 The use of the unit value index method also eliminates the need for any further quality adjustment. This index calculation method is rarely used in the CPI and can only be applied in cases where it is assumed that the average quality represented remains constant through time.^Note 

7.7 The use of overlap pricing can also eliminate or significantly reduce the need to make explicit quality adjustments. This implicit method allows for the reduction of unexpected disappearances of sampled POs and ensures that new representative products can be introduced into the sample before the replaced ones disappear from the market or become unrepresentative. The overlap pricing method is most commonly used in conjunction with the profiles method, enabling the collection of a replacement profile before the obsolescence of an existing one.

7.8 Overall mean imputation is another implicit method used in the CPI to make quality adjustments between the prices of POs entering and exiting the sample. With this method, the price movement applied to entering POs is based on the observed average price movement of all other POs for the same representative product. Overall mean imputation relies on the assumption that the donor POs are comparable to the PO being imputed.

7.9 The link-to-show-no-change method for quality adjustment, another indirect method, involves forcing a price relative of unity (equals no price change) when replacement POs enter the sample. Currently, this practice is being reduced across the CPI because it introduces a degree of undue price stability in the index.^Note 

7.10 Quantity adjustment entails accounting for changes in the quantity (e.g. package size, number of tissue ply, etc.) of observed POs. This is another implicit method of quality adjustment because it is assumed that the quality per standardized unit is the same over time.

7.11 Quantity adjustment is the default treatment for nearly all of the POs in the food major aggregate as well as some of the products in the household operations, and personal care supplies and equipment aggregates.

7.12 For the majority of elementary indices, not covered by the implicit methods described above, it is necessary to make explicit quality adjustments when POs enter or exit the sample.

7.13 To make the appropriate quality comparison, Statistics Canada is usually guided by market valuations of the two POs. Where possible, the two POs are compared in terms of the quality features they offer to consumers. A PO is thought to provide a range of features to the consumer which, grouped together, determine the market price.^Note  This general framework is the basis for many of the explicit quality adjustment methods described below.

7.14 The CPI relies on the hedonic quality adjustment technique for certain elementary aggregates, notably in the case of high-technology goods or services. Currently, the CPI uses hedonic quality adjustment for the computer equipment, software and supplies, Internet access services and rent indices. The hedonic method of quality adjustment is most appropriate for products whose markets are competitive and experience rapid turnover, and where the characteristics of these products change quickly but are readily and consistently observable.

7.15 The hedonic method is applied in the case of forced replacements. This approach assumes that a relationship exists between the price of a PO and its characteristics. Hedonic specifications have to be defined using standard regression techniques.^Note  In period t (when a previously observed PO is no longer available) a regression is used to estimate the unobserved price for the entering PO in period t-1. The estimation of the t-1 price is based on quality differences between the entering and exiting POs, as well as the t-1 price of the exiting PO.

7.16 A semi-log hedonic regression is used for the computer equipment, software and supplies index. It takes the general form:

$$\ln \left(p_n^t\right)={\beta }_0+{\displaystyle \sum _{i=1}^k{\beta }_i}{X}_{i,n}^t+e_n^t\text{\hspace{1em}\hspace{1em}\hspace{1em}(7.1)}$$

where:

${\beta }_i$ is a range of effects for a set of $k$ characteristics ${\text{X}}_{i,n}^t$, $i=1,2,\dots ,k$, that are used to explain variations in the natural log of the price.

7.17 Coefficients of the semi-log hedonic regression are estimated once a year using product characteristics data and retail prices obtained from the Internet and third party databases. All other things being equal, a coefficient represents the impact of a given product characteristic on the price level.

7.18 For the Internet access services elementary (IAS) index, a pure matched-sample cannot properly account for the rapid technological change and marketing practices that characterize the Internet access industry in Canada. Therefore, a symmetric hedonic method is used to adjust the prices of both entering and exiting Internet access services plans.^Note  For the regression model specification, characteristics are transformed as appropriate. Unlike the method for Computer equipment, software and supplies index, coefficients are estimated at every collection period from sets of plans that are used to calculate the index and Internet plan weights.

7.19 For IAS, rather than estimating a single multiple regression, three separate simple regressions are estimated at every collection period. In each of these regressions, the dependent variable, log price, is regressed on the intercept term and a single explanatory variable consisting of either log download speed, log upload speed or log usage cap.

7.20 Least squares are used to solve for the $B$  vector of parameters in the following formulation:

$$\ln p_i^t=B•X_i^t+{\epsilon }_i$$

where

$p_i^t$  is the price of plan $i$   from period $t$ ,

${\epsilon }_i$  is a random error term with an expected value of zero, and

$X_i$ is plan $i$ ’s characteristic (either log download speed, log upload speed or log usage cap).^Note 

7.21 Once all three regressions have been estimated, results from each of the regressions are used to predict a price for each plan, leading to three predicted prices. A weighted average of these three predicted prices is calculated as a single predicted price; the weights are defined such that a regression with a higher value of the coefficient of determination R squared will have more weight. The missing prices of entering and exiting plans are imputed. The missing price of plan $i$ i in period $t$  from Internet Service Provider (ISP) $h$  is calculated as $p_{ih}^t={\widehat{p}}_{ih}^t\times A_{ih}^t$ . Here $A_{ih}^t$  is an adjustment factor calculated from the plans available in period $t$ from ISP $h$  while ${\widehat{p}}_{ih}^t$  is the imputed average predicted price.^Note 

7.22 For the rent index, a hedonic model is estimated using monthly cross-sections of the Labour Force Survey (LFS) data at the national level. The lowest geographical level indices are constructed using average characteristics as quantities and estimated coefficients as prices, while the higher level indices use weighted averages of lower level estimated expenditures.

7.23 The hedonic model for the rent index is a log-linear regression in which the explanatory variables include observed unit characteristics, such as the number of bedrooms, as well as locational characteristics captured by postal codes. The regression specification is as follows:

$$y^{\text{*}}={\beta }_0+{\beta }_{1}services+{\beta }_{2}age+{\beta }_{3}bedrooms+{\beta }_{4}dwelling+{\beta }_{5}FSA+ϵ$$

where  $y^{\text{*}}$  is the log of observed rent, $services$  represents whether the rent cost includes furniture, a washing machine, refrigerator, cable, or heat, $age$  represents the age of building, $bedrooms$  represents the number of bedrooms, $dwelling$   represents the type of the building, and $FSA$  is a vector of dummies defined from the first three digits of the postal code that corresponds to a neighborhood (in urban areas) or a region (in rural areas).

7.24 The option cost method is another explicit approach for making quality adjustments to entering POs in the CPI sample. This technique relies on having data about the specific costs for adding options or quality characteristics to a product. In this explicit method, an adjustment to the last observed price of the exiting PO is made so that it can be compared with the observed price of the entering PO. The option cost method is most commonly used for products where the manufacturer or retailer provides pricing details for the available product characteristics. The CPI uses the option cost method in the elementary aggregates corresponding to the purchase of passenger vehicles index.

7.25 Expert judgment has, in the past, been a predominant practice for explicit quality adjustment in the CPI. This relies upon an employee with expertise in a particular product market to assess and give a valuation to differences in quality between exiting and entering POs. However, the practice of quality adjustment by expert judgment is not arbitrary^Note  and follows procedural guidelines for choosing the most plausible quality ratio between exiting and entering POs. The expert judgment method is primarily used for elementary indices under the clothing and footwear major aggregate.

The option cost and expert judgment explicit approaches to quality adjustment are used in the CPI for cases where a complex decision has to be made, and where it is not appropriate to apply an implicit method such as overall mean imputation.