Prices Analytical Series:
Updated Methodology for the Compilation of the Cellular Services Price Index (CSPI)

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Overview

The Consumer Price Index (CPI) measures price change by comparing the cost of a fixed basket of consumer goods and services through time. To produce a CPI that accurately reflects the experience of Canadians, Statistics Canada regularly updates the methodologies of various components of the CPI. The method used to calculate the CPI follows accepted international standards. It is also regularly reviewed internally and by experts outside the agency, and adjusted as needed to ensure it meets best practices.

The Cellular services price index (CSPI) is part of the Household operations, furnishings and equipment index, one of the eight major components of the CPI. It represents 1.22% of the most recent CPI basket based on 2023 expenditures.^{Note 1}

Statistics Canada prioritizes the accuracy and timeliness elements of quality in measuring price change. As part of its modernization initiative, the agency has been working with major Canadian wireless services providers (WSPs) to obtain transaction data for wireless plans. This initiative is aimed at improving the quality of the CSPI by expanding the sample and incorporating hedonic quality adjustment methods and plan level weights.

Thanks to this collaboration, Statistics Canada now receives monthly transaction data containing plan level information from WSPs with several retail brands across Canada.^{Note 2} Since not all WSPs in the market provide the agency with transaction data, the CSPI will continue to use web-collected data, which will be combined with transaction data.

This document details the methodology used to incorporate transaction data in the CSPI. The result is a “hybrid” index that combines the transaction data from participating WSPs with the web collected data from the other sampled WSPs.

Scope of the CSPI

The CSPI measures the monthly change in the prices of services associated with a cellular device. These include local and long-distance voice calls, text messaging, and internet access.^{Note 3} Miscellaneous fees, such as activation fees, overage charges, and roaming charges are excluded.^{Note 4} The cost of the cellular device is also excluded.^{Note 5} It is important to note that the services included in the CSPI have evolved with the consumption patterns of Canadians over the years.

Outlets

In each province or territory, prices are collected from all major WSPs, which collectively account for over 90% of the total provincial or territorial revenue. Within each province or territory, WSPs are weighted by their provincial or territorial market share, calculated in terms of revenue. Weighting the WSPs by their market share aims at ensuring the representativeness of the index. Revenue data are obtained from the Annual Survey of Telecommunications (AST), conducted jointly by Statistics Canada and the Canadian Radio-Television and Telecommunications Commission (CRTC).^{Note 6} The WSPs’ weights at the provincial and territorial levels are updated annually to reflect their current market shares.

Data

Web collected data

Canadian consumers have few WSPs to select from, and each retail brand within a WSP offers a limited number of cellular service plans on its website. Given the dynamic nature of the market, the consumer profile method is used, where prices for several consumer profiles, or representative bundles of cellular services, are tracked over time.^{Note 7} The method of pricing the same consumer profile over time ensures constant quantity and quality of services, and that the index reflects pure price change. The set of consumer profiles in use are designed to best reflect cellular services usage patterns of Canadian households and are regularly updated to ensure that they remain relevant. New profiles can be added, or old ones removed based on market share shifts or technological changes in the telecommunication industry. Table 1 includes two examples of representative consumer profiles.

For each retail brand in each province and territory, one plan is matched to each consumer profile. The plan must meet the consumer profile’s minimum specifications. While it may exceed the specifications, it must never fail to meet them. Out of all the plans that meet the specifications of a profile, the price of the least expensive plan is used. For the purposes of the CSPI, a (web-collected) plan is defined by brand, number of minutes and texts, data allowance, network type, international calling, and price status (regular or on special). Plan prices and features are collected each month from the websites of the WSPs’ retail brands. The following are excluded from collection due to low market share or measurement complexities: bundled plans, family plans, and prepaid plans.^{Note 8}

Transaction data

Each month, Statistics Canada receives a file from participating WSPs that contains information on wireless plans from each of their retail brands across Canada. All in-market (postpaid and prepaid) wireless plans, and the most popular legacy plans are included.^{Note 9} Statistics Canada’s objective is to achieve full market coverage with transaction data for each WSPs. However, given that some WSP can only provide a subset of their data, a minimum of 70% coverage of a WSP’s total market is acceptable.

For each plan, the following features are provided:

All plan features (except for Plan Availability and Subscriber Count) for a given plan remain constant over time. A plan’s availability status could change from ‘in-market’ to ‘legacy’ when the retail brand stops advertising it on its website and offering it to new subscribers. Any modification by the retail brand to an existing plan is introduced in the dataset as a new observation with a new Plan ID.^{Note 10}

Data processing

Web collected data

Once a plan has been selected for a consumer profile, it will be priced every month until the retail brand either stops advertising it or makes significant modifications to its features (e.g., adding bonus data). In both situations, a quality adjustment is done before proceeding.

Transaction data

Tracking plans to manage churn

To track plans over time, a “unique plan ID” is created for each observation in the dataset by concatenating the Plan ID, Geography, Retail Brand, and Plan Type features.^{Note 11} Note that the ‘Plan Availability’ feature is not included in this derived unique plan ID, because retail brands routinely stop offering certain plans to new subscribers but will continue to provide services to active subscribers on these “legacy” plans.

Given that the inclusion of any legacy plan in the file is contingent on its popularity, legacy plans that fail to reach a certain threshold of subscribers in each month will naturally drop out of the data file for that month. At the same time, in-market plans that become legacy plans in the current month may not appear in the list of the most popular legacy plans in the following month. This dynamic over time results in plan-level churn. It is important to note that the disappearance of a legacy plan from the monthly file does not mean that the plan no longer has any subscribers.   

To reduce the impact of churn on the index, the following actions are taken during data processing, grounded on information provided by WSPs that plan features do not change once a plan is launched in the market and has active subscribers.

1) Carry forward:

1. Legacy plan: A legacy plan that is in the previous month (T₀) but not in the current month (T₁) gets its feature information (e.g., data allowance, MRC, etc. ) carried forward to T₁. The plan’s disappearance in T₁ is likely due to the plan losing subscribers between the two periods. The missing legacy plan’s T₀ subscriber counts are carried forward to T₁ if they are less than the subscriber counts of the least popular legacy plan in T₁. Otherwise, the subscriber counts of the least popular legacy plan in T₁ is used.^{Note 12}
2. In-market plan: In-market plans missing in T₁ but present in T₀ have their feature information carried forward to T₁. These missing plans likely had their Availability switched to “legacy”, and thus, continue to exist in the market but were not popular enough to be included in the list of the most popular legacy plans in T₁.

2) Carry backward: If a legacy plan is in T₁ but not T₀, its feature information is carried backward to create a record in T₀. This situation is likely due to the plan not having enough subscribers to place it among the most popular legacy plans in T₀. The presence of the plan in the T₁ file is likely because the subscriber counts of other legacy plans dropped in T₁.  

Table 3 summarizes the actions for the cases described above:

Assigning comparable plans to service packages

Sample analysis of plans has revealed that retail brands often launch promotional plans with the same features as existing plans, but at different prices. A secondary processing step of assigning these types of plans into a “service package” (SP) is necessary in the compilation of the index. A service package is comprised of one or more plans which have the same values for the following features:

Note that a service package can contain both in-market and legacy plans, since the Availability feature is not used to assign plans into service packages. Each service package’s price is calculated as the weighted arithmetic average of all its plans’ MRCs. Individual plans’ subscriber counts are used as weights.

An example of a service package is given in Table 5 below. Service package “A” contains all 5G postpaid plans offered by Retail Brand 1 in Province A, having a data allowance of 50 GB, unlimited nationwide talk and text, and unlimited and shareable data. There are two plans in the service package (Plan X and Plan Y) and the weighted average price is $89.00.

Service packages are the fundamental building blocks on which pure price change of transaction data is measured. They also serve to classify the data into two distinct observation types:^{Note 13}

1) Continuing:  service packages which are available in both T₀ and T₁.

2) Entering: service packages which are available in T₁ but not in T₀.

Entering service packages are not carried backward to T₀ since they are composed of new (in-market) plans. Thus, T₀ prices for entering service packages are imputed via hedonic regression.

The monthly file is comprised mostly of continuing service packages given that — a small number of service packages enter the sample every month. In addition, most entering or new service packages do not attract sufficiently large numbers of subscribers to be significant in terms of market share. However, some service packages gain larger numbers of new subscribers during certain months (in particular, during select statutory holidays or back to school events) when retailers usually offer new plans at promotional prices or with updated features (e.g., data allowances).

Quality adjustment for new plans and service packages

According to the Wireless Code^{Note 14}, WSPs cannot change the terms and conditions of postpaid wireless plans while subscribers are still under contract. Therefore, their retail brands will frequently replace existing plans with new plans, instead of modifying them. When they introduce new plans that offer larger data allowances or additional features (e.g., international calling, faster transmission speeds, etc.), some of the new plans can quickly become popular with consumers looking to switch from their current cellular plans. In this context, there is a need to apply quality adjustment methods to predict missing T₀ prices and thus, account for price change that would otherwise be missed if the index were based on a matched model approach only.^{Note 15}

Web collected data

When a retail brand stops advertising a plan that was being priced for a consumer profile, the least expensive plan that fits the profile is selected. While Canadians might not always choose the cheapest plan that meets their needs, it is more reasonable to assume this behavior than to assume that consumers make no effort to minimize their costs. Quality adjustment using the option cost approach is then used to estimate the price of the replacement plan in T₀. This adjustment is based on price per GB and is controlled within the WSP’s retail brand and geography. If the replacement plan existed in T_0, then no imputation is performed and the actual T₀ price is used instead. 

Transaction data

Hedonic regression can be used to impute T₀ prices of new service packages in T₁ by estimating the statistical relationship between prices and product characteristics. The regression model uses the multivariate adaptive regression splines (MARS) algorithm to predict prices.^{Note 16} The MARS algorithm was chosen because it produced more accurate predictions, with the lowest Root Squared Mean Error (RMSE) for out-of-sample predictions compared to the other algorithms that were reviewed.^{Note 17}

The general hedonic regression model is:

$$(1)\ln (MR{C}_i)=f(X_i)+{\epsilon }_i$$

where:

$X_i$  consists of the following explanatory features used to explain the (log-transformed) MRC for service package $i$ :  Retail Brand, Plan Type, Data, IsMinUnlimited, IsSMSUnlimited, IsDataUnlimited, IsDataShareable, IncludesCANUS, and is5G.^{Note 18}

Service packages in the T₀ file, composed of in-market plans only, are used to estimate a hedonic regression model in every province or territory. The estimated regression model is used to predict T₀ prices of new service packages entering the provincial or territorial market in T₁. Legacy plans in the T₀ file are not used to estimate the model because they were not offered in the market in T₀ and thus reflect prices from a period prior to T_0.^{Note 19} Between 30 to 80 service packages are used to estimate the provincial and territorial models each month.

Index aggregation

After the missing prices have been estimated, current period prices are directly compared with the preceding period’s prices to construct price relatives.^{Note 20} The price relatives are then aggregated in several stages:

Stage 1: Retail brand level

Web collected data

The price relatives for each consumer profile are aggregated using an unweighted geometric mean to produce a price relative for a retail brand in a province or territory. The profiles are not weighted at this level due to lack of appropriate weight information for WSPs not providing transaction data. The equation below shows the calculation of month-to-month price change for retail brand A:

$$(2)I_A^{t-1:t}={\left({\displaystyle \prod _{i=1}^n\frac{p_{i,t}}{p_{i,t-1}}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}$$

where:

$I_A^{t-1:t}$   is the Jevons price index for retail brand A between period t–1 and t^{Note 21}
$p_{i,t}$  is the price of consumer profile i in period t
$n$  is the number of consumer profiles priced for retail brand A

Transaction data

Given the availability of quantity information in the form of subscriber counts, the price relatives for each service package are aggregated using a weighted geometric mean to produce a price relative for a retail brand in a province or territory. Each service package's price relative is weighted by its average revenue share over T₀ and T₁. A plan's monthly revenue is the product of the plan’s subscriber counts and its MRC. Thus, the monthly revenue of a service package is the sum of all monthly revenues for all plans in that service package. The equation below shows the calculation of month-to-month price change for retail brand B:

$$(3)I_B^{t-1:t}={{\displaystyle \prod _{i=1}^n\left(\frac{p_{i,t}}{p_{i,t-1}}\right)}}^{\frac{1}{2}\left[\frac{p_{i,t-1}{q}_{i,t-1}}{{\sum }_{j=1}^n\left(p_{j,t-1}{q}_{j,t-1}\right)}+\frac{p_{i,t}{q}_{i,t}}{{\sum }_{j=1}^n\left(p_{j,t}{q}_{j,t}\right)}\right]}$$

where:

$I_B^{t-1:t}$  is the Törnqvist – Theil price index for retail brand B between period t–1 and t^{Note 22}
$p_{i,t}$  is the price of service package i in period t
$q_{i,t}$  is the number of subscribers of service package i in period t
$n$   is the number of service packages priced for retail brand B

Stage 2: Provincial/territorial level

The transaction data price relatives are then combined with the web collected data price relatives from the other retail brands in the same province or territory using a weighted geometric mean to produce a hybrid provincial or territorial price relative. The resulting provincial or territorial index is a hybrid index because it is compiled using transaction data for some WSPs’ retail brands and manually web collected data for other WSPs’ retail brands in the same market. Provincial or territorial retail brand weights are based on the latest revenue data from the AST. The equation below shows the calculation of price change for province X:

$$(4)I_X^{t-1:t}={\displaystyle \prod _{k=1}^m{\left(I_k^{t-1:t}\right)}^{w_k}}$$

where:

$I_X^{t-1:t}$   is the Geometric Young price index for province X between period t–1 and t^{Note 23}
$I_k^{t-1:t}$  is the price change of retail brand k in province X
${}^{w_k}$  is the revenue share of retail brand k in province X
$m$  is the number of retail brand in province X

Stage 3: Canada level

The Canada level price relative is obtained by computing the weighted arithmetic mean of all provincial and territorial relatives. Weights for this aggregation are sourced from the National Household Final Consumption Expenditure (HFCE) dataset.^{Note 24} Figure 1 below shows the aggregation scheme for the CSPI.

In summary

This methodology for a hybrid index will be used for incorporating transaction data in the CSPI. Transaction data from WSPs are a comprehensive source of information that can be used to enhance the index. They include a larger volume and type of plans each month and thus, represent a more complete picture of the market. The subscriber counts are used to calculate more accurate measures of price change. Finally, the larger sample size allows the implementation of a hedonic imputation model using the MARS algorithm for quality adjustment. Given that not all WSPs in the market have agreed to provide the agency with transaction data, the hybrid CSPI will continue to use web-collected data alongside the transaction data. The incorporation of transaction data into the currently published CSPI will lead to an improvement in the quality of the index.

Note to users

As part of Statistics Canada’s rigorous and ongoing efforts to maintain the quality and relevance of the CPI, this technical paper explains the data and methodology for including transaction data in the CPI’s cellular services price index.

This enhancement improves the quality of the data, while ensuring the representativeness of prices paid by Canadian consumers. Users should exercise caution when interpreting the year-over-year change for the first 12 months following the implementation of a new methodology and data source.

Users are also advised to exercise caution when making provincial/territorial comparisons. The market shares of the sampled wireless service providers vary across provinces and territories, and price changes derived from transaction data may differ from price changes derived from web-collected data as transaction data includes monthly charges for in-market and legacy plans, while web-collected data only contains monthly charges for advertised plans. The hybrid cellular services price index in each province or territory is affected by the market shares of the wireless service providers from which Statistics Canada is receiving transaction data.

Statistics Canada continues to work with price experts, national statistical organizations, and other partners to ensure data and methods used in the calculation of the CPI are aligned with international standards and best practices. To maintain the accuracy and relevance of the CPI, the agency will continue to monitor prices for cellular services and to acquire transaction data from additional wireless service providers.

For additional information or to provide comments on the proposed enhancement, users may contact the Consumer Prices Division at statcan.cpddisseminationunit-dpcunitedediffusion.statcan@statcan.gc.ca.