Consumer Price Index: The Bank of Canada's Preferred Measures of Core Inflation
Methodology Document

Overview

The consumer price index (CPI) plays a key role in the Bank of Canada's conduct of monetary policy.

In 1991, the Bank of Canada and the Government of Canada jointly established an inflation-targeting framework for the conduct of monetary policy. This framework is reviewed every five years, with the most recent renewal occurring in October 2016. Based on this framework, the Bank of Canada conducts monetary policy aimed at keeping inflation, as measured by the change in the All-items CPI, at 2 per cent, the midpoint of an inflation-control range of 1 to 3 per cent.

To help it achieve this target, the Bank of Canada uses a set of measures of core inflation. The purpose of these measures is to capture persistent price movements by eliminating transitory or sector-specific fluctuations in some components of the CPI. From 2001 until the most recent renewal of the inflation control target, the Bank of Canada's focal measure of core inflation was the All-items CPI excluding eight of its most volatile components (as defined by the Bank of Canada) as well as the effect of changes in indirect taxes on the remaining components (CPIX). For more information, see the Bank of Canada Review article (Macklem [2001]).

As discussed in the Renewal of the Inflation-Control Target – Background Information, the Bank of Canada has identified three preferred measures of core inflation to help assess underlying inflation in Canada.Note 1 The Bank of Canada chose these three measures based primarily on analysis conducted in 2015 by its researchers (Khan, Morel and Sabourin [2015]). While the Bank's emphasis will be on these three measures, Statistics Canada will continue to calculate and publish CPIX.

Although no measure of core inflation was superior across all the evaluation criteria, three measures showed the best performance. Based on the results of this analysis, the Bank of Canada decided to change its approach by jointly using all three measures: i) a measure based on the trimmed mean (CPI-trim); ii) a measure based on the weighted median (CPI-median); and, iii) a measure based on the common component (CPI-common). For more information on how the three measures were chosen, see the background document on the renewal of the inflation-control target (Bank of Canada [2016]). In the rest of this document, we will present detailed information on the methodologies and data used to produce these measures of core inflation.Note 2

Reference period

These measures are expressed as a year-over-year percentage change (i.e., comparing any month in a given year to the same month in the previous year). Accordingly, they are not available in the form of an index level and do not have a reference period (e.g., 2002=100).

Data sources and methodologies

The three preferred measures of core inflation are computed by Statistics Canada using data from the CPI Survey. For more information on the data sources, error detection, imputation rules, estimation and calculation of price indexes, quality evaluation of the data collected, and data disclosure control for the CPI survey, see the description of this survey. Below, we will describe the CPI data used and the methods for calculating these three measures of core inflation.

The three measures require historical series of consumer price indexes based on the disaggregation of the All-items CPI into a fixed number of components. These components are exhaustive and mutually exclusive. Therefore, the sum of their respective weights in the CPI basket is equal to 100. These measures are based on a 55-component disaggregation of the CPI basket; a complete list of these components is provided in Table A1 in the appendix of this document. These historical series are available on a monthly basis. Owing to data limitations, these 55 components are calculated since January 1989.Note 3 Since we use price indexes calculated at the national level, the three measures are only calculated at that level of detail.

The consumer price indexes of the 55 components are first adjusted to remove the effect of changes in indirect taxes.

Measure of core inflation based on the trimmed mean (CPI-trim)

CPI-trim excludes from the 55 components those whose monthly rates of change in the CPI are located in the tails of the distribution of the monthly rates of change of all the price indexes in a given month. This measure is calculated as a weighted arithmetic average of the price changes of the non-excluded components. The weight of a component corresponds to its weight in the CPI basket at the basket link month. The procedure for calculating CPI-trim every month can be described as follows.

Step 1: The historical series of price indexes for the 55 components, adjusted to remove the effect of changes in indirect taxes, are seasonally adjusted. For more information on the seasonal adjustment methodology, see the "Revisions and seasonal adjustment" section below.

Step 2: We obtain the distribution of all monthly inflation rates calculated for the 55 components based on the percentage changes in price indexes for the current month versus those for the previous month. These monthly inflation rates are then sorted in ascending order (i.e., from lowest to highest). By ranking all the components' weights and monthly inflation rates together in this order, components with the lowest inflation rates are excluded, which accounts for 20 per centNote 4 of the total CPI basket. The same process is used to exclude components with the highest inflation rates, up to 20 per centNote 5 of the basket.

Step 3: We calculate a monthly trimmed inflation rate,  CPI-trim t m/m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdbGaaeiuaiaabMeacaqGTaGaaeiDaiaabkhacaqGPbGaaeyB a8aadaqhaaWcbaWdbiaadshaa8aabaWdbiaad2gacaGGVaGaamyBaa aaaaa@40EF@ , defined as the weighted arithmetic average of monthly inflation rates for components not excluded in Step 2, which make up 60 per cent of the total CPI basket. The weight of the excluded components will always be 40 per cent of the total CPI basket, but the excluded components are not necessarily the same from month to month.

Step 4: We produce the annual inflation rate for a given month,  CPI-trim t y/y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdbGaaeiuaiaabMeacaqGTaGaaeiDaiaabkhacaqGPbGaaeyB a8aadaqhaaWcbaWdbiaadshaa8aabaWdbiaadMhacaGGVaGaamyEaa aaaaa@4107@ , using the cumulative monthly trimmed inflation rates for the 12-month period ending in the current month. The following formula is used for this purpose:

CPI-trim t y/y =( ( 1+ CPI-trim t11 m/m 100 )×( 1+ CPI-trim t10 m/m 100 )××( 1+ CPI-trim t m/m 100 )1 )×100. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdbGaaeiuaiaabMeacaqGTaGaaeiDaiaabkhacaqGPbGaaeyB a8aadaqhaaWcbaWdbiaadshaa8aabaWdbiaadMhacaGGVaGaamyEaa aakiabg2da9maabmaapaqaa8qadaqadaWdaeaapeGaaGymaiabgUca Rmaalaaapaqaa8qacaqGdbGaaeiuaiaabMeacaqGTaGaaeiDaiaabk hacaqGPbGaaeyBa8aadaqhaaWcbaWdbiaadshacqGHsislcaaIXaGa aGymaaWdaeaapeGaamyBaiaac+cacaWGTbaaaaGcpaqaa8qacaaIXa GaaGimaiaaicdaaaaacaGLOaGaayzkaaGaey41aq7aaeWaa8aabaWd biaaigdacqGHRaWkdaWcaaWdaeaapeGaae4qaiaabcfacaqGjbGaae ylaiaabshacaqGYbGaaeyAaiaab2gapaWaa0baaSqaa8qacaWG0bGa eyOeI0IaaGymaiaaicdaa8aabaWdbiaad2gacaGGVaGaamyBaaaaaO WdaeaapeGaaGymaiaaicdacaaIWaaaaaGaayjkaiaawMcaaiabgEna 0kabgAci8kabgEna0oaabmaapaqaa8qacaaIXaGaey4kaSYaaSaaa8 aabaWdbiaaboeacaqGqbGaaeysaiaab2cacaqG0bGaaeOCaiaabMga caqGTbWdamaaDaaaleaapeGaamiDaaWdaeaapeGaamyBaiaac+caca WGTbaaaaGcpaqaa8qacaaIXaGaaGimaiaaicdaaaaacaGLOaGaayzk aaGaeyOeI0IaaGymaaGaayjkaiaawMcaaiabgEna0kaaigdacaaIWa GaaGimaiaac6caaaa@88E3@

In other words, the annual inflation rate,  CPI-trim t y/y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdbGaaeiuaiaabMeacaqGTaGaaeiDaiaabkhacaqGPbGaaeyB a8aadaqhaaWcbaWdbiaadshaa8aabaWdbiaadMhacaGGVaGaamyEaa aaaaa@4107@ , measured for a given month t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaaaa@36F0@  is calculated as the cumulative monthly trimmed inflation rates over the 12-month period ending in month  t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaaaa@36F0@ .

Measure of core inflation based on the weighted median (CPI-median)

CPI-median represents, for a given month, the price change corresponding to the 50th percentile (in terms of CPI basket weights) of the distribution of price changes of the 55 components. As with CPI-trim, the weight of a component is represented by its weight in the CPI basket at the basket link month. The method for processing data for the CPI-median is similar to that for CPI-trim. The procedure for calculating CPI-median every month can be described as follows.

Step 1: The historical series of price indexes for the 55 components, adjusted to remove the effect of changes in indirect taxes, are seasonally adjusted. For more information on the seasonal adjustment methodology, see the "Revisions and seasonal adjustment" section below.

Step 2: We obtain the distribution of all monthly inflation rates calculated for the 55 components based on the percentage changes in price indexes for the current month versus those for the previous month. These monthly inflation rates are then sorted in ascending order (i.e., from lowest to highest). By ranking all the components' weights and inflation rates together in this order, we identify the monthly inflation rate located at the 50th percentileNote 6 (in terms of CPI basket weights) of the distribution of the monthly inflation rates for the 55 components. This value represents the monthly inflation rate based on the weighted median,  CPI-median t m/m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdbGaaeiuaiaabMeacaqGTaGaaeyBaiaabwgacaqGKbGaaeyA aiaabggacaqGUbWdamaaDaaaleaapeGaamiDaaWdaeaapeGaamyBai aac+cacaWGTbaaaaaa@42A7@ . The component corresponding to the weighted median value is not necessarily the same from month to month. This approach is similar to that for CPI-trim because it eliminates all the weighted monthly price variations at both the bottom and top of the distribution of price changes in any given month, except the price change for the component that is the midpoint of that distribution.

Step 3: We produce the annual inflation rate,  CPI-median t y/y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdbGaaeiuaiaabMeacaqGTaGaaeyBaiaabwgacaqGKbGaaeyA aiaabggacaqGUbWdamaaDaaaleaapeGaamiDaaWdaeaapeGaamyEai aac+cacaWG5baaaaaa@42BF@ , for a given month, using the cumulative monthly inflation rates based on the weighted median for the 12-month period ending in the current month. The following formula is used for this purpose:

CPI-median t y/y =( ( 1+ CPI-median t11 m/m 100 )×( 1+ CPI-median t10 m/m 100 )××( 1+ CPI-median t m/m 100 )1 )×100. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdbGaaeiuaiaabMeacaqGTaGaaeyBaiaabwgacaqGKbGaaeyA aiaabggacaqGUbWdamaaDaaaleaapeGaamiDaaWdaeaapeGaamyEai aac+cacaWG5baaaOGaeyypa0ZaaeWaa8aabaWdbmaabmaapaqaa8qa caaIXaGaey4kaSYaaSaaa8aabaWdbiaaboeacaqGqbGaaeysaiaab2 cacaqGTbGaaeyzaiaabsgacaqGPbGaaeyyaiaab6gapaWaa0baaSqa a8qacaWG0bGaeyOeI0IaaGymaiaaigdaa8aabaWdbiaad2gacaGGVa GaamyBaaaaaOWdaeaapeGaaGymaiaaicdacaaIWaaaaaGaayjkaiaa wMcaaiabgEna0oaabmaapaqaa8qacaaIXaGaey4kaSYaaSaaa8aaba WdbiaaboeacaqGqbGaaeysaiaab2cacaqGTbGaaeyzaiaabsgacaqG PbGaaeyyaiaab6gapaWaa0baaSqaa8qacaWG0bGaeyOeI0IaaGymai aaicdaa8aabaWdbiaad2gacaGGVaGaamyBaaaaaOWdaeaapeGaaGym aiaaicdacaaIWaaaaaGaayjkaiaawMcaaiabgEna0kabgAci8kabgE na0oaabmaapaqaa8qacaaIXaGaey4kaSYaaSaaa8aabaWdbiaaboea caqGqbGaaeysaiaab2cacaqGTbGaaeyzaiaabsgacaqGPbGaaeyyai aab6gapaWaa0baaSqaa8qacaWG0baapaqaa8qacaWGTbGaai4laiaa d2gaaaaak8aabaWdbiaaigdacaaIWaGaaGimaaaaaiaawIcacaGLPa aacqGHsislcaaIXaaacaGLOaGaayzkaaGaey41aqRaaGymaiaaicda caaIWaGaaiOlaaaa@8FC3@

In other words, the value of the annual inflation rate,  CPI-median t y/y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdbGaaeiuaiaabMeacaqGTaGaaeyBaiaabwgacaqGKbGaaeyA aiaabggacaqGUbWdamaaDaaaleaapeGaamiDaaWdaeaapeGaamyEai aac+cacaWG5baaaaaa@42BF@ , in a given month  t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaaaa@36F0@ is calculated as the cumulative monthly inflation rates based on the weighted median over the 12-month period ending in month  t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaaaa@36F0@ .

Measure of core inflation based on the common component (CPI-common)

CPI-common is a measure that tracks common price changes across the 55 components in the CPI basket.

As with CPI-trim and CPI-median, the input data for CPI-common are the CPI series for the 55 components adjusted to remove the effect of changes in indirect taxes. In addition, we use the historical series of the All-items CPI adjusted to remove the effect of changes in indirect taxes to scale CPI-common to the inflation rate. Unlike CPI-trim and CPI-median, this measure is based on year-over-year percentage changes in price indexes. Therefore, the price index series are not seasonally adjusted when calculating CPI-common.

This measure is based on a factor model. Factor models are statistical methods that represent the variation in a set of variables as the sum of one or more factors representing co-movements across variables and an idiosyncratic term capturing the part unexplained by this (those) common factor(s). In the context of estimating core inflation, these models are used to separate the common source underlying the changes in CPI series from idiosyncratic elements that are related to sector-specific events (Khan, Morel and Sabourin [2013]).Note 7 For each of the 55 components,  i=1,2,...,55 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaiabg2 da9iaaigdacaGGSaGaaGOmaiaacYcacaGGUaGaaiOlaiaac6cacaGG SaGaaGynaiaaiwdaaaa@3F06@ , the model is written as follows (in the case of one common factor):

π i,t = Λ i F t + ε i,t ;   i=1,2,...,55;  t=1,2,...,T, MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHapaCpaWaaSbaaSqaa8qacaWGPbGaaiilaiaadshaa8aabeaa k8qacqGH9aqpcqqHBoatpaWaaSbaaSqaa8qacaWGPbaapaqabaGcpe GaamOra8aadaWgaaWcbaWdbiaadshaa8aabeaak8qacqGHRaWkcqaH 1oqzpaWaaSbaaSqaa8qacaWGPbGaaiilaiaadshaa8aabeaakiaacU dacaqGGaGaaeiiaiaabccacaWGPbGaeyypa0JaaGymaiaacYcacaaI YaGaaiilaiaac6cacaGGUaGaaiOlaiaacYcacaaI1aGaaGynaiaacU dacaqGGaGaaeiiaiaadshacqGH9aqpcaaIXaGaaiilaiaaikdacaGG SaGaaiOlaiaac6cacaGGUaGaaiilaiaadsfacaGGSaaaaa@5D59@

where  T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaaaa@36D0@  represents the total number of time periods available,  π i,t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHapaCpaWaaSbaaSqaa8qacaWGPbGaaiilaiaadshaa8aabeaa aaa@3AC5@  represents the inflation rate of component  i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E5@  for the period  t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaaaa@36F0@ , which is related to the common factor  F t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamiDaaWdaeqaaaaa@3835@  through factor loading  Λ i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqqHBoatpaWaaSbaaSqaa8qacaWGPbaapaqabaaaaa@38D4@ , and  ε i,t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaH1oqzpaWaaSbaaSqaa8qacaWGPbGaaiilaiaadshaa8aabeaa aaa@3AAF@  is an idiosyncratic error term representing sector-specific disturbances that are uncorrelated with the common factor. In this model, the measure of core inflation is then defined as follows:

π ˜ t =Λ F t  , MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacuaHapaCpaGbaGaadaWgaaWcbaWdbiaadshaa8aabeaak8qacqGH 9aqpcqqHBoatcaWGgbWdamaaBaaaleaapeGaamiDaaWdaeqaaOGaae iiaiaabYcaaaa@3F45@

where  Λ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqqHBoataaa@378C@  is the matrix of factor loadings. For more information, see Khan et al. (2013).

In practice, CPI-common is calculated using the entire historical data of price index series and by following the steps below.

Step 1: We calculate annual inflation rates for the 55 components and for the All-items CPI excluding the effect of changes in indirect taxes. In a given month, the annual inflation rate for a given component is defined as the year-over-year percentage change in the price index for that month.

Step 2: The historical series of annual inflation rates for the 55 components are standardized. In other words, the historical series of annual inflation rates for each component is centred with respect to its average and then divided by its standard deviation.

Step 3: A factor model is estimated using data from the 55 historical series of annual standardized inflation rates. The principal components method is used for this purpose (Stock and Watson [2002a, 2002b]). This method involves creating 55 new variables, called principal components, each explaining a fraction of the variation found in all 55-historical series of annual inflation rates. The first principal component, which is associated with the highest eigenvalue, is the one that best explains the variation in the 55 historical series of annual inflation rates over the entire observation period. Only the first principal component is used in calculating CPI-common.Note 8

Step 4: The final step is to scale the first principal component to the inflation rate. The measure of core inflation based on the common component, CPI-common, is defined and calculated as the series of predicted values from the simple linear regression of the annual inflation rates of the All-items CPI excluding the effect of changes in indirect taxes (obtained in Step 1) on an intercept and on the first principal component calculated in Step 3.

Since CPI-common is based on a factor model, a standardization and a linear regression requiring all data available, the historical values for this measure are subject to revisions. An analysis of the magnitude of the revisions, reported in a Bank of Canada's Staff Working Paper (Khan et al. [2013]), suggests that revisions are relatively negligible.

Revisions and seasonal adjustment

These three measures of core inflation, CPI-trim, CPI-median and CPI-common, are subject to revision. For CPI-median and CPI-trim, this results from the fact that these measures are based on seasonally adjusted price index series. For CPI-common, revisions are due to the statistical technique used as the factor model is estimated over all available historical data.

When Statistics Canada introduces the CPI-trim and CPI-median measures in its November 2016 CPI release, 44 of the 55 historical series will be identified as seasonally adjusted, whereas others do not present any identifiable seasonal pattern. Since the technical parameters for seasonal adjustment are updated once a year, the number of series that are seasonally adjusted may change in the future depending on the historical series available that have (or do not have) an identifiable seasonal pattern. As with other CPI series, the approach used for seasonal adjustment involves each series to be seasonally adjusted separately. For more information, see the section "Revisions and seasonal adjustment" in the CPI detailed information document.

The seasonally adjusted CPI series are subject to revision. Every month, the seasonally adjusted data for the previous seven years are revised.Note 9 However, the models underlying the seasonal adjustment procedure are regularly revisited; as a result, they will be revised and updated when necessary.

Data accuracy

As with the CPI in general, statistical reliability is difficult to evaluate for the three preferred measures of core inflation. First, a statistical reliability indicator is not available for the price index series used as inputs to these measures. In addition, calculating these measures is complex, which makes it more difficult to evaluate their statistical reliability. For more information on the evaluation of the CPI data accuracy, see this Statistics Canada publication. In practice, since the three measures are based on price index series calculated at the national level, their level of accuracy should be relatively comparable to that of All-items CPI.

References

Bank of Canada. 2016. Renewal of the Inflation-Control Target—Background Information—October 2016. Ottawa. Bank of Canada.

Khan, M., L. Morel and P. Sabourin. 2013. "The Common Component of CPI: An Alternative Measure of Underlying Inflation for Canada", Bank of Canada Staff Working Paper No. 2013-35.

Khan, M., L. Morel and P. Sabourin. 2015. "A Comprehensive Evaluation of Measures of Core Inflation for Canada", Bank of Canada Staff Discussion Paper No. 2015-12.

Macklem, T. 2001. "A New Measure of Core Inflation", Bank of Canada Review, Autumn 2001, pp. 3-12.

Statistics Canada, Consumer Price Index (CPI), Detailed information document, monthly frequency. Ottawa. Statistics Canada.

Stock, J. H. and M. W. Watson. 2002a. "Macroeconomic Forecasting Using Diffusion Indexes", Journal of Business and Economic Statistics, 20, pp. 147-62.

Stock, J. H. and M. W. Watson. 2002b. "Forecasting Using Principal Components from a Large Number of Predictors", Journal of the American Statistical Association, 97, pp. 1167-79.

Appendix

Table A1
The 55 components used for the calculation of the Bank of Canada’s preferred measures of core inflation
Table summary
This table displays the results of The 55 components used for the calculation of the Bank of Canada’s preferred measures of core inflation. The information is grouped by Category number (appearing as row headers), Category description (appearing as column headers).
Category number Category description
1 Meat
2 Fish, seafood and other marine products
3 Dairy products and eggs
4 Bakery and cereal products (excluding baby food)
5 Fruit, fruit preparations and nuts
6 Vegetables and vegetable preparations
7 Other food products and non-alcoholic beverages
8 Food purchased from restaurants
9 Rented accommodation
10 Mortgage interest cost
11 Homeowners' replacement cost
12 Property taxes and other special charges
13 Homeowners' home and mortgage insurance
14 Homeowners' maintenance and repairs
15 Other owned accommodation expensesNote *
16 Electricity
17 Water
18 Natural gas
19 Fuel oil and other fuels
20 Communications
21 Child care and housekeeping services
22 Household cleaning products
23 Paper, plastic and aluminum foil supplies
24 Other household goods and services
25 Furniture
26 Household textiles
27 Household equipment
28 Services related to household furnishings and equipment
29 Clothing
30 Footwear
31 Clothing accessories, watches and jewellery
32 Clothing material, notions and services
33 Purchase of passenger vehicles
34 Leasing of passenger vehiclesNote *
35 Rental of passenger vehicles
36 Gasoline
37 Passenger vehicle parts, maintenance and repairs
38 Other passenger vehicle operating expenses
39 Local and commuter transportation
40 Inter-city transportation
41 Health care goods
42 Health care services
43 Personal care supplies and equipment
44 Personal care services
45 Recreational equipment and services (excluding recreational vehicles)
46 Purchase of recreational vehicles and outboard motors
47 Operation of recreational vehicles
48 Home entertainment equipment, parts and services
49 Travel services
50 Other cultural and recreational services
51 Education
52 Reading material (excluding textbooks)
53 Alcoholic beverages served in licensed establishments
54 Alcoholic beverages purchased from stores
55 Tobacco products and smokers' supplies
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