1 Assessing the Reliability of the 2005 CPI Basket Update in Canada Using Bortkiewicz-Szulc Decomposition By Alan Chaffe, Mathieu Lequain and Gerry O’Donnell Statistics Canada Prices Division Presented by Gerry O’Donnell May 16, 2008

2 Outline Bortkiewicz-Szulc decomposition  benefits  the theorem in brief Bortkiewicz-Szulc applied to CPI 2005 basket update  method  high-level results  detailed results other uses

3 Why do Bortkiewicz-Szulc Decomposition? Canadian CPI program: Bortkiewicz-Szulc analysis for over 30 years structured analysis of p 0 q 0, p 1 /p 0, p 1 q 1 to understand relationships between high and low levels of aggregation test aggregate index vs. economic expectations quantity index available framework for outlier detection possible uses for modelling expenditures what could have been – if alternative baskets used

4 Bortkiewicz Decomposition derived by Ladislaus Von Bortkiewicz in 1920s proved divergence between Paasche ( P P = ∑p 1 q 1 / ∑ p 0 q 1 ) & Laspeyres ( P L = ∑p 1 q 0 / ∑ p 0 q 0 ) determined by 3 factors:  coefficient of correlation, r pqw0, between price & quantity relatives  coefficient of variation of price relatives (standard deviation of price relatives as ratio of mean price relative)  coefficient of variation of quantity relatives (standard deviation of quantity relatives as ratio of mean quantity relative) CVs always > 0 coefficient of correlation determines direction of divergence r pqw0 < 0 in most markets - buyers dominate

5 Bortkiewicz-Szulc Decomposition by Elements extension of Bortkiewicz decomposition by Bohdan Szulc in 1950s contribution of each element to divergence between Paasche & Laspeyres derived from product of:  relative difference in price movements from the average price movement  relative difference in quantity shifts from the average quantity shift  element’s proportional weight in earlier basket

6 Canadian CPI and Bortkiewicz- Szulc Decomposition Canadian CPI  chain fixed-basket (Lowe) index  basket updates every four to five years  updated to 2001 basket in , & 2005 basket in  based on Survey of Household Spending (SHS) Bortkiewicz-Szulc decomposition  introduced to CPI by Szulc  analysis of weighting patterns for basket updates since 1974

7 Bortkiewicz-Szulc 2005: Method use value matrix for each basic class p 0 q 0, p 1 q 0, p 1 q 1 are known calculate  p 0 q 1 = p 1 q 1 * p 0 q 0 / p 1 q 0  p 1 /p 0 = p 1 q 0 / p 0 q 0 = p 1 q 1 / p 0 q 1  q 1 /q 0 = p 1 q 1 / p 1 q 0 = p 0 q 1 / p 0 q 0 e.g. cigarettes: p 0 q 1 = p 1 q 1 * p 0 q 0 / p 1 q 0 = 7262M * 7052M / 12003M = 4267M p 1 /p 0 = p 1 q 0 / p 0 q 0 = 12003M / 7052M = p 1 q 1 / p 0 q 1 = 7262M / 4267M = q 1 /q 0 = p 1 q 1 / p 1 q 0 = 7262M / 12003M = p 0 q 1 / p 0 q 0 = 4267M / 7052M = Prices in year Quantities in year 01 0p0q0p0q0 p0q1p0q1 1p1q0p1q0 p1q1p1q1 Prices in year Quantities in year $7,052 M$4,267 M 2005$12,003 M$7,262 M mapped 170 basic classes in 2001 basket to 173 classes in 2005 at Canada level result: 164 basic & pseudo classes

8 Bortkiewicz-Szulc 2005 Results Paasche < Laspeyres  P P = ∑p 2005 q 2005 / ∑ p 2001 q 2005 =  P L = ∑p 2005 q 2001 / ∑ p 2001 q 2001 =  (P P - P L ) / P L =  Q P = , Q L = meets expectations - demand factors outweigh supply factors consistent with previous basket updates Bortkiewicz identity: price & quantity relatives negatively related

9 Bortkiewicz-Szulc 2005 Results: Contributions contribution of each basic class to divergence between P P & P L : bubble plot relating 113 basic + pseudo classes each of 3 factors observable in plot  p 1 /p 0 & P L  q 1 /q 0 & Q L  bubbles sized by weight suggests substitution at basic class level most points lie close to curve outliers apparent Scatter Plot of Price and Quantity Changes, , for Non-food Basket Items Sized by 2001 Basket Weight (p 2001 q 2001 )

10 Bortkiewicz-Szulc 2005 Results: Negative Contributors computers (p↓51%, q↑150%, cont ) & video equipment (p↓22%, q↑99%, cont )  increased adoption of digital lifestyle cigarettes (p↑70%, q↓39%, cont )  aggressive tax ↑ contributed to cut in smoking rates from 26% to 22% gasoline (p↑31%, q↑7.5%, cont )  supply and disposition of refined petroleum products, cubic metres ↑5.2%

11 Bortkiewicz-Szulc 2005 Results: Positive Contributors other owned accommodation expenses (p↑20%, q↑38%, cont )  includes expenses on real estate commissions, legal fees, transfer taxes  revived real estate market natural gas (p↑12%, q↑44%, cont )  continuing shift from oil to gas, even though gas prices ↑ above average tuition fees (p↑22%, q↑18%, cont )  19% ↑ in enrolment  “double cohort” in Ontario – grades 12 & 13 graduate in same year air transportation (p↑14%, q↑31%, cont )  25% ↑ in passenger miles

12 Bortkiewicz-Szulc 2005 Results: Outliers weighting discrepancies found using Bortkiewicz- Szulc  gifts of clothing corrected in time for update  other tobacco products (p↑71%, q↑102%) expenditures increased 245% cigars included in 2005 found after basket update  other home entertainment (p↑7%, q↓50%) non-PC video game systems, accessories, and games moved into video equipment basic class in 2005

13 Bortkiewicz-Szulc 2005 Results: Food no Food Expenditure Survey in 2005 for basic class weights allocated food weights using results in little variation in quantity, due to possibility of modelling quantity shifts and expenditures using non-food results, under certain assumptions

14 Bortkiewicz-Szulc Decomposition: Other Uses to compare indexes from alternate baskets  different geographies  different demographic groups seniors vs. non-seniors high income vs. low income 1992 basket – expansion of coverage from larger cities to urban + rural to measure substitution at different levels of aggregation

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