Assessing the Reliability of the 2005 CPI Basket Update in Canada Using Bortkiewicz-Szulc Decomposition

1. Assessing the Reliability of the 2005 CPI Basket Update in Canada Using Bortkiewicz-SzulcDecomposition 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 p0q0, p1/p0, p1q1 • 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 (PP = ∑p1q1/ ∑ p0q1 ) & Laspeyres (PL = ∑p1q0/ ∑ p0q0) determined by 3 factors: • coefficient of correlation, rpqw0, 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 • rpqw0 < 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 200301, & 2005 basket in 200705 • 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 • mapped 170 basic classes in 2001 basket to 173 classes in 2005 at Canada level • result: 164 basic & pseudo classes • use value matrix for each basic class • p0q0, p1q0, p1q1 are known • calculate • p0q1 = p1q1 * p0q0 / p1q0 • p1/p0 = p1q0 / p0q0 = p1q1 / p0q1 • q1/q0 = p1q1 / p1q0 = p0q1 / p0q0 • e.g. cigarettes: • p0q1 = p1q1 * p0q0 / p1q0 = 7262M * 7052M / 12003M = 4267M • p1/p0 = p1q0 / p0q0 = 12003M / 7052M = p1q1 / p0q1 = 7262M / 4267M = 1.7020 • q1/q0 = p1q1 / p1q0 = 7262M / 12003M = p0q1 / p0q0 = 4267M / 7052M = 0.6051

8. Bortkiewicz-Szulc 2005 Results • Paasche < Laspeyres • PP = ∑p2005q2005/ ∑ p2001q2005 = 1.0724 • PL = ∑p2005q2001/ ∑ p2001q2001 = 1.0907 • (PP - PL) / PL = -0.0168 • QP = 1.1222, QL = 1.1413 • 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 Scatter Plot of Price and Quantity Changes, 2001-2005, for Non-food Basket Items Sized by 2001 Basket Weight (p2001q2001) • contribution of each basic class to divergence between PP & PL : • bubble plot relating 113 basic + pseudo classes • each of 3 factors observable in plot • p1/p0 & PL • q1/q0 & QL • bubbles sized by weight • suggests substitution at basic class level • most points lie close to curve • outliers apparent

10. Bortkiewicz-Szulc 2005 Results:Negative Contributors • computers (p↓51%, q↑150%, cont. -0.0056) & video equipment (p↓22%, q↑99%, cont. -0.0010) • increased adoption of digital lifestyle • cigarettes (p↑70%, q↓39%, cont. -0.0040) • aggressive tax ↑ contributed to cut in smoking rates from 26% to 22% • gasoline (p↑31%, q↑7.5%, cont. -0.0005) • supply and disposition of refined petroleum products, cubic metres ↑5.2% 2001-2005

11. Bortkiewicz-Szulc 2005 Results:Positive Contributors • other owned accommodation expenses (p↑20%, q↑38%, cont. +0.0002) • includes expenses on real estate commissions, legal fees, transfer taxes • revived real estate market • natural gas (p↑12%, q↑44%, cont. +0.0001) • continuing shift from oil to gas, even though gas prices ↑ above average • tuition fees (p↑22%, q↑18%, cont. +0.0001) • 19% ↑ in enrolment • “double cohort” in Ontario – grades 12 & 13 graduate in same year • air transportation (p↑14%, q↑31%, cont. +0.0001) • 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

15. Comments & Questions? • Contact • gerry.odonnell@statcan.ca • (613) 951-6891