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

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Canadian CPI program: Bortkiewicz-Szulc analysis for over 30 years. structured ... CVs always 0. coefficient of correlation determines direction of divergence ... – PowerPoint PPT presentation

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Title: 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-SzulcDecomposi
tion
  • By
  • Alan Chaffe, Mathieu Lequain and Gerry ODonnell
  • Statistics Canada
  • Prices Division
  • Presented by Gerry ODonnell
  • 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 gt 0
  • coefficient of correlation determines direction
    of divergence
  • rpqw0 lt 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
  • elements 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

Prices in year Quantities in year Quantities in year
Prices in year 0 1
0 p0q0 p0q1
1 p1q0 p1q1
Prices in year Quantities in year Quantities in year
Prices in year 2001 2005
2001 7,052 M 4,267 M
2005 12,003 M 7,262 M
8
Bortkiewicz-Szulc 2005 Results
  • Paasche lt 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 ResultsContributions
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 ResultsNegative
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 ResultsPositive
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 ResultsOutliers
  • 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 ResultsFood
  • 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 DecompositionOther 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_at_statcan.ca
  • (613) 951-6891
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