1 assessing the reliability of the 2005 cpi basket update in canada using bortkiewicz-szulc...
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Assessing the Reliability of the 2005 CPI Basket Update in Canada Using Bortkiewicz-SzulcDecomposition
By Alan Chaffe, Mathieu Lequain and Gerry O’DonnellStatistics CanadaPrices Division
Presented by Gerry O’DonnellMay 16, 2008
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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
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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
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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
L
qw
L
pw
pqwL
LP
QPr
P
PP 00
0
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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
ii
ii
ii
L
Lii
L
Lii
L
LP
qp
qp
Q
Qqq
P
Ppp
P
PP00
000101
*)(
*)(
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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
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Bortkiewicz-Szulc 2005: Method
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
0 1
0 p0q0 p0q1
1 p1q0 p1q1
Prices in year
Quantities in year
2001 2005
2001 $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
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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
0168.01993.0*1317.0*6389.000
0
L
qw
L
pw
pqwL
LP
QPr
P
PP
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Bortkiewicz-Szulc 2005 Results:Contributions
ii
ii
ii
L
Lii
L
Lii
L
LP
qp
qp
Q
Qqq
P
Ppp
P
PP00
000101
*)(
*)(
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
Scatter Plot of Price and Quantity Changes, 2001-2005, for Non-food Basket ItemsSized by 2001 Basket Weight (p2001q2001)
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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
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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
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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
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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
20012005
2005200520012005
20012005
20012005
20052005
0
1
*
qp
qpqp
qp
qp
qpq
q
FFFF
FF
FFqp
qp
qpqp 20052005
20012005
2001200520052005 *
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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
