ICES III, June, 2007 Zdenek Patak & Jack Lothian, Statistics Canada ENHANCING THE QUALITY OF PRICE INDEXES – A SAMPLING PERSPECTIVE
Mar 27, 2015
ICES III, June, 2007
Zdenek Patak & Jack Lothian, Statistics Canada
ENHANCING THE QUALITY OF PRICE INDEXES – A SAMPLING
PERSPECTIVE
Outline
Motivation Catalyst for change A word on sample design Canadian Service Producer Price Index (SPPI)
– Wholesale component
Simulation study Remarks
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Motivation
Discussion with methodologists on best probability sample design for index surveys
– Stratified Probability Proportional to Size (PPS)
– Stratified Simple Random Sampling Without Replacement (SRSWOR)
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Stratified PPS
Large units selected with higher probability believed to drive index
If economic weight inversely proportional to sampling weight index is simple average
Possible drawback – Accuracy of size measure– Could lead to outlier problems
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Stratified SRSWOR
Size measure less important– Reduces outlier problem– Stratum “jumpers” easy to handle
Wealth of literature on all aspects of design Largest units selected as take-alls Larger units selected with high probability
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Catalyst for change
Boskin report (1996) on state of US CPI– Impetus for revision of procedures
More emphasis on data quality More emphasis on reacting to change More emphasis on quality indicators
– Impetus for enhancing methodology
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A word on sample design
Historically most common sample designs– Purposive– Cut-off
Probability sample designs– Stratified PPS– Stratified SRSWOR ? a possibility
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Judgmental and Cut-off sample designs
Easy to implement but requires good industry knowledge– Which units to select – different experts may select
different samples– What represents satisfactory coverage
Cannot compute statistical quality indicators– Sampling bias may be difficult to estimate– Variance = 0
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Probability sample designs
Can produce statistical quality indicators– Coefficients of Variation– Confidence intervals
Handle non-response, imputation and outlier detection in a consistent, scientific manner
Do not depend on judgment Typically stratified PPS but is stratified SRSWOR a
viable alternative?
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Canadian SPPI – Wholesale component
Probability sample – Stratified PPS– Frame stratified by NAICS ~ 33,000 est– Sample ~ 3,000 est
Size variable – Revenue
Collect monthly prices for 3 representative items on quarterly basis– Complete “triplets” form basis for frame used for
simulation study
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Simulation study
Only complete observations – triplets – used– Observations pooled across time– Largest outliers removed
Data replicated to approximate original frame– More where small revenue– Less where larger revenue
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Laspeyres index
Base period economic weights Index is weighted mean Upward economic bias typically
0
0 00
0
np q E nP p q
pL w
p
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Paasche index
Current period economic weights Index is weighted harmonic mean Downward economic bias typically
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0
1n nP
n E nn
p qP
p q pw
p
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Simulation study – Stratified PPS
Stratified PPS sampling (Poisson)– Proportional to revenue available on most frames– Proportional to variable of interest gross margin
(available on simulation frame)
– Allocate 3,000 units Neyman X-proportional
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Simulation study – Stratified PPS
Generate 5,000 samples Compute Laspeyres index at national and industry
levels Vary simulation parameters
– Economic weight Revenue Gross margin
– Weight adjustment
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Simulation study – Stratified SRSWOR
Use Lavallée-Hidiroglou for optimal stratification– Take-all stratum– Two take-some strata
Neyman allocation (3,000 units) Repeat steps as described in Stratified PPS section
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Simulation results I
Geomean at unit levelTrade Group Bias (SRS) Std Dev (SRS) Bias (PPS) Std Dev (PPS)
A 0.006 0.009 0.006 0.008
B -0.024 0.004 -0.024 0.004
C -0.004 0.005 -0.004 0.001
D 0.017 0.006 0.018 0.001
E -0.003 0.004 -0.002 0.004
F 0.009 0.005 0.009 0.004
G 0.017 0.011 0.016 0.010
H 0.001 0.004 0.001 0.004
I -0.092 0.008 -0.093 0.003
J 0.007 0.002 0.007 0.001
Overall -0.007 0.002 -0.006 0.00117
Simulation results II
Arithmetic mean at unit level (~ Laspeyres)Trade Group Bias (SRS) Std Dev (SRS) Bias (PPS) Std Dev (PPS)
A 0.016 0.010 0.015 0.010
B -0.016 0.004 -0.016 0.004
C -0.001 0.005 -0.001 0.001
D 0.021 0.006 0.021 0.001
E 0.003 0.004 0.003 0.004
F 0.020 0.005 0.021 0.004
G 0.042 0.012 0.040 0.011
H 0.007 0.004 0.007 0.005
I -0.072 0.009 -0.073 0.004
J 0.017 0.002 0.017 0.002
Overall 0.001 0.002 0.000 0.00118
Remarks
Negligible differences between Stratified PPS (Poisson) and Stratified SRSWOR– True in ideal setting? need to expand simulation study– What happens when real life phenomena are
incorporated? imperfect size measure, non-response, misclassification, etc.
– Holds for Laspeyres would same hold for “true” index?
Another option Stratified PPSWOR
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ENHANCING THE QUALITY OF PRICE INDEXES – A SAMPLING PERSPECTIVE
Pour de plus amples informations ou pour obtenir une copie en anglais du document veuillez contacter…
For more information, or to obtain an English copy of the presentation, please contact:
Statistique StatisticsCanada Canada Zdenek Patak
Courriel / Email: [email protected]