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

2

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)

3

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

4

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

10

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: zdenek.patak@statcan.ca