1. By: Saad Rais, Statistics Canada Zdenek Patak, Statistics Canada
Statistics Canada’s Survey Methodology for the New Services Producer Price Index Surveys
By: Saad Rais, Statistics Canada
Zdenek Patak, Statistics Canada
Statistique Statistics
Canada Canada

2. Outline of Presentation
Introduction
Sampling Design
Estimation
Outlier Detection
Conclusion

3. Introduction What is a Price Index? What is its purpose?
Proportionate change in the price of goods or services over time
What is its purpose?
Deflator
Indicator

4. Introduction Users: Examples: Government departments Private companies
Economists, analysts, researchers etc.
Examples:
Consumer Price Index
Import and Export Price Index
Producer Price Index

5. Introduction Price Indices in Canada
Price indices were mostly limited to the goods sector
Service industry accounted for 75% of employment and 68% of the GDP in Canada
Five year plan to produce a set of Services Producer Price Indices (SPPI)
Focus on a survey methodology that is based on sound statistical principles

6. Sampling Design Two Stage Design: Sampling of businesses
Sampling of items within each business

7. Sampling Scheme Common method: Judgmental sampling
Straightforward sampling and estimation
Absence of a complete reliable frame
Limited resources
Statistical quality measures cannot be calculated

8. Sampling Scheme Cut-off sampling
Yields a sample with the optimal coverage of some size measure variable – revenue in our surveys
Susceptible to biased estimates
No sample rotation

9. Sampling Scheme
Stratified Simple Random Sampling Without Replacement (Stratified SRSWOR)
Common Sampling scheme for business surveys
A probability sample
Abundance of literature
Size stratification
Each unit has equal probability of selection

10. Sampling Scheme Probability Proportional-to-Size (PPS) Sampling
Probability sampling
High revenue coverage in sample
Requires appropriate size measure
Not robust to errors in measure of size

11. Sampling Scheme Sequential Poisson Sampling
All the desirable properties of Poisson Sampling
Additional benefit: fixed sample size

12. Sampling Design First-Stage Frame Primary Sampling Unit
Statistics Canada’s Business Register
Primary Sampling Unit
Varied from survey to survey, ranging from establishment, company, enterprise
Primary Stratification
By industry line
Sometimes by province

13. Sampling Design Stratum Allocation
x – optimal allocation, where x = unit revenue (Särndal, et al., (1992))
Adjustment for over-allocation (Cochran (1977))
Adjustment for under-allocation

14. Sampling Design Sample Size
Based on availability of resources and expert knowledge and experience
No previous or related data available to anticipate response rate or target a CV to estimate a sample size
Improvements to sample size will be made after obtaining sufficient data

15. Sampling Design Size Stratification
TN units: the smallest revenue-generating units that contribute to 5% of the applicable primary stratum.
TA units: Any units for which
TS units: Units for which

16. Sampling Design Second Stage Sampling: Selection of Items
PPS sampling scheme
Requires a list of items for each business unit
Resource intensive, high response burden
Therefore a judgmental sample is selected
Concerns:
No variance estimation
Sampling bias could result from not pricing representative items

17. Estimation
Estimation in 2 stages:
Elemental Indices
Aggregate Indices

18. Estimation Elemental Index: Jevons Index
Exhibits desirable economic and axiomatic properties
Closer to Fisher’s index
Cannot use zero or negative prices

19. Estimation Target Aggregate Index: Laspeyres Index Ratio Estimator:
where
Ratio Estimator:

20. Estimation Cancellation of economic weights and sampling weights:
However, in the presence of non-responding units, cancellation of weights does not occur.

21. Estimation Variance Estimation:
Approximated using the Taylor linearization method:
In Poisson sampling, since when , the formula reduces to:
where

22. Outlier Detection α-trimming Interquartile range
Proportion α is removed from tails
Requires prior knowledge to be efficient
Interquartile range
Handles up to 25% aberrant observations
Construct robust z-score to identify outliers
MAD (Median Absolute Deviation)
Handles up to 50% aberrant observations

23. Conclusion Current and future projects
Research on the efficiency of PPS sampling versus SRSWOR sampling
Outlier detection methods
Imputation methods
Bootstrap variance estimation

24. Conclusion Services industry is an integral component of our economy
We are currently in the pilot/developmental stage of index production
With the collection of data, efficiencies in the sample size, and further research will help improve our methodology

25. Thank You Saad Rais E-Mail: saad.rais@statcan.ca
Pour de plus amples informations ou pour obtenir une
copie en français du document veuillez contacter:
For more information, or to obtain a French copy of the
presentation, please contact:
Saad Rais
Statistique Statistics
Canada Canada