Statistics Canada’s Survey Methodology for the New Services Producer Price Index Surveys

1. 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? • Proportionate change in the price of goods or services over time What is its purpose? • Deflator • Indicator

4. Introduction Users: • 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 • 2003 - 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 • 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 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 • 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 • Construct robust z-score to identify outliers

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 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 E-Mail: saad.rais@statcan.ca Statistique Statistics Canada Canada