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Outline of Presentation
Introduction Sampling Design Estimation Outlier Detection Conclusion

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Estimation Estimation in 2 stages: Elemental Indices Aggregate Indices

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

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

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

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

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

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

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