Statistics Canada

1
Statistics Canadas Survey Methodology for the
New Services Producer Price Index Surveys

• By Saad Rais, Statistics Canada
• Zdenek Patak, Statistics Canada

Statistique Statistics Canada Canada
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Outline of Presentation

• Introduction
• Sampling Design
• Estimation
• Outlier Detection
• Conclusion

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Introduction

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

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Introduction

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

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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

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Sampling Design

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

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Sampling Scheme

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

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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

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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

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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

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Sampling Scheme

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

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Sampling Design

• First-Stage Frame
• Statistics Canadas Business Register
• Primary Sampling Unit
• Varied from survey to survey, ranging from
  establishment, company, enterprise
• Primary Stratification
• By industry line
• Sometimes by province

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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

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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

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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

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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

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Estimation

• Estimation in 2 stages
• Elemental Indices
• Aggregate Indices

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Estimation

• Elemental Index Jevons Index
• Exhibits desirable economic and axiomatic
  properties
• Closer to Fishers index
• Cannot use zero or negative prices

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Estimation

• Target Aggregate Index Laspeyres Index
• where
• Ratio Estimator

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Estimation

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

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Estimation

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

where
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Outlier Detection

• a-trimming
• Proportion a 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

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Conclusion

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

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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

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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_at_statcan.ca
Statistique Statistics Canada Canada