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

By: Saad Rais, Statistics CanadaZdenek Patak, Statistics

Canada

Statistique StatisticsCanada 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 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

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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 DesignSecond 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 Fisher’s 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:

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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

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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 YouPour 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 thepresentation, please contact:

Statistique StatisticsCanada Canada

Saad RaisE-Mail: saad.rais@statcan.ca