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 1

Outline of Presentation

     Introduction Sampling Design Estimation Outlier Detection Conclusion 2

Introduction

What is a Price Index?

 Proportionate change in the price of goods or services over time What is its purpose?

 Deflator  Indicator 3

Introduction

Users:  Government departments   Private companies Economists, analysts, researchers etc.

Examples:   Consumer Price Index Import and Export Price Index  Producer Price Index 4

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 5

Sampling Design

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

Sampling Scheme

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

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 8

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 9

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 10

Sampling Scheme

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

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 12

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 13

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 14

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 

i

  1

i

 1 15

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 16

Estimation

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

Estimation

Elemental Index: Jevons Index

P J

(

t

/ 0  )   

p i t



p i b

1  /

n

   

p t i p i b

 1  /

n

  

p i

(

t

/

b

)  1 /

n

Exhibits desirable economic and axiomatic properties   Closer to Fisher’s index Cannot use zero or negative prices 18

Estimation

Target Aggregate Index: Laspeyres Index

I L

(

t

/ 0 ) 

i N

  1

P i t Q i

0

i N

  1

P i

0

Q i

0 

i N

  1

r i

0

P i

(

t

/ 0 )

i N

  1

r i

0 Ratio Estimator: where

r i

0 

P i

0

Q i

0 

revenue I

ˆ

L

(

t

/ 0 ) 

i n

  1

r i

0

P i

(

t

/ 0 )

i n

  1

r i

0 / 

i

/ 

i



Y

ˆ

X

ˆ 19

Estimation

Cancellation of economic weights and sampling weights:

i n

  1

r i

0

P i

(

t

/ 0 )

i n

  1

r i

0 / 

i

/ 

i



i n

  1

r i

0

P i

(

t

/ 0 )

nr i

0

i n

  1

r i

0

R nr i

0

R



i n

  1

P i

(

t

/ 0 )

i n

  1 1 However, in the presence of non-responding units, cancellation of weights does not occur.

20

Estimation

Variance Estimation: Approximated using the Taylor linearization method:

v I

ˆ

L

(

t



i

 

j s



ij

 

i

 

ij j e i

(

t

 /

i

0 )

e

(

t j

/ 0 ) 

j

where

e i

(

t

/ 0 ) 

y i

(

t

/ 0 ) 

X

ˆ

I

ˆ

L

(

t

/ 0 )

x i

formula reduces to: 

ij

 

i



v I

ˆ  

L

)  

i s

( 1  

i

)   

e i

(

t

 /

i

0 )    2

i



j

21

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 22

Conclusion

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

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 24

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: [email protected]

Statistique Statistics Canada Canada 25